importance of experiments in scientific method

What is the Scientific Method: How does it work and why is it important?

The scientific method is a systematic process involving steps like defining questions, forming hypotheses, conducting experiments, and analyzing data. It minimizes biases and enables replicable research, leading to groundbreaking discoveries like Einstein's theory of relativity, penicillin, and the structure of DNA. This ongoing approach promotes reason, evidence, and the pursuit of truth in science.

Updated on November 18, 2023

Beginning in elementary school, we are exposed to the scientific method and taught how to put it into practice. As a tool for learning, it prepares children to think logically and use reasoning when seeking answers to questions.

Rather than jumping to conclusions, the scientific method gives us a recipe for exploring the world through observation and trial and error. We use it regularly, sometimes knowingly in academics or research, and sometimes subconsciously in our daily lives.

In this article we will refresh our memories on the particulars of the scientific method, discussing where it comes from, which elements comprise it, and how it is put into practice. Then, we will consider the importance of the scientific method, who uses it and under what circumstances.

What is the scientific method?

The scientific method is a dynamic process that involves objectively investigating questions through observation and experimentation . Applicable to all scientific disciplines, this systematic approach to answering questions is more accurately described as a flexible set of principles than as a fixed series of steps.

The following representations of the scientific method illustrate how it can be both condensed into broad categories and also expanded to reveal more and more details of the process. These graphics capture the adaptability that makes this concept universally valuable as it is relevant and accessible not only across age groups and educational levels but also within various contexts.

Steps in the scientific method

While the scientific method is versatile in form and function, it encompasses a collection of principles that create a logical progression to the process of problem solving:

• Define a question : Constructing a clear and precise problem statement that identifies the main question or goal of the investigation is the first step. The wording must lend itself to experimentation by posing a question that is both testable and measurable.
• Gather information and resources : Researching the topic in question to find out what is already known and what types of related questions others are asking is the next step in this process. This background information is vital to gaining a full understanding of the subject and in determining the best design for experiments. 
• Form a hypothesis : Composing a concise statement that identifies specific variables and potential results, which can then be tested, is a crucial step that must be completed before any experimentation. An imperfection in the composition of a hypothesis can result in weaknesses to the entire design of an experiment.
• Perform the experiments : Testing the hypothesis by performing replicable experiments and collecting resultant data is another fundamental step of the scientific method. By controlling some elements of an experiment while purposely manipulating others, cause and effect relationships are established.
• Analyze the data : Interpreting the experimental process and results by recognizing trends in the data is a necessary step for comprehending its meaning and supporting the conclusions. Drawing inferences through this systematic process lends substantive evidence for either supporting or rejecting the hypothesis.
• Report the results : Sharing the outcomes of an experiment, through an essay, presentation, graphic, or journal article, is often regarded as a final step in this process. Detailing the project's design, methods, and results not only promotes transparency and replicability but also adds to the body of knowledge for future research.
• Retest the hypothesis : Repeating experiments to see if a hypothesis holds up in all cases is a step that is manifested through varying scenarios. Sometimes a researcher immediately checks their own work or replicates it at a future time, or another researcher will repeat the experiments to further test the hypothesis.

Where did the scientific method come from?

Oftentimes, ancient peoples attempted to answer questions about the unknown by:

• Making simple observations
• Discussing the possibilities with others deemed worthy of a debate
• Drawing conclusions based on dominant opinions and preexisting beliefs

For example, take Greek and Roman mythology. Myths were used to explain everything from the seasons and stars to the sun and death itself.

However, as societies began to grow through advancements in agriculture and language, ancient civilizations like Egypt and Babylonia shifted to a more rational analysis for understanding the natural world. They increasingly employed empirical methods of observation and experimentation that would one day evolve into the scientific method . 

In the 4th century, Aristotle, considered the Father of Science by many, suggested these elements , which closely resemble the contemporary scientific method, as part of his approach for conducting science:

• Study what others have written about the subject.
• Look for the general consensus about the subject.
• Perform a systematic study of everything even partially related to the topic.

By continuing to emphasize systematic observation and controlled experiments, scholars such as Al-Kindi and Ibn al-Haytham helped expand this concept throughout the Islamic Golden Age . 

In his 1620 treatise, Novum Organum , Sir Francis Bacon codified the scientific method, arguing not only that hypotheses must be tested through experiments but also that the results must be replicated to establish a truth. Coming at the height of the Scientific Revolution, this text made the scientific method accessible to European thinkers like Galileo and Isaac Newton who then put the method into practice.

As science modernized in the 19th century, the scientific method became more formalized, leading to significant breakthroughs in fields such as evolution and germ theory. Today, it continues to evolve, underpinning scientific progress in diverse areas like quantum mechanics, genetics, and artificial intelligence.

Why is the scientific method important?

The history of the scientific method illustrates how the concept developed out of a need to find objective answers to scientific questions by overcoming biases based on fear, religion, power, and cultural norms. This still holds true today.

By implementing this standardized approach to conducting experiments, the impacts of researchers’ personal opinions and preconceived notions are minimized. The organized manner of the scientific method prevents these and other mistakes while promoting the replicability and transparency necessary for solid scientific research.

The importance of the scientific method is best observed through its successes, for example: 

• “ Albert Einstein stands out among modern physicists as the scientist who not only formulated a theory of revolutionary significance but also had the genius to reflect in a conscious and technical way on the scientific method he was using.” Devising a hypothesis based on the prevailing understanding of Newtonian physics eventually led Einstein to devise the theory of general relativity .
• Howard Florey “Perhaps the most useful lesson which has come out of the work on penicillin has been the demonstration that success in this field depends on the development and coordinated use of technical methods.” After discovering a mold that prevented the growth of Staphylococcus bacteria, Dr. Alexander Flemimg designed experiments to identify and reproduce it in the lab, thus leading to the development of penicillin .
• James D. Watson “Every time you understand something, religion becomes less likely. Only with the discovery of the double helix and the ensuing genetic revolution have we had grounds for thinking that the powers held traditionally to be the exclusive property of the gods might one day be ours. . . .” By using wire models to conceive a structure for DNA, Watson and Crick crafted a hypothesis for testing combinations of amino acids, X-ray diffraction images, and the current research in atomic physics, resulting in the discovery of DNA’s double helix structure .

Final thoughts

As the cases exemplify, the scientific method is never truly completed, but rather started and restarted. It gave these researchers a structured process that was easily replicated, modified, and built upon. 

While the scientific method may “end” in one context, it never literally ends. When a hypothesis, design, methods, and experiments are revisited, the scientific method simply picks up where it left off. Each time a researcher builds upon previous knowledge, the scientific method is restored with the pieces of past efforts.

By guiding researchers towards objective results based on transparency and reproducibility, the scientific method acts as a defense against bias, superstition, and preconceived notions. As we embrace the scientific method's enduring principles, we ensure that our quest for knowledge remains firmly rooted in reason, evidence, and the pursuit of truth.

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The Scientific Method was first used during the Scientific Revolution (1500-1700). The method combined theoretical knowledge such as mathematics with practical experimentation using scientific instruments, results analysis and comparisons, and finally peer reviews, all to better determine how the world around us works. In this way, hypotheses were rigorously tested, and laws could be formulated which explained observable phenomena. The goal of this scientific method was to not only increase human knowledge but to do so in a way that practically benefitted everyone and improved the human condition.

A New Approach: Bacon 's Vision

Francis Bacon (1561-1626) was an English philosopher, statesman, and author. He is considered one of the founders of modern scientific research and scientific method, even as "the father of modern science " because he proposed a new combined method of empirical (observable) experimentation and shared data collection so that humanity might finally discover all of nature's secrets and improve itself. Bacon championed the need for systematic and detailed empirical study, as this was the only way to increase humanity's understanding and, for him, more importantly, gain control of nature. This approach sounds quite obvious today, but at the time, the highly theoretical approach of the Greek philosopher Aristotle (l. 384-322 BCE) still dominated thought. Verbal arguments had become more important than what could actually be seen in the world. Further, natural philosophers had become preoccupied with why things happen instead of first ascertaining what was happening in nature.

Bacon rejected the current backward-looking approach to knowledge, that is, the seemingly never-ending attempt to prove the ancients right. Instead, new thinkers and experimenters, said Bacon, should act like the new navigators who had pushed beyond the limits of the known world. Christopher Columbus (1451-1506) had shown there was land across the Atlantic Ocean. Vasco da Gama (c. 1469-1524) had explored the globe in the other direction. Scientists, as we would call them today, had to be similarly bold. Old knowledge had to be rigorously tested to see that it was worth keeping. New knowledge had to be acquired by thoroughly testing nature without preconceived ideas. Reason had to be applied to data collected from experiments, and the same data had to be openly shared with other thinkers so that it could be tested again, comparing it to what others had discovered. Finally, this knowledge must then be used to improve the human condition; otherwise, it was no use pursuing it in the first place. This was Bacon's vision. What he proposed did indeed come about but with three notable factors added to the scientific method. These were mathematics, hypotheses, and technology.

The Importance of Experiments & Instruments

Experiments had always been carried out by thinkers, from ancient figures like Archimedes (l. 287-212 BCE) to the alchemists of the Middle Ages, but their experiments were usually haphazard, and very often thinkers were trying to prove a preconceived idea. In the Scientific Revolution, experimentation became a more systematic and multi-layered activity involving many different people. This more rigorous approach to gathering observable data was also a reaction against traditional activities and methods such as magic, astrology, and alchemy , all ancient and secret worlds of knowledge-gathering that now came under attack.

At the outset of the Scientific Revolution, experiments were any sort of activity carried out to see what would happen, a sort of anything-goes approach to satisfying scientific curiosity. It is important to note, though, that the modern meaning of scientific experiment is rather different, summarised here by W. E. Burns: "the creation of an artificial situation designed to study scientific principles held to apply in all situations" (95). It is fair to say, though, that the modern approach to experimentation, with its highly specialised focus where only one specific hypothesis is being tested, would not have become possible without the pioneering experimenters of the Scientific Revolution.

The first well-documented practical experiment of our period was made by William Gilbert using magnets; he published his findings in 1600 in On the Magnet . The work was pioneering because "Central to Gilbert's enterprise was the claim that you could reproduce his experiments and confirm his results: his book was, in effect, a collection of experimental recipes" (Wootton, 331).

There remained sceptics of experimentation, those who stressed that the senses could be misled when the reason of the mind could not be. One such doubter was René Descartes (1596-1650), but if anything, he and other natural philosophers who questioned the value of the work of the practical experimenters were responsible for creating a lasting new division between philosophy and what we would today call science. The term "science" was still not widely used in the 17th century, instead, many experimenters referred to themselves as practitioners of "experimental philosophy". The first use in English of the term "experimental method" was in 1675.

The first truly international effort in coordinated experiments involved the development of the barometer. This process began with the efforts of the Italian Evangelista Torricelli (1608-1647) in 1643. Torricelli discovered that mercury could be raised within a glass tube when one end of that tube was placed in a container of mercury. The air pressure on the mercury in the container pushed the mercury in the tube up around 30 inches (76 cm) higher than the level in the container. In 1648, Blaise Pascal (1623-1662) and his brother-in- law Florin Périer conducted experiments using similar apparatus, but this time tested under different atmospheric pressures by setting up the devices at a variety of altitudes on the side of a mountain. The scientists noted that the level of the mercury in the glass tube fell the higher up the mountain readings were taken.

The Anglo-Irish chemist Robert Boyle (1627-1691) named the new instrument a barometer and conclusively demonstrated the effect of air pressure by using a barometer inside an air pump where a vacuum was established. Boyle formulated a principle which became known as 'Boyle's Law'. This law states that the pressure exerted by a certain quantity of air varies inversely in proportion to its volume (provided temperatures are constant). The story of the development of the barometer became typical throughout the Scientific Revolution: natural phenomena were observed, instruments were invented to measure and understand these observable facts, scientists collaborated (sometimes even competed), and so they extended the work of each other until, finally, a universal law could be devised which explained what was being seen. This law could then be used as a predictive device in future experiments.

Experiments like Robert Boyle's air pump demonstrations and Isaac Newton 's use of a prism to demonstrate white light is made up of different coloured light continued the trend of experimentation to prove, test, and adjust theories. Further, these endeavours highlight the importance of scientific instruments in the new method of inquiry. The scientific method was employed to invent useful and accurate instruments, which were, in turn, used in further experiments. The invention of the telescope (c. 1608), microscope (c. 1610), barometer (1643), thermometer (c. 1650), pendulum clock (1657), air pump (1659), and balance spring watch (1675) all allowed fine measurements to be made which previously had been impossible. New instruments meant that a whole new range of experiments could be carried out. Whole new specialisations of study became possible, such as meteorology, microscopic anatomy, embryology, and optics.

The scientific method came to involve the following key components:

• conducting practical experiments
• conducting experiments without prejudice of what they should prove
• using deductive reasoning (creating a generalisation from specific examples) to form a hypothesis (untested theory), which is then tested by an experiment, after which the hypothesis might be accepted, altered, or rejected based on empirical (observable) evidence
• conducting multiple experiments and doing so in different places and by different people to confirm the reliability of the results
• an open and critical review of the results of an experiment by peers
• the formulation of universal laws (inductive reasoning or logic) using, for example, mathematics
• a desire to gain practical benefits from scientific experiments and a belief in the idea of scientific progress

(Note: the above criteria are expressed in modern linguistic terms, not necessarily those terms 17th-century scientists would have used since the revolution in science also caused a revolution in the language to describe it).

Scientific Institutions

The scientific method really took hold when it became institutionalised, that is, when it was endorsed and employed by official institutions like the learned societies where thinkers tested their theories in the real world and worked collaboratively. The first such society was the Academia del Cimento in Florence, founded in 1657. Others soon followed, notably the Royal Academy of Sciences in Paris in 1667. Four years earlier, London had gained its own academy with the foundation of the Royal Society . The founding fellows of this society credited Bacon with the idea, and they were keen to follow his principles of scientific method and his emphasis on sharing and communicating scientific data and results. The Berlin Academy was founded in 1700 and the St. Petersburg Academy in 1724. These academies and societies became the focal points of an international network of scientists who corresponded, read each other's works, and even visited each other as the new scientific method took hold.

Official bodies were able to fund expensive experiments and assemble or commission new equipment. They showed these experiments to the public, a practice that illustrates that what was new here was not the act of discovery but the creation of a culture of discovery. Scientists went much further than a real-time audience and ensured their results were printed for a far wider (and more critical) readership in journals and books. Here, in print, the experiments were described in great detail, and the results were presented for all to see. In this way, scientists were able to create "virtual witnesses" to their experiments. Now, anyone who cared to be could become a participant in the development of knowledge acquired through science.

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Bibliography

• Burns, William E. The Scientific Revolution in Global Perspective. Oxford University Press, 2015.
• Burns, William E. The Scientific Revolution. ABC-CLIO, 2001.
• Bynum, William F. & Browne, Janet & Porter, Roy. Dictionary of the History of Science . Princeton University Press, 1982.
• Henry, John. The Scientific Revolution and the Origins of Modern Science . Red Globe Press, 2008.
• Jardine, Lisa. Ingenious Pursuits. Nan A. Talese, 1999.
• Moran, Bruce T. Distilling Knowledge. Harvard University Press, 2006.
• Wootton, David. The Invention of Science. Harper, 2015.

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Scientific Method

Science is an enormously successful human enterprise. The study of scientific method is the attempt to discern the activities by which that success is achieved. Among the activities often identified as characteristic of science are systematic observation and experimentation, inductive and deductive reasoning, and the formation and testing of hypotheses and theories. How these are carried out in detail can vary greatly, but characteristics like these have been looked to as a way of demarcating scientific activity from non-science, where only enterprises which employ some canonical form of scientific method or methods should be considered science (see also the entry on science and pseudo-science ). Others have questioned whether there is anything like a fixed toolkit of methods which is common across science and only science. Some reject privileging one view of method as part of rejecting broader views about the nature of science, such as naturalism (Dupré 2004); some reject any restriction in principle (pluralism).

Scientific method should be distinguished from the aims and products of science, such as knowledge, predictions, or control. Methods are the means by which those goals are achieved. Scientific method should also be distinguished from meta-methodology, which includes the values and justifications behind a particular characterization of scientific method (i.e., a methodology) — values such as objectivity, reproducibility, simplicity, or past successes. Methodological rules are proposed to govern method and it is a meta-methodological question whether methods obeying those rules satisfy given values. Finally, method is distinct, to some degree, from the detailed and contextual practices through which methods are implemented. The latter might range over: specific laboratory techniques; mathematical formalisms or other specialized languages used in descriptions and reasoning; technological or other material means; ways of communicating and sharing results, whether with other scientists or with the public at large; or the conventions, habits, enforced customs, and institutional controls over how and what science is carried out.

While it is important to recognize these distinctions, their boundaries are fuzzy. Hence, accounts of method cannot be entirely divorced from their methodological and meta-methodological motivations or justifications, Moreover, each aspect plays a crucial role in identifying methods. Disputes about method have therefore played out at the detail, rule, and meta-rule levels. Changes in beliefs about the certainty or fallibility of scientific knowledge, for instance (which is a meta-methodological consideration of what we can hope for methods to deliver), have meant different emphases on deductive and inductive reasoning, or on the relative importance attached to reasoning over observation (i.e., differences over particular methods.) Beliefs about the role of science in society will affect the place one gives to values in scientific method.

The issue which has shaped debates over scientific method the most in the last half century is the question of how pluralist do we need to be about method? Unificationists continue to hold out for one method essential to science; nihilism is a form of radical pluralism, which considers the effectiveness of any methodological prescription to be so context sensitive as to render it not explanatory on its own. Some middle degree of pluralism regarding the methods embodied in scientific practice seems appropriate. But the details of scientific practice vary with time and place, from institution to institution, across scientists and their subjects of investigation. How significant are the variations for understanding science and its success? How much can method be abstracted from practice? This entry describes some of the attempts to characterize scientific method or methods, as well as arguments for a more context-sensitive approach to methods embedded in actual scientific practices.

1. Overview and organizing themes

2. historical review: aristotle to mill, 3.1 logical constructionism and operationalism, 3.2. h-d as a logic of confirmation, 3.3. popper and falsificationism, 3.4 meta-methodology and the end of method, 4. statistical methods for hypothesis testing, 5.1 creative and exploratory practices.

• 5.2 Computer methods and the ‘new ways’ of doing science

6.1 “The scientific method” in science education and as seen by scientists

6.2 privileged methods and ‘gold standards’, 6.3 scientific method in the court room, 6.4 deviating practices, 7. conclusion, other internet resources, related entries.

This entry could have been given the title Scientific Methods and gone on to fill volumes, or it could have been extremely short, consisting of a brief summary rejection of the idea that there is any such thing as a unique Scientific Method at all. Both unhappy prospects are due to the fact that scientific activity varies so much across disciplines, times, places, and scientists that any account which manages to unify it all will either consist of overwhelming descriptive detail, or trivial generalizations.

The choice of scope for the present entry is more optimistic, taking a cue from the recent movement in philosophy of science toward a greater attention to practice: to what scientists actually do. This “turn to practice” can be seen as the latest form of studies of methods in science, insofar as it represents an attempt at understanding scientific activity, but through accounts that are neither meant to be universal and unified, nor singular and narrowly descriptive. To some extent, different scientists at different times and places can be said to be using the same method even though, in practice, the details are different.

Whether the context in which methods are carried out is relevant, or to what extent, will depend largely on what one takes the aims of science to be and what one’s own aims are. For most of the history of scientific methodology the assumption has been that the most important output of science is knowledge and so the aim of methodology should be to discover those methods by which scientific knowledge is generated.

Science was seen to embody the most successful form of reasoning (but which form?) to the most certain knowledge claims (but how certain?) on the basis of systematically collected evidence (but what counts as evidence, and should the evidence of the senses take precedence, or rational insight?) Section 2 surveys some of the history, pointing to two major themes. One theme is seeking the right balance between observation and reasoning (and the attendant forms of reasoning which employ them); the other is how certain scientific knowledge is or can be.

Section 3 turns to 20 th century debates on scientific method. In the second half of the 20 th century the epistemic privilege of science faced several challenges and many philosophers of science abandoned the reconstruction of the logic of scientific method. Views changed significantly regarding which functions of science ought to be captured and why. For some, the success of science was better identified with social or cultural features. Historical and sociological turns in the philosophy of science were made, with a demand that greater attention be paid to the non-epistemic aspects of science, such as sociological, institutional, material, and political factors. Even outside of those movements there was an increased specialization in the philosophy of science, with more and more focus on specific fields within science. The combined upshot was very few philosophers arguing any longer for a grand unified methodology of science. Sections 3 and 4 surveys the main positions on scientific method in 20 th century philosophy of science, focusing on where they differ in their preference for confirmation or falsification or for waiving the idea of a special scientific method altogether.

In recent decades, attention has primarily been paid to scientific activities traditionally falling under the rubric of method, such as experimental design and general laboratory practice, the use of statistics, the construction and use of models and diagrams, interdisciplinary collaboration, and science communication. Sections 4–6 attempt to construct a map of the current domains of the study of methods in science.

As these sections illustrate, the question of method is still central to the discourse about science. Scientific method remains a topic for education, for science policy, and for scientists. It arises in the public domain where the demarcation or status of science is at issue. Some philosophers have recently returned, therefore, to the question of what it is that makes science a unique cultural product. This entry will close with some of these recent attempts at discerning and encapsulating the activities by which scientific knowledge is achieved.

Attempting a history of scientific method compounds the vast scope of the topic. This section briefly surveys the background to modern methodological debates. What can be called the classical view goes back to antiquity, and represents a point of departure for later divergences. [ 1 ]

We begin with a point made by Laudan (1968) in his historical survey of scientific method:

Perhaps the most serious inhibition to the emergence of the history of theories of scientific method as a respectable area of study has been the tendency to conflate it with the general history of epistemology, thereby assuming that the narrative categories and classificatory pigeon-holes applied to the latter are also basic to the former. (1968: 5)

To see knowledge about the natural world as falling under knowledge more generally is an understandable conflation. Histories of theories of method would naturally employ the same narrative categories and classificatory pigeon holes. An important theme of the history of epistemology, for example, is the unification of knowledge, a theme reflected in the question of the unification of method in science. Those who have identified differences in kinds of knowledge have often likewise identified different methods for achieving that kind of knowledge (see the entry on the unity of science ).

Different views on what is known, how it is known, and what can be known are connected. Plato distinguished the realms of things into the visible and the intelligible ( The Republic , 510a, in Cooper 1997). Only the latter, the Forms, could be objects of knowledge. The intelligible truths could be known with the certainty of geometry and deductive reasoning. What could be observed of the material world, however, was by definition imperfect and deceptive, not ideal. The Platonic way of knowledge therefore emphasized reasoning as a method, downplaying the importance of observation. Aristotle disagreed, locating the Forms in the natural world as the fundamental principles to be discovered through the inquiry into nature ( Metaphysics Z , in Barnes 1984).

Aristotle is recognized as giving the earliest systematic treatise on the nature of scientific inquiry in the western tradition, one which embraced observation and reasoning about the natural world. In the Prior and Posterior Analytics , Aristotle reflects first on the aims and then the methods of inquiry into nature. A number of features can be found which are still considered by most to be essential to science. For Aristotle, empiricism, careful observation (but passive observation, not controlled experiment), is the starting point. The aim is not merely recording of facts, though. For Aristotle, science ( epistêmê ) is a body of properly arranged knowledge or learning—the empirical facts, but also their ordering and display are of crucial importance. The aims of discovery, ordering, and display of facts partly determine the methods required of successful scientific inquiry. Also determinant is the nature of the knowledge being sought, and the explanatory causes proper to that kind of knowledge (see the discussion of the four causes in the entry on Aristotle on causality ).

In addition to careful observation, then, scientific method requires a logic as a system of reasoning for properly arranging, but also inferring beyond, what is known by observation. Methods of reasoning may include induction, prediction, or analogy, among others. Aristotle’s system (along with his catalogue of fallacious reasoning) was collected under the title the Organon . This title would be echoed in later works on scientific reasoning, such as Novum Organon by Francis Bacon, and Novum Organon Restorum by William Whewell (see below). In Aristotle’s Organon reasoning is divided primarily into two forms, a rough division which persists into modern times. The division, known most commonly today as deductive versus inductive method, appears in other eras and methodologies as analysis/​synthesis, non-ampliative/​ampliative, or even confirmation/​verification. The basic idea is there are two “directions” to proceed in our methods of inquiry: one away from what is observed, to the more fundamental, general, and encompassing principles; the other, from the fundamental and general to instances or implications of principles.

The basic aim and method of inquiry identified here can be seen as a theme running throughout the next two millennia of reflection on the correct way to seek after knowledge: carefully observe nature and then seek rules or principles which explain or predict its operation. The Aristotelian corpus provided the framework for a commentary tradition on scientific method independent of science itself (cosmos versus physics.) During the medieval period, figures such as Albertus Magnus (1206–1280), Thomas Aquinas (1225–1274), Robert Grosseteste (1175–1253), Roger Bacon (1214/1220–1292), William of Ockham (1287–1347), Andreas Vesalius (1514–1546), Giacomo Zabarella (1533–1589) all worked to clarify the kind of knowledge obtainable by observation and induction, the source of justification of induction, and best rules for its application. [ 2 ] Many of their contributions we now think of as essential to science (see also Laudan 1968). As Aristotle and Plato had employed a framework of reasoning either “to the forms” or “away from the forms”, medieval thinkers employed directions away from the phenomena or back to the phenomena. In analysis, a phenomena was examined to discover its basic explanatory principles; in synthesis, explanations of a phenomena were constructed from first principles.

During the Scientific Revolution these various strands of argument, experiment, and reason were forged into a dominant epistemic authority. The 16 th –18 th centuries were a period of not only dramatic advance in knowledge about the operation of the natural world—advances in mechanical, medical, biological, political, economic explanations—but also of self-awareness of the revolutionary changes taking place, and intense reflection on the source and legitimation of the method by which the advances were made. The struggle to establish the new authority included methodological moves. The Book of Nature, according to the metaphor of Galileo Galilei (1564–1642) or Francis Bacon (1561–1626), was written in the language of mathematics, of geometry and number. This motivated an emphasis on mathematical description and mechanical explanation as important aspects of scientific method. Through figures such as Henry More and Ralph Cudworth, a neo-Platonic emphasis on the importance of metaphysical reflection on nature behind appearances, particularly regarding the spiritual as a complement to the purely mechanical, remained an important methodological thread of the Scientific Revolution (see the entries on Cambridge platonists ; Boyle ; Henry More ; Galileo ).

In Novum Organum (1620), Bacon was critical of the Aristotelian method for leaping from particulars to universals too quickly. The syllogistic form of reasoning readily mixed those two types of propositions. Bacon aimed at the invention of new arts, principles, and directions. His method would be grounded in methodical collection of observations, coupled with correction of our senses (and particularly, directions for the avoidance of the Idols, as he called them, kinds of systematic errors to which naïve observers are prone.) The community of scientists could then climb, by a careful, gradual and unbroken ascent, to reliable general claims.

Bacon’s method has been criticized as impractical and too inflexible for the practicing scientist. Whewell would later criticize Bacon in his System of Logic for paying too little attention to the practices of scientists. It is hard to find convincing examples of Bacon’s method being put in to practice in the history of science, but there are a few who have been held up as real examples of 16 th century scientific, inductive method, even if not in the rigid Baconian mold: figures such as Robert Boyle (1627–1691) and William Harvey (1578–1657) (see the entry on Bacon ).

It is to Isaac Newton (1642–1727), however, that historians of science and methodologists have paid greatest attention. Given the enormous success of his Principia Mathematica and Opticks , this is understandable. The study of Newton’s method has had two main thrusts: the implicit method of the experiments and reasoning presented in the Opticks, and the explicit methodological rules given as the Rules for Philosophising (the Regulae) in Book III of the Principia . [ 3 ] Newton’s law of gravitation, the linchpin of his new cosmology, broke with explanatory conventions of natural philosophy, first for apparently proposing action at a distance, but more generally for not providing “true”, physical causes. The argument for his System of the World ( Principia , Book III) was based on phenomena, not reasoned first principles. This was viewed (mainly on the continent) as insufficient for proper natural philosophy. The Regulae counter this objection, re-defining the aims of natural philosophy by re-defining the method natural philosophers should follow. (See the entry on Newton’s philosophy .)

To his list of methodological prescriptions should be added Newton’s famous phrase “ hypotheses non fingo ” (commonly translated as “I frame no hypotheses”.) The scientist was not to invent systems but infer explanations from observations, as Bacon had advocated. This would come to be known as inductivism. In the century after Newton, significant clarifications of the Newtonian method were made. Colin Maclaurin (1698–1746), for instance, reconstructed the essential structure of the method as having complementary analysis and synthesis phases, one proceeding away from the phenomena in generalization, the other from the general propositions to derive explanations of new phenomena. Denis Diderot (1713–1784) and editors of the Encyclopédie did much to consolidate and popularize Newtonianism, as did Francesco Algarotti (1721–1764). The emphasis was often the same, as much on the character of the scientist as on their process, a character which is still commonly assumed. The scientist is humble in the face of nature, not beholden to dogma, obeys only his eyes, and follows the truth wherever it leads. It was certainly Voltaire (1694–1778) and du Chatelet (1706–1749) who were most influential in propagating the latter vision of the scientist and their craft, with Newton as hero. Scientific method became a revolutionary force of the Enlightenment. (See also the entries on Newton , Leibniz , Descartes , Boyle , Hume , enlightenment , as well as Shank 2008 for a historical overview.)

Not all 18 th century reflections on scientific method were so celebratory. Famous also are George Berkeley’s (1685–1753) attack on the mathematics of the new science, as well as the over-emphasis of Newtonians on observation; and David Hume’s (1711–1776) undermining of the warrant offered for scientific claims by inductive justification (see the entries on: George Berkeley ; David Hume ; Hume’s Newtonianism and Anti-Newtonianism ). Hume’s problem of induction motivated Immanuel Kant (1724–1804) to seek new foundations for empirical method, though as an epistemic reconstruction, not as any set of practical guidelines for scientists. Both Hume and Kant influenced the methodological reflections of the next century, such as the debate between Mill and Whewell over the certainty of inductive inferences in science.

The debate between John Stuart Mill (1806–1873) and William Whewell (1794–1866) has become the canonical methodological debate of the 19 th century. Although often characterized as a debate between inductivism and hypothetico-deductivism, the role of the two methods on each side is actually more complex. On the hypothetico-deductive account, scientists work to come up with hypotheses from which true observational consequences can be deduced—hence, hypothetico-deductive. Because Whewell emphasizes both hypotheses and deduction in his account of method, he can be seen as a convenient foil to the inductivism of Mill. However, equally if not more important to Whewell’s portrayal of scientific method is what he calls the “fundamental antithesis”. Knowledge is a product of the objective (what we see in the world around us) and subjective (the contributions of our mind to how we perceive and understand what we experience, which he called the Fundamental Ideas). Both elements are essential according to Whewell, and he was therefore critical of Kant for too much focus on the subjective, and John Locke (1632–1704) and Mill for too much focus on the senses. Whewell’s fundamental ideas can be discipline relative. An idea can be fundamental even if it is necessary for knowledge only within a given scientific discipline (e.g., chemical affinity for chemistry). This distinguishes fundamental ideas from the forms and categories of intuition of Kant. (See the entry on Whewell .)

Clarifying fundamental ideas would therefore be an essential part of scientific method and scientific progress. Whewell called this process “Discoverer’s Induction”. It was induction, following Bacon or Newton, but Whewell sought to revive Bacon’s account by emphasising the role of ideas in the clear and careful formulation of inductive hypotheses. Whewell’s induction is not merely the collecting of objective facts. The subjective plays a role through what Whewell calls the Colligation of Facts, a creative act of the scientist, the invention of a theory. A theory is then confirmed by testing, where more facts are brought under the theory, called the Consilience of Inductions. Whewell felt that this was the method by which the true laws of nature could be discovered: clarification of fundamental concepts, clever invention of explanations, and careful testing. Mill, in his critique of Whewell, and others who have cast Whewell as a fore-runner of the hypothetico-deductivist view, seem to have under-estimated the importance of this discovery phase in Whewell’s understanding of method (Snyder 1997a,b, 1999). Down-playing the discovery phase would come to characterize methodology of the early 20 th century (see section 3 ).

Mill, in his System of Logic , put forward a narrower view of induction as the essence of scientific method. For Mill, induction is the search first for regularities among events. Among those regularities, some will continue to hold for further observations, eventually gaining the status of laws. One can also look for regularities among the laws discovered in a domain, i.e., for a law of laws. Which “law law” will hold is time and discipline dependent and open to revision. One example is the Law of Universal Causation, and Mill put forward specific methods for identifying causes—now commonly known as Mill’s methods. These five methods look for circumstances which are common among the phenomena of interest, those which are absent when the phenomena are, or those for which both vary together. Mill’s methods are still seen as capturing basic intuitions about experimental methods for finding the relevant explanatory factors ( System of Logic (1843), see Mill entry). The methods advocated by Whewell and Mill, in the end, look similar. Both involve inductive generalization to covering laws. They differ dramatically, however, with respect to the necessity of the knowledge arrived at; that is, at the meta-methodological level (see the entries on Whewell and Mill entries).

3. Logic of method and critical responses

The quantum and relativistic revolutions in physics in the early 20 th century had a profound effect on methodology. Conceptual foundations of both theories were taken to show the defeasibility of even the most seemingly secure intuitions about space, time and bodies. Certainty of knowledge about the natural world was therefore recognized as unattainable. Instead a renewed empiricism was sought which rendered science fallible but still rationally justifiable.

Analyses of the reasoning of scientists emerged, according to which the aspects of scientific method which were of primary importance were the means of testing and confirming of theories. A distinction in methodology was made between the contexts of discovery and justification. The distinction could be used as a wedge between the particularities of where and how theories or hypotheses are arrived at, on the one hand, and the underlying reasoning scientists use (whether or not they are aware of it) when assessing theories and judging their adequacy on the basis of the available evidence. By and large, for most of the 20 th century, philosophy of science focused on the second context, although philosophers differed on whether to focus on confirmation or refutation as well as on the many details of how confirmation or refutation could or could not be brought about. By the mid-20 th century these attempts at defining the method of justification and the context distinction itself came under pressure. During the same period, philosophy of science developed rapidly, and from section 4 this entry will therefore shift from a primarily historical treatment of the scientific method towards a primarily thematic one.

Advances in logic and probability held out promise of the possibility of elaborate reconstructions of scientific theories and empirical method, the best example being Rudolf Carnap’s The Logical Structure of the World (1928). Carnap attempted to show that a scientific theory could be reconstructed as a formal axiomatic system—that is, a logic. That system could refer to the world because some of its basic sentences could be interpreted as observations or operations which one could perform to test them. The rest of the theoretical system, including sentences using theoretical or unobservable terms (like electron or force) would then either be meaningful because they could be reduced to observations, or they had purely logical meanings (called analytic, like mathematical identities). This has been referred to as the verifiability criterion of meaning. According to the criterion, any statement not either analytic or verifiable was strictly meaningless. Although the view was endorsed by Carnap in 1928, he would later come to see it as too restrictive (Carnap 1956). Another familiar version of this idea is operationalism of Percy William Bridgman. In The Logic of Modern Physics (1927) Bridgman asserted that every physical concept could be defined in terms of the operations one would perform to verify the application of that concept. Making good on the operationalisation of a concept even as simple as length, however, can easily become enormously complex (for measuring very small lengths, for instance) or impractical (measuring large distances like light years.)

Carl Hempel’s (1950, 1951) criticisms of the verifiability criterion of meaning had enormous influence. He pointed out that universal generalizations, such as most scientific laws, were not strictly meaningful on the criterion. Verifiability and operationalism both seemed too restrictive to capture standard scientific aims and practice. The tenuous connection between these reconstructions and actual scientific practice was criticized in another way. In both approaches, scientific methods are instead recast in methodological roles. Measurements, for example, were looked to as ways of giving meanings to terms. The aim of the philosopher of science was not to understand the methods per se , but to use them to reconstruct theories, their meanings, and their relation to the world. When scientists perform these operations, however, they will not report that they are doing them to give meaning to terms in a formal axiomatic system. This disconnect between methodology and the details of actual scientific practice would seem to violate the empiricism the Logical Positivists and Bridgman were committed to. The view that methodology should correspond to practice (to some extent) has been called historicism, or intuitionism. We turn to these criticisms and responses in section 3.4 . [ 4 ]

Positivism also had to contend with the recognition that a purely inductivist approach, along the lines of Bacon-Newton-Mill, was untenable. There was no pure observation, for starters. All observation was theory laden. Theory is required to make any observation, therefore not all theory can be derived from observation alone. (See the entry on theory and observation in science .) Even granting an observational basis, Hume had already pointed out that one could not deductively justify inductive conclusions without begging the question by presuming the success of the inductive method. Likewise, positivist attempts at analyzing how a generalization can be confirmed by observations of its instances were subject to a number of criticisms. Goodman (1965) and Hempel (1965) both point to paradoxes inherent in standard accounts of confirmation. Recent attempts at explaining how observations can serve to confirm a scientific theory are discussed in section 4 below.

The standard starting point for a non-inductive analysis of the logic of confirmation is known as the Hypothetico-Deductive (H-D) method. In its simplest form, a sentence of a theory which expresses some hypothesis is confirmed by its true consequences. As noted in section 2 , this method had been advanced by Whewell in the 19 th century, as well as Nicod (1924) and others in the 20 th century. Often, Hempel’s (1966) description of the H-D method, illustrated by the case of Semmelweiss’ inferential procedures in establishing the cause of childbed fever, has been presented as a key account of H-D as well as a foil for criticism of the H-D account of confirmation (see, for example, Lipton’s (2004) discussion of inference to the best explanation; also the entry on confirmation ). Hempel described Semmelsweiss’ procedure as examining various hypotheses explaining the cause of childbed fever. Some hypotheses conflicted with observable facts and could be rejected as false immediately. Others needed to be tested experimentally by deducing which observable events should follow if the hypothesis were true (what Hempel called the test implications of the hypothesis), then conducting an experiment and observing whether or not the test implications occurred. If the experiment showed the test implication to be false, the hypothesis could be rejected. If the experiment showed the test implications to be true, however, this did not prove the hypothesis true. The confirmation of a test implication does not verify a hypothesis, though Hempel did allow that “it provides at least some support, some corroboration or confirmation for it” (Hempel 1966: 8). The degree of this support then depends on the quantity, variety and precision of the supporting evidence.

Another approach that took off from the difficulties with inductive inference was Karl Popper’s critical rationalism or falsificationism (Popper 1959, 1963). Falsification is deductive and similar to H-D in that it involves scientists deducing observational consequences from the hypothesis under test. For Popper, however, the important point was not the degree of confirmation that successful prediction offered to a hypothesis. The crucial thing was the logical asymmetry between confirmation, based on inductive inference, and falsification, which can be based on a deductive inference. (This simple opposition was later questioned, by Lakatos, among others. See the entry on historicist theories of scientific rationality. )

Popper stressed that, regardless of the amount of confirming evidence, we can never be certain that a hypothesis is true without committing the fallacy of affirming the consequent. Instead, Popper introduced the notion of corroboration as a measure for how well a theory or hypothesis has survived previous testing—but without implying that this is also a measure for the probability that it is true.

Popper was also motivated by his doubts about the scientific status of theories like the Marxist theory of history or psycho-analysis, and so wanted to demarcate between science and pseudo-science. Popper saw this as an importantly different distinction than demarcating science from metaphysics. The latter demarcation was the primary concern of many logical empiricists. Popper used the idea of falsification to draw a line instead between pseudo and proper science. Science was science because its method involved subjecting theories to rigorous tests which offered a high probability of failing and thus refuting the theory.

A commitment to the risk of failure was important. Avoiding falsification could be done all too easily. If a consequence of a theory is inconsistent with observations, an exception can be added by introducing auxiliary hypotheses designed explicitly to save the theory, so-called ad hoc modifications. This Popper saw done in pseudo-science where ad hoc theories appeared capable of explaining anything in their field of application. In contrast, science is risky. If observations showed the predictions from a theory to be wrong, the theory would be refuted. Hence, scientific hypotheses must be falsifiable. Not only must there exist some possible observation statement which could falsify the hypothesis or theory, were it observed, (Popper called these the hypothesis’ potential falsifiers) it is crucial to the Popperian scientific method that such falsifications be sincerely attempted on a regular basis.

The more potential falsifiers of a hypothesis, the more falsifiable it would be, and the more the hypothesis claimed. Conversely, hypotheses without falsifiers claimed very little or nothing at all. Originally, Popper thought that this meant the introduction of ad hoc hypotheses only to save a theory should not be countenanced as good scientific method. These would undermine the falsifiabililty of a theory. However, Popper later came to recognize that the introduction of modifications (immunizations, he called them) was often an important part of scientific development. Responding to surprising or apparently falsifying observations often generated important new scientific insights. Popper’s own example was the observed motion of Uranus which originally did not agree with Newtonian predictions. The ad hoc hypothesis of an outer planet explained the disagreement and led to further falsifiable predictions. Popper sought to reconcile the view by blurring the distinction between falsifiable and not falsifiable, and speaking instead of degrees of testability (Popper 1985: 41f.).

From the 1960s on, sustained meta-methodological criticism emerged that drove philosophical focus away from scientific method. A brief look at those criticisms follows, with recommendations for further reading at the end of the entry.

Thomas Kuhn’s The Structure of Scientific Revolutions (1962) begins with a well-known shot across the bow for philosophers of science:

History, if viewed as a repository for more than anecdote or chronology, could produce a decisive transformation in the image of science by which we are now possessed. (1962: 1)

The image Kuhn thought needed transforming was the a-historical, rational reconstruction sought by many of the Logical Positivists, though Carnap and other positivists were actually quite sympathetic to Kuhn’s views. (See the entry on the Vienna Circle .) Kuhn shares with other of his contemporaries, such as Feyerabend and Lakatos, a commitment to a more empirical approach to philosophy of science. Namely, the history of science provides important data, and necessary checks, for philosophy of science, including any theory of scientific method.

The history of science reveals, according to Kuhn, that scientific development occurs in alternating phases. During normal science, the members of the scientific community adhere to the paradigm in place. Their commitment to the paradigm means a commitment to the puzzles to be solved and the acceptable ways of solving them. Confidence in the paradigm remains so long as steady progress is made in solving the shared puzzles. Method in this normal phase operates within a disciplinary matrix (Kuhn’s later concept of a paradigm) which includes standards for problem solving, and defines the range of problems to which the method should be applied. An important part of a disciplinary matrix is the set of values which provide the norms and aims for scientific method. The main values that Kuhn identifies are prediction, problem solving, simplicity, consistency, and plausibility.

An important by-product of normal science is the accumulation of puzzles which cannot be solved with resources of the current paradigm. Once accumulation of these anomalies has reached some critical mass, it can trigger a communal shift to a new paradigm and a new phase of normal science. Importantly, the values that provide the norms and aims for scientific method may have transformed in the meantime. Method may therefore be relative to discipline, time or place

Feyerabend also identified the aims of science as progress, but argued that any methodological prescription would only stifle that progress (Feyerabend 1988). His arguments are grounded in re-examining accepted “myths” about the history of science. Heroes of science, like Galileo, are shown to be just as reliant on rhetoric and persuasion as they are on reason and demonstration. Others, like Aristotle, are shown to be far more reasonable and far-reaching in their outlooks then they are given credit for. As a consequence, the only rule that could provide what he took to be sufficient freedom was the vacuous “anything goes”. More generally, even the methodological restriction that science is the best way to pursue knowledge, and to increase knowledge, is too restrictive. Feyerabend suggested instead that science might, in fact, be a threat to a free society, because it and its myth had become so dominant (Feyerabend 1978).

An even more fundamental kind of criticism was offered by several sociologists of science from the 1970s onwards who rejected the methodology of providing philosophical accounts for the rational development of science and sociological accounts of the irrational mistakes. Instead, they adhered to a symmetry thesis on which any causal explanation of how scientific knowledge is established needs to be symmetrical in explaining truth and falsity, rationality and irrationality, success and mistakes, by the same causal factors (see, e.g., Barnes and Bloor 1982, Bloor 1991). Movements in the Sociology of Science, like the Strong Programme, or in the social dimensions and causes of knowledge more generally led to extended and close examination of detailed case studies in contemporary science and its history. (See the entries on the social dimensions of scientific knowledge and social epistemology .) Well-known examinations by Latour and Woolgar (1979/1986), Knorr-Cetina (1981), Pickering (1984), Shapin and Schaffer (1985) seem to bear out that it was social ideologies (on a macro-scale) or individual interactions and circumstances (on a micro-scale) which were the primary causal factors in determining which beliefs gained the status of scientific knowledge. As they saw it therefore, explanatory appeals to scientific method were not empirically grounded.

A late, and largely unexpected, criticism of scientific method came from within science itself. Beginning in the early 2000s, a number of scientists attempting to replicate the results of published experiments could not do so. There may be close conceptual connection between reproducibility and method. For example, if reproducibility means that the same scientific methods ought to produce the same result, and all scientific results ought to be reproducible, then whatever it takes to reproduce a scientific result ought to be called scientific method. Space limits us to the observation that, insofar as reproducibility is a desired outcome of proper scientific method, it is not strictly a part of scientific method. (See the entry on reproducibility of scientific results .)

By the close of the 20 th century the search for the scientific method was flagging. Nola and Sankey (2000b) could introduce their volume on method by remarking that “For some, the whole idea of a theory of scientific method is yester-year’s debate …”.

Despite the many difficulties that philosophers encountered in trying to providing a clear methodology of conformation (or refutation), still important progress has been made on understanding how observation can provide evidence for a given theory. Work in statistics has been crucial for understanding how theories can be tested empirically, and in recent decades a huge literature has developed that attempts to recast confirmation in Bayesian terms. Here these developments can be covered only briefly, and we refer to the entry on confirmation for further details and references.

Statistics has come to play an increasingly important role in the methodology of the experimental sciences from the 19 th century onwards. At that time, statistics and probability theory took on a methodological role as an analysis of inductive inference, and attempts to ground the rationality of induction in the axioms of probability theory have continued throughout the 20 th century and in to the present. Developments in the theory of statistics itself, meanwhile, have had a direct and immense influence on the experimental method, including methods for measuring the uncertainty of observations such as the Method of Least Squares developed by Legendre and Gauss in the early 19 th century, criteria for the rejection of outliers proposed by Peirce by the mid-19 th century, and the significance tests developed by Gosset (a.k.a. “Student”), Fisher, Neyman & Pearson and others in the 1920s and 1930s (see, e.g., Swijtink 1987 for a brief historical overview; and also the entry on C.S. Peirce ).

These developments within statistics then in turn led to a reflective discussion among both statisticians and philosophers of science on how to perceive the process of hypothesis testing: whether it was a rigorous statistical inference that could provide a numerical expression of the degree of confidence in the tested hypothesis, or if it should be seen as a decision between different courses of actions that also involved a value component. This led to a major controversy among Fisher on the one side and Neyman and Pearson on the other (see especially Fisher 1955, Neyman 1956 and Pearson 1955, and for analyses of the controversy, e.g., Howie 2002, Marks 2000, Lenhard 2006). On Fisher’s view, hypothesis testing was a methodology for when to accept or reject a statistical hypothesis, namely that a hypothesis should be rejected by evidence if this evidence would be unlikely relative to other possible outcomes, given the hypothesis were true. In contrast, on Neyman and Pearson’s view, the consequence of error also had to play a role when deciding between hypotheses. Introducing the distinction between the error of rejecting a true hypothesis (type I error) and accepting a false hypothesis (type II error), they argued that it depends on the consequences of the error to decide whether it is more important to avoid rejecting a true hypothesis or accepting a false one. Hence, Fisher aimed for a theory of inductive inference that enabled a numerical expression of confidence in a hypothesis. To him, the important point was the search for truth, not utility. In contrast, the Neyman-Pearson approach provided a strategy of inductive behaviour for deciding between different courses of action. Here, the important point was not whether a hypothesis was true, but whether one should act as if it was.

Similar discussions are found in the philosophical literature. On the one side, Churchman (1948) and Rudner (1953) argued that because scientific hypotheses can never be completely verified, a complete analysis of the methods of scientific inference includes ethical judgments in which the scientists must decide whether the evidence is sufficiently strong or that the probability is sufficiently high to warrant the acceptance of the hypothesis, which again will depend on the importance of making a mistake in accepting or rejecting the hypothesis. Others, such as Jeffrey (1956) and Levi (1960) disagreed and instead defended a value-neutral view of science on which scientists should bracket their attitudes, preferences, temperament, and values when assessing the correctness of their inferences. For more details on this value-free ideal in the philosophy of science and its historical development, see Douglas (2009) and Howard (2003). For a broad set of case studies examining the role of values in science, see e.g. Elliott & Richards 2017.

In recent decades, philosophical discussions of the evaluation of probabilistic hypotheses by statistical inference have largely focused on Bayesianism that understands probability as a measure of a person’s degree of belief in an event, given the available information, and frequentism that instead understands probability as a long-run frequency of a repeatable event. Hence, for Bayesians probabilities refer to a state of knowledge, whereas for frequentists probabilities refer to frequencies of events (see, e.g., Sober 2008, chapter 1 for a detailed introduction to Bayesianism and frequentism as well as to likelihoodism). Bayesianism aims at providing a quantifiable, algorithmic representation of belief revision, where belief revision is a function of prior beliefs (i.e., background knowledge) and incoming evidence. Bayesianism employs a rule based on Bayes’ theorem, a theorem of the probability calculus which relates conditional probabilities. The probability that a particular hypothesis is true is interpreted as a degree of belief, or credence, of the scientist. There will also be a probability and a degree of belief that a hypothesis will be true conditional on a piece of evidence (an observation, say) being true. Bayesianism proscribes that it is rational for the scientist to update their belief in the hypothesis to that conditional probability should it turn out that the evidence is, in fact, observed (see, e.g., Sprenger & Hartmann 2019 for a comprehensive treatment of Bayesian philosophy of science). Originating in the work of Neyman and Person, frequentism aims at providing the tools for reducing long-run error rates, such as the error-statistical approach developed by Mayo (1996) that focuses on how experimenters can avoid both type I and type II errors by building up a repertoire of procedures that detect errors if and only if they are present. Both Bayesianism and frequentism have developed over time, they are interpreted in different ways by its various proponents, and their relations to previous criticism to attempts at defining scientific method are seen differently by proponents and critics. The literature, surveys, reviews and criticism in this area are vast and the reader is referred to the entries on Bayesian epistemology and confirmation .

5. Method in Practice

Attention to scientific practice, as we have seen, is not itself new. However, the turn to practice in the philosophy of science of late can be seen as a correction to the pessimism with respect to method in philosophy of science in later parts of the 20 th century, and as an attempted reconciliation between sociological and rationalist explanations of scientific knowledge. Much of this work sees method as detailed and context specific problem-solving procedures, and methodological analyses to be at the same time descriptive, critical and advisory (see Nickles 1987 for an exposition of this view). The following section contains a survey of some of the practice focuses. In this section we turn fully to topics rather than chronology.

A problem with the distinction between the contexts of discovery and justification that figured so prominently in philosophy of science in the first half of the 20 th century (see section 2 ) is that no such distinction can be clearly seen in scientific activity (see Arabatzis 2006). Thus, in recent decades, it has been recognized that study of conceptual innovation and change should not be confined to psychology and sociology of science, but are also important aspects of scientific practice which philosophy of science should address (see also the entry on scientific discovery ). Looking for the practices that drive conceptual innovation has led philosophers to examine both the reasoning practices of scientists and the wide realm of experimental practices that are not directed narrowly at testing hypotheses, that is, exploratory experimentation.

Examining the reasoning practices of historical and contemporary scientists, Nersessian (2008) has argued that new scientific concepts are constructed as solutions to specific problems by systematic reasoning, and that of analogy, visual representation and thought-experimentation are among the important reasoning practices employed. These ubiquitous forms of reasoning are reliable—but also fallible—methods of conceptual development and change. On her account, model-based reasoning consists of cycles of construction, simulation, evaluation and adaption of models that serve as interim interpretations of the target problem to be solved. Often, this process will lead to modifications or extensions, and a new cycle of simulation and evaluation. However, Nersessian also emphasizes that

creative model-based reasoning cannot be applied as a simple recipe, is not always productive of solutions, and even its most exemplary usages can lead to incorrect solutions. (Nersessian 2008: 11)

Thus, while on the one hand she agrees with many previous philosophers that there is no logic of discovery, discoveries can derive from reasoned processes, such that a large and integral part of scientific practice is

the creation of concepts through which to comprehend, structure, and communicate about physical phenomena …. (Nersessian 1987: 11)

Similarly, work on heuristics for discovery and theory construction by scholars such as Darden (1991) and Bechtel & Richardson (1993) present science as problem solving and investigate scientific problem solving as a special case of problem-solving in general. Drawing largely on cases from the biological sciences, much of their focus has been on reasoning strategies for the generation, evaluation, and revision of mechanistic explanations of complex systems.

Addressing another aspect of the context distinction, namely the traditional view that the primary role of experiments is to test theoretical hypotheses according to the H-D model, other philosophers of science have argued for additional roles that experiments can play. The notion of exploratory experimentation was introduced to describe experiments driven by the desire to obtain empirical regularities and to develop concepts and classifications in which these regularities can be described (Steinle 1997, 2002; Burian 1997; Waters 2007)). However the difference between theory driven experimentation and exploratory experimentation should not be seen as a sharp distinction. Theory driven experiments are not always directed at testing hypothesis, but may also be directed at various kinds of fact-gathering, such as determining numerical parameters. Vice versa , exploratory experiments are usually informed by theory in various ways and are therefore not theory-free. Instead, in exploratory experiments phenomena are investigated without first limiting the possible outcomes of the experiment on the basis of extant theory about the phenomena.

The development of high throughput instrumentation in molecular biology and neighbouring fields has given rise to a special type of exploratory experimentation that collects and analyses very large amounts of data, and these new ‘omics’ disciplines are often said to represent a break with the ideal of hypothesis-driven science (Burian 2007; Elliott 2007; Waters 2007; O’Malley 2007) and instead described as data-driven research (Leonelli 2012; Strasser 2012) or as a special kind of “convenience experimentation” in which many experiments are done simply because they are extraordinarily convenient to perform (Krohs 2012).

5.2 Computer methods and ‘new ways’ of doing science

The field of omics just described is possible because of the ability of computers to process, in a reasonable amount of time, the huge quantities of data required. Computers allow for more elaborate experimentation (higher speed, better filtering, more variables, sophisticated coordination and control), but also, through modelling and simulations, might constitute a form of experimentation themselves. Here, too, we can pose a version of the general question of method versus practice: does the practice of using computers fundamentally change scientific method, or merely provide a more efficient means of implementing standard methods?

Because computers can be used to automate measurements, quantifications, calculations, and statistical analyses where, for practical reasons, these operations cannot be otherwise carried out, many of the steps involved in reaching a conclusion on the basis of an experiment are now made inside a “black box”, without the direct involvement or awareness of a human. This has epistemological implications, regarding what we can know, and how we can know it. To have confidence in the results, computer methods are therefore subjected to tests of verification and validation.

The distinction between verification and validation is easiest to characterize in the case of computer simulations. In a typical computer simulation scenario computers are used to numerically integrate differential equations for which no analytic solution is available. The equations are part of the model the scientist uses to represent a phenomenon or system under investigation. Verifying a computer simulation means checking that the equations of the model are being correctly approximated. Validating a simulation means checking that the equations of the model are adequate for the inferences one wants to make on the basis of that model.

A number of issues related to computer simulations have been raised. The identification of validity and verification as the testing methods has been criticized. Oreskes et al. (1994) raise concerns that “validiation”, because it suggests deductive inference, might lead to over-confidence in the results of simulations. The distinction itself is probably too clean, since actual practice in the testing of simulations mixes and moves back and forth between the two (Weissart 1997; Parker 2008a; Winsberg 2010). Computer simulations do seem to have a non-inductive character, given that the principles by which they operate are built in by the programmers, and any results of the simulation follow from those in-built principles in such a way that those results could, in principle, be deduced from the program code and its inputs. The status of simulations as experiments has therefore been examined (Kaufmann and Smarr 1993; Humphreys 1995; Hughes 1999; Norton and Suppe 2001). This literature considers the epistemology of these experiments: what we can learn by simulation, and also the kinds of justifications which can be given in applying that knowledge to the “real” world. (Mayo 1996; Parker 2008b). As pointed out, part of the advantage of computer simulation derives from the fact that huge numbers of calculations can be carried out without requiring direct observation by the experimenter/​simulator. At the same time, many of these calculations are approximations to the calculations which would be performed first-hand in an ideal situation. Both factors introduce uncertainties into the inferences drawn from what is observed in the simulation.

For many of the reasons described above, computer simulations do not seem to belong clearly to either the experimental or theoretical domain. Rather, they seem to crucially involve aspects of both. This has led some authors, such as Fox Keller (2003: 200) to argue that we ought to consider computer simulation a “qualitatively different way of doing science”. The literature in general tends to follow Kaufmann and Smarr (1993) in referring to computer simulation as a “third way” for scientific methodology (theoretical reasoning and experimental practice are the first two ways.). It should also be noted that the debates around these issues have tended to focus on the form of computer simulation typical in the physical sciences, where models are based on dynamical equations. Other forms of simulation might not have the same problems, or have problems of their own (see the entry on computer simulations in science ).

In recent years, the rapid development of machine learning techniques has prompted some scholars to suggest that the scientific method has become “obsolete” (Anderson 2008, Carrol and Goodstein 2009). This has resulted in an intense debate on the relative merit of data-driven and hypothesis-driven research (for samples, see e.g. Mazzocchi 2015 or Succi and Coveney 2018). For a detailed treatment of this topic, we refer to the entry scientific research and big data .

6. Discourse on scientific method

Despite philosophical disagreements, the idea of the scientific method still figures prominently in contemporary discourse on many different topics, both within science and in society at large. Often, reference to scientific method is used in ways that convey either the legend of a single, universal method characteristic of all science, or grants to a particular method or set of methods privilege as a special ‘gold standard’, often with reference to particular philosophers to vindicate the claims. Discourse on scientific method also typically arises when there is a need to distinguish between science and other activities, or for justifying the special status conveyed to science. In these areas, the philosophical attempts at identifying a set of methods characteristic for scientific endeavors are closely related to the philosophy of science’s classical problem of demarcation (see the entry on science and pseudo-science ) and to the philosophical analysis of the social dimension of scientific knowledge and the role of science in democratic society.

One of the settings in which the legend of a single, universal scientific method has been particularly strong is science education (see, e.g., Bauer 1992; McComas 1996; Wivagg & Allchin 2002). [ 5 ] Often, ‘the scientific method’ is presented in textbooks and educational web pages as a fixed four or five step procedure starting from observations and description of a phenomenon and progressing over formulation of a hypothesis which explains the phenomenon, designing and conducting experiments to test the hypothesis, analyzing the results, and ending with drawing a conclusion. Such references to a universal scientific method can be found in educational material at all levels of science education (Blachowicz 2009), and numerous studies have shown that the idea of a general and universal scientific method often form part of both students’ and teachers’ conception of science (see, e.g., Aikenhead 1987; Osborne et al. 2003). In response, it has been argued that science education need to focus more on teaching about the nature of science, although views have differed on whether this is best done through student-led investigations, contemporary cases, or historical cases (Allchin, Andersen & Nielsen 2014)

Although occasionally phrased with reference to the H-D method, important historical roots of the legend in science education of a single, universal scientific method are the American philosopher and psychologist Dewey’s account of inquiry in How We Think (1910) and the British mathematician Karl Pearson’s account of science in Grammar of Science (1892). On Dewey’s account, inquiry is divided into the five steps of

(i) a felt difficulty, (ii) its location and definition, (iii) suggestion of a possible solution, (iv) development by reasoning of the bearing of the suggestions, (v) further observation and experiment leading to its acceptance or rejection. (Dewey 1910: 72)

Similarly, on Pearson’s account, scientific investigations start with measurement of data and observation of their correction and sequence from which scientific laws can be discovered with the aid of creative imagination. These laws have to be subject to criticism, and their final acceptance will have equal validity for “all normally constituted minds”. Both Dewey’s and Pearson’s accounts should be seen as generalized abstractions of inquiry and not restricted to the realm of science—although both Dewey and Pearson referred to their respective accounts as ‘the scientific method’.

Occasionally, scientists make sweeping statements about a simple and distinct scientific method, as exemplified by Feynman’s simplified version of a conjectures and refutations method presented, for example, in the last of his 1964 Cornell Messenger lectures. [ 6 ] However, just as often scientists have come to the same conclusion as recent philosophy of science that there is not any unique, easily described scientific method. For example, the physicist and Nobel Laureate Weinberg described in the paper “The Methods of Science … And Those By Which We Live” (1995) how

The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend. (1995: 8)

Interview studies with scientists on their conception of method shows that scientists often find it hard to figure out whether available evidence confirms their hypothesis, and that there are no direct translations between general ideas about method and specific strategies to guide how research is conducted (Schickore & Hangel 2019, Hangel & Schickore 2017)

Reference to the scientific method has also often been used to argue for the scientific nature or special status of a particular activity. Philosophical positions that argue for a simple and unique scientific method as a criterion of demarcation, such as Popperian falsification, have often attracted practitioners who felt that they had a need to defend their domain of practice. For example, references to conjectures and refutation as the scientific method are abundant in much of the literature on complementary and alternative medicine (CAM)—alongside the competing position that CAM, as an alternative to conventional biomedicine, needs to develop its own methodology different from that of science.

Also within mainstream science, reference to the scientific method is used in arguments regarding the internal hierarchy of disciplines and domains. A frequently seen argument is that research based on the H-D method is superior to research based on induction from observations because in deductive inferences the conclusion follows necessarily from the premises. (See, e.g., Parascandola 1998 for an analysis of how this argument has been made to downgrade epidemiology compared to the laboratory sciences.) Similarly, based on an examination of the practices of major funding institutions such as the National Institutes of Health (NIH), the National Science Foundation (NSF) and the Biomedical Sciences Research Practices (BBSRC) in the UK, O’Malley et al. (2009) have argued that funding agencies seem to have a tendency to adhere to the view that the primary activity of science is to test hypotheses, while descriptive and exploratory research is seen as merely preparatory activities that are valuable only insofar as they fuel hypothesis-driven research.

In some areas of science, scholarly publications are structured in a way that may convey the impression of a neat and linear process of inquiry from stating a question, devising the methods by which to answer it, collecting the data, to drawing a conclusion from the analysis of data. For example, the codified format of publications in most biomedical journals known as the IMRAD format (Introduction, Method, Results, Analysis, Discussion) is explicitly described by the journal editors as “not an arbitrary publication format but rather a direct reflection of the process of scientific discovery” (see the so-called “Vancouver Recommendations”, ICMJE 2013: 11). However, scientific publications do not in general reflect the process by which the reported scientific results were produced. For example, under the provocative title “Is the scientific paper a fraud?”, Medawar argued that scientific papers generally misrepresent how the results have been produced (Medawar 1963/1996). Similar views have been advanced by philosophers, historians and sociologists of science (Gilbert 1976; Holmes 1987; Knorr-Cetina 1981; Schickore 2008; Suppe 1998) who have argued that scientists’ experimental practices are messy and often do not follow any recognizable pattern. Publications of research results, they argue, are retrospective reconstructions of these activities that often do not preserve the temporal order or the logic of these activities, but are instead often constructed in order to screen off potential criticism (see Schickore 2008 for a review of this work).

Philosophical positions on the scientific method have also made it into the court room, especially in the US where judges have drawn on philosophy of science in deciding when to confer special status to scientific expert testimony. A key case is Daubert vs Merrell Dow Pharmaceuticals (92–102, 509 U.S. 579, 1993). In this case, the Supreme Court argued in its 1993 ruling that trial judges must ensure that expert testimony is reliable, and that in doing this the court must look at the expert’s methodology to determine whether the proffered evidence is actually scientific knowledge. Further, referring to works of Popper and Hempel the court stated that

ordinarily, a key question to be answered in determining whether a theory or technique is scientific knowledge … is whether it can be (and has been) tested. (Justice Blackmun, Daubert v. Merrell Dow Pharmaceuticals; see Other Internet Resources for a link to the opinion)

But as argued by Haack (2005a,b, 2010) and by Foster & Hubner (1999), by equating the question of whether a piece of testimony is reliable with the question whether it is scientific as indicated by a special methodology, the court was producing an inconsistent mixture of Popper’s and Hempel’s philosophies, and this has later led to considerable confusion in subsequent case rulings that drew on the Daubert case (see Haack 2010 for a detailed exposition).

The difficulties around identifying the methods of science are also reflected in the difficulties of identifying scientific misconduct in the form of improper application of the method or methods of science. One of the first and most influential attempts at defining misconduct in science was the US definition from 1989 that defined misconduct as

fabrication, falsification, plagiarism, or other practices that seriously deviate from those that are commonly accepted within the scientific community . (Code of Federal Regulations, part 50, subpart A., August 8, 1989, italics added)

However, the “other practices that seriously deviate” clause was heavily criticized because it could be used to suppress creative or novel science. For example, the National Academy of Science stated in their report Responsible Science (1992) that it

wishes to discourage the possibility that a misconduct complaint could be lodged against scientists based solely on their use of novel or unorthodox research methods. (NAS: 27)

This clause was therefore later removed from the definition. For an entry into the key philosophical literature on conduct in science, see Shamoo & Resnick (2009).

The question of the source of the success of science has been at the core of philosophy since the beginning of modern science. If viewed as a matter of epistemology more generally, scientific method is a part of the entire history of philosophy. Over that time, science and whatever methods its practitioners may employ have changed dramatically. Today, many philosophers have taken up the banners of pluralism or of practice to focus on what are, in effect, fine-grained and contextually limited examinations of scientific method. Others hope to shift perspectives in order to provide a renewed general account of what characterizes the activity we call science.

One such perspective has been offered recently by Hoyningen-Huene (2008, 2013), who argues from the history of philosophy of science that after three lengthy phases of characterizing science by its method, we are now in a phase where the belief in the existence of a positive scientific method has eroded and what has been left to characterize science is only its fallibility. First was a phase from Plato and Aristotle up until the 17 th century where the specificity of scientific knowledge was seen in its absolute certainty established by proof from evident axioms; next was a phase up to the mid-19 th century in which the means to establish the certainty of scientific knowledge had been generalized to include inductive procedures as well. In the third phase, which lasted until the last decades of the 20 th century, it was recognized that empirical knowledge was fallible, but it was still granted a special status due to its distinctive mode of production. But now in the fourth phase, according to Hoyningen-Huene, historical and philosophical studies have shown how “scientific methods with the characteristics as posited in the second and third phase do not exist” (2008: 168) and there is no longer any consensus among philosophers and historians of science about the nature of science. For Hoyningen-Huene, this is too negative a stance, and he therefore urges the question about the nature of science anew. His own answer to this question is that “scientific knowledge differs from other kinds of knowledge, especially everyday knowledge, primarily by being more systematic” (Hoyningen-Huene 2013: 14). Systematicity can have several different dimensions: among them are more systematic descriptions, explanations, predictions, defense of knowledge claims, epistemic connectedness, ideal of completeness, knowledge generation, representation of knowledge and critical discourse. Hence, what characterizes science is the greater care in excluding possible alternative explanations, the more detailed elaboration with respect to data on which predictions are based, the greater care in detecting and eliminating sources of error, the more articulate connections to other pieces of knowledge, etc. On this position, what characterizes science is not that the methods employed are unique to science, but that the methods are more carefully employed.

Another, similar approach has been offered by Haack (2003). She sets off, similar to Hoyningen-Huene, from a dissatisfaction with the recent clash between what she calls Old Deferentialism and New Cynicism. The Old Deferentialist position is that science progressed inductively by accumulating true theories confirmed by empirical evidence or deductively by testing conjectures against basic statements; while the New Cynics position is that science has no epistemic authority and no uniquely rational method and is merely just politics. Haack insists that contrary to the views of the New Cynics, there are objective epistemic standards, and there is something epistemologically special about science, even though the Old Deferentialists pictured this in a wrong way. Instead, she offers a new Critical Commonsensist account on which standards of good, strong, supportive evidence and well-conducted, honest, thorough and imaginative inquiry are not exclusive to the sciences, but the standards by which we judge all inquirers. In this sense, science does not differ in kind from other kinds of inquiry, but it may differ in the degree to which it requires broad and detailed background knowledge and a familiarity with a technical vocabulary that only specialists may possess.

• Aikenhead, G.S., 1987, “High-school graduates’ beliefs about science-technology-society. III. Characteristics and limitations of scientific knowledge”, Science Education , 71(4): 459–487.
• Allchin, D., H.M. Andersen and K. Nielsen, 2014, “Complementary Approaches to Teaching Nature of Science: Integrating Student Inquiry, Historical Cases, and Contemporary Cases in Classroom Practice”, Science Education , 98: 461–486.
• Anderson, C., 2008, “The end of theory: The data deluge makes the scientific method obsolete”, Wired magazine , 16(7): 16–07
• Arabatzis, T., 2006, “On the inextricability of the context of discovery and the context of justification”, in Revisiting Discovery and Justification , J. Schickore and F. Steinle (eds.), Dordrecht: Springer, pp. 215–230.
• Barnes, J. (ed.), 1984, The Complete Works of Aristotle, Vols I and II , Princeton: Princeton University Press.
• Barnes, B. and D. Bloor, 1982, “Relativism, Rationalism, and the Sociology of Knowledge”, in Rationality and Relativism , M. Hollis and S. Lukes (eds.), Cambridge: MIT Press, pp. 1–20.
• Bauer, H.H., 1992, Scientific Literacy and the Myth of the Scientific Method , Urbana: University of Illinois Press.
• Bechtel, W. and R.C. Richardson, 1993, Discovering complexity , Princeton, NJ: Princeton University Press.
• Berkeley, G., 1734, The Analyst in De Motu and The Analyst: A Modern Edition with Introductions and Commentary , D. Jesseph (trans. and ed.), Dordrecht: Kluwer Academic Publishers, 1992.
• Blachowicz, J., 2009, “How science textbooks treat scientific method: A philosopher’s perspective”, The British Journal for the Philosophy of Science , 60(2): 303–344.
• Bloor, D., 1991, Knowledge and Social Imagery , Chicago: University of Chicago Press, 2 nd edition.
• Boyle, R., 1682, New experiments physico-mechanical, touching the air , Printed by Miles Flesher for Richard Davis, bookseller in Oxford.
• Bridgman, P.W., 1927, The Logic of Modern Physics , New York: Macmillan.
• –––, 1956, “The Methodological Character of Theoretical Concepts”, in The Foundations of Science and the Concepts of Science and Psychology , Herbert Feigl and Michael Scriven (eds.), Minnesota: University of Minneapolis Press, pp. 38–76.
• Burian, R., 1997, “Exploratory Experimentation and the Role of Histochemical Techniques in the Work of Jean Brachet, 1938–1952”, History and Philosophy of the Life Sciences , 19(1): 27–45.
• –––, 2007, “On microRNA and the need for exploratory experimentation in post-genomic molecular biology”, History and Philosophy of the Life Sciences , 29(3): 285–311.
• Carnap, R., 1928, Der logische Aufbau der Welt , Berlin: Bernary, transl. by R.A. George, The Logical Structure of the World , Berkeley: University of California Press, 1967.
• –––, 1956, “The methodological character of theoretical concepts”, Minnesota studies in the philosophy of science , 1: 38–76.
• Carrol, S., and D. Goodstein, 2009, “Defining the scientific method”, Nature Methods , 6: 237.
• Churchman, C.W., 1948, “Science, Pragmatics, Induction”, Philosophy of Science , 15(3): 249–268.
• Cooper, J. (ed.), 1997, Plato: Complete Works , Indianapolis: Hackett.
• Darden, L., 1991, Theory Change in Science: Strategies from Mendelian Genetics , Oxford: Oxford University Press
• Dewey, J., 1910, How we think , New York: Dover Publications (reprinted 1997).
• Douglas, H., 2009, Science, Policy, and the Value-Free Ideal , Pittsburgh: University of Pittsburgh Press.
• Dupré, J., 2004, “Miracle of Monism ”, in Naturalism in Question , Mario De Caro and David Macarthur (eds.), Cambridge, MA: Harvard University Press, pp. 36–58.
• Elliott, K.C., 2007, “Varieties of exploratory experimentation in nanotoxicology”, History and Philosophy of the Life Sciences , 29(3): 311–334.
• Elliott, K. C., and T. Richards (eds.), 2017, Exploring inductive risk: Case studies of values in science , Oxford: Oxford University Press.
• Falcon, Andrea, 2005, Aristotle and the science of nature: Unity without uniformity , Cambridge: Cambridge University Press.
• Feyerabend, P., 1978, Science in a Free Society , London: New Left Books
• –––, 1988, Against Method , London: Verso, 2 nd edition.
• Fisher, R.A., 1955, “Statistical Methods and Scientific Induction”, Journal of The Royal Statistical Society. Series B (Methodological) , 17(1): 69–78.
• Foster, K. and P.W. Huber, 1999, Judging Science. Scientific Knowledge and the Federal Courts , Cambridge: MIT Press.
• Fox Keller, E., 2003, “Models, Simulation, and ‘computer experiments’”, in The Philosophy of Scientific Experimentation , H. Radder (ed.), Pittsburgh: Pittsburgh University Press, 198–215.
• Gilbert, G., 1976, “The transformation of research findings into scientific knowledge”, Social Studies of Science , 6: 281–306.
• Gimbel, S., 2011, Exploring the Scientific Method , Chicago: University of Chicago Press.
• Goodman, N., 1965, Fact , Fiction, and Forecast , Indianapolis: Bobbs-Merrill.
• Haack, S., 1995, “Science is neither sacred nor a confidence trick”, Foundations of Science , 1(3): 323–335.
• –––, 2003, Defending science—within reason , Amherst: Prometheus.
• –––, 2005a, “Disentangling Daubert: an epistemological study in theory and practice”, Journal of Philosophy, Science and Law , 5, Haack 2005a available online . doi:10.5840/jpsl2005513
• –––, 2005b, “Trial and error: The Supreme Court’s philosophy of science”, American Journal of Public Health , 95: S66-S73.
• –––, 2010, “Federal Philosophy of Science: A Deconstruction-and a Reconstruction”, NYUJL & Liberty , 5: 394.
• Hangel, N. and J. Schickore, 2017, “Scientists’ conceptions of good research practice”, Perspectives on Science , 25(6): 766–791
• Harper, W.L., 2011, Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Cosmology , Oxford: Oxford University Press.
• Hempel, C., 1950, “Problems and Changes in the Empiricist Criterion of Meaning”, Revue Internationale de Philosophie , 41(11): 41–63.
• –––, 1951, “The Concept of Cognitive Significance: A Reconsideration”, Proceedings of the American Academy of Arts and Sciences , 80(1): 61–77.
• –––, 1965, Aspects of scientific explanation and other essays in the philosophy of science , New York–London: Free Press.
• –––, 1966, Philosophy of Natural Science , Englewood Cliffs: Prentice-Hall.
• Holmes, F.L., 1987, “Scientific writing and scientific discovery”, Isis , 78(2): 220–235.
• Howard, D., 2003, “Two left turns make a right: On the curious political career of North American philosophy of science at midcentury”, in Logical Empiricism in North America , G.L. Hardcastle & A.W. Richardson (eds.), Minneapolis: University of Minnesota Press, pp. 25–93.
• Hoyningen-Huene, P., 2008, “Systematicity: The nature of science”, Philosophia , 36(2): 167–180.
• –––, 2013, Systematicity. The Nature of Science , Oxford: Oxford University Press.
• Howie, D., 2002, Interpreting probability: Controversies and developments in the early twentieth century , Cambridge: Cambridge University Press.
• Hughes, R., 1999, “The Ising Model, Computer Simulation, and Universal Physics”, in Models as Mediators , M. Morgan and M. Morrison (eds.), Cambridge: Cambridge University Press, pp. 97–145
• Hume, D., 1739, A Treatise of Human Nature , D. Fate Norton and M.J. Norton (eds.), Oxford: Oxford University Press, 2000.
• Humphreys, P., 1995, “Computational science and scientific method”, Minds and Machines , 5(1): 499–512.
• ICMJE, 2013, “Recommendations for the Conduct, Reporting, Editing, and Publication of Scholarly Work in Medical Journals”, International Committee of Medical Journal Editors, available online , accessed August 13 2014
• Jeffrey, R.C., 1956, “Valuation and Acceptance of Scientific Hypotheses”, Philosophy of Science , 23(3): 237–246.
• Kaufmann, W.J., and L.L. Smarr, 1993, Supercomputing and the Transformation of Science , New York: Scientific American Library.
• Knorr-Cetina, K., 1981, The Manufacture of Knowledge , Oxford: Pergamon Press.
• Krohs, U., 2012, “Convenience experimentation”, Studies in History and Philosophy of Biological and BiomedicalSciences , 43: 52–57.
• Kuhn, T.S., 1962, The Structure of Scientific Revolutions , Chicago: University of Chicago Press
• Latour, B. and S. Woolgar, 1986, Laboratory Life: The Construction of Scientific Facts , Princeton: Princeton University Press, 2 nd edition.
• Laudan, L., 1968, “Theories of scientific method from Plato to Mach”, History of Science , 7(1): 1–63.
• Lenhard, J., 2006, “Models and statistical inference: The controversy between Fisher and Neyman-Pearson”, The British Journal for the Philosophy of Science , 57(1): 69–91.
• Leonelli, S., 2012, “Making Sense of Data-Driven Research in the Biological and the Biomedical Sciences”, Studies in the History and Philosophy of the Biological and Biomedical Sciences , 43(1): 1–3.
• Levi, I., 1960, “Must the scientist make value judgments?”, Philosophy of Science , 57(11): 345–357
• Lindley, D., 1991, Theory Change in Science: Strategies from Mendelian Genetics , Oxford: Oxford University Press.
• Lipton, P., 2004, Inference to the Best Explanation , London: Routledge, 2 nd edition.
• Marks, H.M., 2000, The progress of experiment: science and therapeutic reform in the United States, 1900–1990 , Cambridge: Cambridge University Press.
• Mazzochi, F., 2015, “Could Big Data be the end of theory in science?”, EMBO reports , 16: 1250–1255.
• Mayo, D.G., 1996, Error and the Growth of Experimental Knowledge , Chicago: University of Chicago Press.
• McComas, W.F., 1996, “Ten myths of science: Reexamining what we think we know about the nature of science”, School Science and Mathematics , 96(1): 10–16.
• Medawar, P.B., 1963/1996, “Is the scientific paper a fraud”, in The Strange Case of the Spotted Mouse and Other Classic Essays on Science , Oxford: Oxford University Press, 33–39.
• Mill, J.S., 1963, Collected Works of John Stuart Mill , J. M. Robson (ed.), Toronto: University of Toronto Press
• NAS, 1992, Responsible Science: Ensuring the integrity of the research process , Washington DC: National Academy Press.
• Nersessian, N.J., 1987, “A cognitive-historical approach to meaning in scientific theories”, in The process of science , N. Nersessian (ed.), Berlin: Springer, pp. 161–177.
• –––, 2008, Creating Scientific Concepts , Cambridge: MIT Press.
• Newton, I., 1726, Philosophiae naturalis Principia Mathematica (3 rd edition), in The Principia: Mathematical Principles of Natural Philosophy: A New Translation , I.B. Cohen and A. Whitman (trans.), Berkeley: University of California Press, 1999.
• –––, 1704, Opticks or A Treatise of the Reflections, Refractions, Inflections & Colors of Light , New York: Dover Publications, 1952.
• Neyman, J., 1956, “Note on an Article by Sir Ronald Fisher”, Journal of the Royal Statistical Society. Series B (Methodological) , 18: 288–294.
• Nickles, T., 1987, “Methodology, heuristics, and rationality”, in Rational changes in science: Essays on Scientific Reasoning , J.C. Pitt (ed.), Berlin: Springer, pp. 103–132.
• Nicod, J., 1924, Le problème logique de l’induction , Paris: Alcan. (Engl. transl. “The Logical Problem of Induction”, in Foundations of Geometry and Induction , London: Routledge, 2000.)
• Nola, R. and H. Sankey, 2000a, “A selective survey of theories of scientific method”, in Nola and Sankey 2000b: 1–65.
• –––, 2000b, After Popper, Kuhn and Feyerabend. Recent Issues in Theories of Scientific Method , London: Springer.
• –––, 2007, Theories of Scientific Method , Stocksfield: Acumen.
• Norton, S., and F. Suppe, 2001, “Why atmospheric modeling is good science”, in Changing the Atmosphere: Expert Knowledge and Environmental Governance , C. Miller and P. Edwards (eds.), Cambridge, MA: MIT Press, 88–133.
• O’Malley, M., 2007, “Exploratory experimentation and scientific practice: Metagenomics and the proteorhodopsin case”, History and Philosophy of the Life Sciences , 29(3): 337–360.
• O’Malley, M., C. Haufe, K. Elliot, and R. Burian, 2009, “Philosophies of Funding”, Cell , 138: 611–615.
• Oreskes, N., K. Shrader-Frechette, and K. Belitz, 1994, “Verification, Validation and Confirmation of Numerical Models in the Earth Sciences”, Science , 263(5147): 641–646.
• Osborne, J., S. Simon, and S. Collins, 2003, “Attitudes towards science: a review of the literature and its implications”, International Journal of Science Education , 25(9): 1049–1079.
• Parascandola, M., 1998, “Epidemiology—2 nd -Rate Science”, Public Health Reports , 113(4): 312–320.
• Parker, W., 2008a, “Franklin, Holmes and the Epistemology of Computer Simulation”, International Studies in the Philosophy of Science , 22(2): 165–83.
• –––, 2008b, “Computer Simulation through an Error-Statistical Lens”, Synthese , 163(3): 371–84.
• Pearson, K. 1892, The Grammar of Science , London: J.M. Dents and Sons, 1951
• Pearson, E.S., 1955, “Statistical Concepts in Their Relation to Reality”, Journal of the Royal Statistical Society , B, 17: 204–207.
• Pickering, A., 1984, Constructing Quarks: A Sociological History of Particle Physics , Edinburgh: Edinburgh University Press.
• Popper, K.R., 1959, The Logic of Scientific Discovery , London: Routledge, 2002
• –––, 1963, Conjectures and Refutations , London: Routledge, 2002.
• –––, 1985, Unended Quest: An Intellectual Autobiography , La Salle: Open Court Publishing Co..
• Rudner, R., 1953, “The Scientist Qua Scientist Making Value Judgments”, Philosophy of Science , 20(1): 1–6.
• Rudolph, J.L., 2005, “Epistemology for the masses: The origin of ‘The Scientific Method’ in American Schools”, History of Education Quarterly , 45(3): 341–376
• Schickore, J., 2008, “Doing science, writing science”, Philosophy of Science , 75: 323–343.
• Schickore, J. and N. Hangel, 2019, “‘It might be this, it should be that…’ uncertainty and doubt in day-to-day science practice”, European Journal for Philosophy of Science , 9(2): 31. doi:10.1007/s13194-019-0253-9
• Shamoo, A.E. and D.B. Resnik, 2009, Responsible Conduct of Research , Oxford: Oxford University Press.
• Shank, J.B., 2008, The Newton Wars and the Beginning of the French Enlightenment , Chicago: The University of Chicago Press.
• Shapin, S. and S. Schaffer, 1985, Leviathan and the air-pump , Princeton: Princeton University Press.
• Smith, G.E., 2002, “The Methodology of the Principia”, in The Cambridge Companion to Newton , I.B. Cohen and G.E. Smith (eds.), Cambridge: Cambridge University Press, 138–173.
• Snyder, L.J., 1997a, “Discoverers’ Induction”, Philosophy of Science , 64: 580–604.
• –––, 1997b, “The Mill-Whewell Debate: Much Ado About Induction”, Perspectives on Science , 5: 159–198.
• –––, 1999, “Renovating the Novum Organum: Bacon, Whewell and Induction”, Studies in History and Philosophy of Science , 30: 531–557.
• Sober, E., 2008, Evidence and Evolution. The logic behind the science , Cambridge: Cambridge University Press
• Sprenger, J. and S. Hartmann, 2019, Bayesian philosophy of science , Oxford: Oxford University Press.
• Steinle, F., 1997, “Entering New Fields: Exploratory Uses of Experimentation”, Philosophy of Science (Proceedings), 64: S65–S74.
• –––, 2002, “Experiments in History and Philosophy of Science”, Perspectives on Science , 10(4): 408–432.
• Strasser, B.J., 2012, “Data-driven sciences: From wonder cabinets to electronic databases”, Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences , 43(1): 85–87.
• Succi, S. and P.V. Coveney, 2018, “Big data: the end of the scientific method?”, Philosophical Transactions of the Royal Society A , 377: 20180145. doi:10.1098/rsta.2018.0145
• Suppe, F., 1998, “The Structure of a Scientific Paper”, Philosophy of Science , 65(3): 381–405.
• Swijtink, Z.G., 1987, “The objectification of observation: Measurement and statistical methods in the nineteenth century”, in The probabilistic revolution. Ideas in History, Vol. 1 , L. Kruger (ed.), Cambridge MA: MIT Press, pp. 261–285.
• Waters, C.K., 2007, “The nature and context of exploratory experimentation: An introduction to three case studies of exploratory research”, History and Philosophy of the Life Sciences , 29(3): 275–284.
• Weinberg, S., 1995, “The methods of science… and those by which we live”, Academic Questions , 8(2): 7–13.
• Weissert, T., 1997, The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem , New York: Springer Verlag.
• William H., 1628, Exercitatio Anatomica de Motu Cordis et Sanguinis in Animalibus , in On the Motion of the Heart and Blood in Animals , R. Willis (trans.), Buffalo: Prometheus Books, 1993.
• Winsberg, E., 2010, Science in the Age of Computer Simulation , Chicago: University of Chicago Press.
• Wivagg, D. & D. Allchin, 2002, “The Dogma of the Scientific Method”, The American Biology Teacher , 64(9): 645–646

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Blackmun opinion , in Daubert v. Merrell Dow Pharmaceuticals (92–102), 509 U.S. 579 (1993).
• Scientific Method at philpapers. Darrell Rowbottom (ed.).
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Science and the scientific method: Definitions and examples

Here's a look at the foundation of doing science — the scientific method.

The scientific method

Hypothesis, theory and law, a brief history of science, additional resources, bibliography.

Science is a systematic and logical approach to discovering how things in the universe work. It is also the body of knowledge accumulated through the discoveries about all the things in the universe. 

The word "science" is derived from the Latin word "scientia," which means knowledge based on demonstrable and reproducible data, according to the Merriam-Webster dictionary . True to this definition, science aims for measurable results through testing and analysis, a process known as the scientific method. Science is based on fact, not opinion or preferences. The process of science is designed to challenge ideas through research. One important aspect of the scientific process is that it focuses only on the natural world, according to the University of California, Berkeley . Anything that is considered supernatural, or beyond physical reality, does not fit into the definition of science.

When conducting research, scientists use the scientific method to collect measurable, empirical evidence in an experiment related to a hypothesis (often in the form of an if/then statement) that is designed to support or contradict a scientific theory .

"As a field biologist, my favorite part of the scientific method is being in the field collecting the data," Jaime Tanner, a professor of biology at Marlboro College, told Live Science. "But what really makes that fun is knowing that you are trying to answer an interesting question. So the first step in identifying questions and generating possible answers (hypotheses) is also very important and is a creative process. Then once you collect the data you analyze it to see if your hypothesis is supported or not."

The steps of the scientific method go something like this, according to Highline College :

• Make an observation or observations.
• Form a hypothesis — a tentative description of what's been observed, and make predictions based on that hypothesis.
• Test the hypothesis and predictions in an experiment that can be reproduced.
• Analyze the data and draw conclusions; accept or reject the hypothesis or modify the hypothesis if necessary.
• Reproduce the experiment until there are no discrepancies between observations and theory. "Replication of methods and results is my favorite step in the scientific method," Moshe Pritsker, a former post-doctoral researcher at Harvard Medical School and CEO of JoVE, told Live Science. "The reproducibility of published experiments is the foundation of science. No reproducibility — no science."

Some key underpinnings to the scientific method:

• The hypothesis must be testable and falsifiable, according to North Carolina State University . Falsifiable means that there must be a possible negative answer to the hypothesis.
• Research must involve deductive reasoning and inductive reasoning . Deductive reasoning is the process of using true premises to reach a logical true conclusion while inductive reasoning uses observations to infer an explanation for those observations.
• An experiment should include a dependent variable (which does not change) and an independent variable (which does change), according to the University of California, Santa Barbara .
• An experiment should include an experimental group and a control group. The control group is what the experimental group is compared against, according to Britannica .

The process of generating and testing a hypothesis forms the backbone of the scientific method. When an idea has been confirmed over many experiments, it can be called a scientific theory. While a theory provides an explanation for a phenomenon, a scientific law provides a description of a phenomenon, according to The University of Waikato . One example would be the law of conservation of energy, which is the first law of thermodynamics that says that energy can neither be created nor destroyed. 

A law describes an observed phenomenon, but it doesn't explain why the phenomenon exists or what causes it. "In science, laws are a starting place," said Peter Coppinger, an associate professor of biology and biomedical engineering at the Rose-Hulman Institute of Technology. "From there, scientists can then ask the questions, 'Why and how?'"

Laws are generally considered to be without exception, though some laws have been modified over time after further testing found discrepancies. For instance, Newton's laws of motion describe everything we've observed in the macroscopic world, but they break down at the subatomic level.

This does not mean theories are not meaningful. For a hypothesis to become a theory, scientists must conduct rigorous testing, typically across multiple disciplines by separate groups of scientists. Saying something is "just a theory" confuses the scientific definition of "theory" with the layperson's definition. To most people a theory is a hunch. In science, a theory is the framework for observations and facts, Tanner told Live Science.

The earliest evidence of science can be found as far back as records exist. Early tablets contain numerals and information about the solar system , which were derived by using careful observation, prediction and testing of those predictions. Science became decidedly more "scientific" over time, however.

1200s: Robert Grosseteste developed the framework for the proper methods of modern scientific experimentation, according to the Stanford Encyclopedia of Philosophy. His works included the principle that an inquiry must be based on measurable evidence that is confirmed through testing.

1400s: Leonardo da Vinci began his notebooks in pursuit of evidence that the human body is microcosmic. The artist, scientist and mathematician also gathered information about optics and hydrodynamics.

1500s: Nicolaus Copernicus advanced the understanding of the solar system with his discovery of heliocentrism. This is a model in which Earth and the other planets revolve around the sun, which is the center of the solar system.

1600s: Johannes Kepler built upon those observations with his laws of planetary motion. Galileo Galilei improved on a new invention, the telescope, and used it to study the sun and planets. The 1600s also saw advancements in the study of physics as Isaac Newton developed his laws of motion.

1700s: Benjamin Franklin discovered that lightning is electrical. He also contributed to the study of oceanography and meteorology. The understanding of chemistry also evolved during this century as Antoine Lavoisier, dubbed the father of modern chemistry , developed the law of conservation of mass.

1800s: Milestones included Alessandro Volta's discoveries regarding electrochemical series, which led to the invention of the battery. John Dalton also introduced atomic theory, which stated that all matter is composed of atoms that combine to form molecules. The basis of modern study of genetics advanced as Gregor Mendel unveiled his laws of inheritance. Later in the century, Wilhelm Conrad Röntgen discovered X-rays , while George Ohm's law provided the basis for understanding how to harness electrical charges.

1900s: The discoveries of Albert Einstein , who is best known for his theory of relativity, dominated the beginning of the 20th century. Einstein's theory of relativity is actually two separate theories. His special theory of relativity, which he outlined in a 1905 paper, " The Electrodynamics of Moving Bodies ," concluded that time must change according to the speed of a moving object relative to the frame of reference of an observer. His second theory of general relativity, which he published as " The Foundation of the General Theory of Relativity ," advanced the idea that matter causes space to curve.

In 1952, Jonas Salk developed the polio vaccine , which reduced the incidence of polio in the United States by nearly 90%, according to Britannica . The following year, James D. Watson and Francis Crick discovered the structure of DNA , which is a double helix formed by base pairs attached to a sugar-phosphate backbone, according to the National Human Genome Research Institute .

2000s: The 21st century saw the first draft of the human genome completed, leading to a greater understanding of DNA. This advanced the study of genetics, its role in human biology and its use as a predictor of diseases and other disorders, according to the National Human Genome Research Institute .

• This video from City University of New York delves into the basics of what defines science.
• Learn about what makes science science in this book excerpt from Washington State University .
• This resource from the University of Michigan — Flint explains how to design your own scientific study.

Merriam-Webster Dictionary, Scientia. 2022. https://www.merriam-webster.com/dictionary/scientia

University of California, Berkeley, "Understanding Science: An Overview." 2022. ​​ https://undsci.berkeley.edu/article/0_0_0/intro_01  

Highline College, "Scientific method." July 12, 2015. https://people.highline.edu/iglozman/classes/astronotes/scimeth.htm  

North Carolina State University, "Science Scripts." https://projects.ncsu.edu/project/bio183de/Black/science/science_scripts.html  

University of California, Santa Barbara. "What is an Independent variable?" October 31,2017. http://scienceline.ucsb.edu/getkey.php?key=6045  

Encyclopedia Britannica, "Control group." May 14, 2020. https://www.britannica.com/science/control-group  

The University of Waikato, "Scientific Hypothesis, Theories and Laws." https://sci.waikato.ac.nz/evolution/Theories.shtml  

Stanford Encyclopedia of Philosophy, Robert Grosseteste. May 3, 2019. https://plato.stanford.edu/entries/grosseteste/  

Encyclopedia Britannica, "Jonas Salk." October 21, 2021. https://www.britannica.com/ biography /Jonas-Salk

National Human Genome Research Institute, "​Phosphate Backbone." https://www.genome.gov/genetics-glossary/Phosphate-Backbone  

National Human Genome Research Institute, "What is the Human Genome Project?" https://www.genome.gov/human-genome-project/What  

‌ Live Science contributor Ashley Hamer updated this article on Jan. 16, 2022.

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What Are The Steps Of The Scientific Method?

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

Learn about our Editorial Process

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

Science is not just knowledge. It is also a method for obtaining knowledge. Scientific understanding is organized into theories.

The scientific method is a step-by-step process used by researchers and scientists to determine if there is a relationship between two or more variables. Psychologists use this method to conduct psychological research, gather data, process information, and describe behaviors.

It involves careful observation, asking questions, formulating hypotheses, experimental testing, and refining hypotheses based on experimental findings.

How it is Used

The scientific method can be applied broadly in science across many different fields, such as chemistry, physics, geology, and psychology. In a typical application of this process, a researcher will develop a hypothesis, test this hypothesis, and then modify the hypothesis based on the outcomes of the experiment.

The process is then repeated with the modified hypothesis until the results align with the observed phenomena. Detailed steps of the scientific method are described below.

Keep in mind that the scientific method does not have to follow this fixed sequence of steps; rather, these steps represent a set of general principles or guidelines.

7 Steps of the Scientific Method

Psychology uses an empirical approach.

Empiricism (founded by John Locke) states that the only source of knowledge comes through our senses – e.g., sight, hearing, touch, etc.

Empirical evidence does not rely on argument or belief. Thus, empiricism is the view that all knowledge is based on or may come from direct observation and experience.

The empiricist approach of gaining knowledge through experience quickly became the scientific approach and greatly influenced the development of physics and chemistry in the 17th and 18th centuries.

Step 1: Make an Observation (Theory Construction)

Every researcher starts at the very beginning. Before diving in and exploring something, one must first determine what they will study – it seems simple enough!

By making observations, researchers can establish an area of interest. Once this topic of study has been chosen, a researcher should review existing literature to gain insight into what has already been tested and determine what questions remain unanswered.

This assessment will provide helpful information about what has already been comprehended about the specific topic and what questions remain, and if one can go and answer them.

Specifically, a literature review might implicate examining a substantial amount of documented material from academic journals to books dating back decades. The most appropriate information gathered by the researcher will be shown in the introduction section or abstract of the published study results.

The background material and knowledge will help the researcher with the first significant step in conducting a psychology study, which is formulating a research question.

This is the inductive phase of the scientific process. Observations yield information that is used to formulate theories as explanations. A theory is a well-developed set of ideas that propose an explanation for observed phenomena.

Inductive reasoning moves from specific premises to a general conclusion. It starts with observations of phenomena in the natural world and derives a general law.

Step 2: Ask a Question

Once a researcher has made observations and conducted background research, the next step is to ask a scientific question. A scientific question must be defined, testable, and measurable.

A useful approach to develop a scientific question is: “What is the effect of…?” or “How does X affect Y?”

To answer an experimental question, a researcher must identify two variables: the independent and dependent variables.

The independent variable is the variable manipulated (the cause), and the dependent variable is the variable being measured (the effect).

An example of a research question could be, “Is handwriting or typing more effective for retaining information?” Answering the research question and proposing a relationship between the two variables is discussed in the next step.

Step 3: Form a Hypothesis (Make Predictions)

A hypothesis is an educated guess about the relationship between two or more variables. A hypothesis is an attempt to answer your research question based on prior observation and background research. Theories tend to be too complex to be tested all at once; instead, researchers create hypotheses to test specific aspects of a theory.

For example, a researcher might ask about the connection between sleep and educational performance. Do students who get less sleep perform worse on tests at school?

It is crucial to think about different questions one might have about a particular topic to formulate a reasonable hypothesis. It would help if one also considered how one could investigate the causalities.

It is important that the hypothesis is both testable against reality and falsifiable. This means that it can be tested through an experiment and can be proven wrong.

The falsification principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory to be considered scientific, it must be able to be tested and conceivably proven false.

To test a hypothesis, we first assume that there is no difference between the populations from which the samples were taken. This is known as the null hypothesis and predicts that the independent variable will not influence the dependent variable.

Examples of “if…then…” Hypotheses:

• If one gets less than 6 hours of sleep, then one will do worse on tests than if one obtains more rest.
• If one drinks lots of water before going to bed, one will have to use the bathroom often at night.
• If one practices exercising and lighting weights, then one’s body will begin to build muscle.

The research hypothesis is often called the alternative hypothesis and predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Although one could state and write a scientific hypothesis in many ways, hypotheses are usually built like “if…then…” statements.

Step 4: Run an Experiment (Gather Data)

The next step in the scientific method is to test your hypothesis and collect data. A researcher will design an experiment to test the hypothesis and gather data that will either support or refute the hypothesis.

The exact research methods used to examine a hypothesis depend on what is being studied. A psychologist might utilize two primary forms of research, experimental research, and descriptive research.

The scientific method is objective in that researchers do not let preconceived ideas or biases influence the collection of data and is systematic in that experiments are conducted in a logical way.

Experimental Research

Experimental research is used to investigate cause-and-effect associations between two or more variables. This type of research systematically controls an independent variable and measures its effect on a specified dependent variable.

Experimental research involves manipulating an independent variable and measuring the effect(s) on the dependent variable. Repeating the experiment multiple times is important to confirm that your results are accurate and consistent.

One of the significant advantages of this method is that it permits researchers to determine if changes in one variable cause shifts in each other.

While experiments in psychology typically have many moving parts (and can be relatively complex), an easy investigation is rather fundamental. Still, it does allow researchers to specify cause-and-effect associations between variables.

Most simple experiments use a control group, which involves those who do not receive the treatment, and an experimental group, which involves those who do receive the treatment.

An example of experimental research would be when a pharmaceutical company wants to test a new drug. They give one group a placebo (control group) and the other the actual pill (experimental group).

Descriptive Research

Descriptive research is generally used when it is challenging or even impossible to control the variables in question. Examples of descriptive analysis include naturalistic observation, case studies , and correlation studies .

One example of descriptive research includes phone surveys that marketers often use. While they typically do not allow researchers to identify cause and effect, correlational studies are quite common in psychology research. They make it possible to spot associations between distinct variables and measure the solidity of those relationships.

Step 5: Analyze the Data and Draw Conclusions

Once a researcher has designed and done the investigation and collected sufficient data, it is time to inspect this gathered information and judge what has been found. Researchers can summarize the data, interpret the results, and draw conclusions based on this evidence using analyses and statistics.

Upon completion of the experiment, you can collect your measurements and analyze the data using statistics. Based on the outcomes, you will either reject or confirm your hypothesis.

Analyze the Data

So, how does a researcher determine what the results of their study mean? Statistical analysis can either support or refute a researcher’s hypothesis and can also be used to determine if the conclusions are statistically significant.

When outcomes are said to be “statistically significant,” it is improbable that these results are due to luck or chance. Based on these observations, investigators must then determine what the results mean.

An experiment will support a hypothesis in some circumstances, but sometimes it fails to be truthful in other cases.

What occurs if the developments of a psychology investigation do not endorse the researcher’s hypothesis? It does mean that the study was worthless. Simply because the findings fail to defend the researcher’s hypothesis does not mean that the examination is not helpful or instructive.

This kind of research plays a vital role in supporting scientists in developing unexplored questions and hypotheses to investigate in the future. After decisions have been made, the next step is to communicate the results with the rest of the scientific community.

This is an integral part of the process because it contributes to the general knowledge base and can assist other scientists in finding new research routes to explore.

If the hypothesis is not supported, a researcher should acknowledge the experiment’s results, formulate a new hypothesis, and develop a new experiment.

We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist that could refute a theory.

Draw Conclusions and Interpret the Data

When the empirical observations disagree with the hypothesis, a number of possibilities must be considered. It might be that the theory is incorrect, in which case it needs altering, so it fully explains the data.

Alternatively, it might be that the hypothesis was poorly derived from the original theory, in which case the scientists were expecting the wrong thing to happen.

It might also be that the research was poorly conducted, or used an inappropriate method, or there were factors in play that the researchers did not consider. This will begin the process of the scientific method again.

If the hypothesis is supported, the researcher can find more evidence to support their hypothesis or look for counter-evidence to strengthen their hypothesis further.

In either scenario, the researcher should share their results with the greater scientific community.

Step 6: Share Your Results

One of the final stages of the research cycle involves the publication of the research. Once the report is written, the researcher(s) may submit the work for publication in an appropriate journal.

Usually, this is done by writing up a study description and publishing the article in a professional or academic journal. The studies and conclusions of psychological work can be seen in peer-reviewed journals such as  Developmental Psychology , Psychological Bulletin, the  Journal of Social Psychology, and numerous others.

Scientists should report their findings by writing up a description of their study and any subsequent findings. This enables other researchers to build upon the present research or replicate the results.

As outlined by the American Psychological Association (APA), there is a typical structure of a journal article that follows a specified format. In these articles, researchers:

• Supply a brief narrative and background on previous research
• Give their hypothesis
• Specify who participated in the study and how they were chosen
• Provide operational definitions for each variable
• Explain the measures and methods used to collect data
• Describe how the data collected was interpreted
• Discuss what the outcomes mean

A detailed record of psychological studies and all scientific studies is vital to clearly explain the steps and procedures used throughout the study. So that other researchers can try this experiment too and replicate the results.

The editorial process utilized by academic and professional journals guarantees that each submitted article undergoes a thorough peer review to help assure that the study is scientifically sound. Once published, the investigation becomes another piece of the current puzzle of our knowledge “base” on that subject.

This last step is important because all results, whether they supported or did not support the hypothesis, can contribute to the scientific community. Publication of empirical observations leads to more ideas that are tested against the real world, and so on. In this sense, the scientific process is circular.

The editorial process utilized by academic and professional journals guarantees that each submitted article undergoes a thorough peer review to help assure that the study is scientifically sound.

Once published, the investigation becomes another piece of the current puzzle of our knowledge “base” on that subject.

By replicating studies, psychologists can reduce errors, validate theories, and gain a stronger understanding of a particular topic.

Step 7: Repeat the Scientific Method (Iteration)

Now, if one’s hypothesis turns out to be accurate, find more evidence or find counter-evidence. If one’s hypothesis is false, create a new hypothesis or try again.

One may wish to revise their first hypothesis to make a more niche experiment to design or a different specific question to test.

The amazingness of the scientific method is that it is a comprehensive and straightforward process that scientists, and everyone, can utilize over and over again.

So, draw conclusions and repeat because the scientific method is never-ending, and no result is ever considered perfect.

The scientific method is a process of:

• Making an observation.
• Forming a hypothesis.
• Making a prediction.
• Experimenting to test the hypothesis.

The procedure of repeating the scientific method is crucial to science and all fields of human knowledge.

Further Information

• Karl Popper – Falsification
• Thomas – Kuhn Paradigm Shift
• Positivism in Sociology: Definition, Theory & Examples
• Is Psychology a Science?
• Psychology as a Science (PDF)

List the 6 steps of the scientific methods in order

• Make an observation (theory construction)
• Ask a question. A scientific question must be defined, testable, and measurable.
• Form a hypothesis (make predictions)
• Run an experiment to test the hypothesis (gather data)
• Analyze the data and draw conclusions
• Share your results so that other researchers can make new hypotheses

What is the first step of the scientific method?

The first step of the scientific method is making an observation. This involves noticing and describing a phenomenon or group of phenomena that one finds interesting and wishes to explain.

Observations can occur in a natural setting or within the confines of a laboratory. The key point is that the observation provides the initial question or problem that the rest of the scientific method seeks to answer or solve.

What is the scientific method?

The scientific method is a step-by-step process that investigators can follow to determine if there is a causal connection between two or more variables.

Psychologists and other scientists regularly suggest motivations for human behavior. On a more casual level, people judge other people’s intentions, incentives, and actions daily.

While our standard assessments of human behavior are subjective and anecdotal, researchers use the scientific method to study psychology objectively and systematically.

All utilize a scientific method to study distinct aspects of people’s thinking and behavior. This process allows scientists to analyze and understand various psychological phenomena, but it also provides investigators and others a way to disseminate and debate the results of their studies.

The outcomes of these studies are often noted in popular media, which leads numerous to think about how or why researchers came to the findings they did.

Why Use the Six Steps of the Scientific Method

The goal of scientists is to understand better the world that surrounds us. Scientific research is the most critical tool for navigating and learning about our complex world.

Without it, we would be compelled to rely solely on intuition, other people’s power, and luck. We can eliminate our preconceived concepts and superstitions through methodical scientific research and gain an objective sense of ourselves and our world.

All psychological studies aim to explain, predict, and even control or impact mental behaviors or processes. So, psychologists use and repeat the scientific method (and its six steps) to perform and record essential psychological research.

So, psychologists focus on understanding behavior and the cognitive (mental) and physiological (body) processes underlying behavior.

In the real world, people use to understand the behavior of others, such as intuition and personal experience. The hallmark of scientific research is evidence to support a claim.

Scientific knowledge is empirical, meaning it is grounded in objective, tangible evidence that can be observed repeatedly, regardless of who is watching.

The scientific method is crucial because it minimizes the impact of bias or prejudice on the experimenter. Regardless of how hard one tries, even the best-intentioned scientists can’t escape discrimination. can’t

It stems from personal opinions and cultural beliefs, meaning any mortal filters data based on one’s experience. Sadly, this “filtering” process can cause a scientist to favor one outcome over another.

For an everyday person trying to solve a minor issue at home or work, succumbing to these biases is not such a big deal; in fact, most times, it is important.

But in the scientific community, where results must be inspected and reproduced, bias or discrimination must be avoided.

When to Use the Six Steps of the Scientific Method ?

One can use the scientific method anytime, anywhere! From the smallest conundrum to solving global problems, it is a process that can be applied to any science and any investigation.

Even if you are not considered a “scientist,” you will be surprised to know that people of all disciplines use it for all kinds of dilemmas.

Try to catch yourself next time you come by a question and see how you subconsciously or consciously use the scientific method.

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Scientific Method

Instructor prep, student protocol.

The scientific method is a framework of techniques and questions that scientists use to investigate phenomena with the aim of making scientific discoveries simple and reproducible. It's been loosely observed by experimenters going as far back as the 4th century BC, but the first properly formalized scientific method was coined during the European Renaissance. Here individuals at the forefront of science like Francis Bacon, Galileo, and Isaac Newton started putting into routine practice the rules that we use to carry out experiments today.

Typically, the first step of the scientific method is to formulate a question, usually after observation of a phenomenon. For example, say you have been raising caterpillars and have noticed that some take longer than others to get to pupation. And you wonder, do the caterpillars develop at different rates depending on the temperature?

This is where the second part of the scientific method comes in, the hypothesis. A hypothesis is an uncertain explanation as to why we observe what we observe, and there are two main types. The first is the experimental or alternative hypothesis, and it implies that there will be a relationship between the variables being investigated, the temperature and caterpillar development, in this case. So, our experimental hypothesis could be that the caterpillars will take longer to go from egg to pupation if they're raised at colder temperatures. Crucially, a good hypothesis will be testable. For our caterpillars, we can change the temperature, and record the time it takes for them to go from egg to pupa, and falsifiable. So, if it takes around the same time for the caterpillars to develop no matter what the temperature, then we can accept that the hypothesis was likely false. The second type of hypothesis is the null hypothesis. This typically speculates that there won't be any observed significant change or difference during the experiment. In our caterpillar example, we would state that the caterpillars will develop at the same rate in each temperature condition.

Once we have our hypotheses, the third step of the scientific method covers experimentation and data collection. In a typical experiment, there will be two types of variables. The independent variable is something directly manipulated by the experimenter. So, with our caterpillars, we are altering the independent variable when we change the temperature. The dependent variable, also known as the response variable, should be affected by the state of the independent variable. So, when we expose our caterpillars to different temperatures, then the response, the dependent variable, is the rate at which they develop.

There are also two main types of data that could be collected to support or falsify the hypotheses. The first is qualitative data, which typically refers to descriptive observations made with the senses, seeing, touching, hearing, smelling, or even tasting. In our experiment, we might record that the caterpillars seem to move around and eat a lot in the normal temperature condition, compared to the cooler one. In contrast to qualitative data, quantitative data can be measured and written down as numbers. So, when we count the number of hours it takes the caterpillar from hatching to finally pupating, this gives us a definite figure. Where possible, it's almost important to have a control condition in any experiment where we manipulate the independent variables. In our caterpillar experiment, we can grow the caterpillars at a set standard room temperature of 21 degrees as a control, because this demonstrates what happens when the caterpillars develop under normal conditions in comparison to experimental settings.

In observational experiments, a control may not be needed or even possible. For example, imagine our caterpillars are now grown up butterflies, feeding on nectar in a flower garden. In our experimental hypothesis, we suggest that they prefer to feed from the big pink flowers, while our null hypothesis suggests they have no preference and will visit the flowers at random. In this case, simply observing and recording the number of times the butterflies visit each flower type will provide enough data to confirm or reject our hypotheses without needing manipulation of any variables or the need for a control.

Once the data have been collected, the next step is to figure out what it all means. Scientists will compare the predictions of their two hypotheses to figure out if they can reject the null hypothesis. This can be done by comparing the values of the dependent variable in the control versus the experimental conditions. If they are not equal, the null hypothesis can be rejected. If the data collected supports a hypothesis, like the caterpillars did take significantly more hours to go from egg to pupa when kept at the cooler climate, then this gives the experimental hypothesis more credibility, but critically it does not indicate that the hypothesis is definitely true, because future experiments may reveal new information.

The final part of the scientific method is where we draw conclusions, and discuss what our findings might mean. Here, scientists might refer to other experiments or other literature to put their findings into context, and come up with explanations of why the results showed what they did. For example, the conclusion could be that the caterpillars like to grow at temperatures closest to their natural habitat. This may, in turn, spiral new questions, like do other species pupate at different rates at different temperatures, too? This may inspire new experiments, which we can test using, you guessed it, the scientific method.

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy underpinning scientific discovery, radically transforming the views of society about nature. During the European Renaissance, individuals such as Francis Bacon, Galileo, and Isaac Newton formalized the concept of the scientific method and put it into practice. Although the scientific method has been revised since its early conceptions, much of the framework and philosophy remains in practice today.

Step 1: The Observation and Question

Prior to investigation, a scientist must define the question to be addressed. This crucial first step in the scientific process involves observing some natural phenomena of interest. This observation should then lead to a number of questions about the phenomena. This stage frequently requires background research necessary to understand the subject matter and past work on similar ideas. Reviewing and evaluating previous research allows scientists to refine their questions to more accurately address gaps in scientific knowledge. Defining a research question and understanding relevant prior research will influence how the scientific method is applied, making it an important first step in the research process.

An everyday example: You are trying to get to school or work and your car won’t start. The thought process that most people go through in that situation clearly mirrors the official scientific method (after you are finished getting upset). First, you make an observation: my car won’t start! The question that follows: why isn’t it working?

Step 2: The Hypothesis

The next step is making a hypothesis, based on prior knowledge. A hypothesis is an “uncertain explanation” or an unproven conjecture that seeks to explain some phenomenon based on knowledge obtained while executing subsequent experiments or observations. Generally, scientists develop multiple hypotheses to address their questions and test them systematically.

All hypotheses must meet certain criteria for the scientific process to work. First, a hypothesis must be testable and falsifiable. This aspect of the hypothesis is critical and of much greater importance than the hypothesis being correct. A testable hypothesis is one that generates testable predictions, addressed through observations or experiments. A falsifiable hypothesis is one that, through observation of conflicting outcomes, can be proven wrong. This allows investigators to gain more confidence over time, not by accumulating evidence showing that a hypothesis is correct, but rather by showing that situations that could establish its falsity do not occur.

Hypotheses come in two forms: null hypotheses and alternative hypotheses. The null hypothesis is tested against the alternative hypothesis and reflects that there will be no observed change in the experiment. The alternative hypothesis is generally the one described in the previous two paragraphs, also referred to as the experimental hypothesis. The alternative hypothesis is the predicted outcome of the experiment. If the null hypothesis is rejected, then this builds evidence for the alternative hypothesis.

An everyday example: Maybe it is freezing outside and therefore it is fairly likely that your car battery is dead. Maybe you know you were low on gas the night before and therefore it is likely that the tank is empty.

Step 3: Experimentation and Data Collection

Either way, the next step is to make more observations or to conduct experiments leading to conclusions. Following the formulation of hypotheses, scientists plan and conduct experiments to test their hypotheses. These experiments provide data that will either support or falsify the hypothesis. Data can be collected from quantitative or qualitative observations. Qualitative information refers to observations that can be made simply using one's senses, be that through sight, sound, taste, smell, or touch. In contrast, quantitative observations are ones in which precise measurements of some type are used to investigate one's hypothesis.

An experiment is a procedure designed to determine whether observations of the real world agree with or refute the derived predictions in the hypothesis. If evidence from an experiment supports a hypothesis, that gives the hypothesis more credibility. This does not indicate that the hypothesis is true, as future experiments may reveal new information about the original hypothesis. Experimental design is another critical step in the scientific method and can have a great effect on the results and conclusions one draws from an experiment. Careful thought and time should be devoted to experimental design and minimizing possible errors. The experiment should be designed so that every variable or factor that could influence the outcome of the experiment be under control of the researcher. Two types of variables are used to describe the conditions in an experiment: the independent and the dependent, or response, variable. The independent variable is directly manipulated or controlled by the scientist and is generally what one predicts will affect the dependent variable. The dependent, or response, variable thus depends on the value of the independent variable. Experiments are generally designed so that one specific factor is manipulated in the experiment in order to illuminate cause and effect relationships.

An everyday example: Does the car still have all of its parts? Is this the right key? What does the gas gauge say? Does a jump start help?

Another important aspect in experimental design is the role of the control treatment, which represents a non-manipulated treatment condition. The control treatment is kept in the same conditions as the experimental treatment, but the experimental manipulation is not applied to the control. For example, if a researcher were testing the effects of soil salinity on plant growth, the soil in the control treatment would have no added salt. The control provides a baseline of “normal” conditions with which to compare the experimental treatments.

Experimental design should also incorporate replicates of each treatment. Repeatability of experimental results is an important part of the scientific method that ensures the validity and accuracy of data. It is quite difficult to control all aspects of an experiment so there is inherent variation in results that cannot be controlled for even under the most carefully designed and controlled experiments. Having replicates enables an investigator to estimate this inherent variation in results. Precise recording and measurement of data is also of great importance for ensuring the accuracy of results and the conclusions one draws from the results.

Step 4: Results and Data Analysis

The next step in the scientific method involves determining what the results from the experiment mean. Scientists compare the predictions of their null hypothesis to that of their alternative hypothesis to determine if they are able to reject the null hypothesis. Rejecting the null hypothesis means that there is a significant probability that values of the dependent variable in the control versus experimental treatments are not equal to each other. If significant differences exist, then one can reject the null hypothesis and accept the alternative hypothesis. Conversely, the investigator may fail to reject the null hypothesis, meaning the treatment has no effect on the results. Before scientists can make any claims about their null hypothesis from their experimental data or observations, statistical tests are required to ensure the validity of the data and further interpretation of the data. Statistical tests allow researchers to determine if there are genuine differences between the control and experimental treatments. From there, they can create figures and tables to illustrate their findings.

Step 5: Conclusions

The last portion of the scientific method involves providing explanations of the results and the conclusions that can be logically drawn from the results. Generally, this step of the scientific process also requires one to revisit scientific literature and compare their results with other experiments or observations on related topics. This allows researchers to put their experiment in a more general context and elaborate on the significance of particular results. Additionally, it allows them to explain how their work fits into a larger context in their discipline.

The scientific process does not stop here! The scientific process works through time as knowledge on topics in science accumulate and drive our understanding of particular mechanisms or processes explaining natural phenomena. If we fail to reject our null hypothesis, then it becomes necessary to revisit the initial stages of the scientific method and try to reformulate our questions and understand why an anticipated result was not attained.

Application of the Scientific Method

The only difference between the use of this method in every-day life and in the laboratory is that scientists carefully document their work, from observation to hypothesis to experiment, and finally conclusions and peer review. In addition, unlike problem solving outside the lab, the scientific method in the lab includes controlled conditions and variables.

Let’s investigate the scientific method using an example from the lab. It is known that plant growth is affected by microbes, such as bacteria and fungi, living in their soil. It is possible to figure out what microbes have which effects by potting plants in completely sterile soil, then adding in microbes one at a time, or in different combinations and measuring the growth of the plant. Now let’s fit this into the terms used to describe the scientific method:

Observation and Question : There are microbes in the soil…do these affect plant growth?

HYPOTHESES:

Experimental: One particular microbe of interest will cause the plants to grow more slowly.

Null: The presence or absence of microbes will have no effect on plant growth

Experiment : set up groups of plants in 1) sterile soil, 2) soil with the microbe added in, and 3) natural soil. Measure the growth of the plants over time, using a ruler.

Conclusion : if the plants in group 2 grow more slowly than the other two, the hypothesis is supported. This needs to be backed up with statistical analysis from many plants to be considered significant. An experiment like this is not legitimate with just one plant per group.

Group 1 is a control which shows the plants can grow in the sterile soil. Group 3 is a control that shows the plants can grow under normal conditions. Group 2 is the experimental group. It would be possible to add different amounts of the microbe, or different microbes, to introduce more variables. The main point is that the researcher has something to which to compare the experimental group- the control group. If the experiment included only group 2 and the researcher determined that the plants “looked sick,” that would be a matter of opinion. The only way to make that observation scientific is to have healthy plants to measure. The type or amount of microbe used is the independent variable , because the researcher has control over it. The size of the plant at the end of the experiment is the dependent or response variable because it is the result.

Ultimately, work like this is published in scientific journals so that other researchers can read about the methods used and conclusions drawn. Publications like this are subject to peer-review, which means that an article won’t be published in a journal until other researchers have checked it out and agree it is well-done. As a community of scientists, general concepts are developed based on observed patterns in the experiments that individual scientists conduct. This results in the development of a scientific theory . This term means that there is a consensus among researchers that a particular concept or process exists. It is important to note that the word theory does not mean the same thing as hypothesis. Once scientists label a concept with this term, it is considered to be true, considering all currently available data. Of course, if a large body of experimentation demonstrates information to the contrary, theories can be modified.

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How the Scientific Method Works

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We hear about the scientific method all the time. Middle and high school students learn about it in science class and use it in research competitions. Advertisers use it to support claims about products ranging from vacuum cleaners to vitamins. And Hollywood portrays it by showing scientists with clipboards and lab coats standing behind microscopes and flasks filled with bubbling liquids.

So why does the scientific method remain such a mystery to so many people? One reason has to do with the name itself. The word "method" implies that there is some sacred formula locked in a vault — a formula available to highly trained scientists and no one else. This is absolutely untrue. The scientific method is something all of us use all of the time. In fact, engaging in the basic activities that make up the scientific method — being curious, asking questions, seeking answers — is a natural part of being human.

­In this article, we'll demystify the scientific method by breaking it down to its basic parts.

We'll explore how the scientific method can be used to solve everyday problems, but we'll also explain why it is so fundamentally critical to the physical and natural sciences. We'll also examine a few examples of how the method has been applied to make landmark discoveries and support groundbreaking theories . But let's start with a basic definition.

Ask a group of people to define "science," and you'll get a lot of different answers. Some will tell you it's a really difficult class wedged between social studies and math. Others will tell you it's a dusty book filled with Latin terms that no one can pronounce. And still others will say it's a useless collection of facts, figures and formulas. Unfortunately, most dictionaries don't shed any significant light on the subject. Here's a typical definition:

Sounds difficult, right? Not if we break this long-winded definition into its most important parts. By doing so, we'll achieve two things: First, we'll support the argument that science isn't mysterious or unattainable. Second, we'll demonstrate that the method of science is really no different than science itself.

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Scientific Method

Reviewed by: BD Editors

The scientific method is a series of processes that people can use to gather knowledge about the world around them, improve that knowledge, and attempt to explain why and/or how things occur. This method involves making observations, forming questions, making hypotheses, doing an experiment, analyzing the data, and forming a conclusion. Every scientific experiment performed is an example of the scientific method in action, but it is also used by non-scientists in everyday situations.

Scientific Method Overview

The scientific method is a process of trying to get as close as possible to the  objective truth . However, part of the process is to constantly refine your conclusions, ask new questions, and continue the search for the rules of the universe. Through the scientific method, scientists are trying to uncover how the world works and discover the laws that make it function in that way. You can use the scientific method to find answers for almost any question, though the scientific method can yield conflicting evidence based on the method of experimentation. In other words, the scientific method is a very useful way to figure things out – though it must be used with caution and care!

Scientific Method Steps

The exact steps of the scientific method vary from source to source , but the general procedure is the same: acquiring knowledge through observation and testing.

Making an Observation

The first step of the scientific method is to make an observation about the world around you. Before hypotheses can be made or experiments can be done, one must first notice and think about some sort of phenomena occurring. The scientific method is used when one does not know why or how something is occurring and wants to uncover the answer. But, before you can form a question you must notice something puzzling in the first place.

Asking a Question

Next, one must ask a question based on their observations. Here are some examples of good questions:

• Why is this thing occurring?
• How is this thing occurring?
• Why or how does it happen this way?

Sometimes this step is listed first in the scientific method, with making an observation (and researching the phenomena in question) listed as second. In reality, both making observations and asking questions tend to happen around the same time.

One can see a confusing occurrence and immediately think, “why is it occurring?” When observations are being made and questions are being formed, it is important to do research to see if others have already answered the question or uncovered information that may help you shape your question. For example, if you find an answer to why something is occurring, you may want to go a step further and figure out how it occurs.

Forming a Hypothesis

A hypothesis is an educated guess to explain the phenomena occurring based on prior observations. It answers the question posed in the previous step. Hypotheses can be specific or more general depending on the question being asked, but all hypotheses must be testable by gathering evidence that can be measured. If a hypothesis is not testable, then it is impossible to perform an experiment to determine whether the hypothesis is supported by evidence.

Performing an Experiment

After forming a hypothesis, an experiment must be set up and performed to test the hypothesis. An experiment must have an independent variable (something that is manipulated by the person doing the experiment), and a dependent variable (the thing being measured which may be affected by the independent variable). All other variables must be controlled so that they do not affect the outcome. During an experiment, data is collected. Data is a set of values; it may be quantitative (e.g. measured in numbers) or qualitative (a description or generalization of the results).

For example, if you were to test the effect of sunlight on plant growth, the amount of light would be the independent variable (the thing you manipulate) and the height of the plants would be the dependent variable (the thing affected by the independent variable). Other factors such as air temperature, amount of water in the soil, and species of plant would have to be kept the same between all of the plants used in the experiment so that you could truly collect data on whether sunlight affects plant growth. The data that you would collect would be quantitative – since you would measure the height of the plant in numbers.

Analyzing Data

After performing an experiment and collecting data, one must analyze the data. Research experiments are usually analyzed with statistical software in order to determine relationships among the data. In the case of a simpler experiment, one could simply look at the data and see how they correlate with the change in the independent variable.

Forming a Conclusion

The last step of the scientific method is to form a conclusion. If the data support the hypothesis, then the hypothesis may be the explanation for the phenomena. However, multiple trials must be done to confirm the results, and it is also important to make sure that the sample size—the number of observations made—is big enough so that the data is not skewed by just a few observations.

If the data do not support the hypothesis, then more observations must be made, a new hypothesis is formed, and the scientific method is used all over again. When a conclusion is drawn, the research can be presented to others to inform them of the findings and receive input about the validity of the conclusion drawn from the research.

Scientific Method Examples

There are very many examples of the use of the scientific method throughout history because it is the basis for all scientific experiments. Scientists have been conducting experiments using the scientific method for hundreds of years.

One such example is Francesco Redi’s experiment on spontaneous generation. In the 17 th Century, when Redi lived, people commonly believed that living things could spontaneously arise from organic material. For example, people believed that maggots were created from meat that was left out to sit. Redi had an alternate hypothesis: that maggots were actually part of the fly life cycle!

He conducted an experiment by leaving four jars of meat out: some uncovered, some covered with muslin, and some sealed completely. Flies got into the uncovered jars and maggots appeared a short time later. The jars that were covered had maggots on the outer surface of the muslin, but not inside the jars. Sealed jars had absolutely no maggots whatsoever.

Redi was able to conclude that maggots did not spontaneously arise in meat. He further confirmed the results by collecting captured maggots and growing them into adult flies. This may seem like common sense today, but back then, people did not know as much about the world, and it is through experiments like these that people uncovered what is now common knowledge.

Scientists use the scientific method in their research, but it is also used by people who aren’t scientists in everyday life. Even if you were not consciously aware of it, you have used the scientific method many times when solving problems around you.

For example, say you are at home and a lightbulb goes out. Noticing that the lightbulb is out is an observation. You would then naturally question, “Why is the lightbulb out?” and come up with possible guesses, or hypotheses. For example, you may hypothesize that the bulb has burned out. Then you would perform a very small experiment in order to test your hypothesis; namely, you would replace the bulb and analyze the data (“Did the light come back on?”).

If the light turned back on, you would conclude that the lightbulb had, in fact, burned out. But if the light still did not work, you would come up with other hypotheses (“The socket doesn’t work”, “Part of the lamp is broken,” “The fuse went out”, etc.) and test those.

1. Which step of the scientific method comes immediately after making observations and asking a question?

2. A scientist is performing an experiment to determine if the amount of light that rodents are exposed to affects their sleep cycle. She places some rodents in a room with 12 hours of light and 12 hours of darkness, some in a room with 24-hour light, and some in 24-hour darkness. What is the independent variable in this experiment?

3. What is the last step of the scientific method?

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Scientific Method

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The scientific method is a series of steps followed by scientific investigators to answer specific questions about the natural world. It involves making observations, formulating a hypothesis , and conducting scientific experiments . Scientific inquiry starts with an observation followed by the formulation of a question about what has been observed. The steps of the scientific method are as follows:

Observation

The first step of the scientific method involves making an observation about something that interests you. This is very important if you are doing a science project because you want your project to be focused on something that will hold your attention. Your observation can be on anything from plant movement to animal behavior, as long as it is something you really want to know more about.​ This is where you come up with the idea for your science project.

Once you've made your observation, you must formulate a question about what you have observed. Your question should tell what it is that you are trying to discover or accomplish in your experiment. When stating your question you should be as specific as possible.​ For example, if you are doing a project on plants , you may want to know how plants interact with microbes. Your question may be: Do plant spices inhibit bacterial growth ?

The hypothesis is a key component of the scientific process. A hypothesis is an idea that is suggested as an explanation for a natural event, a particular experience, or a specific condition that can be tested through definable experimentation. It states the purpose of your experiment, the variables used, and the predicted outcome of your experiment. It is important to note that a hypothesis must be testable. That means that you should be able to test your hypothesis through experimentation .​ Your hypothesis must either be supported or falsified by your experiment. An example of a good hypothesis is: If there is a relation between listening to music and heart rate, then listening to music will cause a person's resting heart rate to either increase or decrease.

Once you've developed a hypothesis, you must design and conduct an experiment that will test it. You should develop a procedure that states very clearly how you plan to conduct your experiment. It is important that you include and identify a controlled variable or dependent variable in your procedure. Controls allow us to test a single variable in an experiment because they are unchanged. We can then make observations and comparisons between our controls and our independent variables (things that change in the experiment) to develop an accurate conclusion.​

The results are where you report what happened in the experiment. That includes detailing all observations and data made during your experiment. Most people find it easier to visualize the data by charting or graphing the information.​

The final step of the scientific method is developing a conclusion. This is where all of the results from the experiment are analyzed and a determination is reached about the hypothesis. Did the experiment support or reject your hypothesis? If your hypothesis was supported, great. If not, repeat the experiment or think of ways to improve your procedure.

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What Is the Scientific Method?

The scientific method is a systematic way of conducting experiments or studies so that you can explore the things you observe in the world and answer questions about them. The scientific method, also known as the hypothetico-deductive method, is a series of steps that can help you accurately describe the things you observe or improve your understanding of them.

Ultimately, your goal when you use the scientific method is to:

• Find a cause-and-effect relationship by asking a question about something you observed
• Collect as much evidence as you can about what you observed, as this can help you explore the connection between your evidence and what you observed
• Determine if all your evidence can be combined to answer your question in a way that makes sense

Francis Bacon and René Descartes are usually credited with formalizing the process in the 16th and 17th centuries. The two philosophers argued that research shouldn’t be guided by preset metaphysical ideas of how reality works. They supported the use of inductive reasoning to come up with hypotheses and understand new things about reality.

Scientific Method Steps

The scientific method is a step-by-step problem-solving process. These steps include:

Observe the world around you. This will help you come up with a topic you are interested in and want to learn more about. In many cases, you already have a topic in mind because you have a related question for which you couldn't find an immediate answer.

Either way, you'll start the process by finding out what people before you already know about the topic, as well as any questions that people are still asking about. You may need to look up and read books and articles from academic journals or talk to other people so that you understand as much as you possibly can about your topic. This will help you with your next step.

Ask questions. Asking questions about what you observed and learned from reading and talking to others can help you figure out what the "problem" is. Scientists try to ask questions that are both interesting and specific and can be answered with the help of a fairly easy experiment or series of experiments. Your question should have one part (called a variable) that you can change in your experiment and another variable that you can measure. Your goal is to design an experiment that is a "fair test," which is when all the conditions in the experiment are kept the same except for the one you change (called the experimental or independent variable).

Form a hypothesis and make predictions based on it.  A hypothesis is an educated guess about the relationship between two or more variables in your question. A good hypothesis lets you predict what will happen when you test it in an experiment. Another important feature of a good hypothesis is that, if the hypothesis is wrong, you should be able to show that it's wrong. This is called falsifiability. If your experiment shows that your prediction is true, then your hypothesis is supported by your data.

Test your prediction by doing an experiment or making more observations.  The way you test your prediction depends on what you are studying. The best support comes from an experiment, but in some cases, it's too hard or impossible to change the variables in an experiment. Sometimes, you may need to do descriptive research where you gather more observations instead of doing an experiment. You will carefully gather notes and measurements during your experiments or studies, and you can share them with other people interested in the same question as you. Ideally, you will also repeat your experiment a couple more times because it's possible to get a result by chance, but it's less possible to get the same result more than once by chance.

Draw a conclusion. You will analyze what you already know about your topic from your literature research and the data gathered during your experiment. This will help you decide if the conclusion you draw from your data supports or contradicts your hypothesis. If your results contradict your hypothesis, you can use this observation to form a new hypothesis and make a new prediction. This is why scientific research is ongoing and scientific knowledge is changing all the time. It's very common for scientists to get results that don't support their hypotheses. In fact, you sometimes learn more about the world when your experiments don't support your hypotheses because it leads you to ask more questions. And this time around, you already know that one possible explanation is likely wrong.

Use your results to guide your next steps (iterate). For instance, if your hypothesis is supported, you may do more experiments to confirm it. Or you could come up with a hypothesis about why it works this way and design an experiment to test that. If your hypothesis is not supported, you can come up with another hypothesis and do experiments to test it. You'll rarely get the right hypothesis in one go. Most of the time, you'll have to go back to the hypothesis stage and try again. Every attempt offers you important information that helps you improve your next round of questions, hypotheses, and predictions.

Share your results. Scientific research isn't something you can do on your own; you must work with other people to do it.   You may be able to do an experiment or a series of experiments on your own, but you can't come up with all the ideas or do all the experiments by yourself .

Scientists and researchers usually share information by publishing it in a scientific journal or by presenting it to their colleagues during meetings and scientific conferences. These journals are read and the conferences are attended by other researchers who are interested in the same questions. If there's anything wrong with your hypothesis, prediction, experiment design, or conclusion, other researchers will likely find it and point it out to you.

It can be scary, but it's a critical part of doing scientific research. You must let your research be examined by other researchers who are as interested and knowledgeable about your question as you. This process helps other researchers by pointing out hypotheses that have been proved wrong and why they are wrong. It helps you by identifying flaws in your thinking or experiment design. And if you don't share what you've learned and let other people ask questions about it, it's not helpful to your or anyone else's understanding of what happens in the world.

Scientific Method Example

Here's an everyday example of how you can apply the scientific method to understand more about your world so you can solve your problems in a helpful way.

Let's say you put slices of bread in your toaster and press the button, but nothing happens. Your toaster isn't working, but you can't afford to buy a new one right now. You might be able to rescue it from the trash can if you can figure out what's wrong with it. So, let's figure out what's wrong with your toaster.

Observation. Your toaster isn't working to toast your bread.

Ask a question. In this case, you're asking, "Why isn't my toaster working?" You could even do a bit of preliminary research by looking in the owner's manual for your toaster. The manufacturer has likely tested your toaster model under many conditions, and they may have some ideas for where to start with your hypothesis.

Form a hypothesis and make predictions based on it. Your hypothesis should be a potential explanation or answer to the question that you can test to see if it's correct. One possible explanation that we could test is that the power outlet is broken. Our prediction is that if the outlet is broken, then plugging it into a different outlet should make the toaster work again.

Test your prediction by doing an experiment or making more observations. You plug the toaster into a different outlet and try to toast your bread.

If that works, then your hypothesis is supported by your experimental data. Results that support your hypothesis don't prove it right; they simply suggest that it's a likely explanation. This uncertainty arises because, in the real world, we can't rule out the possibility of mistakes, wrong assumptions, or weird coincidences affecting the results. If the toaster doesn’t work even after plugging it into a different outlet, then your hypothesis is not supported and it's likely the wrong explanation.

Use your results to guide your next steps (iteration). If your toaster worked, you may decide to do further tests to confirm it or revise it. For example, you could plug something else that you know is working into the first outlet to see if that stops working too. That would be further confirmation that your hypothesis is correct.

If your toaster failed to toast when plugged into the second outlet, you need a new hypothesis. For example, your next hypothesis might be that the toaster has a shorted wire. You could test this hypothesis directly if you have the right equipment and training, or you could take it to a repair shop where they could test that hypothesis for you.

Share your results. For this everyday example, you probably wouldn't want to write a paper, but you could share your problem-solving efforts with your housemates or anyone you hire to repair your outlet or help you test if the toaster has a short circuit.

What the Scientific Method Is Used For

The scientific method is useful whenever you need to reason logically about your questions and gather evidence to support your problem-solving efforts. So, you can use it in everyday life to answer many of your questions; however, when most people think of the scientific method, they likely think of using it to:

Describe how nature works . It can be hard to accurately describe how nature works because it's almost impossible to account for every variable that's involved in a natural process. Researchers may not even know about many of the variables that are involved. In some cases, all you can do is make assumptions. But you can use the scientific method to logically disprove wrong assumptions by identifying flaws in the reasoning.

Do scientific research in a laboratory to develop things such as new medicines.

Develop critical thinking skills.  Using the scientific method may help you develop critical thinking in your daily life because you learn to systematically ask questions and gather evidence to find answers. Without logical reasoning, you might be more likely to have a distorted perspective or bias. Bias is the inclination we all have to favor one perspective (usually our own) over another.

The scientific method doesn't perfectly solve the problem of bias, but it does make it harder for an entire field to be biased in the same direction. That's because it's unlikely that all the people working in a field have the same biases. It also helps make the biases of individuals more obvious because if you repeatedly misinterpret information in the same way in multiple experiments or over a period, the other people working on the same question will notice. If you don't correct your bias when others point it out to you, you'll lose your credibility. Other people might then stop believing what you have to say.

Why Is the Scientific Method Important?

When you use the scientific method, your goal is to do research in a fair, unbiased, and repeatable way. The scientific method helps meet these goals because:

It's a systematic approach to problem-solving. It can help you figure out where you're going wrong in your thinking and research if you're not getting helpful answers to your questions. Helpful answers solve problems and keep you moving forward. So, a systematic approach helps you improve your problem-solving abilities if you get stuck.

It can help you solve your problems.  The scientific method helps you isolate problems by focusing on what's important. In addition, it can help you make your solutions better every time you go through the process.

It helps you eliminate (or become aware of) your personal biases.  It can help you limit the influence of your own personal, preconceived notions . A big part of the process is considering what other people already know and think about your question. It also involves sharing what you've learned and letting other people ask about your methods and conclusions. At the end of the process, even if you still think your answer is best, you have considered what other people know and think about the question.

The scientific method is a systematic way of conducting experiments or studies so that you can explore the world around you and answer questions using reason and evidence. It's a step-by-step problem-solving process that involves: (1) observation, (2) asking questions, (3) forming hypotheses and making predictions, (4) testing your hypotheses through experiments or more observations, (5) using what you learned through experiment or observation to guide further investigation, and (6) sharing your results.

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Scientific Method Steps in Psychology Research

Steps, Uses, and Key Terms

Verywell / Theresa Chiechi

How do researchers investigate psychological phenomena? They utilize a process known as the scientific method to study different aspects of how people think and behave.

When conducting research, the scientific method steps to follow are:

• Observe what you want to investigate
• Ask a research question and make predictions
• Test the hypothesis and collect data
• Examine the results and draw conclusions
• Report and share the results 

This process not only allows scientists to investigate and understand different psychological phenomena but also provides researchers and others a way to share and discuss the results of their studies.

Generally, there are five main steps in the scientific method, although some may break down this process into six or seven steps. An additional step in the process can also include developing new research questions based on your findings.

What Is the Scientific Method?

What is the scientific method and how is it used in psychology?

The scientific method consists of five steps. It is essentially a step-by-step process that researchers can follow to determine if there is some type of relationship between two or more variables.

By knowing the steps of the scientific method, you can better understand the process researchers go through to arrive at conclusions about human behavior.

Scientific Method Steps

While research studies can vary, these are the basic steps that psychologists and scientists use when investigating human behavior.

The following are the scientific method steps:

Step 1. Make an Observation

Before a researcher can begin, they must choose a topic to study. Once an area of interest has been chosen, the researchers must then conduct a thorough review of the existing literature on the subject. This review will provide valuable information about what has already been learned about the topic and what questions remain to be answered.

A literature review might involve looking at a considerable amount of written material from both books and academic journals dating back decades.

The relevant information collected by the researcher will be presented in the introduction section of the final published study results. This background material will also help the researcher with the first major step in conducting a psychology study: formulating a hypothesis.

Step 2. Ask a Question

Once a researcher has observed something and gained some background information on the topic, the next step is to ask a question. The researcher will form a hypothesis, which is an educated guess about the relationship between two or more variables

For example, a researcher might ask a question about the relationship between sleep and academic performance: Do students who get more sleep perform better on tests at school?

In order to formulate a good hypothesis, it is important to think about different questions you might have about a particular topic.

You should also consider how you could investigate the causes. Falsifiability is an important part of any valid hypothesis. In other words, if a hypothesis was false, there needs to be a way for scientists to demonstrate that it is false.

Step 3. Test Your Hypothesis and Collect Data

Once you have a solid hypothesis, the next step of the scientific method is to put this hunch to the test by collecting data. The exact methods used to investigate a hypothesis depend on exactly what is being studied. There are two basic forms of research that a psychologist might utilize: descriptive research or experimental research.

Descriptive research is typically used when it would be difficult or even impossible to manipulate the variables in question. Examples of descriptive research include case studies, naturalistic observation , and correlation studies. Phone surveys that are often used by marketers are one example of descriptive research.

Correlational studies are quite common in psychology research. While they do not allow researchers to determine cause-and-effect, they do make it possible to spot relationships between different variables and to measure the strength of those relationships. 

Experimental research is used to explore cause-and-effect relationships between two or more variables. This type of research involves systematically manipulating an independent variable and then measuring the effect that it has on a defined dependent variable .

One of the major advantages of this method is that it allows researchers to actually determine if changes in one variable actually cause changes in another.

While psychology experiments are often quite complex, a simple experiment is fairly basic but does allow researchers to determine cause-and-effect relationships between variables. Most simple experiments use a control group (those who do not receive the treatment) and an experimental group (those who do receive the treatment).

Step 4. Examine the Results and Draw Conclusions

Once a researcher has designed the study and collected the data, it is time to examine this information and draw conclusions about what has been found.  Using statistics , researchers can summarize the data, analyze the results, and draw conclusions based on this evidence.

So how does a researcher decide what the results of a study mean? Not only can statistical analysis support (or refute) the researcher’s hypothesis; it can also be used to determine if the findings are statistically significant.

When results are said to be statistically significant, it means that it is unlikely that these results are due to chance.

Based on these observations, researchers must then determine what the results mean. In some cases, an experiment will support a hypothesis, but in other cases, it will fail to support the hypothesis.

So what happens if the results of a psychology experiment do not support the researcher's hypothesis? Does this mean that the study was worthless?

Just because the findings fail to support the hypothesis does not mean that the research is not useful or informative. In fact, such research plays an important role in helping scientists develop new questions and hypotheses to explore in the future.

After conclusions have been drawn, the next step is to share the results with the rest of the scientific community. This is an important part of the process because it contributes to the overall knowledge base and can help other scientists find new research avenues to explore.

Step 5. Report the Results

The final step in a psychology study is to report the findings. This is often done by writing up a description of the study and publishing the article in an academic or professional journal. The results of psychological studies can be seen in peer-reviewed journals such as  Psychological Bulletin , the  Journal of Social Psychology ,  Developmental Psychology , and many others.

The structure of a journal article follows a specified format that has been outlined by the  American Psychological Association (APA) . In these articles, researchers:

• Provide a brief history and background on previous research
• Present their hypothesis
• Identify who participated in the study and how they were selected
• Provide operational definitions for each variable
• Describe the measures and procedures that were used to collect data
• Explain how the information collected was analyzed
• Discuss what the results mean

Why is such a detailed record of a psychological study so important? By clearly explaining the steps and procedures used throughout the study, other researchers can then replicate the results. The editorial process employed by academic and professional journals ensures that each article that is submitted undergoes a thorough peer review, which helps ensure that the study is scientifically sound.

Once published, the study becomes another piece of the existing puzzle of our knowledge base on that topic.

Before you begin exploring the scientific method steps, here's a review of some key terms and definitions that you should be familiar with:

• Falsifiable : The variables can be measured so that if a hypothesis is false, it can be proven false
• Hypothesis : An educated guess about the possible relationship between two or more variables
• Variable : A factor or element that can change in observable and measurable ways
• Operational definition : A full description of exactly how variables are defined, how they will be manipulated, and how they will be measured

Uses for the Scientific Method

The  goals of psychological studies  are to describe, explain, predict and perhaps influence mental processes or behaviors. In order to do this, psychologists utilize the scientific method to conduct psychological research. The scientific method is a set of principles and procedures that are used by researchers to develop questions, collect data, and reach conclusions.

Goals of Scientific Research in Psychology

Researchers seek not only to describe behaviors and explain why these behaviors occur; they also strive to create research that can be used to predict and even change human behavior.

Psychologists and other social scientists regularly propose explanations for human behavior. On a more informal level, people make judgments about the intentions, motivations , and actions of others on a daily basis.

While the everyday judgments we make about human behavior are subjective and anecdotal, researchers use the scientific method to study psychology in an objective and systematic way. The results of these studies are often reported in popular media, which leads many to wonder just how or why researchers arrived at the conclusions they did.

Examples of the Scientific Method

Now that you're familiar with the scientific method steps, it's useful to see how each step could work with a real-life example.

Say, for instance, that researchers set out to discover what the relationship is between psychotherapy and anxiety .

• Step 1. Make an observation : The researchers choose to focus their study on adults ages 25 to 40 with generalized anxiety disorder.
• Step 2. Ask a question : The question they want to answer in their study is: Do weekly psychotherapy sessions reduce symptoms in adults ages 25 to 40 with generalized anxiety disorder?
• Step 3. Test your hypothesis : Researchers collect data on participants' anxiety symptoms . They work with therapists to create a consistent program that all participants undergo. Group 1 may attend therapy once per week, whereas group 2 does not attend therapy.
• Step 4. Examine the results : Participants record their symptoms and any changes over a period of three months. After this period, people in group 1 report significant improvements in their anxiety symptoms, whereas those in group 2 report no significant changes.
• Step 5. Report the results : Researchers write a report that includes their hypothesis, information on participants, variables, procedure, and conclusions drawn from the study. In this case, they say that "Weekly therapy sessions are shown to reduce anxiety symptoms in adults ages 25 to 40."

Of course, there are many details that go into planning and executing a study such as this. But this general outline gives you an idea of how an idea is formulated and tested, and how researchers arrive at results using the scientific method.

Erol A. How to conduct scientific research ? Noro Psikiyatr Ars . 2017;54(2):97-98. doi:10.5152/npa.2017.0120102

University of Minnesota. Psychologists use the scientific method to guide their research .

Shaughnessy, JJ, Zechmeister, EB, & Zechmeister, JS. Research Methods In Psychology . New York: McGraw Hill Education; 2015.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

The Crucial Role of Experiment in Modern Research

What is the importance of experiment in conducting modern research? Why should students engage in experiments more than just descriptive studies? This article discusses the importance, common experimental designs, and the prospects of experiments as a tool to discover new things.

Table of Contents

The pursuit of knowledge and the desire to understand the world around us consistently propels us into a realm of perpetual investigative processes and rigorous scientific examinations. A tool that largely occupies this realm is ‘experimentation.’ The very essence of scientific inquiry, experimentation is a methodological examination with the heart and soul rooted in observation and empirical analysis.

Understanding its nature, significance, methodologies, challenges, and its futuristic perspectives can pave the way for groundbreaking discoveries and advancements in multiple disciplines. Consisting of diverse designs and techniques, each with its particular strengths and applicability, experimental practices serve as the backbone of scientific and academic research – shaping our understanding, informing our decisions, and ultimately, refining the human experience.

The Nature and Importance of Experiment

Fundamentally, a scientific experiment is the nucleus driving the scientific method. The underlying principle rests on the dialectic of observation, formulation of hypotheses, prediction, testing through experimentation, and analysis. Several noteworthy contributions to scientific knowledge have been produced from this rigorous methodological framework.

Experimentation provides a vital platform for testing hypotheses and theories in a controlled environment, thereby ensuring the reliability and validity of the results. A scientific experiment that is well-conceived and meticulously executed offers a clear snapshot of the cause-and-effect relationships under investigation.

Four Key Attributes of a Scientific Experiment

1. reproducibility.

One of the key attributes of a scientific experiment is its reproducibility . This critical element underscores the importance of credibility and verifiability in science, as reproducibility essentially forms the acid test for the validation of research findings. The beauty of this paradigm lies in its democratizing effect, bridging the gap between independent investigators and established scientific frameworks.

2. Falcifiability

3. ethically sound.

Although the role of scientific experiments is unquestionably pivotal, it is equally important to maintain a persistent focus on ethical considerations . Responsible conduct of research promotes trust in the scientific process, ensuring that the pursuit of knowledge is not compromised by institutional shortcuts or personal biases.

4. Has limitations and challenges

Experimental designs and techniques, key experimental designs and techniques.

The cornerstone of scientific research requires profound comprehension of experimental designs and techniques. Ingeniously constructed, these designs embody the heart of experimental studies, offering invaluable insights, identifying causal inferences, and articulating a slight difference in relationships between variables. Prominent varieties of these designs and techniques include randomized controlled trials (RCTs) , quasi-experiments , and single-subject designs , each possessing distinct advantages and attributes.

1. Randomized Controlled Trials

2. quasi-experiments.

Closely associated yet inherently distinct, quasi-experiments , are observable in circumstances where random assignment is unrealizable or unethical. Quasi-experiments align identification of causal connections without compromising ethical boundaries.

3. Single-Subject Designs

Venturing towards single-subject designs , they place emphasis on the individual rather than the collective . By reversing the traditional large sample mentality, these designs promote the examination of behavioral changes within a single entity over time.

Modifications of the Common Experimental Designs

Each technique buttresses the conceptual skeleton of experimental designs with a distinct perspective. Blinded and double-blinded trials , cross-over designs , and factorial experiments stand as indispensable experimental modifications methodical in their approach.

For instance, blinded trials eliminate bias by concealing treatment assignment from participants, while cross-over designs enable participants to serve as their own controls, enhancing statistical efficacy.

Challenges in Conducting Experiments and Mitigation Strategies

Now that we have delved into the fundamental importance and role of scientific experiments, systematic design systems, and associated challenges in the scientific realm, let’s further venture into the complexities and difficulties inherent in conducting experiments. Overcoming these challenges can significantly enhance the quality and integrity of research outcomes.

Challenges of Experiments

Mitigation practices, the role of sample size.

The sample size in a study bears heavily on the statistical power of the experiment, which in turn impacts the reliability of results. A challenge often encountered is in securing a sufficiently large sample that can statistically represent the larger population.

Steps such as blinded designs , where either the participants, the researchers, or both do not know which individuals are in the control or experimental group, can help mitigate bias. Double-blind experimental designs offer an even more rigorous control against bias.

Lack of Randomization

Although the detailed planning and execution of experiments may seem daunting, tackling these challenges head-on is integral to scientific integrity and progress. Cumulative understanding and meticulous adaptation within constraints can yield highly reliable and valid results, propelling scientific inquiry towards new horizons. Such is the art and science of scientific experimentation.

The Future of Experimentation

The use of artificial intelligence, refinement and augmentation of experimental designs.

Moreover, these adjustments could catalyze efforts towards enhancing reproducibility and mitigating reproducibility crisis.

Computational Simulations

Herein, pivotal will be the design and implementation of AI-guided adaptive experimentation, where the computer algorithm leads the determination of experimental conditions based on real-time data.

Virtual Reality

Public participation, issues confronting experimentation.

In this rapidly-changing experimental landscape, various challenges also become apparent. Issues of data privacy, cybersecurity, and possible misuse of AI could pose significant hurdles.

Technological Concerns

Navigating through the colossal maze that is experimentation can be daunting. Still, it is essential for unlocking the doors to understanding our complex world.

Understanding this, alongside the challenges and mitigation strategies, equips one with a well-rounded perspective, paving the way for novel thought processes and innovative solutions. Here, we have journeyed through the science and art of experimentation but let this be only a catalyst spurring us into the future of perpetual understanding and progressive discovery.

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What makes content go viral six intriguing reasons derived from 6,956 articles, a research on in-service training activities, teaching efficacy, job satisfaction and attitude, contingent valuation method example: vehicle owners’ willingness to pay for maintenance costs to improve air quality, about the author, patrick regoniel.

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The Scientific Method: A Need for Something Better?

Here is the last part of the triptych that started with the “Perspectives” on brainstorming that was followed by the one on verbal overshadowing. I have decided to keep this for last because it deals with and in many ways attempts to debunk the use of the scientific method as the Holy Grail of research. Needless to say, the topic is controversial and will anger some.

In the “natural sciences,” advances occur through research that employs the scientific method. Just imagine trying to publish an original investigation or getting funds for a project without using it! Although research in the pure (fundamental) sciences (eg, biology, physics, and chemistry) must adhere to it, investigations pertaining to soft (a pejorative term) sciences (eg, sociology, economics, and anthropology) do not use it and yet produce valid ideas important enough to be published in peer-reviewed journals and even win Nobel Prizes.

The scientific method is better thought of as a set of “methods” or different techniques used to prove or disprove 1 or more hypotheses. A hypothesis is a proposed explanation for observed phenomena. These phenomena are, in general, empirical—that is, they are gathered by observation and/or experimentation. “Hypothesis” is a term often confused with “theory.” A theory is the end result of a previously tested hypothesis, meaning a proved set of principles that explain observed phenomena. Thus, a hypothesis is sometimes called a “working hypothesis,” to avoid this confusion. A working hypothesis needs to be proved or disproved by investigation. The entire approach employed to validate a hypothesis is more broadly called the “hypothetico-deductivism” method. Not all hypotheses are proved by empirical testing, and most of what we know and accept as truth about the economy and ancient civilizations is solely based on … just observation and thoughts. Conversely, the deep thinkers in the non-natural disciplines see many things wrong with the scientific method because it does not entirely reflect the chaotic environment that we live in—that is, the scientific method is rigid and constrained in its design and produces results that are isolated from real environments and that only address specific issues.

One of the most important features of the scientific method is its repeatability. The experiments performed to prove a working hypothesis must clearly record all details so that others may replicate them and eventually allow the hypothesis to become widely accepted. Objectivity must be used in experiments to reduce bias. “Bias” refers to the inclination to favor one perspective over others. The opposite of bias is “neutrality,” and all experiments (and their peer review) need to be devoid of bias and be neutral. In medicine, bias is also a part of conflict of interest and produces corrupt results. In medicine, conflict of interest is often due to relationships with the pharmaceutical/device industries. The American Journal of Neuroradiology ( AJNR ), as do most other serious journals, requires that contributors fill out the standard disclosure form regarding conflict of interest proposed by the International Committee of Medical Journal Editors, and it publishes these at the end of articles. 1

Like many other scientific advances, the scientific method originated in the Muslim world. About 1000 years ago, the Iraqi mathematician Ibn al-Haytham was already using it. In the Western world, the scientific method was first welcomed by astronomers such as Galileo and Kepler, and after the 17th century, its use became widespread. As we now know it, the scientific method dates only from the 1930s. The first step in the scientific method is observation from which one formulates a question. From that question, the hypothesis is generated. A hypothesis must be phrased in a way that it can be proved or disproved (“falsifiable”). The so-called “null hypothesis” represents the default position. For example, if you are trying to prove the relationship between 2 phenomena, the null hypothesis may be a statement that there is no relationship between the observed phenomena. The next step is to test the hypothesis via 1 or more experiments. The best experiments, at least in medicine, are those that are blinded and accompanied by control groups (not submitted to the same experiments). Third is the analysis of the data obtained. The results may support the working hypothesis or “falsify” (disprove) it, leading to the creation of a new hypothesis again to be tested scientifically. Not surprising, the structure of abstracts and articles published in AJNR and other scientific journals reflects the 4 steps in the scientific method (Background and Purpose, Materials and Methods, Results, and Conclusions). Another way in which our journals adhere to the scientific method is peer review—that is, every part of the article must be open to review by others who look for possible mistakes and biases. The last part of the modern scientific method is publication.

Despite its rigid structure, the scientific method still depends on the most human capabilities: creativity, imagination, and intelligence; and without these, it cannot exist. Documentation of experiments is always flawed because everything cannot be recorded. One of the most significant problems with the scientific method is the lack of importance placed on observations that lie outside of the main hypothesis (related to lateral thinking). No matter how carefully you record what you observe, if these observations are not also submitted to the method, they cannot be accepted. This is a common problem found by paleontologists who really have no way of testing their observations; yet many of their observations (primary and secondary) are accepted as valid. Also, think about the works of Sigmund Freud that led to improved understanding of psychological development and related disorders; most were based just on observations. Many argue that because the scientific method discards observations extemporaneous to it, this actually limits the growth of scientific knowledge. Because a hypothesis only reflects current knowledge, data that contradict it may be discarded only to later become important.

Because the scientific method is basically a “trial-and-error” scheme, progress is slow. In older disciplines, there may not have been enough knowledge to develop good theories, which led to the creation of bad theories that have resulted in significant delay of progress. It can also be said that progress is many times fortuitous; while one is trying to test a hypothesis, completely unexpected and often accidental results lead to new discoveries. Just imagine how many important data have been discarded because the results did not fit the initial hypothesis.

A lot of time goes into the trial-and-error phase of an experiment, so why do it when we already know perfectly well what to expect from the results? Just peruse AJNR , and most proposed hypotheses are proved true! Hypotheses proved false are never sexy, and journals are generally not interested in publishing such studies. In the scientific method, unexpected results are not trusted, while expected and understood ones are immediately trusted. The fact that we do “this” to observe “that” may be very misleading in the long run. 2 However, in reality, many controversies could have been avoided if instead of calling it “The Scientific Method,” we simply would have called it “A Scientific Method,” leaving space for development of other methods and acceptance of those used by other disciplines. Some argue that it was called “scientific” because the ones who invented it were arrogant and pretentious.

The term “science” comes from the Latin “scientia,” meaning knowledge. Aristotle equated science with reliability because it could be rationally and logically explained. Curiously, science was, for many centuries, a part of the greater discipline of philosophy. In the 14th and 15th centuries, “natural philosophy” was born; by the start of the 17th century, it had become “natural sciences.” It was during the 16th century that Francis Bacon popularized the inductive reasoning methods that would thereafter become known as the scientific method. Western reasoning is based on our faith in truth, many times absolute truth. Beginning assumptions that then become hypotheses are subjectively accepted as being true; thus, the scientific method took longer to be accepted by Eastern civilizations whose concept of truth differs from ours. It is possible that the scientific method is the greatest unifying activity of the human race. Although medicine and philosophy have been separated from each other by centuries, there is a current trend to unite both again.

The specialty of psychiatry did not become “scientific” until the widespread use of medications and therapeutic procedures offered the possibility of being examined by the scientific method. In the United States and Europe, the number of psychoanalysts has progressively declined; and most surprising, philosophers are taking their place. 3 The benefits philosophy offers are that it puts patients first, supports new models of service delivery, and reconnects researchers in different disciplines (it is the advances in neurosciences that demand answers to the more abstract questions that define a human “being”). Philosophy provides psychiatrists with much-needed generic thinking skills; and because philosophy is more widespread than psychiatry and recognizes its importance, it provides a more universal and open environment. 4 This is an example of a soft discipline merging with a hard one (medicine) for the improvement of us all. However, this is not the case in other areas.

For about 10 years, the National Science Foundation has sponsored the “Empirical Implications of Theoretical Models” initiative in political science. 5 A major complaint is that most political science literature consists of noncumulative empirical studies and very few have a “formal” component. The formal part refers to accumulation of data and use of statistics to prove or disprove an observation (thus, the use of the scientific method). For academics in political science, the problem is that some journals no longer accept publications that are based on unproven theoretic models, and this poses a significant problem to the “non-natural” sciences. 6 In this case, the social sciences try to emulate the “hard” sciences, and this may not be the best approach. These academics and others think that using the scientific method in such instances emphasizes predictions rather than ideas, focuses learning on material activities rather than on a deep understanding of a subject, and lacks epistemic framing relevant to a discipline. 7 So, is there a better approach than the scientific method?

A provocative method called “model-based inquiry” respects the precepts of the scientific method (that knowledge is testable, revisable, explanatory, conjectural, and generative). 7 While the scientific method attempts to find patterns in natural phenomena, the model-based inquiry method attempts to develop defensible explanations. This new system sees models as tools for explanations and not explanations proper and allows going beyond data; thus, new hypotheses, new concepts, and new predictions can be generated at any point along the inquiry, something not allowed within the rigidity of the traditional scientific method.

In a different approach, the National Science Foundation charged scientists, philosophers, and educators from the University of California at Berkeley to come up with a “dynamic” alternative to the scientific method. 8 The proposed method accepts input from serendipitous occurrences and emphasizes that science is a dynamic process engaging many individuals and activities. Unlike the traditional scientific method, this new one accepts data that do not fit into organized and neat conclusions. Science is about discovery, not the justifications it seems to emphasize. 9

Obviously, I am not proposing that we immediately get rid of the traditional scientific method. Until another one is proved better, it should continue to be the cornerstone of our endeavors. However, in a world where information will grow more in the next 50 years than in the past 400 years, where the Internet has 1 trillion links, where 300 billion e-mail messages are generated every day, and 200 million Tweets occur daily, ask yourself whether it is still valid to use the same scientific method that was invented nearly 400 years ago?

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The 6 Scientific Method Steps and How to Use Them

General Education

When you’re faced with a scientific problem, solving it can seem like an impossible prospect. There are so many possible explanations for everything we see and experience—how can you possibly make sense of them all? Science has a simple answer: the scientific method.

The scientific method is a method of asking and answering questions about the world. These guiding principles give scientists a model to work through when trying to understand the world, but where did that model come from, and how does it work?

In this article, we’ll define the scientific method, discuss its long history, and cover each of the scientific method steps in detail.

What Is the Scientific Method?

At its most basic, the scientific method is a procedure for conducting scientific experiments. It’s a set model that scientists in a variety of fields can follow, going from initial observation to conclusion in a loose but concrete format.

The number of steps varies, but the process begins with an observation, progresses through an experiment, and concludes with analysis and sharing data. One of the most important pieces to the scientific method is skepticism —the goal is to find truth, not to confirm a particular thought. That requires reevaluation and repeated experimentation, as well as examining your thinking through rigorous study.

There are in fact multiple scientific methods, as the basic structure can be easily modified.  The one we typically learn about in school is the basic method, based in logic and problem solving, typically used in “hard” science fields like biology, chemistry, and physics. It may vary in other fields, such as psychology, but the basic premise of making observations, testing, and continuing to improve a theory from the results remain the same.

The History of the Scientific Method

The scientific method as we know it today is based on thousands of years of scientific study. Its development goes all the way back to ancient Mesopotamia, Greece, and India.

The Ancient World

In ancient Greece, Aristotle devised an inductive-deductive process , which weighs broad generalizations from data against conclusions reached by narrowing down possibilities from a general statement. However, he favored deductive reasoning, as it identifies causes, which he saw as more important.

Aristotle wrote a great deal about logic and many of his ideas about reasoning echo those found in the modern scientific method, such as ignoring circular evidence and limiting the number of middle terms between the beginning of an experiment and the end. Though his model isn’t the one that we use today, the reliance on logic and thorough testing are still key parts of science today.

The Middle Ages

The next big step toward the development of the modern scientific method came in the Middle Ages, particularly in the Islamic world. Ibn al-Haytham, a physicist from what we now know as Iraq, developed a method of testing, observing, and deducing for his research on vision. al-Haytham was critical of Aristotle’s lack of inductive reasoning, which played an important role in his own research.

Other scientists, including Abū Rayhān al-Bīrūnī, Ibn Sina, and Robert Grosseteste also developed models of scientific reasoning to test their own theories. Though they frequently disagreed with one another and Aristotle, those disagreements and refinements of their methods led to the scientific method we have today.

Following those major developments, particularly Grosseteste’s work, Roger Bacon developed his own cycle of observation (seeing that something occurs), hypothesis (making a guess about why that thing occurs), experimentation (testing that the thing occurs), and verification (an outside person ensuring that the result of the experiment is consistent).

After joining the Franciscan Order, Bacon was granted a special commission to write about science; typically, Friars were not allowed to write books or pamphlets. With this commission, Bacon outlined important tenets of the scientific method, including causes of error, methods of knowledge, and the differences between speculative and experimental science. He also used his own principles to investigate the causes of a rainbow, demonstrating the method’s effectiveness.

Scientific Revolution

Throughout the Renaissance, more great thinkers became involved in devising a thorough, rigorous method of scientific study. Francis Bacon brought inductive reasoning further into the method, whereas Descartes argued that the laws of the universe meant that deductive reasoning was sufficient. Galileo’s research was also inductive reasoning-heavy, as he believed that researchers could not account for every possible variable; therefore, repetition was necessary to eliminate faulty hypotheses and experiments.

All of this led to the birth of the Scientific Revolution , which took place during the sixteenth and seventeenth centuries. In 1660, a group of philosophers and physicians joined together to work on scientific advancement. After approval from England’s crown , the group became known as the Royal Society, which helped create a thriving scientific community and an early academic journal to help introduce rigorous study and peer review.

Previous generations of scientists had touched on the importance of induction and deduction, but Sir Isaac Newton proposed that both were equally important. This contribution helped establish the importance of multiple kinds of reasoning, leading to more rigorous study.

As science began to splinter into separate areas of study, it became necessary to define different methods for different fields. Karl Popper was a leader in this area—he established that science could be subject to error, sometimes intentionally. This was particularly tricky for “soft” sciences like psychology and social sciences, which require different methods. Popper’s theories furthered the divide between sciences like psychology and “hard” sciences like chemistry or physics.

Paul Feyerabend argued that Popper’s methods were too restrictive for certain fields, and followed a less restrictive method hinged on “anything goes,” as great scientists had made discoveries without the Scientific Method. Feyerabend suggested that throughout history scientists had adapted their methods as necessary, and that sometimes it would be necessary to break the rules. This approach suited social and behavioral scientists particularly well, leading to a more diverse range of models for scientists in multiple fields to use.

The Scientific Method Steps

Though different fields may have variations on the model, the basic scientific method is as follows:

#1: Make Observations 

Notice something, such as the air temperature during the winter, what happens when ice cream melts, or how your plants behave when you forget to water them.

#2: Ask a Question

Turn your observation into a question. Why is the temperature lower during the winter? Why does my ice cream melt? Why does my toast always fall butter-side down?

This step can also include doing some research. You may be able to find answers to these questions already, but you can still test them!

#3: Make a Hypothesis

A hypothesis is an educated guess of the answer to your question. Why does your toast always fall butter-side down? Maybe it’s because the butter makes that side of the bread heavier.

A good hypothesis leads to a prediction that you can test, phrased as an if/then statement. In this case, we can pick something like, “If toast is buttered, then it will hit the ground butter-first.”

#4: Experiment

Your experiment is designed to test whether your predication about what will happen is true. A good experiment will test one variable at a time —for example, we’re trying to test whether butter weighs down one side of toast, making it more likely to hit the ground first.

The unbuttered toast is our control variable. If we determine the chance that a slice of unbuttered toast, marked with a dot, will hit the ground on a particular side, we can compare those results to our buttered toast to see if there’s a correlation between the presence of butter and which way the toast falls.

If we decided not to toast the bread, that would be introducing a new question—whether or not toasting the bread has any impact on how it falls. Since that’s not part of our test, we’ll stick with determining whether the presence of butter has any impact on which side hits the ground first.

#5: Analyze Data

After our experiment, we discover that both buttered toast and unbuttered toast have a 50/50 chance of hitting the ground on the buttered or marked side when dropped from a consistent height, straight down. It looks like our hypothesis was incorrect—it’s not the butter that makes the toast hit the ground in a particular way, so it must be something else.

Since we didn’t get the desired result, it’s back to the drawing board. Our hypothesis wasn’t correct, so we’ll need to start fresh. Now that you think about it, your toast seems to hit the ground butter-first when it slides off your plate, not when you drop it from a consistent height. That can be the basis for your new experiment.

#6: Communicate Your Results

Good science needs verification. Your experiment should be replicable by other people, so you can put together a report about how you ran your experiment to see if other peoples’ findings are consistent with yours.

This may be useful for class or a science fair. Professional scientists may publish their findings in scientific journals, where other scientists can read and attempt their own versions of the same experiments. Being part of a scientific community helps your experiments be stronger because other people can see if there are flaws in your approach—such as if you tested with different kinds of bread, or sometimes used peanut butter instead of butter—that can lead you closer to a good answer.

A Scientific Method Example: Falling Toast

We’ve run through a quick recap of the scientific method steps, but let’s look a little deeper by trying again to figure out why toast so often falls butter side down.

#1: Make Observations

At the end of our last experiment, where we learned that butter doesn’t actually make toast more likely to hit the ground on that side, we remembered that the times when our toast hits the ground butter side first are usually when it’s falling off a plate.

The easiest question we can ask is, “Why is that?”

We can actually search this online and find a pretty detailed answer as to why this is true. But we’re budding scientists—we want to see it in action and verify it for ourselves! After all, good science should be replicable, and we have all the tools we need to test out what’s really going on.

Why do we think that buttered toast hits the ground butter-first? We know it’s not because it’s heavier, so we can strike that out. Maybe it’s because of the shape of our plate?

That’s something we can test. We’ll phrase our hypothesis as, “If my toast slides off my plate, then it will fall butter-side down.”

Just seeing that toast falls off a plate butter-side down isn’t enough for us. We want to know why, so we’re going to take things a step further—we’ll set up a slow-motion camera to capture what happens as the toast slides off the plate.

We’ll run the test ten times, each time tilting the same plate until the toast slides off. We’ll make note of each time the butter side lands first and see what’s happening on the video so we can see what’s going on.

When we review the footage, we’ll likely notice that the bread starts to flip when it slides off the edge, changing how it falls in a way that didn’t happen when we dropped it ourselves.

That answers our question, but it’s not the complete picture —how do other plates affect how often toast hits the ground butter-first? What if the toast is already butter-side down when it falls? These are things we can test in further experiments with new hypotheses!

Now that we have results, we can share them with others who can verify our results. As mentioned above, being part of the scientific community can lead to better results. If your results were wildly different from the established thinking about buttered toast, that might be cause for reevaluation. If they’re the same, they might lead others to make new discoveries about buttered toast. At the very least, you have a cool experiment you can share with your friends!

Key Scientific Method Tips

Though science can be complex, the benefit of the scientific method is that it gives you an easy-to-follow means of thinking about why and how things happen. To use it effectively, keep these things in mind!

Don’t Worry About Proving Your Hypothesis

One of the important things to remember about the scientific method is that it’s not necessarily meant to prove your hypothesis right. It’s great if you do manage to guess the reason for something right the first time, but the ultimate goal of an experiment is to find the true reason for your observation to occur, not to prove your hypothesis right.

Good science sometimes means that you’re wrong. That’s not a bad thing—a well-designed experiment with an unanticipated result can be just as revealing, if not more, than an experiment that confirms your hypothesis.

Be Prepared to Try Again

If the data from your experiment doesn’t match your hypothesis, that’s not a bad thing. You’ve eliminated one possible explanation, which brings you one step closer to discovering the truth.

The scientific method isn’t something you’re meant to do exactly once to prove a point. It’s meant to be repeated and adapted to bring you closer to a solution. Even if you can demonstrate truth in your hypothesis, a good scientist will run an experiment again to be sure that the results are replicable. You can even tweak a successful hypothesis to test another factor, such as if we redid our buttered toast experiment to find out whether different kinds of plates affect whether or not the toast falls butter-first. The more we test our hypothesis, the stronger it becomes!

What’s Next?

Want to learn more about the scientific method? These important high school science classes will no doubt cover it in a variety of different contexts.

Test your ability to follow the scientific method using these at-home science experiments for kids !

Need some proof that science is fun? Try making slime

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What is the scientific method?

The scientific method is the process of objectively establishing facts through testing and experimentation. The basic process involves making an observation, forming a hypothesis, making a prediction, conducting an experiment and finally analyzing the results. The principals of the scientific method can be applied in many areas, including scientific research, business and technology.

Steps of the scientific method

The scientific method uses a series of steps to establish facts or create knowledge. The overall process is well established, but the specifics of each step may change depending on what is being examined and who is performing it. The scientific method can only answer questions that can be proven or disproven through testing.

Make an observation or ask a question. The first step is to observe something that you would like to learn about or ask a question that you would like answered. These can be specific or general. Some examples would be "I observe that our total available network bandwidth drops at noon every weekday" or "How can we increase our website registration numbers?" Taking the time to establish a well-defined question will help you in later steps.

Gather background information. This involves doing research into what is already known about the topic. This can also involve finding if anyone has already asked the same question.

Create a hypothesis. A hypothesis is an explanation for the observation or question. If proven later, it can become a fact. Some examples would be "Our employees watching online videos during lunch is using our internet bandwidth" or "Our website visitors don't see our registration form."

Create a prediction and perform a test. Create a testable prediction based on the hypothesis. The test should establish a noticeable change that can be measured or observed using empirical analysis. It is also important to control for other variables during the test. Some examples would be "If we block video-sharing sites, our available bandwidth will not go down significantly during lunch" or "If we make our registration box bigger, a greater percentage of visitors will register for our website than before the change."

Analyze the results and draw a conclusion. Use the metrics established before the test see if the results match the prediction. For example, "After blocking video-sharing sites, our bandwidth utilization only went down by 10% from before; this is not enough of a change to be the primary cause of the network congestion" or "After increasing the size of the registration box, the percent of sign-ups went from 2% of total page views to 5%, showing that making the box larger results in more registrations."

Share the conclusion or decide what question to ask next: Document the results of your experiment. By sharing the results with others, you also increase the total body of knowledge available. Your experiment may have also led to other questions, or if your hypothesis is disproven you may need to create a new one and test that. For example, "Because user activity is not the cause of excessive bandwidth use, we now suspect that an automated process is running at noon every day."

Using the scientific method in technology and computers

The scientific method is incredibly valuable in technology and related fields. It is obviously used in research and development, but it is also useful in day-to-day operations. Because almost everything can be quantified, testing hypotheses can be easy.

Most modern computer systems are complicated and difficult to troubleshoot. Using the scientific method of hypothesis and testing can greatly simplify the process of tracking down errors and it can help find areas of improvement. It can also help when you evaluate new technologies before implementation.

Using the scientific method in business

Many business processes benefit when using the scientific method. Shifting business landscapes and complex business relationships can make behaviors hard to predict or act counter to previous history. Instead of using gut feelings or previous experience, a scientific approach can help businesses grow. Big data initiative can make business information more available and easier to test with.

The scientific method can be applied in many areas. Customer satisfaction and retention numbers can be analyzed and tested upon. Profitability and finance numbers can be analyzed to form new conclusions. Making predictions on changing business practices and checking the results will help to identify and measure success or failure of the initiatives.

Common pitfalls in using the scientific method

The scientific method is a powerful tool. Like any tool, though, if it is misused it can cause more damage than good.

The scientific method can only be used for testable phenomenon. This is known as falsifiability . While much in nature can be tested and measured, some areas of human experience are beyond objective observation.

Both proving and disproving the hypothesis are equally valid outcomes of testing. It is possible to ignore the outcome or inject bias to skew the results of a test in a way that will fit the hypothesis. Data in opposition to the hypothesis should not be discounted.

It is important to control for other variables and influences during testing to not skew the results. While difficult, not accounting for these could produce invalid data. For example, testing bandwidth during a holiday or measuring registrations during a sale event may introduce other factors that influence the outcome.

Another common pitfall is mixing correlation with causation. While two data points may seem to be connected, it is not necessarily true that once is directly influenced by the other. For example, an ice cream stand in town sees drops in business on the hottest days. While the data may look like the hotter the weather, the less people want ice cream, the reality is that more people are going to the beach on those days and less are in town.

History of the scientific method

The discovery of the scientific method is not credited to any single person, but there are a few notable figures who contributed to its development.

The Greek philosopher Aristotle is considered to be one of the earliest proponents of logic and cycles of observation and deduction in recorded history. Ibn al-Haytham, a mathematician, established stringent testing methodologies in pursuit of facts and truth, and he recorded his findings.

During the Renaissance, many thinkers and scientists continued developing rational methods of establishing facts. Sir Francis Bacon emphasized the importance of  inductive reasoning . Sir Isaac Newton relied on both inductive and  deductive reasoning  to explain the results of his experiments, and Galileo Galilei emphasized the idea that results should be repeatable.

Other well-known contributors to the scientific method include Karl Popper, who introduced the concept of falsifiability, and Charles Darwin, who is known for using multiple communication channels to share his conclusions.

See also: falsifiability , pseudoscience , empirical analysis , validated learning , OODA loop , black swan event , deep learning .

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The crucial role of the scientific method & experimental design in engineering innovation.

When it comes to wastewater treatment systems, owners demand reliability and effectiveness, but getting from concept to solution is not always a straight path. For this reason, the application of the scientific method 1 (SM) and rigorous experimental design 2 (ED) are essential for advancing engineering designs and ensuring reliable, efficient and innovative engineering solutions.

SM in Engineering

The scientific method can be defined as a process of systematic inquiry using observation, hypothesis, experimentation, analysis and conclusion. Even though most of us are first introduced to SM in grade school, few of us use it in real life, real work and real problem solving on a daily, weekly or even monthly basis.

Even so, having a systematic laboratory investigative mechanism is a cornerstone of engineering practice, as it:

Ensures accuracy with precision and repeatability

Enhances problem solving with a structured approach to identifying and analyzing problems and solutions

Builds credibility and trust through the scientific rigor of engineering studies that can be peer reviewed, critiqued and discussed

Facilitates innovation by allowing scientists and engineers to develop creative and effective solutions to complex problems as well as keys to discovering new methods and technologies 1

ED in Engineering

Experimental design in engineering refers to the structured planning of experiments to investigate and validate hypothesized engineered solutions to users’ wastewater problems. The goal is to gather empirical data that can be analyzed to draw valid and reliable conclusions to make informed decisions. When done correctly, it validates assumptions with experimental data or uncovers unforeseen problems early in the low-cost laboratory study rather than later in the commercial plant, when high-cost modifications are required.

Good ED always states a clear objective that defines the problem to be solved and a hypothetical solution based upon previous experience, literature review and industry knowledge. Good ED includes variables, controls and replicas to statistically validate results. It includes, with constraints where needed, state-of-the-industry approaches to solving wastewater problems.

When design of experiment (DOE or ED) is done correctly, it optimizes efficiency and performance of the tested processes and/or products, facilitates development of innovative technologies and solutions and ensures accurate, reproducible results—all while helping to improve the quality of engineered designs and systems. Careful planning leads to meaningful insights and better developed engineered solutions.

Use of SM & ED to Solve a Mine Wastewater Treatment Problem

To better show the role of SM and ED in engineering, here is an example of how these processes were used in the development of a wastewater treatment system for a mine tailings waste stream. In this example, what began as a series of laboratory studies for a mining application ultimately led to the invention of a new selenium-reducing fixed bed bioreactor (Se FBBR) that found use in other applications and the refining industry.

Solution development began in the lab with isolation and observation of anoxic selenium-reducing bacteria (Se-RB) in a mine tailings waste stream (Image 1). Process scientists used SM principles to test hypotheses and better understand the Se-RB culture’s growth dynamics. Based on these experiments, the scientists learned these selenate-reducing bacteria (Se-RB) were also denitrifier bacteria, meaning they were able to grow by reducing nitrate and nitrite in the absence of dissolved oxygen. Additional lab studies were also conducted to determine the best external carbon source to support selenate reduction (a glycerin-based carbon source) as well as the optimal nutrient requirements, temperature and pH range for bacterial growth.

Through rigorous scientific experimentation, process scientists also discovered that the addition of too much external carbon led to overproduction of hydrogen sulfide, which was an unexpected and undesirable result. This observation enabled the team to innovate a novel aeration/no-aeration sequencing of operational regimes to select and promote growth of the desirable Se-RBs while limiting or killing the growth of unwanted sulfate-reducing bacteria (SRBs). Conceived based on SM and ED principles, these well-designed lab studies allowed the team to investigate potential solutions before testing them in the field, which helped to prevent any surprise findings from cropping up later in the engineering and design process. The analysis from the lab studies led to a full-scale process design and mathematical model, followed by an on-site pilot study (Image 2) to demonstrate and validate the hypothetical model.

A few years later, the selenium FBBR technology developed through this series of lab studies was again put to work, this time for removing selenate from a refinery wastewater stream. The refinery wastewater stream had selenate levels that exceeded limits for discharge into a local surface water stream. Due to high levels of sulfate also present in the wastewater, the selective Se-RBs were needed to out-compete SRBs to preferentially remove selenate while forming minimal hydrogen sulfide.

Challenges & Mitigations

From a water treatment professional’s perspective, the usual challenges to applying the SM and ED in engineering systems include securing the trust of the user to invest in a customized solution-development study, accurately estimating the time and cost of the lab study, obtaining and evaluating the best representative wastewater samples in the lab and designing the sequence of lab experiments to the end solution.

Some lab studies are so clear and conclusive that full-scale engineering and warranty can follow, while other studies necessitate an on-site field study to validate the designed approach. In these cases, the field study allows the team to gauge system performance while treating daily plant variations in wastewater concentrations, flow rates, loads and effluent quality. From there, a process warranty can follow. Even if all these phases are needed, a scientifically sound approach is often well worth it in the end, as it can prevent delays and added costs due to unforeseen issues with a solution concept.

Other Examples

SM and ED principles can be leveraged in nearly any type of wastewater treatment system design process. Recent examples of wastewater treatment solutions achieved through application of SM and ED include:

An extensive river remedial action laboratory study involving contaminated sediment dewatering and treatment with subsequent large-scale engineering system design and offer

Conducting a large jar test study to determine the optimal method for removing multiple metals from a highly variable wastewater stream

Conducting a lab study on cyanide and nickel removal from a novel wastewater to support on-site treatment and eliminate expensive disposal costs

Performing a laboratory respirometer study to examine growth kinetics of denitrification bacteria in refinery nitrogen-bearing cooling tower blowdown water

In each of these cases, conducting well-designed laboratory studies at the outset of the project yielded a smooth design and build process thereafter, including the building of a full-scale moving bed bioreactor for treatment of a complex cooling tower blowdown stream. These and other experiences demonstrate the value of using both SM and ED for engagements between wastewater treatment solution providers and users.

The use of scientific rigor in wastewater treatment studies with experimental design is extremely important for engineering wastewater treatment solutions and systems. Solution providers should take deliberate efforts to foster a culture of inquiry and experimentation in their approach to wastewater treatment problem solving and solution development.

Adopting SM and ED as standard engineering practice and education will benefit solution providers and clients alike by encouraging earlier detection of problematic issues, more comprehensive problem solving and greater innovation in the engineering process.

Scientific Method, en.wikipedia.org/wiki/scientific method. Elements of inquiry, overview and factors of scientific inquiry.

Introduction to Engineering Experimentation, 3rd ed., 2010. Wheeler & Ganji; sections 12.1.2 through 12.1.6, pp. 423-424.

Further reading: Activated Sludge Technologies for Treating Industrial Wastewaters, Design & Troubleshooting, 2014. Echenfelder & Cleary. Ch 7 section on Treatability Studies (pp. 144-145) and Process Modeling (pp. 163-164).

Bill Sheridan is a senior process design scientist and subject matter expert for Technologies, Inc. He has received four biological wastewater treatment technology patents and has led the licensing of two of those biotechnologies. Additionally, Sheridan has led or conducted close to 100 laboratory treatability studies as well as dozens of field pilot demonstrations and engineering design studies, audits and consultations. He may be reached at [email protected].

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Understanding Science

How science REALLY works...

Frequently asked questions about how science works

The Understanding Science site is assembling an expanded list of FAQs for the site and you can contribute. Have a question about how science works, what science is, or what it’s like to be a scientist? Send it to  [email protected] !

Expand the individual panels to reveal the answers or Expand all | Collapse all

What is the scientific method?

The “scientific method” is traditionally presented in the first chapter of science textbooks as a simple, linear, five- or six-step procedure for performing scientific investigations. Although the Scientific Method captures the core logic of science (testing ideas with evidence), it misrepresents many other aspects of the true process of science — the dynamic, nonlinear, and creative ways in which science is actually done. In fact, the Scientific Method more accurately describes how science is summarized  after the fact  — in textbooks and journal articles — than how scientific research is actually performed. Teachers may ask that students use the format of the scientific method to write up the results of their investigations (e.g., by reporting their  question, background information, hypothesis, study design, data analysis,  and  conclusion ), even though the process that students went through in their investigations may have involved many iterations of questioning, background research, data collection, and data analysis and even though the students’ “conclusions” will always be tentative ones. To learn more about how science really works and to see a more accurate representation of this process, visit  The  real  process of science .

Why do scientists often seem tentative about their explanations?

Scientists often seem tentative about their explanations because they are aware that those explanations could change if new evidence or perspectives come to light. When scientists write about their ideas in journal articles, they are expected to carefully analyze the evidence for and against their ideas and to be explicit about alternative explanations for what they are observing. Because they are trained to do this for their scientific writing, scientist often do the same thing when talking to the press or a broader audience about their ideas. Unfortunately, this means that they are sometimes misinterpreted as being wishy-washy or unsure of their ideas. Even worse, ideas supported by masses of evidence are sometimes discounted by the public or the press because scientists talk about those ideas in tentative terms. It’s important for the public to recognize that, while provisionality is a fundamental characteristic of scientific knowledge, scientific ideas supported by evidence are trustworthy. To learn more about provisionality in science, visit our page describing  how science builds knowledge . To learn more about how this provisionality can be misinterpreted, visit a section of the  Science toolkit .

Why is peer review useful?

Peer review helps assure the quality of published scientific work: that the authors haven’t ignored key ideas or lines of evidence, that the study was fairly-designed, that the authors were objective in their assessment of their results, etc. This means that even if you are unfamiliar with the research presented in a particular peer-reviewed study, you can trust it to meet certain standards of scientific quality. This also saves scientists time in keeping up-to-date with advances in their fields by weeding out untrustworthy studies. Peer-reviewed work isn’t necessarily correct or conclusive, but it does meet the standards of science. To learn more, visit  Scrutinizing science .

What is the difference between independent and dependent variables?

In an experiment, the independent variables are the factors that the experimenter manipulates. The dependent variable is the outcome of interest—the outcome that depends on the experimental set-up. Experiments are set-up to learn more about how the independent variable does or does not affect the dependent variable. So, for example, if you were testing a new drug to treat Alzheimer’s disease, the independent variable might be whether or not the patient received the new drug, and the dependent variable might be how well participants perform on memory tests. On the other hand, to study how the temperature, volume, and pressure of a gas are related, you might set up an experiment in which you change the volume of a gas, while keeping the temperature constant, and see how this affects the gas’s pressure. In this case, the independent variable is the gas’s volume, and the dependent variable is the pressure of the gas. The temperature of the gas is a controlled variable. To learn more about experimental design, visit Fair tests: A do-it-yourself guide .

What is a control group?

In scientific testing, a control group is a group of individuals or cases that is treated in the same way as the experimental group, but that is not exposed to the experimental treatment or factor. Results from the experimental group and control group can be compared. If the control group is treated very similarly to the experimental group, it increases our confidence that any difference in outcome is caused by the presence of the experimental treatment in the experimental group. For an example, visit our side trip  Fair tests in the field of medicine .

What is the difference between a positive and a negative control group?

A negative control group is a control group that is not exposed to the experimental treatment or to any other treatment that is expected to have an effect. A positive control group is a control group that is not exposed to the experimental treatment but that is exposed to some other treatment that is known to produce the expected effect. These sorts of controls are particularly useful for validating the experimental procedure. For example, imagine that you wanted to know if some lettuce carried bacteria. You set up an experiment in which you wipe lettuce leaves with a swab, wipe the swab on a bacterial growth plate, incubate the plate, and see what grows on the plate. As a negative control, you might just wipe a sterile swab on the growth plate. You would not expect to see any bacterial growth on this plate, and if you do, it is an indication that your swabs, plates, or incubator are contaminated with bacteria that could interfere with the results of the experiment. As a positive control, you might swab an existing colony of bacteria and wipe it on the growth plate. In this case, you  would  expect to see bacterial growth on the plate, and if you do not, it is an indication that something in your experimental set-up is preventing the growth of bacteria. Perhaps the growth plates contain an antibiotic or the incubator is set to too high a temperature. If either the positive or negative control does not produce the expected result, it indicates that the investigator should reconsider his or her experimental procedure. To learn more about experimental design, visit  Fair tests: A do-it-yourself guide .

What is a correlational study, and how is it different from an experimental study?

In a correlational study, a scientist looks for associations between variables (e.g., are people who eat lots of vegetables less likely to suffer heart attacks than others?) without manipulating any variables (e.g., without asking a group of people to eat more or fewer vegetables than they usually would). In a correlational study, researchers may be interested in any sort of statistical association — a positive relationship among variables, a negative relationship among variables, or a more complex one. Correlational studies are used in many fields (e.g., ecology, epidemiology, astronomy, etc.), but the term is frequently associated with psychology. Correlational studies are often discussed in contrast to experimental studies. In experimental studies, researchers do manipulate a variable (e.g., by asking one group of people to eat more vegetables and asking a second group of people to eat as they usually do) and investigate the effect of that change. If an experimental study is well-designed, it can tell a researcher more about the cause of an association than a correlational study of the same system can. Despite this difference, correlational studies still generate important lines of evidence for testing ideas and often serve as the inspiration for new hypotheses. Both types of study are very important in science and rely on the same logic to relate evidence to ideas. To learn more about the basic logic of scientific arguments, visit  The core of science .

What is the difference between deductive and inductive reasoning?

Deductive reasoning involves logically extrapolating from a set of premises or hypotheses. You can think of this as logical “if-then” reasoning. For example, IF an asteroid strikes Earth, and IF iridium is more prevalent in asteroids than in Earth’s crust, and IF nothing else happens to the asteroid iridium afterwards, THEN there will be a spike in iridium levels at Earth’s surface. The THEN statement is the logical consequence of the IF statements. Another case of deductive reasoning involves reasoning from a general premise or hypothesis to a specific instance. For example, based on the idea that all living things are built from cells, we might  deduce  that a jellyfish (a specific example of a living thing) has cells. Inductive reasoning, on the other hand, involves making a generalization based on many individual observations. For example, a scientist who samples rock layers from the Cretaceous-Tertiary (KT) boundary in many different places all over the world and always observes a spike in iridium may  induce  that all KT boundary layers display an iridium spike. The logical leap from many individual observations to one all-inclusive statement isn’t always warranted. For example, it’s possible that, somewhere in the world, there is a KT boundary layer without the iridium spike. Nevertheless, many individual observations often make a strong case for a more general pattern. Deductive, inductive, and other modes of reasoning are all useful in science. It’s more important to understand the logic behind these different ways of reasoning than to worry about what they are called.

What is the difference between a theory and a hypothesis?

Scientific theories are broad explanations for a wide range of phenomena, whereas hypotheses are proposed explanations for a fairly narrow set of phenomena. The difference between the two is largely one of breadth. Theories have broader explanatory power than hypotheses do and often integrate and generalize many hypotheses. To be accepted by the scientific community, both theories and hypotheses must be supported by many different lines of evidence. However, both theories and hypotheses may be modified or overturned if warranted by new evidence and perspectives.

What is a null hypothesis?

A null hypothesis is usually a statement asserting that there is no difference or no association between variables. The null hypothesis is a tool that makes it possible to use certain statistical tests to figure out if another hypothesis of interest is likely to be accurate or not. For example, if you were testing the idea that sugar makes kids hyperactive, your null hypothesis might be that there is no difference in the amount of time that kids previously given a sugary drink and kids previously given a sugar-substitute drink are able to sit still. After making your observations, you would then perform a statistical test to determine whether or not there is a significant difference between the two groups of kids in time spent sitting still.

What is Ockhams's razor?

Ockham’s razor is an idea with a long philosophical history. Today, the term is frequently used to refer to the principle of parsimony — that, when two explanations fit the observations equally well, a simpler explanation should be preferred over a more convoluted and complex explanation. Stated another way, Ockham’s razor suggests that, all else being equal, a straightforward explanation should be preferred over an explanation requiring more assumptions and sub-hypotheses. Visit  Competing ideas: Other considerations  to read more about parsimony.

What does science have to say about ghosts, ESP, and astrology?

Rigorous and well controlled scientific investigations 1  have examined these topics and have found  no  evidence supporting their usual interpretations as natural phenomena (i.e., ghosts as apparitions of the dead, ESP as the ability to read minds, and astrology as the influence of celestial bodies on human personalities and affairs) — although, of course, different people interpret these topics in different ways. Science can investigate such phenomena and explanations only if they are thought to be part of the natural world. To learn more about the differences between science and astrology, visit  Astrology: Is it scientific?  To learn more about the natural world and the sorts of questions and phenomena that science can investigate, visit  What’s  natural ?  To learn more about how science approaches the topic of ESP, visit  ESP: What can science say?

Has science had any negative effects on people or the world in general?

Knowledge generated by science has had many effects that most would classify as positive (e.g., allowing humans to treat disease or communicate instantly with people half way around the world); it also has had some effects that are often considered negative (e.g., allowing humans to build nuclear weapons or pollute the environment with industrial processes). However, it’s important to remember that the process of science and scientific knowledge are distinct from the uses to which people put that knowledge. For example, through the process of science, we have learned a lot about deadly pathogens. That knowledge might be used to develop new medications for protecting people from those pathogens (which most would consider a positive outcome), or it might be used to build biological weapons (which many would consider a negative outcome). And sometimes, the same application of scientific knowledge can have effects that would be considered both positive and negative. For example, research in the first half of the 20th century allowed chemists to create pesticides and synthetic fertilizers. Supporters argue that the spread of these technologies prevented widespread famine. However, others argue that these technologies did more harm than good to global food security. Scientific knowledge itself is neither good nor bad; however, people can choose to use that knowledge in ways that have either positive or negative effects. Furthermore, different people may make different judgments about whether the overall impact of a particular piece of scientific knowledge is positive or negative. To learn more about the applications of scientific knowledge, visit  What has science done for you lately?

1 For examples, see:

• Milton, J., and R. Wiseman. 1999. Does psi exist? Lack of replication of an anomalous process of information transfer.  Psychological Bulletin  125:387-391.
• Carlson, S. 1985. A double-blind test of astrology.  Nature  318:419-425.
• Arzy, S., M. Seeck, S. Ortigue, L. Spinelli, and O. Blanke. 2006. Induction of an illusory shadow person.  Nature  443:287.
• Gassmann, G., and D. Glindemann. 1993. Phosphane (PH 3 ) in the biosphere.  Angewandte Chemie International Edition in English  32:761-763.

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• Published: 08 August 2024

Superconductivity in CaH \(_{6}\) and ThH \(_{10}\) through fully ab initio Eliashberg method and self-consistent Green’s function

• Alwan Abdillah Darussalam 1 &
• Takashi Koretsune 1  

Scientific Reports volume  14 , Article number:  18399 ( 2024 ) Cite this article

Metrics details

• Electronic properties and materials
• Superconducting properties and materials
• Theoretical physics

Pressurized hydrogen-based superconductors are phonon-mediated superconductors that exhibit high phonon frequencies. In these superconductors, in addition to the density of states (DOS) at the Fermi energy ( \(E_F\) ), the energy dependence of the DOS around \(E_F\) becomes important for evaluating their transition temperature ( \(T_c\) ). Systems with peak structures in the DOS around \(E_F\) , such as \(Im\bar{3}m\) H \(_{3}\) S and \(Fm\bar{3}m\) LaH \(_{10}\) , highlight this point. We use the fully ab initio Eliashberg method to investigate this phenomenon in \(Im\bar{3}m\) CaH \(_{6}\) and \(Fm\bar{3}m\) ThH \(_{10}\) with a dip structure in their DOS around \(E_F\) . Our calculated \(T_c\) values (225–235 K for CaH \(_{6}\) at 200 GPa and 156–158 K for ThH \(_{10}\) at 170 GPa) are quantitatively consistent with the experimental results. Remarkably, our results from the self-consistent treatment of the electron Green’s function contrasts with those cases with a peak structure in the DOS. This finding unifies the understanding of how DOS structures influence the evaluation of \(T_c\) .

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Introduction.

The discovery of pressurized hydrogen-based superconductors ( M H \(_x\) ) with measured high transition temperature ( \(T_c\) ) has revolutionized the field of condensed matter physics. The superconductivity in M H \(_x\) can be explained by the conventional phonon-mediated superconductivity theory. H, as the lightest element, provides high phonon frequencies ( \(\sim 1000\) K) that lead to high \(T_c\) following the inverse square root of the atomic mass 1 . The advancement of high-pressure experimental techniques allows for the structure stabilization of H in atomic form in M H \(_x\) materials. Remarkably, theoretical and experimental studies of M H \(_x\) are consistent with each other, and the former has been the precedent. Some notable materials that show this predictability are H \(_{3}\) S 2 , 3 , 4 , LaH \(_{10}\) 5 , 6 , 7 , YH \(_{6}\) and YH \(_{9}\) 8 , 9 , 10 , 11 , ThH \(_{10}\) 12 , 13 , and CaH \(_{6}\) 14 , 15 , 16 . Despite the notable consistency between theoretical studies and experimental measurements on \(T_c\) , those theoretical studies often employed an adjustable parameter to include the Coulomb interaction.

The standard approach to predicting \(T_c\) is based on the strong-coupling extension of BCS theory introduced by Eliashberg 17 , 18 , following the approximation method proposed by Migdal 19 . One can employ Eliashberg equations when the electron–phonon spectral function is provided. The simplest and most widely used solution to Eliashberg equations is the McMillan–Allen–Dynes formula 20 , 21 :

This formula approximates the electronic density of states (DOS) being constant to the value at its Fermi energy ( \(E_F\) ). The formula has contained phonon-induced mass renormalization ( \(1 + \lambda _\text {ep}\) ) and the Coulomb interaction with the retardation effect, \(\mu _c^*\) . The latter is often treated as an adjustable parameter encompassing the pseudo-Coulomb potential. Therefore, the McMillan–Allen–Dynes often employs a semi-empirical, adjustable \(\mu _c^*\) with a typical value 0.10–0.13. However, the value of \(\mu _c^*\) that reproduces experimental \(T_c\) varies by materials 22 , 23 . A more sophisticated approach is indispensable to understanding and predicting the superconducting \(T_c\) . One approach to calculate \(\mu _c^*\) with the retardation effect is often discussed in literature as 24 :

Equation ( 2 ) describes how the bare Coulomb potential \(\mu _c\) is rescaled considering the order of electron energy scale \(\omega _\text {e}\) and the order of phonon energy scale \(\omega _\text {p}\) . Although a first-principles study for \(\mu _c^*\) has been conducted 25 , determining cutoff energies is not straightforward.

Recently, fully ab initio methods to calculate \(T_c\) were developed: the density functional theory for superconductors (SCDFT) 26 , 27 , and a direct solution to the original temperature Eliashberg equations 28 . By employing these non-empirical methods, it is possible to evaluate the effects that are neglected in the conventional approach and compare them with experiments. For example, the plasmon effect 29 and the spin-fluctuation effect 23 , 30 , which comes from the screened Coulomb interaction beyond the static random phase approximation (RPA), have been discussed in the framework of SCDFT. On the other hand, a direct solution of the original Eliashberg method (the fully ab initio Eliashberg method) includes energy-dependent DOS calculation and self-consistent mass renormalization. These features are advantageous in materials with a strong energy dependence of their DOS around \(E_F\) . One can see this renormalization affects \(T_c\) of H \(_{3}\) S and LaH \(_{10}\) superconductors 28 , 31 , in which the Van Hove singularity peak exists around \(E_F\) . In those studies, the self-consistently treated renormalization gives 8-16 \(\%\) gain in the calculated \(T_c\) than a one-shot renormalization. Nevertheless, only a few hydrogen-based materials were studied using a fully ab initio method 28 , 31 , 32 , 33 , 34 .

In this report, the ability of the fully ab initio Eliashberg method is further examined through a direct comparison with experimental data. We extend the use of the method to calculate \(T_c\) of materials with energy-dependency of the DOS around \(E_F\) featuring a dip structure: \(Im\bar{3}m\) CaH \(_{6}\) (experimental \(T_c = 215\) K at 172 GPa 15 ) and \(Fm\bar{3}m\) ThH \(_{10}\) (experimental \(T_c = 161\) K at 170 GPa 13 ). Our fully ab initio calculation results not only show a quantitative agreement with the reported \(T_c\) from experiments but also are consistent with previous semi-empirical theoretical studies 12 , 14 , 35 , 36 , 37 , 38 . In addition, we show that the self-consistent treatment of the mass renormalization leads to a reduction in \(T_c\) , which is reasonably the reverse for systems where DOS features a peak structure.

Theoretical framework: fully ab-initio Eliashberg theory

Eliashberg theory 17 , 18 describes the superconducting system in Green’s function formalism. The theory considers the method of simplifying the electron–phonon interaction part as proposed by Migdal 19 . Green’s function of electrons is derived in a square matrix form comprised of normal functions G as diagonal elements and anomalous functions F as the off-diagonal elements. In correspondence, there is a self-energy matrix consisting of normal self-energy \(\Sigma\) and anomalous self-energy \(\Delta\) . The anomalous part describes the existence of the superconducting gap at temperature \(T < T_c\) and reads zero at \(T > T_c\) . In our study, we use the linearized version of the temperature Eliashberg equations 18 with the band structure of electron and phonon are calculated based on the density functional theory (DFT) 28 as:

Here, \(\xi _j({\varvec{k}}) = \tilde{\varepsilon }_j({\varvec{k}}) - \mu\) , where \(\tilde{\varepsilon }_j({\varvec{k}})\) is the electron dispersion function at band j with momentum \({\varvec{k}}\) , and \(i\omega _n = i(2n + 1)\pi T\) , is the fermion Matsubara frequency for integer index n . One may write \(i\nu _m \equiv i\omega _{n} - i\omega _{n^\prime } = i2m\pi T\) as a transfer of the boson Matsubara frequency for integer index m and, in this case, along with a momentum transfer \({\varvec{q}} = {\varvec{k}} - {\varvec{k}}^\prime\) . In general, performing calculations using Matsubara Green’s functions involves significant computational expenses. We mitigate this issue by sparsely sampling Matsubara frequency points utilizing the compact basis called the intermediate-representation (IR) basis 39 , 40 , 41 .

The interaction propagators, \(D_{jj^\prime }({\varvec{q}}; i\nu _{m})\) , are also comprised of density functional quantities. We only write electron–phonon interaction part, \(D^\text {ep}_{jj^\prime }\) , in the normal self-energy (Eq. ( 5 )) because the DFT calculation has included the normal self-energy caused by the screened Coulomb interaction. In the anomalous self-energy (Eq. ( 6 )), we write both \(D^\text {ep}_{jj^\prime }\) and a considerable screened electron–electron (Coulomb) repulsion in the pairing channel sought from the random phase approximation (RPA), \(D^\text {ee, RPA}_{jj^\prime }\) . The screened Coulomb repulsion in our work is approximated to be static ( \(i\nu _{m}=0)\) ) and independent of the spin index, therefore neglecting the possibility of the plasmon and spin-fluctuation mechanism.

One can see that this fully ab initio Eliashberg method can be viewed as a relatively straightforward method for calculating superconducting state. In particular, the method facilitates the self-consistent determination of electron normal Green’s function as expressed in Eqs. ( 3 ) and ( 5 ). In principle, the self-consistent treatment is the more realistic approach as the electronic state and energy are allowed to relax considering the environment of systems. The role of self-consistency is particularly significant in systems with large phonon frequencies and a strong energy-dependent feature in DOS around \(E_F\) 28 , 31 . In cases where DOS is relatively uniform, this self-consistency can be simplified into a one-shot treatment.

We breakdown the self-consistent treatment of \(G_{j}({\varvec{k}}; i\omega _n)\) as follows.

where the electron-self energy for each stage \(s \ge 1\) is given by,

Initially, one can consider a guess Green’s function from a non-interacting case \(G^0_{j}({\varvec{k}}; i\omega _n)\) to obtain the one-shot self-energy \(\Sigma ^1_{j}({\varvec{k}}; i\omega _n)\) and calculating the one-shot Green’s function \(G^1_{j}({\varvec{k}}; i\omega _n)\) . At this stage, we reached the one-shot treatment. The self-consistent Green’s function is obtained by continuing the process until \(G_{j}({\varvec{k}}; i\omega _n)\) and \(\Sigma _{j}({\varvec{k}}; i\omega _n)\) only change insignificantly. It should be noted that the chemical potential \(\mu\) is always updated after calculating the self-energy so that the number of electrons does not change during the calculation.

DFT Calculations

DFT calculations were performed to obtain electronic energy dispersion \(\tilde{\varepsilon }_{j}({\varvec{k}})\) and electron wavefunctions \(\tilde{\psi }_{j}({\varvec{k}})\) employing Q uantum ESPRESSO packages 42 . DFPT calculations were performed to obtain phonon frequency dispersion \(\tilde{\omega }^\gamma ({\varvec{q}})\) and electron–phonon matrix elements \(\tilde{g}^\gamma _{j{\varvec{k}} j^\prime {\varvec{k}} - {\varvec{q}}}({\varvec{q}})\) 43 from the response of \(\tilde{\psi }_{j{\varvec{k}}}({\varvec{r}})\) for each phonon branch \(\gamma\) . Based on these quantities, we construct our electron Green’s function \(G_{j}({\varvec{k}}; i\omega _n)\) and the interaction propagators \(D_{j}({\varvec{q}}; i\nu _{m})\) . We note that due to DFT, the normal self-energy from the screened electron–electron (Coulomb) interaction is already included in the band structure.

The electron–phonon interaction is given as

where \(\tilde{g}^\gamma _{jj^\prime }({\varvec{q}})\) is the momentum-averaged electron–phonon matrix element,

The screened electron–electron (Coulomb) interaction in the pairing channel is given as

Here, \(\epsilon _{{\varvec{G}} {\varvec{G}}^\prime }({\varvec{q}}; 0)\) is a symmetrized static dielectric function in the reciprocal lattice space \({\varvec{G}}, {\varvec{G}}^\prime\) with unit volume \(\Omega\) . The dielectric quantity is calculated from an RPA-type polarization, considering the electronic energy dispersion \(\tilde{\varepsilon }_{j}({\varvec{k}})\) and density functional pair density \(\tilde{\rho }_{j{\varvec{k}} j^\prime {\varvec{k}} - {\varvec{q}}}({\varvec{G}})\) 44 :

\(D^\text {ep}_{jj^\prime }({\varvec{q}}; i\omega _n)\) and \(D^\text {ee}_{jj^\prime }({\varvec{q}}; 0)\) enter into Eliashberg equations in a rather complicated convolutions. For the analysis purpose, we quantify these contributions by employing the Eliashberg spectral function \(\alpha ^2F(\omega )\) and the introducing the dimensionless strength parameter of the electron–phonon interaction as \(\lambda _\text {ep}\) , in the case of \(D^\text {ep}_{jj^\prime }({\varvec{q}}; 0)\) :

Similarly, we employ the strength of Coulomb repulsion in the pairing channel to quantify \(D^\text {ee}_{jj^\prime }({\varvec{q}}; 0)\) :

In order to calculate these quantities with good accuracy, we use the weighted average method 45 . Here, \(\delta (\tilde{\xi })\) is a delta function calculated within the Hermite–Gaussian smearing method 46 with smearing width 0.010 Ry. \(N(0)=\sum \nolimits _{j {\varvec{k}} } \delta (\tilde{\xi }_{j{\varvec{k}}})\) essentially is the DOS at \(E_F\) . Due to the DFT calculation, \(\tilde{g}^\gamma _{j{\varvec{k}} j^\prime {\varvec{k}} - {\varvec{q}}}({\varvec{q}})\) includes the renormalization from the screened Coulomb interaction. On the other hand, \(\mu _\text {ee}\) is a bare Coulomb potential without any screening contributions from phonon. Therefore, one expects \(\mu _\text {ee}\) to be larger than the pseudo-Coulomb potential \(\mu _c^*\) .

In the DFT calculations, we first employ a \(16 \times 16 \times 16\) \({\varvec{k}}\) -mesh. Later, the obtained quantities such as \(\tilde{g}^\gamma _{j{\varvec{k}} j^\prime {\varvec{k}} - {\varvec{q}}}({\varvec{q}})\) and \(D^\text {ee}_{j{\varvec{k}} j^\prime {\varvec{k}} - {\varvec{q}}}({\varvec{q}};0)\) are interpolated into the electronic structure of fine \({\varvec{k}}\) -meshes to calculate the \({\varvec{k}}\) summation. For \(Im\bar{3}m\) CaH \(_{6}\) , projector-augmented wave (PAW) 47 pseudopotentials and plane-wave basis are employed where cutoff energies for wavefunction and charge density are 50 Ry and 500 Ry. For \(Fm\bar{3}m\) ThH \(_{10}\) , ultrasoft 48 pseudopotentials and plane-wave basis are employed where cutoff energies for wavefunction and charge density are 60 Ry and 600 Ry. The pseudopotentials are provided in the PS library 49 and are chosen by considering the standard solid-state pseudopotential (SSSP) precision 50 .

Intermediate-Representation Basis

We expand the Matsubara Green’s function for each statistic:

where \(U_l^F(i\omega _n)\) and \(U_l^B(i\nu _{m})\) act as universal functions that carry the dynamical properties of fermion and boson. The expansion in principle goes over \(l_\text {max} = \infty\) points. However, it has been shown that the expansion coefficients \(G_l\) and \(D_l\) decay rapidly 51 , and the feature of Green’s function can be reproduced using a small value \(l_\text {max}\) by employing the precomputed IR basis library 39 , 40 , 41 . In addition, one stores the iteration results in the static expansion coefficients (amplitudes) \(G_l\) and \(D_l\) that further accelerate the conventional Fourier convolution of frequency basis.

In this paper, we present the result of a non-empirical \(T_c\) calculation by a fully ab initio Eliashberg method of two hydrogen-based compounds: \(Fm\bar{3}m\) ThH \(_{10}\) and \(Im\bar{3}m\) CaH \(_{6}\) . Both of these materials have been experimentally confirmed for their thermodynamic stability and high \(T_c\) under high pressure 13 , 15 , 16 , following their initial theoretical predictions 12 , 14 , 35 . In particular, their DOS \(N(E-E_F)\) calculated from DFT show an energy-dependent dip feature around \(E_F\) as shown in Fig.  1 a,b. Here, one can see two comparable densities of states per number of atoms \(E_F\) . However, the dip structure in the DOS of ThH \(_{10}\) is more prominent than that in the DOS of CaH \(_{6}\) . This prominence is shown by the fitted quadratic curve in the range of \(-\)  0.5 to 0.5 eV. The second derivatives of the obtained curves are 0.018 (eV) \(^{-3}\) for CaH \(_{6}\) and 0.030 (eV) \(^{-3}\) for ThH \(_{10}\) . The phonon band structure and the Eliashberg function \(\alpha ^2F(\omega )\) for both compounds are shown in Fig.  2 .

( a , b ) Electronic DOS \(N(E-E_F)\) of \(Im\bar{3}m\) CaH \(_{6}\) and \(Fm\bar{3}m\) ThH \(_{10}\) at 200 GPa calculated by DFT with tetrahedron method using a \(96 \times 96 \times 96\) \({\varvec{k}}\) -mesh (solid line). The number of atoms normalizes the vertical axis. A quadratic function is fitted to \(N(E-E_F)\) in the range of \(\pm 0.5\) eV around the \(E_F\) (dashed line). In addition, a calculated \(N(E-E_F)\) of \(Fm\bar{3}m\) ThH \(_{10}\) considering spin-orbit interaction is plotted (thin dotted line). ( c ) Eigenvalue \(\varphi (T)\) of superconducting gap function as expressed in Eq. ( 20 ). Eigenvalue problem is calculated using a \(96 \times 96 \times 96\) \({\varvec{k}}\) -mesh and a \(8 \times 8 \times 8\) \({\varvec{q}}\) -point.

Phonon band structure and Eliashberg spectral function \(\alpha ^2F(\omega )\) of \(Im\bar{3}m\) CaH \(_{6}\) ( a , b ) and \(Fm\bar{3}m\) ThH \(_{10}\) (c, d) at 200 GPa calculated by density functional perturbation theory (DFPT) using \(96 \times 96 \times 96\) \({\varvec{k}}\) -mesh and a \(8 \times 8 \times 8\) \({\varvec{q}}\) -point.

To calculate \(T_c\) , the linearized anomalous Green’s function, as in Eq. ( 4 ), is substituted to Eq. ( 6 ). This substitution constructs an eigenvalue equation with respect to the superconducting gap function \(\Delta _{j} ({\varvec{k}};i\omega _n)\) :

We have introduced an eigenvalue parameter denoted by \(\varphi (T)\) corresponding to the eigenvector \(\Delta _{j}({\varvec{k}}; i\omega _n)\) . The eigenvalue represents the pairing state as seen from the entire operation on the left-hand side of Eq. ( 20 ) with respect to the \(\Delta _{j}({\varvec{k}}; i\omega _n)\) . By decreasing temperature, \(\varphi (T)\) increases, and it should reach unity at \(T_c\) to give the solution of the linearized Eliashberg equations. In short, we use \(\varphi (T_c) = 1\) to determine \(T_c\) . In our framework, since the Green’s function and other variables depend on the Matsubara frequencies over a fine \({\varvec{k}}\) -mesh, storing this information becomes the primary bottleneck. In this sense, intermediate-representation (IR) basis is helpful 39 , 40 , 52 . On the other hand, the computational time is manageable. For example, a calculation employing \(96\times 96\times 96\) \(\varvec{k}\) -points and \(8\times 8\times 8\) \(\varvec{q}\) -points takes a few days to obtain \(T_c\) under one condition.

The calculation of eigenvalue includes the evaluation of electron normal Green’s function \(G_{j}({\varvec{k}};i\omega _n)\) . The fully ab initio Eliashberg method allows for the evaluation of \(G_{j}({\varvec{k}};i\omega _n)\) from either the self-consistent treatment, as in Eq. ( 9 ), or from a one-shot treatment, as in Eq. ( 8 ).

In practice, \(T_c\) is determined by a numerical calculation by evaluating the eigenvalue \(\varphi (T)\) for some range of decreasing temperatures, as shown in Fig.  1 c. Here we have calculated \(\varphi (T)\) of ThH \(_{10}\) and CaH \(_{6}\) at 200 GPa starting from \(T=300\) K. The calculation stops at temperature T that gives \(\varphi (T)\) slightly exceeds unity. From this point, \(T_c\) is determined through a simple interpolation. Figure  1 c also shows the results from self-consistent and one-shot treatment, with the prior yields lower calculated \(\varphi (T)\) compared to the latter. This discrepancy results in lower values of \(T_c\) . Specifically, the self-consistent (one-shot) treatment leads to a calculated \(T_c\) of 225 K (235 K) in CaH \(_{6}\) and 137 K (142 K) in ThH \(_{10}\) as summarized in Table  1 .

The corresponding interaction parameters \(\lambda _\text {ep}\) and \(\mu _\text {ee}\) , are also listed as references. For both systems, we employ \(96\times 96\times 96\) \({\varvec{k}}\) -mesh for solving the Eliashberg equations, \(16 \times 16 \times 16\) \({\varvec{k}}\) -mesh for calculating the electronic structure \(\tilde{\varepsilon }_{j}({\varvec{k}})\) , wave functions \(\tilde{\psi }_{j{\varvec{k}}}({\varvec{r}})\) , and \(8 \times 8 \times 8\) \({\varvec{q}}\) -mesh for calculating the electron–phonon and the screened Coulomb scattering matrix. Our results in the self-consistent treatment indicate the reverse for cases of H \(_{3}\) S and LaH \(_{10}\) where \(T_c\) from the self-consistent treatment is higher than those from the one-shot treatment 28 , 31 .

The experimental \(T_c\) data of CaH \(_{6}\) is available within the pressure range of 150–200 GPa 15 , 16 , with the highest \(T_c\) recorded being \(\sim 215\)  K at 172 GPa. In the case of ThH \(_{10}\) , it is only reported that the experimental \(T_c\) is \(\sim 161\)  K at 170 GPa and \(\sim 159\)  K at 174 GPa 13 . For a better comparison, we perform calculations for both systems at 170, 200, and 250 GPa employing \(96\times 96\times 96\) \({\varvec{k}}\) -mesh and \(8 \times 8 \times 8\) \({\varvec{q}}\) -mesh. \(T_c\) from our calculation results, along with the available experimental reports for CaH \(_{6}\) and ThH \(_{10}\) are presented in Fig.  3 . We also employed both self-consistent and one-shot treatments, where \(T_c\) from the prior is consistently lower than \(T_c\) from the latter. The calculated \(T_c\) for CaH \(_{6}\) are 236–246 K compared to the experimental value of \(\sim\)  212–214 K at 170 GPa, and 225–235 K compared to \(\sim\)  205 K at 200 GPa. The deviation in both pressures is \(\sim 20\)  K (10 \(\%\) ), indicating a similar pressure dependence in this range. For ThH \(_{10}\) , the calculated \(T_c\) of 156–158 K at 170 GPa is nearly equal to its experimental \(T_c\) of 161 K.

We remark other previous semi-empirical calculations of in CaH \(_{6}\) , which resulted in \(T_c\) range of 198–240 K (adjusted \(\mu _c^*\)  = 0.13–0.16) from Eliashberg methods 14 , 38 , 53 , and that in ThH \(_{10}\) , which resulted in \(T_c\) of 205 K from Eliashberg method and 150.5 K from McMillan–Allen–Dynes formula (adjusted \(\mu _c^*=0.15\) ) 12 . Our fully ab initio results for CaH \(_{6}\) are comparable to these studies while we do not employ adjustable parameter \(\mu _c^*\) .

Superconducting transition temperature \(T_c\) calculated from the fully ab initio Eliashberg method (this work) of \(Im\bar{3}m\) CaH \(_{6}\) and \(Fm\bar{3}m\) ThH \(_{10}\) compared to the reported experimental data points. Experimental data is obtained from Ma et al. 15 (plus marker), Li et al. 16 (diamond marker), for \(Im\bar{3}m\) CaH \(_{6}\) , and Semenok et al. 13 (star marker), for \(Fm\bar{3}m\) ThH \(_{10}\) .

Superconducting transition temperature \(T_c\) from the fully ab initio Eliashberg theory upon \({\varvec{k}}\) -mesh and \({\varvec{q}}\) -mesh choices. \(T_c\) of \(Im\bar{3}m\) CaH \(_{6}\) (triangle markers) and \(Fm\bar{3}m\) ThH \(_{10}\) (pentagon markers) are calculated at 200 GPa. On the horizontal axis, \(N_k\) denotes the volume of a cubic \({\varvec{k}}\) -mesh in which the Eliashberg equation is solved. Inset shows the electron–phonon interaction strength \(\lambda _\text {ep}\) with an identical horizontal axis for each system that is indicated with the same marker.

In order to examine the precision of calculation, the dependence of \(T_c\) on the number of \({\varvec{k}}\) -points and \({\varvec{q}}\) -points are considered. Figure  4 shows the convergence of the calculated \(T_c\) of CaH \(_{6}\) and ThH \(_{10}\) upon increasing the sampling point in the \({\varvec{k}}\) -mesh and \({\varvec{q}}\) -mesh. An interpolation is employed for interaction terms calculated in coarse \({\varvec{q}}\) -meshes ( \(N_q = 4^3\) and \(N_q = 8^3\) ) for the phonon calculation and a medium \({\varvec{k}}\) -mesh ( \(N_k^\text {med.} = 16^3\) ) for the electronic structure calculation to the fine \({\varvec{k}}\) -mesh of the Eliashberg equations. Here, we have set the calculation \({\varvec{k}}\) -meshes as integer multiples of \(16 \times 16 \times 16\) \({\varvec{k}}\) -mesh.

Our calculations generally converge at calculation with \(64 \times 64 \times 64\) \({\varvec{k}}\) -points and \(8 \times 8 \times 8\) \({\varvec{q}}\) -points. Notably, in calculations with \(4 \times 4 \times 4\) \({\varvec{q}}\) -points, the results for ThH \(_{10}\) already show good convergence with respect to \({\varvec{k}}\) -mesh, whereas the results for CaH \(_{6}\) still show a fluctuating variation. We found that all variations of \(T_c\) , including the fluctuating one, resemble \({\varvec{k}}\) -mesh dependence of electron–phonon interaction strength \(\lambda _\text {ep}\) , indicating that \({\varvec{k}}\) -mesh dependence of \(T_c\) mainly comes from the electron–phonon interaction. Thus, the convergence of the fully ab initio Eliashberg method conserves that of \(\lambda _\text {ep}\) , which depends on the DFPT calculation. We can see that this method is not only non-empirical but also an extension of the McMillan–Allen–Dynes formula. The energy-dependent DOS calculation chooses the proper number of relevant electronic states for the superconductivity at \(E_F\) . On the other hand, self-consistency acts as a correction factor regarding the more proper and realistic treatment of electron–phonon interaction. In addition, the static screened Coulomb interaction is calculated employing \(16 \times 16 \times 16\) medium \({\varvec{k}}\) -mesh and identical for all plots in each \({\varvec{q}}\) -mesh. \(\mu _\text {ee}\) does not change upon increasing the number of \({\varvec{k}}\) -points.

In Fig.  4 , we have also plotted \(T_c\) from both self-consistent and one-shot treatments. Upon achieving convergence, the difference between the results from self-consistent and one-shot treatments persists in calculation employing \(4\times 4\times 4\) and \(8 \times 8 \times 8\) \({\varvec{q}}\) -meshes, in conjunction with a sufficiently fine \({\varvec{k}}\) -mesh.

Our discussion begins with the comparison of our calculation results with the experimental results, as shown in Fig.  3 . The calculated \(T_c\) of CaH \(_{6}\) is slightly higher than the experimental results, even after the introduction of adequately large \(96\times 96\times 96\) \({\varvec{k}}\) -points and \(8\times 8\times 8\) \({\varvec{q}}\) -points. In this case, the discrepancy in \(T_c\) might be attributed to the use of harmonic approximation for the calculation of the electron–phonon interaction. A recent anharmonic calculation has demonstrated the phonon hardening effect, in which the electron–phonon interaction becomes small and, in turn, reduces \(T_c\) of CaH \(_{6}\) from 240 to 190 K 37 . In the case of ThH \(_{10}\) , the calculated \(T_c\) is in good agreement with the experimental \(T_c\) . Although there are no theoretical studies about the anharmonic effect in ThH \(_{10}\) , our result suggests that this effect is insignificant, which is beyond the scope of our research. We shall remark the sizeable contributions from d and f -orbitals to the DOS of ThH \(_{10}\) . Nevertheless, these contributions do not affect spin-orbit interactions around \(E_F\) . We observed no change upon calculating the DOS with or without spin-orbit interaction.

In the subsequent analysis, we explore the impact of self-consistent treatment compared to the one-shot treatment for these two materials. Our results show that the self-consistent treatment, hereafter the self-consistency, leads to a lower \(T_c\) , which is in contrast to the cases when a peak feature is present in the DOS 28 , 31 . In other words, we find that the effect of self-consistency on \(T_c\) behaves oppositely: an increase in the peaked-DOS system and a decrease in the dipped-DOS system. In addition, the effect of self-consistency is not solely reflected by the prominence of the DOS feature shown in Fig.  1 a,b. Even though the dip structure in ThH \(_{10}\) is more evident than in CaH \(_{6}\) , the effect of the self-consistency is smaller. Namely, the self-consistency reduces \(T_c\) of CaH \(_{6}\) and ThH \(_{10}\) by \(\sim 4.4\%\) and \(\sim 3.7\%\) . Since \(T_c\) is determined by the combination of the DOS and the electron–phonon interaction, the prominence of the DOS feature should be scaled by the strength of the electron–phonon interaction. Indeed, ThH \(_{10}\) does not exhibit a large \(\lambda _\text {ep}\) (0.78–1.3) despite a large N (0) (0.50–0.56 states/eV). Its \(\alpha ^2F(\omega )\) spectrum also exhibits relatively low intensity. Therefore, we suggest that the energy dependence of the DOS becomes more important in the self-consistent treatment when the electron–phonon interaction is stronger.

Renormalization function \(Z(i\omega _n)\) of CaH \(_{6}\) and ThH \(_{10}\) at pressure of 200 GPa as \(T=T_c\) . The maximum value of the renormalization function lies at the zeroth frequency \(i\omega _0 = i\pi T_c\) . The values of \(Z(i\pi T_c)\) and their ratio from self-consistent to one-shot treatment are stated.

In systems with a peak in the DOS, it has been considered that the increase of \(T_c\) after the self-consistency is related to the decrease of renormalization function:

where \(Z(i\omega _n)\) of H \(_3\) S decrease by \(7.5\%\) 28 . Here, \(\Sigma _{j}({\varvec{k}}; i\omega _n)\) is solely due to the electron–phonon interactions as explained by Eq. ( 5 ). We have plotted \(Z(i\omega _n)\) of CaH \(_{6}\) and ThH \(_{10}\) in Fig.  5 . The renormalization at the zeroth frequency index \(Z(i\pi T_c)\) is comparable to \(1+\lambda _\text {ep}\) that can explain the larger \(Z(i\omega _n)\) in CaH \(_{6}\) than that in ThH \(_{10}\) . In our cases of systems exhibiting a dip feature in the DOS, the self-consistency leads to an increase of \(Z(i\omega _n)\) than that in the one-shot treatment. The ratios of \(Z(i\omega _n)\) from the self-consistent to the one-shot treatment is 1.020 for CaH \(_{6}\) and 1.017 for ThH \(_{10}\) . An increase in \(Z(i\omega _n)\) corresponds to a larger mass enhancement of electron, which in turn reduces \(T_c\) . This mass enhancement influences the electron Green’s function \(G_{j}(i\omega _n)\) , which, according to Eq. ( 20 ), yields a lower eigenvalue \(\varphi (T)\) , as shown in Fig.  1 c. The reduction in \(\varphi (T)\) is likely due to the interaction of phonons with electron quasiparticles with shorter lifetimes after the additional mass enhancement.

We have investigated the fully ab initio Eliashberg method and its self-consistency in \(Im\bar{3}m\) CaH \(_{6}\) and \(Fm\bar{3}m\) ThH \(_{10}\) systems. The calculated \(T_c\)  = 225–235 K of CaH \(_{6}\) at 200 GPa and \(T_c\)  = 156–158 K of ThH \(_{10}\) at 170 GPa are consistent with experimental \(T_c\) 13 , 15 , 16 . The dip structure in DOS around \(E_F\) in these systems guides the self-consistency to the small but persistent decrease of \(T_c\) (compared to the one-shot treatment) around 3–4 \(\%\) . This effect might rely on the sharpness of the peak/dip structure and the strength of electron–phonon interaction. We shall note that only studies of the singular peak structure observed notable increases in \(T_c\) of H \(_{3}\) S and LaH \(_{10}\) (8–16 \(\%\) , \(\lambda _\text {ep}\)  = 1.79–2.01), and even in the case of relatively flat (featureless) DOS, it still leads to a small increase in \(T_c\) of \(T_c\) of H \(_{2}\) S and MgB \(_{2}\) (4–5 \(\%\) , \(\lambda _\text {ep}\)  = 0.73–0.86) 28 , 31 . These phenomena might be the reason why the rather shallow dip structure does not have a significant decrease in \(T_c\) in our calculations despite its persistent effect.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108 , 1175–1204. https://doi.org/10.1103/PhysRev.108.1175 (1957).

Article   ADS   MathSciNet   CAS   Google Scholar  

Li, Y., Hao, J., Liu, H., Li, Y. & Ma, Y. The metallization and superconductivity of dense hydrogen sulfide. J. Chem. Phys. https://doi.org/10.1063/1.4874158 (2014).

Article   PubMed   PubMed Central   Google Scholar  

Duan, D. et al. Pressure-induced metallization of dense (H \(_2\) S) \(_2\) H \(_2\) with high- \(T_c\) superconductivity. Sci. Rep. 4 , 6968. https://doi.org/10.1038/srep06968 (2014).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Drozdov, A. P., Eremets, M. I., Troyan, I. A., Ksenofontov, V. & Shylin, S. I. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Nature 525 , 73–76. https://doi.org/10.1038/nature14964 (2015).

Article   ADS   CAS   PubMed   Google Scholar  

Liu, H., Naumov, I. I., Hoffmann, R., Ashcroft, N. W. & Hemley, R. J. Potential high- \(T_c\) superconducting lanthanum and yttrium hydrides at high pressure. Proc. Natl. Acad. Sci. USA 114 , 6990–6995. https://doi.org/10.1073/pnas.1704505114 (2017).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Drozdov, A. P. et al. Superconductivity at 250 K in lanthanum hydride under high pressures. Nature 569 , 528–531. https://doi.org/10.1038/s41586-019-1201-8 (2019).

Somayazulu, M. et al. Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures. Phys. Rev. Lett. 122 , 027001. https://doi.org/10.1103/PhysRevLett.122.027001 (2019).

Li, Y. et al. Pressure-stabilized superconductive yttrium hydrides. Sci. Rep. 5 , 9948. https://doi.org/10.1038/srep09948 (2015).

Peng, F. et al. Hydrogen Clathrate structures in rare earth hydrides at high pressures: Possible route to room-temperature superconductivity. Phys. Rev. Lett. 119 , 107001. https://doi.org/10.1103/PhysRevLett.119.107001 (2017).

Article   ADS   PubMed   Google Scholar  

Troyan, I. A. et al. Anomalous high-temperature superconductivity in YH \(_6\) . Adv. Mater. 33 , 2006832. https://doi.org/10.1002/adma.202006832 (2021).

Article   CAS   Google Scholar  

Kong, P. et al. Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure. Nat. Commun. 12 , 5075. https://doi.org/10.1038/s41467-021-25372-2 (2021).

Kvashnin, A. G., Semenok, D. V., Kruglov, I. A., Wrona, I. A. & Oganov, A. R. High-temperature superconductivity in a Th-H system under pressure conditions. ACS Appl. Mater. Interfaces 10 , 43809–43816. https://doi.org/10.1021/acsami.8b17100 (2018).

Article   CAS   PubMed   Google Scholar  

Semenok, D. V. et al. Superconductivity at 161 K in thorium hydride ThH \(_{10}\) : Synthesis and properties. Mater. Today 33 , 36–44. https://doi.org/10.1016/j.mattod.2019.10.005 (2020).

Wang, H., Tse, J. S., Tanaka, K., Iitaka, T. & Ma, Y. Superconductive sodalite-like clathrate calcium hydride at high pressures. Proc. Natl. Acad. Sci. 109 , 6463–6466. https://doi.org/10.1073/pnas.1118168109 (2012).

Article   ADS   PubMed   PubMed Central   Google Scholar  

Ma, L. et al. High-temperature superconducting phase in clathrate calcium hydride CaH \(_{6}\) up to 215 K at a pressure of 172 GPa. Phys. Rev. Lett. 128 , 167001. https://doi.org/10.1103/PhysRevLett.128.167001 (2022).

Li, Z. et al. Superconductivity above 200 K discovered in superhydrides of calcium. Nat. Commun. 13 , 1–5. https://doi.org/10.1038/s41467-022-30454-w (2022).

Article   ADS   CAS   Google Scholar  

Eliashberg, G. Interactions between electrons and lattice vibrations in a superconductor. Soviet Phys. J. Exp. Theor. Phys. 11 , 696–702 (1960).

MathSciNet   Google Scholar  

Eliashberg, G. M. Temperature Green’s function for electrons in a superconductor. Soviet Phys. J. Exp. Theor. Phys. 12 , 1000–1002 (1961).

Google Scholar  

Migdal, A. B. Interactions between electrons and lattice vibrations in a normal metal. Soviet Phys. J. Exp. Theor. Phys. 7 , 1438–1446 (1958).

McMillan, W. L. Transition temperature of strong-coupled superconductors. Phys. Rev. 167 , 331–344. https://doi.org/10.1103/PhysRev.167.331 (1968).

Allen, P. B. & Dynes, R. C. Transition temperature of strong-coupled superconductors reanalyzed. Phys. Rev. B 12 , 905–922. https://doi.org/10.1103/PhysRevB.12.905 (1975).

Savrasov, S. Y. & Savrasov, D. Y. Electron–phonon interactions and related physical properties of metals from linear-response theory. Phys. Rev. B 54 , 16487–16501. https://doi.org/10.1103/PhysRevB.54.16487 (1996).

Kawamura, M., Hizume, Y. & Ozaki, T. Benchmark of density functional theory for superconductors in elemental materials. Phys. Rev. B 101 , 134511. https://doi.org/10.1103/PhysRevB.101.134511 (2020).

Morel, P. & Anderson, P. W. Calculation of the superconducting state parameters with retarded electron–phonon interaction. Phys. Rev. 125 , 1263–1271. https://doi.org/10.1103/PhysRev.125.1263 (1962).

Article   ADS   Google Scholar  

Lee, K.-H., Chang, K. J. & Cohen, M. L. First-principles calculations of the Coulomb pseudopotential \(\mu ^*\) : Application to Al. Phys. Rev. B 52 , 1425–1428. https://doi.org/10.1103/PhysRevB.52.1425 (1995).

Lüders, M. et al. Ab initio theory of superconductivity. I. Density functional formalism and approximate functionals. Phys. Rev. B 72 , 024545. https://doi.org/10.1103/PhysRevB.72.024545 (2005).

Marques, M. A. L. et al. Ab initio theory of superconductivity. II. Application to elemental metals. Phys. Rev. B 72 , 024546. https://doi.org/10.1103/PhysRevB.72.024546 (2005).

Sano, W., Koretsune, T., Tadano, T., Akashi, R. & Arita, R. Effect of Van Hove singularities on high- \(T_c\) superconductivity in H \(_3\) S. Phys. Rev. B 93 , 094525. https://doi.org/10.1103/PhysRevB.93.094525 (2016).

Akashi, R. & Arita, R. Development of density-functional theory for a plasmon-assisted superconducting state: Application to lithium under high pressures. Phys. Rev. Lett. 111 , 057006. https://doi.org/10.1103/PhysRevLett.111.057006 (2013).

Tsutsumi, K., Hizume, Y., Kawamura, M., Akashi, R. & Tsuneyuki, S. Effect of spin fluctuations on superconductivity in V and Nb: A first-principles study. Phys. Rev. B 102 , 1–10. https://doi.org/10.1103/PhysRevB.102.214515 (2020).

Article   Google Scholar  

Wang, T., Nomoto, T., Koretsune, T. & Arita, R. Importance of self-consistency in first-principles Eliashberg calculation for superconducting transition temperature. J. Phys. Chem. Solids 178 , 111348. https://doi.org/10.1016/j.jpcs.2023.111348 (2023).

Akashi, R., Kawamura, M., Tsuneyuki, S., Nomura, Y. & Arita, R. First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydrides. Phys. Rev. B 91 , 224513. https://doi.org/10.1103/PhysRevB.91.224513 (2015).

Flores-Livas, J. A., Sanna, A. & Gross, E. K. High temperature superconductivity in sulfur and selenium hydrides at high pressure. Eur. Phys. J. B 89 , 63. https://doi.org/10.1140/epjb/e2016-70020-0 (2016).

Errea, I. et al. Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride. Nature 578 , 66–69. https://doi.org/10.1038/s41586-020-1955-z (2020).

Tanaka, K., Tse, J. S. & Liu, H. Electron-phonon coupling mechanisms for hydrogen-rich metals at high pressure. Phys. Rev. B 96 , 100502. https://doi.org/10.1103/PhysRevB.96.100502 (2017).

Boudabia, S. et al. First principles study and reconsideration of the mechanical and dynamic stability of hydrogen-rich compound cI14-CaH6 high critical temperature superconductor under pressure. Phys. C 587 , 1353899. https://doi.org/10.1016/j.physc.2021.1353899 (2021).

Hou, P., Huo, Z. & Duan, D. Quantum and anharmonic effects in superconducting \(Im\bar{3}m\) CaH \(_{6}\) under high pressure: A first-principles study. J. Phys. Chem. C 127 , 23980–23987. https://doi.org/10.1021/acs.jpcc.3c06664 (2023).

Lucrezi, R. et al. Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides. Commun. Phys. 7 , 33. https://doi.org/10.1038/s42005-024-01528-6 (2024).

Shinaoka, H., Otsuki, J., Ohzeki, M. & Yoshimi, K. Compressing Green’s function using intermediate representation between imaginary-time and real-frequency domains. Phys. Rev. B 96 , 035147. https://doi.org/10.1103/PhysRevB.96.035147 (2017).

Chikano, N., Yoshimi, K., Otsuki, J. & Shinaoka, H. irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function. Comput. Phys. Commun. 240 , 181–188. https://doi.org/10.1016/j.cpc.2019.02.006 (2019).

Wallerberger, M. et al. sparse-ir: Optimal compression and sparse sampling of many-body propagators. SoftwareX 21 , 101266. https://doi.org/10.1016/j.softx.2022.101266 (2023).

Giannozzi, P. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21 , 395502. https://doi.org/10.1088/0953-8984/21/39/395502 (2009).

Article   PubMed   Google Scholar  

Baroni, S., de Gironcoli, S., Corso, A. D. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73 , 515–562. https://doi.org/10.1103/RevModPhys.73.515 (2001).

Hybertsen, M. S. & Louie, S. G. Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators. Phys. Rev. B 35 , 5585–5601. https://doi.org/10.1103/PhysRevB.35.5585 (1987).

Koretsune, T. & Arita, R. Efficient method to calculate the electron-phonon coupling constant and superconducting transition temperature. Comput. Phys. Commun. 220 , 239–242. https://doi.org/10.1016/j.cpc.2017.07.011 (2017).

Methfessel, M. & Paxton, A. T. High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B 40 , 3616–3621. https://doi.org/10.1103/PhysRevB.40.3616 (1989).

Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50 , 17953–17979. https://doi.org/10.1103/PhysRevB.50.17953 (1994).

Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41 , 7892–7895. https://doi.org/10.1103/PhysRevB.41.7892 (1990).

Corso, A. D. Pseudopotentials periodic table: From H to Pu. Comput. Mater. Sci. 95 , 337–350. https://doi.org/10.1016/j.commatsci.2014.07.043 (2014).

Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N. & Marzari, N. Precision and efficiency in solid-state pseudopotential calculations. npj Comput. Mater. 4 , 72. https://doi.org/10.1038/s41524-018-0127-2 (2018).

Li, J. et al. Sparse sampling approach to efficient ab initio calculations at finite temperature. Phys. Rev. B 101 , 035144. https://doi.org/10.1103/PhysRevB.101.035144 (2020).

Wang, T. et al. Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors. Phys. Rev. B 102 , 134503. https://doi.org/10.1103/PhysRevB.102.134503 (2020).

Jeon, H. et al. Electron-phonon coupling and superconductivity in an alkaline earth hydride CaH \(_{6}\) at high pressures. New J. Phys. 24 , 083048. https://doi.org/10.1088/1367-2630/ac8a0c (2022).

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Acknowledgements

This work was supported by the Japan Science and Technology Agency (JST), the establishment of university fellowships towards the creation of science and technology innovation, Grant Nos. JPMJSP2114 and JSPS KAKENHI Grant Nos. 21H01003, 22K03447, and 23H04869.

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Darussalam, A.A., Koretsune, T. Superconductivity in CaH \(_{6}\) and ThH \(_{10}\) through fully ab initio Eliashberg method and self-consistent Green’s function. Sci Rep 14 , 18399 (2024). https://doi.org/10.1038/s41598-024-69190-0

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DOI : https://doi.org/10.1038/s41598-024-69190-0

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