experiment or trial

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How to distinguish trial and experiment?

How to distinguish trial and experiment in probability? I have checked Ross's definition and wikipedia's intro on the definition of them for a while, but not quite get it till now. What is the difference of them? And when it comes to Bernoulli trail or Bernoulli experiment , do we call Bernoulli trial, or Bernoulli trials, or Bernoulli experiment, or Bernoulli experiments?

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• random-variables

• $\begingroup$ The short answer is "context". A trial can be reframed /recontexualised into an experiment, and vice versa. For example, the 3-trial experiment Mary flipping three coins might be one trial of the 2-trial experiment Mary and John each flipping 3 coins. $\endgroup$ –  ryang Commented Aug 9, 2022 at 9:53

3 Answers 3

Strictly speaking, any particular performance of a random experiment is called a trial.

We know that a random experiment can be repeated under similar conditions. One such specific repetition of the experiment is what is meant by a trial. So if I consider a random experiment of tossing a fair coin twice, then one particular toss will be referred to as a trial.

• $\begingroup$ 1) If consider an experiment "toss a coin and then toss a dice", is each "sub-experiment", though being quite different kind, still called a trial? 2) Is there a standard name for something like "composed experiment" (or "successive experiment"?), refering to succesively performing some experiment, and such process forms an experiment? The text I only have is Ross', I remember he didn't give a name for this, weird. $\endgroup$ –  Eric Commented Jun 4, 2018 at 18:10
• $\begingroup$ @Eric (1) Yes, an experiment can comprise different types of trials, so its sample space could be $\{1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T\}.$ I wish the terminology had a specific word for a trial's outcome (say, $H$), because I often find myself informally saying "sub-outcome" to distinguish it from the experiment's outcome (say, $2H$). $\endgroup$ –  ryang Commented Dec 10, 2020 at 17:31

I am giving my description on the basis of the notes taken during my probability class.

Any particular performance of a random experiment is a trial.

By Experiment or Trial in the subject of probability, we mean a random experiment unless otherwise specified. Each trial results in one or more outcomes.

For example

$1)$ Tossing $4$ coins

$2)$ Picking $3$ balls from a bag containing $10$ balls $4$ of which are red and $6$ blue

$3)$ Rolling a die

Trial vs Experiment

Many times we use the words trials and experiment synonymously. Both trial and experiment mean something that is done in anticipation of a result. However, we sometimes use the two terms together attributing a slightly different sense to the two terms.

Where you are required to differentiate between a trial and an experiment, consider the experiment to be larger entity formed by the combination of a number of trials.

For example,

$1)$ In the experiment of tossing $4$ coins, wew may consider tossing each coin as a trail and therefore say that there are $4$ trails in the experiment.

$2)$ In the experiment of picking $3$ balls from a bag containing $10$ balls $4$ of which are red and $6$ blue, we can consider picking each ball to be an event and therefore say that there are $3$ trails in the experiment.

• $\begingroup$ I see. I find that there may be two opposite way to think about such question, which is better, or equally good? One is as you mentioned: given an experiement, we can divide it into many "trials" to analyze it, if necessary. The other, we treat every single step as an experiment, and think about the whole successive performance of them as a combined experiment. For the latter, do we use the term like "composite experiment" or "combined experiment" or "successive experiment" an experiment that is made by doing many subexperiments? ... $\endgroup$ –  Eric Commented Jun 11, 2018 at 5:21
• $\begingroup$ ...I saw Feller informally used it in his text, but he didn't explicitly give a defintion for such thing. $\endgroup$ –  Eric Commented Jun 11, 2018 at 5:21
• $\begingroup$ To be clear, a question bumped into my mind. Adam, Brian, Cody three people both shoot an arrow to the same target. An arrow for each person. Suppose the rate they can successifully hit the target are $0.9$, $0.7$ and $0.5$ respect, and consider their shoot don't affect each other. What is the probability that these three person both successifully hit the target? For such question, should we consider the sample space as $\{(H,H,H),~(H,H,L),~(H,L,H),~(H,L,L),~\cdots\cdots,~(L,L,L)\}$ (ps: $H$ for hit, and $L$ for lost), and the event that Adam hit means $\{(H,H,H),~(H,H,L),~(H,L,H),~(H,L,L)\}$? $\endgroup$ –  Eric Commented Jun 11, 2018 at 5:26
• $\begingroup$ @Eric Yes re: the suggested sample space and event re: Adam,Brian, Cody. $\endgroup$ –  ryang Commented Dec 10, 2020 at 17:36

Experiment is the some activity whose outcomes are sometimes known to us and sometimes not. For example, "After many experiments Edison was able to invent an electric bulb. This was an experiment in which were not having any idea about what will be the outcome. Experiment in which we know that our outcome will from some possible out comes that are known to us, for example, when we roll a dice, we know that, the outcome will be either from "1,2,3,4,5,6". There will be know outcome other than these six numbers. We call such experiments as random experiments. Trial - When we repeat a experiment many times, then each of that performed experiment is known as trail. Use following link for reference- https://www.cuemath.com/data/terms-of-probability/

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Trial, Experiment, Event, Result/Outcome - Probability

By Experiment or Trial in the subject of probability, we mean a Random experiment unless otherwise specified.

Each trial results in one or more outcomes

• Tossing 4 coins
• Picking 3 balls from a bag containing 10 balls 4 of which are red and 6 blue
• Rolling a die

Trial vs. Experiment

Both trial and experiment mean something that is done in anticipation of a result.

However, we sometimes use the two terms together attributing a slightly different sense to the two terms.

Where you are required to differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the combination of a number of trials.

• In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there are 4 trials in the experiment.
• In the experiment of picking 3 balls from a bag containing 10 balls 4 of which are red and 6 blue, we can consider picking each ball to be an event and therefore say that there are 3 trials in the experiment.

Event or Outcome

• Something that results.
• A result that is caused by some previous action

The results or outcomes or observations of an experiment are called events.

They are generally represented by the capital letters of English Alphabets.

Though we know the possible outcomes of a random experiment, we cannot predict which of these will occur/happen in a conduct of the experiment/trial.

There are two possible Events or Outcomes:

• Event "A" : The Event of getting a head
• Event "B" : The Event of getting a tail

In the experiment of throwing a die

There are six possible Events or Outcomes:

• Event "A" : The Event of the die showing up 1 on its face
• Event "B" : The Event of the die showing up 2 on its face
• Event "E" : The Event of the die showing up 5 on its face
• Event "F" : The Event of the die showing up 6 on its face

There are two possible Events or Outcomes [If we view the Event or Outcome in different sense]

• Event "M" : The Event of the die showing up an even number on its face
• Event "N" : The Event of the die showing up an odd number on its face

There are three possible Events or Outcomes [If we view the Event or Outcome in another sense]

• Event "P" : The Event of the die showing up a number divisible by 2
• Event "Q" : The Event of the die showing up 1
• Event "R" : The Event of the die showing up a non even prime number i.e. 3 or 5

An Event is what we define it to be

The same experiment can be interpreted in a number of different ways to define different types of events within the experiment.

The number of possible events or outcomes in an experiment are dependent on what we define the event to be.

If getting a digit is defined as an event, there are six possible events or outcomes.

If getting an even number and getting an odd number are defined to be the events, there are only two possible Events or Outcomes

If getting a number divisible by 2 is an event, getting 1 is another event and getting a non even prime number is another event, then there are three possible Events or Outcomes.

How To Calculate Experimental Probability: Step-By-Step Guide With Examples

Experimental probability.

Experimental probability is an approach to calculating the likelihood of an event occurring based on the results of an experiment or trial. This method involves conducting multiple trials or tests of an experiment and then calculating the probability of an event occurring based on the frequency of its occurrence in those trials.

Here are the steps involved in determining experimental probability:

1. Define the event: Start by defining the event for which you want to calculate the probability. For example, if you are flipping a coin, the event could be getting heads.

2. Conduct the experiment: Carry out the experiment by flipping the coin a predetermined number of times. For example, if you want to flip the coin 10 times, then do so and record the results.

3. Count the number of occurrences: Count the number of times the event occurred during the experiment. For example, if you flipped the coin 10 times and got heads 4 of those times, then the number of occurrences of the event (heads) is 4.

4. Calculate the experimental probability: Determine the experimental probability by dividing the number of occurrences by the total number of trials. In this example, the experimental probability of getting heads is 4/10, or 0.4 (or 40%).

5. Repeat and refine: To increase the accuracy of your results, continue repeating the experiment multiple times and refining your calculations.

In summary, experimental probability involves conducting an experiment or trial, counting the number of times an event occurs, and then calculating the probability of the event based on the frequency of its occurrence.

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Experiments, Sample Spaces, Events, and Probability Laws

• First Online: 28 May 2023

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In this chapter, we provide some fundamental definitions concerning the probability concept. First, we give information about experiments, sample spaces, and events and then introduce probability laws. Succeeding the explanation of probability laws, the concept of conditional probability is explained together with solved examples.

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Gazi, O. (2023). Experiments, Sample Spaces, Events, and Probability Laws. In: Introduction to Probability and Random Variables. Springer, Cham. https://doi.org/10.1007/978-3-031-31816-0_1

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Experimental vs Quasi-Experimental Design: Which to Choose?

Here’s a table that summarizes the similarities and differences between an experimental and a quasi-experimental study design:

What is a quasi-experimental design?

A quasi-experimental design is a non-randomized study design used to evaluate the effect of an intervention. The intervention can be a training program, a policy change or a medical treatment.

Unlike a true experiment, in a quasi-experimental study the choice of who gets the intervention and who doesn’t is not randomized. Instead, the intervention can be assigned to participants according to their choosing or that of the researcher, or by using any method other than randomness.

Having a control group is not required, but if present, it provides a higher level of evidence for the relationship between the intervention and the outcome.

(for more information, I recommend my other article: Understand Quasi-Experimental Design Through an Example ) .

Examples of quasi-experimental designs include:

• One-Group Posttest Only Design
• Static-Group Comparison Design
• One-Group Pretest-Posttest Design
• Separate-Sample Pretest-Posttest Design

What is an experimental design?

An experimental design is a randomized study design used to evaluate the effect of an intervention. In its simplest form, the participants will be randomly divided into 2 groups:

• A treatment group: where participants receive the new intervention which effect we want to study.
• A control or comparison group: where participants do not receive any intervention at all (or receive some standard intervention).

Randomization ensures that each participant has the same chance of receiving the intervention. Its objective is to equalize the 2 groups, and therefore, any observed difference in the study outcome afterwards will only be attributed to the intervention – i.e. it removes confounding.

(for more information, I recommend my other article: Purpose and Limitations of Random Assignment ).

Examples of experimental designs include:

• Posttest-Only Control Group Design
• Pretest-Posttest Control Group Design
• Solomon Four-Group Design
• Matched Pairs Design
• Randomized Block Design

When to choose an experimental design over a quasi-experimental design?

Although many statistical techniques can be used to deal with confounding in a quasi-experimental study, in practice, randomization is still the best tool we have to study causal relationships.

Another problem with quasi-experiments is the natural progression of the disease or the condition under study — When studying the effect of an intervention over time, one should consider natural changes because these can be mistaken with changes in outcome that are caused by the intervention. Having a well-chosen control group helps dealing with this issue.

So, if losing the element of randomness seems like an unwise step down in the hierarchy of evidence, why would we ever want to do it?

This is what we’re going to discuss next.

When to choose a quasi-experimental design over a true experiment?

The issue with randomness is that it cannot be always achievable.

So here are some cases where using a quasi-experimental design makes more sense than using an experimental one:

• If being in one group is believed to be harmful for the participants , either because the intervention is harmful (ex. randomizing people to smoking), or the intervention has a questionable efficacy, or on the contrary it is believed to be so beneficial that it would be malevolent to put people in the control group (ex. randomizing people to receiving an operation).
• In cases where interventions act on a group of people in a given location , it becomes difficult to adequately randomize subjects (ex. an intervention that reduces pollution in a given area).
• When working with small sample sizes , as randomized controlled trials require a large sample size to account for heterogeneity among subjects (i.e. to evenly distribute confounding variables between the intervention and control groups).

Further reading

• Statistical Software Popularity in 40,582 Research Papers
• Checking the Popularity of 125 Statistical Tests and Models
• Objectives of Epidemiology (With Examples)
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Why Should We Make Multiple Trials of an Experiment?

10 Characteristics of a Science Experiment

When you have an idea, and you want to know if it is true, a simple experiment can give you a quick result. But how do you know for sure that your idea will hold up based on one experiment? A multitude of tests can narrow the chance that your original idea simply doesn’t hold water.

Scientific Method

Asking questions about the natural world is a human trait that has propelled the species into space and the deepest depths of the ocean. The scientific method is used by biologists and other scientists to explore the world, and it begins with an observation. The original observation turns into a multitude of questions, which leads to a hypothesis. The hypothesis part is where the true test of the original observation yields facts and findings of the truth of the original thought. The experiments completed to prove the hypothesis can open new ideas, explore previously undiscovered expanses and lead the observer in new directions. The experiments are the heart of the hypothesis. The outcomes can either uphold or undo the hypothesis.

Experiments Matter

When the conditions of an experiment are under control the scientist is able to better understand the outcome of the test. It’s not always possible to control all of the conditions of a test, particularly when first starting out in proving the hypothesis. If a controlled experiment is impractical or can’t be done due to ethical reasons, a hypothesis may be tested by making predictions about patterns that should arise if in fact the hypothesis is true. The scientist collects data from as many patterns they can test or push to be tested within reason. The more experiments completed by the scientist the stronger the principle is for the hypothesis.

Variables and Variation

There are two types of variables when running tests: independent and dependent. An experiment with two groups, such as using water on one set of plants and nothing on a second set, has independent and dependent variables. The group that receives water, in this example, is the independent variable because it does not depend on happenstance. The scientist applies the water by choice. The dependent variable is the response that is measured in an experiment to show if the treatment had any affect. The lack of water on the set of plants shows whether the application by the scientist changes the outcome so therefore it depends on the independent variable.

This experiment needs to be done more than once due to the potential for variation, meaning some of the plants could have had disease or other outside variable that spoiled the experiment unbeknownst to the scientist conducting the experiment. The more samples presented at each test the better chance the scientist has of coming to a solid conclusion with little room for error.

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Making statistics intuitive

Observational Study vs Experiment with Examples

By Jim Frost 1 Comment

Comparing Observational Studies vs Experiments

Observational studies and experiments are two standard research methods for understanding the world. Both research designs collect data and use statistical analysis to understand relationships between variables. Beyond that commonality, they are vastly different and have dissimilar sets of pros and cons.

Experiments are controlled investigations where researchers actively manipulate one or more variables to observe the effect on another variable, all within a carefully controlled environment. Researchers must be able to control the treatment condition each subject experiences. Experiments typically use randomization to equalize the experimental groups at the start of the study to control potential confounders.

In this post, we’ll compare an observational study vs experiment, highlighting their definitions, strengths, and when to use them effectively. I work through an example showing how a study can use either approach to answer the same research question.

Learn more about Experimental Design: Definition and Types and Confounding Variable Bias .

Strengths of Observational Studies

Real-World Insights : Observational studies reflect real-world scenarios, providing valuable insights into how things naturally occur. Well-designed observational studies have high external validity , specifically ecological validity .

Does Not Require Randomization : Observational studies shine when researchers can’t manipulate treatment conditions or ethical constraints prevent randomization. For example, studying the long-term effects of smoking requires an observational approach because we can’t ethically assign people to smoke or abstain from smoking.

Cost-Effective : Observational studies are generally less expensive and time-consuming than experiments.

Longitudinal Research : They are well-suited for long-term studies or those tracking trends over time.

Strengths of Experiments

Causality : Experiments are the gold standard for establishing causality. By controlling variables and randomly assigning treatment conditions to participants, researchers can confidently attribute changes to the manipulated factor . Well-designed experiments have high internal validity . Learn more about Correlation vs. Causation: Understanding the Differences .

Controlled Environment : Experiments offer a controlled environment, reducing the influence of confounding variables and enhancing the reliability of results.

Replicability : Well-designed experiments are often easier to replicate, increasing researchers’ ability to compare and confirm results.

Randomization : Random assignment in experiments minimizes bias, ensuring all groups are comparable. Learn more about Random Assignment in Experiments .

When to Choose Observational Studies vs Experiments

Observational studies vs experiments are two vital tools in the statistician ’s arsenal, each offering unique advantages.

Experiments excel in establishing causality, controlling variables, and minimizing the impact of confounders. However, they are more expensive and randomly assigning subjects to the treatment groups is impossible in some settings. Learn more about Randomized Controlled Trials .

Meanwhile, observational studies provide real-world insights, are less expensive, and do not require randomization but are more susceptible to the effects of confounders. Identifying causal relationships is problematic in these studies. Learn more about Observational Studies: Definition & Examples  and Correlational Studies .

Observational studies can be prospective or retrospective studies . On the other hand, randomized experiments must be prospective studies .

The choice between an observational study vs experiment hinges on your research objectives, the context in which you’re working, available time and resources, and your ability to assign subjects to the experimental groups and control other variables.

If you’re looking for a middle ground choice between observational studies vs experiments, consider using a quasi-experimental design. These methods don’t require you to randomly assign participants to the experimental groups and still allow you to draw better causal conclusions about an intervention than an observational study. Learn more about Quasi-Experimental Design Overview & Examples .

Understanding their strengths and differences will help you make the right choice for your statistical endeavors.

Observational Study vs Experiment Example

Suppose you want to assess the health benefits of consuming a daily multivitamin. Let’s explore how an observational study vs experiment would evaluate this research question and their pros and cons.

An observational study will recruit subjects and have them record their vitamin consumption, various health outcomes, and, ideally, record confounding variables. The participants choose whether or not to take vitamins during the study based on their existing habits. Some medical measurements might occur in a lab setting, but researchers are not administering treatments (vitamins). Then, using statistical models, researchers can evaluate the relationship between vitamin consumption and health outcomes while controlling for potential confounders they measured.

An experiment will recruit subjects and then randomly assign them to the treatment group that takes daily vitamins or the control group taking a placebo . Randomization controls all confounders whether the researchers know of them or not. Finally, the researchers compare the treatment to the control group. Learn more about Control Groups in Experiments .

Most vitamin studies are observational because the randomization process would be challenging to implement, and it raises ethical concerns in this context. The random assignment process would override the participants’ preferences for taking vitamins by randomly forcing subjects to consume vitamins or placebos for decades . That’s how long it takes for the differences in health outcomes to manifest. Consequently, enforcing the rigid protocol for so long would be difficult and unethical.

For an observational study, a critical downside is that the pre-existing differences between those who do and do not take vitamins daily comprise a pretty long list of health-related habits and medical measures. Any of them can potentially explain the difference in outcomes instead of the vitamin consumption!

As you can see, using an observational study vs experiment involves many tradeoffs! Let’s close with a table that summarizes the differences.

Differences between an Observational Study and Experiment

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Reader Interactions

October 22, 2023 at 11:17 pm

Well stated: ” Both research designs collect data and use statistical analysis to understand relationships between variables” I was not familiar with the terms research designs. 😀

PS, I am already receiving all your wonderful mailing. I binge-read them every few weeks. I am planning on getting your other two books when I can. Thanks, and Cheers!

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Random Experiments

A random experiment is a type of experiment that has multiple possible outcomes. Such an experiment can be repeated many times. In probability theory, once the random experiment has been performed multiple times then the experimental probabilities of various outcomes can be calculated.

An example of a random experiment is a Bernoulli trial in which there are exactly two possible outcomes. Any outcome of a random experiment cannot be predicted until the experiment has been performed. In this article, we will learn more about a random experiment, its definition, and various associated examples.

What are Random Experiments in Probability?

A random experiment is a very important part of probability theory. This is because probability theory is based on the assumption that an experiment is random and can be repeated several times under the same condition. An experiment in probability will have a sample space, a set of events as well as the probabilities of occurrence of those events.

Random Experiments Definition

Random experiments can be defined as experiments that can be performed many times under the same conditions and their outcome cannot be predicted with complete certainty. In order words, in a random experiment, all the possible outcomes are known, however, its exact outcome cannot be precisely predicted in advance. There are certain terms associated with random experiments that are given as follows:

• Sample space: A sample space can be defined as the list of all possible outcomes of a random experiment.
• Outcome: An outcome is a possible result of the random experiment.
• Event: An event is a possible outcome of an experiment and forms a subset of the sample space.
• Trial: When a random experiment is repeated many times each one is known as a trial.

Random Experiments Example

Suppose a coin is tossed. The two possible outcomes are getting a head or a tail. The outcome of this experiment cannot be predicted before it has been performed. Furthermore, it can be conducted many times under the same conditions. Thus, tossing a coin is an example of a random experiment.

Another random experiment example is that of rolling a dice . There can be 6 possible outcomes {1, 2, 3, 4, 5, 6}. However, none of the outcomes can be exactly predicted.

How to Find Probability of Random Experiments?

Probability can be defined as the likelihood of occurrence of an outcome of a random experiment. The formula for finding the probability is given as the number of favorable outcomes divided by the total number of possible outcomes of that random experiment. Suppose the probability of getting exactly two heads needs to be determined when a fair coin is tossed twice. The steps to find the probability are as follows:

• Step 1: Determine the sample space of the random experiment or the total number of outcomes. The sample space of a coin tossed twice is given as {HH, HT, TH, TT}. Thus, the total number of outcomes are 4.
• Step 2: Find the number of favorable outcomes. As the probability of getting exactly two heads needs to be determined the number of favorable outcomes is 1.
• Step 3: Apply the probability formula. Thus, the probability of getting two heads is 1 / 4 or 0.25.

Related Articles:

• Experimental Probability
• Probability Rules
• Probability and Statistics

Important Notes on Random Experiments

• A random experiment is an experiment whose outcome cannot be predicted.
• A random experiment can be performed several times under the same condition.
• The probability of a random experiment can be given by the number of favorable outcomes / total number of outcomes.

Examples on Random Experiments

Example 2: Can picking a card from a pack of cards be classified as a random experiment?

Solution: As picking a card can be done multiple times thus, this experiment can be conducted many times.

As any card can be picked up, hence, the outcome of the experiment cannot be predicted

Thus, it is a random experiment,

Answer: Picking a card from a pack of cards is a random experiment

Example 3: If there are 3 green balls, 4 red balls, and 5 pink balls in a bag then what is the probability of drawing a pink ball?

Solution: There are a total of 12 balls in the bag.

As there are 5 pink balls thus, the number of favorable outcomes is 5

P(Pink) = favorable outcomes / total number of outcomes

Answer: The probability of drawing a pink ball is 5 / 12.

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FAQs on Random Experiments

What are random experiments.

Random experiments are experiments that can be performed several times and the outcome cannot be predicted beforehand.

What is the Random Experiment Sample Space and Event?

A sample space of a random experiment enlists all the possible outcomes of that experiment. However, an event is a set of possible outcomes of a random experiment that is a subset of the sample space.

What are the Two Conditions that Random Experiments Must Satisfy?

For experiments to be random experiments they must satisfy the following two conditions:

• The experiment can be arbitrarily repeated many times under the same conditions.
• The outcome of each trial of a random experiment cannot be predicted before the experiment has been performed.

What is the Formula to Find the Probability of an Outcome of a Random Experiment?

The likelihood of occurrence of any outcome of a random experiment can be calculated by the formula number of favorable outcomes / total number of outcomes.

What are the Steps to Find the Probability of a Random Experiment?

To find the probability of an outcome the steps are as follows:

• Find the total number of outcomes of the random experiment.
• Find the number of favorable outcomes.
• Divide step 2 by step 3 to determine the probability.

Can Dividing 20 by 5 Be Considered a Random Experiment?

On diving 20 by 5 the outcome will always be 4. Thus, as the outcome is predictable this cannot be classified as a random experiment.

What is a Random Variable and a Random Experiment?

A random variable is a variable that can assume all possible outcomes of a random experiment and its value changes with every trial that is performed.

Experiment vs. Test

What's the difference.

Experiment and test are two methods used to gather information and evaluate hypotheses or theories. However, there are some key differences between the two. An experiment is a controlled procedure that is designed to test a specific hypothesis. It involves manipulating variables and observing the effects to determine cause and effect relationships. On the other hand, a test is a method used to assess the knowledge, skills, or abilities of an individual or a system. It typically involves a set of questions or tasks that are administered to measure performance or proficiency. While experiments are more commonly used in scientific research, tests are often used in educational or professional settings to assess competence or aptitude.

Further Detail

Introduction.

When it comes to scientific research and analysis, two terms that often come up are "experiment" and "test." While they may seem similar at first glance, there are distinct differences between the two. In this article, we will explore the attributes of experiments and tests, highlighting their unique characteristics and purposes.

Definition and Purpose

An experiment is a systematic procedure carried out to investigate a hypothesis or test a specific scientific theory. It involves manipulating variables and observing the outcomes to draw conclusions. Experiments are designed to provide evidence for or against a particular hypothesis and contribute to the advancement of scientific knowledge.

A test, on the other hand, is a procedure performed to assess the performance, functionality, or quality of a product, system, or process. Tests are commonly used in various fields, including technology, engineering, medicine, and education, to ensure that the subject being tested meets specific criteria or standards.

Controlled Variables

In an experiment, researchers carefully control variables to isolate the effect of the independent variable on the dependent variable. By manipulating only one variable while keeping others constant, they can determine the causal relationship between the variables under investigation. This control allows for accurate and reliable results.

Tests, on the other hand, often involve multiple variables that can influence the outcome. While certain variables may be controlled, such as environmental conditions, tests typically focus on assessing the overall performance rather than isolating specific cause-and-effect relationships.

Sample Size and Representativeness

Experiments often require a smaller sample size compared to tests. This is because experiments aim to investigate specific hypotheses and focus on the relationship between variables. By carefully selecting a representative sample, researchers can draw meaningful conclusions about the entire population.

Tests, on the other hand, often require larger sample sizes to ensure statistical significance and generalizability. Since tests aim to assess the overall performance or quality of a subject, a larger sample is needed to account for potential variations and provide a more accurate representation of the population.

Data Collection and Analysis

In experiments, data collection is typically more detailed and specific. Researchers use various methods, such as surveys, observations, or laboratory measurements, to collect quantitative and qualitative data. This data is then analyzed using statistical techniques to determine the significance of the results and draw conclusions.

Tests, on the other hand, often rely on standardized procedures and measurements to collect data. The data collected is usually more focused on specific performance metrics or quality indicators. Analysis of the data may involve comparing the results against predetermined benchmarks or standards to determine whether the subject being tested meets the required criteria.

Timeframe and Flexibility

Experiments are often conducted over an extended period, allowing researchers to observe the effects of variables over time. The timeframe for experiments can range from days to years, depending on the nature of the research question and the variables being investigated. This longer timeframe allows for more in-depth analysis and understanding of complex phenomena.

Tests, on the other hand, are typically conducted within a shorter timeframe. They are often designed to assess the immediate performance or functionality of a subject. Tests are generally more rigid in their procedures and require adherence to specific protocols to ensure consistency and comparability of results.

While experiments and tests share some similarities, such as the systematic approach and the need for reliable results, they serve different purposes and have distinct attributes. Experiments focus on investigating hypotheses, isolating variables, and contributing to scientific knowledge, while tests aim to assess performance, functionality, or quality against predetermined criteria.

Understanding the differences between experiments and tests is crucial for researchers, scientists, and professionals in various fields. By recognizing the unique attributes of each, they can choose the appropriate methodology to answer their research questions or evaluate the subject at hand effectively.

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Frequently asked questions

What’s the difference between correlational and experimental research.

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

Frequently asked questions: Methodology

Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.

Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .

Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.

Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.

Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.

A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”

To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.

Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.

While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.

Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.

Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.

• Convergent validity indicates whether a test that is designed to measure a particular construct correlates with other tests that assess the same or similar construct.
• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related. This type of validity is also called divergent validity .

You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.

• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related

Content validity shows you how accurately a test or other measurement method taps  into the various aspects of the specific construct you are researching.

In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.

The higher the content validity, the more accurate the measurement of the construct.

If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.

Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.

When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.

For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).

On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.

A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.

Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.

Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.

Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .

This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .

Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.

Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .

Snowball sampling is best used in the following cases:

• If there is no sampling frame available (e.g., people with a rare disease)
• If the population of interest is hard to access or locate (e.g., people experiencing homelessness)
• If the research focuses on a sensitive topic (e.g., extramarital affairs)

The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.

Reproducibility and replicability are related terms.

• Reproducing research entails reanalyzing the existing data in the same manner.
• Replicating (or repeating ) the research entails reconducting the entire analysis, including the collection of new data . 
• A successful reproduction shows that the data analyses were conducted in a fair and honest manner.
• A successful replication shows that the reliability of the results is high.

Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.

The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).

Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.

A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.

The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.

Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.

On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.

Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.

However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.

In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .

It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.

While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.

Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.

Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.

Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.

Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.

You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .

When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.

Construct validity is often considered the overarching type of measurement validity ,  because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.

Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.

There are two subtypes of construct validity.

• Convergent validity : The extent to which your measure corresponds to measures of related constructs
• Discriminant validity : The extent to which your measure is unrelated or negatively related to measures of distinct constructs

Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.

The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.

Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.

You can think of naturalistic observation as “people watching” with a purpose.

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.

In statistics, dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation).

As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.

Overall, your focus group questions should be:

• Open-ended and flexible
• Impossible to answer with “yes” or “no” (questions that start with “why” or “how” are often best)
• Unambiguous, getting straight to the point while still stimulating discussion
• Unbiased and neutral

A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when: 

• You already have a very clear understanding of your topic. Perhaps significant research has already been conducted, or you have done some prior research yourself, but you already possess a baseline for designing strong structured questions.
• You are constrained in terms of time or resources and need to analyze your data quickly and efficiently.
• Your research question depends on strong parity between participants, with environmental conditions held constant.

More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.

This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.

The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.

There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.

A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:

• You have prior interview experience. Spontaneous questions are deceptively challenging, and it’s easy to accidentally ask a leading question or make a participant uncomfortable.
• Your research question is exploratory in nature. Participant answers can guide future research questions and help you develop a more robust knowledge base for future research.

An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.

Unstructured interviews are best used when:

• You are an experienced interviewer and have a very strong background in your research topic, since it is challenging to ask spontaneous, colloquial questions.
• Your research question is exploratory in nature. While you may have developed hypotheses, you are open to discovering new or shifting viewpoints through the interview process.
• You are seeking descriptive data, and are ready to ask questions that will deepen and contextualize your initial thoughts and hypotheses.
• Your research depends on forming connections with your participants and making them feel comfortable revealing deeper emotions, lived experiences, or thoughts.

The four most common types of interviews are:

• Structured interviews : The questions are predetermined in both topic and order. 
• Semi-structured interviews : A few questions are predetermined, but other questions aren’t planned.
• Unstructured interviews : None of the questions are predetermined.
• Focus group interviews : The questions are presented to a group instead of one individual.

Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .

In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Triangulation can help:

• Reduce research bias that comes from using a single method, theory, or investigator
• Enhance validity by approaching the same topic with different tools
• Establish credibility by giving you a complete picture of the research problem

But triangulation can also pose problems:

• It’s time-consuming and labor-intensive, often involving an interdisciplinary team.
• Your results may be inconsistent or even contradictory.

There are four main types of triangulation :

• Data triangulation : Using data from different times, spaces, and people
• Investigator triangulation : Involving multiple researchers in collecting or analyzing data
• Theory triangulation : Using varying theoretical perspectives in your research
• Methodological triangulation : Using different methodologies to approach the same topic

Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.

However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure. 

Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.

Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.

Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.

In general, the peer review process follows the following steps: 

• First, the author submits the manuscript to the editor.
• Reject the manuscript and send it back to author, or 
• Send it onward to the selected peer reviewer(s) 
• Next, the peer review process occurs. The reviewer provides feedback, addressing any major or minor issues with the manuscript, and gives their advice regarding what edits should be made. 
• Lastly, the edited manuscript is sent back to the author. They input the edits, and resubmit it to the editor for publication.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.

Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.

Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.

Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.

For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.

After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.

Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.

These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.

Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.

Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.

Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.

In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.

Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.

These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.

Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .

You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.

You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.

Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.

Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.

Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .

These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.

In multistage sampling , you can use probability or non-probability sampling methods .

For a probability sample, you have to conduct probability sampling at every stage.

You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.

Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.

But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .

These are four of the most common mixed methods designs :

• Convergent parallel: Quantitative and qualitative data are collected at the same time and analyzed separately. After both analyses are complete, compare your results to draw overall conclusions. 
• Embedded: Quantitative and qualitative data are collected at the same time, but within a larger quantitative or qualitative design. One type of data is secondary to the other.
• Explanatory sequential: Quantitative data is collected and analyzed first, followed by qualitative data. You can use this design if you think your qualitative data will explain and contextualize your quantitative findings.
• Exploratory sequential: Qualitative data is collected and analyzed first, followed by quantitative data. You can use this design if you think the quantitative data will confirm or validate your qualitative findings.

Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.

Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.

In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.

This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

Quantitative research designs can be divided into two main categories:

• Correlational and descriptive designs are used to investigate characteristics, averages, trends, and associations between variables.
• Experimental and quasi-experimental designs are used to test causal relationships .

Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.

A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.

The priorities of a research design can vary depending on the field, but you usually have to specify:

• Your research questions and/or hypotheses
• Your overall approach (e.g., qualitative or quantitative )
• The type of design you’re using (e.g., a survey , experiment , or case study )
• Your sampling methods or criteria for selecting subjects
• Your data collection methods (e.g., questionnaires , observations)
• Your data collection procedures (e.g., operationalization , timing and data management)
• Your data analysis methods (e.g., statistical tests  or thematic analysis )

A research design is a strategy for answering your   research question . It defines your overall approach and determines how you will collect and analyze data.

Questionnaires can be self-administered or researcher-administered.

Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.

Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.

You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.

Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.

Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.

Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.

While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

Random error  is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .

You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.

Systematic error is generally a bigger problem in research.

With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.

Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.

Random and systematic error are two types of measurement error.

Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).

Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).

On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.

• If you have quantitative variables , use a scatterplot or a line graph.
• If your response variable is categorical, use a scatterplot or a line graph.
• If your explanatory variable is categorical, use a bar graph.

The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.

The difference between explanatory and response variables is simple:

• An explanatory variable is the expected cause, and it explains the results.
• A response variable is the expected effect, and it responds to other variables.

In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:

• A control group that receives a standard treatment, a fake treatment, or no treatment.
• Random assignment of participants to ensure the groups are equivalent.

Depending on your study topic, there are various other methods of controlling variables .

There are 4 main types of extraneous variables :

• Demand characteristics : environmental cues that encourage participants to conform to researchers’ expectations.
• Experimenter effects : unintentional actions by researchers that influence study outcomes.
• Situational variables : environmental variables that alter participants’ behaviors.
• Participant variables : any characteristic or aspect of a participant’s background that could affect study results.

An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.

A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.

In a factorial design, multiple independent variables are tested.

If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.

Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .

Advantages:

• Only requires small samples
• Statistically powerful
• Removes the effects of individual differences on the outcomes

Disadvantages:

• Internal validity threats reduce the likelihood of establishing a direct relationship between variables
• Time-related effects, such as growth, can influence the outcomes
• Carryover effects mean that the specific order of different treatments affect the outcomes

While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .

• Prevents carryover effects of learning and fatigue.
• Shorter study duration.
• Needs larger samples for high power.
• Uses more resources to recruit participants, administer sessions, cover costs, etc.
• Individual differences may be an alternative explanation for results.

Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.

Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.

Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .

If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .

A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.

Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.

Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.

If something is a mediating variable :

• It’s caused by the independent variable .
• It influences the dependent variable
• When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered.

A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.

A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method.

Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.

However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.

There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.

• In single-stage sampling , you collect data from every unit within the selected clusters.
• In double-stage sampling , you select a random sample of units from within the clusters.
• In multi-stage sampling , you repeat the procedure of randomly sampling elements from within the clusters until you have reached a manageable sample.

Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.

The clusters should ideally each be mini-representations of the population as a whole.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.

Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .

If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.

• In a single-blind study , only the participants are blinded.
• In a double-blind study , both participants and experimenters are blinded.
• In a triple-blind study , the assignment is hidden not only from participants and experimenters, but also from the researchers analyzing the data.

Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .

A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.

However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).

For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.

In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).

The process of turning abstract concepts into measurable variables and indicators is called operationalization .

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organize your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organization to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

When conducting research, collecting original data has significant advantages:

• You can tailor data collection to your specific research aims (e.g. understanding the needs of your consumers or user testing your website)
• You can control and standardize the process for high reliability and validity (e.g. choosing appropriate measurements and sampling methods )

However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.

In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.

In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .

In statistical control , you include potential confounders as variables in your regression .

In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!

You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .

• The type of soda – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.

Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .

Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.

Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.

A sampling error is the difference between a population parameter and a sample statistic .

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.

The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).

The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.

Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .

Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.

Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.

Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.

The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .

Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.

Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.

There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .

Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .

External validity is the extent to which your results can be generalized to other contexts.

The validity of your experiment depends on your experimental design .

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Binomial Experiment: Rules, Examples, Steps

What is a binomial experiment.

A binomial experiment is an experiment where you have a fixed number of independent trials with only have two outcomes. For example, the outcome might involve a yes or no answer. If you toss a coin you might ask yourself “Will I get a heads?” and the answer is either yes or no. That’s the basic idea, but in order to call an experiment a binomial experiment you also have to make sure of the following rules.

• You must have a fixed number of trials . This should go without saying; if you don’t have a fixed number of trials you could be tossing that coin forever without stopping. In addition, the results from your experiment will be vastly different if you toss that coin twice (you could get two heads in a row and conclude that you will always get a heads if you toss a coin!) or if you toss it a hundred times .
• Each trial is an independent event . “Independent” means that every time you repeat the trial (i.e. tossing that coin), it’s a fresh new trial and nothing you do has an effect on each coin toss. For example, if you tossed ten coins at a time and removed the coins that landed heads down before throwing again, you’ll affect the probability, because there are fewer coins. There’s nothing wrong with that, but it would not be a binomial experiment. The fact that each trial is independent of each other leads to another important aspect of binomial experiments; the probability remains constant from trial to trial.
• There are only two outcomes. In other words, if you can phrase the experiment as a yes or no answer, then it can be a binomial experiment: Will I get a heads? Can someone find a parking space in the city? Do eggs hard boil in ten minutes?

Binomial Experiment: Examples

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• Tossing a coin a hundred times to see how many land on heads.
• Asking 100 people if they have ever been to Paris.
• Rolling two dice to see if you get a double.

Examples of experiments that are not Binomial Experiments

• Asking 100 people how much they weigh (you’ll have a hundred possible answers, not two).
• Tossing a coin until you get a heads (it could take one toss, or three, or six, so there is not a fixed number of trials). This is actually called a negative binomial experiment .

Binomial experiment: Four Steps

Determining if a question concerns a binomial experiment involves asking yourself four questions about the problem.

Example question: which of the following are binomial experiments?

• Telephone surveying a group of 200 people to ask if they voted for George Bush.
• Counting the average number of dogs seen at a veterinarian’s office daily.
• You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time.
• You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.”

Step 1: Ask yourself: is there a fixed number of trials ?

• For question #1, the answer is yes (200).
• For question #2, the answer is no , so we’re going to discard #2 as a binomial experiment.
• For question #3, the answer is yes , there’s a fixed number of trials (the 50 traffic lights).
• For question #4, the answer is yes (your 6 darts).

Step 2: Ask yourself: Are there only 2 possible outcomes?

• For question #1, the only two possible outcomes are that they did, or they didn’t vote for Mr. Bush, so the answer is yes .
• For question #3, there are 3 possibilities: red, green, and yellow, so it’s not a binomial experiment.
• For question #4, the only possible outcomes are WIN or LOSE, so the answer is yes .

Step 3:  Ask yourself: are the outcomes independent of each other ? In other words, does the outcome of one trial (or one toss, or one question) affect another trial?

• For question #1, the answer is yes : one person saying they did or didn’t vote for Mr. Bush isn’t going to affect the next person’s response.
• For question #4, each time you toss a dart, the number of winning and losing tickets changes, which means, for example, if you win one toss, the probability of winning isn’t 10 to 10 anymore, but 9 to 10, since you already have one of the winning tickets. Since the probability is different, the trials are not independent events , so the answer is no , and question #4 is not a binomial experiment.

Step 4: Does the probability of success remain the same for each trial ?

• For question #1, the answer is yes , each person has a 50% chance of having voted for Mr. Bush.

Question #1 out of the 4 given questions was the only one that was a binomial experiment .

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Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.

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what is trial in my experiment?

I have a basic question about the exact meaning of trial in experimental designs. My experiment includes presenting three rhythmic patterns (each consisting of 5 sounds) to participants and they're supposed to say which one is different from the other two and then we go to the next three rhythms and so on. Now I wanna know if the three presentations at the end of which rating happens are the trial or each of the three rhythms or every single sound in each rhythmic sequence. In fact, I haven't got the exact meaning of trial and I would very much appreciate it if anybody could clarify it.

• experiment-design
• terminology

Trial here is the single experimental unit, we could say the "atom of the experiment", which leads to one observed value each. So here it is

... presenting three rhythmic patterns (each consisting of 5 sounds) to participants and they're supposed to say which one is different from the other two ...

which results in one observed value, which here is an identifier of the different one.

• 1 $\begingroup$ Thanks a lot. So just to make sure, you're saying that in my experiment, every three rhythms at the end of which rating happens is considered one trial. Right? If so what do we call each of the three rhythmic sequences and also each single sound in each rhythm? $\endgroup$ –  Zhaleh Commented Oct 11, 2020 at 20:29
• $\begingroup$ Why do these parts of the trial need a specific name? $\endgroup$ –  kjetil b halvorsen ♦ Commented Oct 11, 2020 at 21:12
• $\begingroup$ I don’t mean they should necessarily have a specific name. I just thought maybe they’re called in a specific way like the trial itself. $\endgroup$ –  Zhaleh Commented Oct 12, 2020 at 23:43

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Synonyms of experiment

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Thesaurus Definition of experiment

Synonyms & Similar Words

• experimentation
• trial and error

Examples of experiment in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'experiment.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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Thesaurus Entries Near experiment

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Cite this Entry

“Experiment.” Merriam-Webster.com Thesaurus , Merriam-Webster, https://www.merriam-webster.com/thesaurus/experiment. Accessed 11 Sep. 2024.

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[ noun ik- sper - uh -m uh nt ; verb ek- sper - uh -ment ]

a chemical experiment; a teaching experiment; an experiment in living.

a product that is the result of long experiment.

Synonyms: investigation , research

• Obsolete. experience .

verb (used without object)

to experiment with a new procedure.

• a test or investigation, esp one planned to provide evidence for or against a hypothesis: a scientific experiment
• the act of conducting such an investigation or test; experimentation; research

a poetic experiment

• an obsolete word for experience
• intr to make an experiment or experiments

/ ĭk-spĕr ′ ə-mənt /

• A test or procedure carried out under controlled conditions to determine the validity of a hypothesis or make a discovery.
• See Note at hypothesis

Derived Forms

• exˈperiˌmenter , noun

Other Words From

• ex·peri·menter ex·peri·mentor ex·peri·men·tator noun
• preex·peri·ment noun
• proex·peri·ment adjective
• reex·peri·ment verb (used without object) noun
• unex·peri·mented adjective

Word History and Origins

Origin of experiment 1

Synonym Study

Example sentences.

IBM hopes that a platform like RoboRXN could dramatically speed up that process by predicting the recipes for compounds and automating experiments.

The hope there is for improved sensitivity in searches for dark matter or experiments that might reveal some long-sought flaws in our standard model of particle physics.

The experiment represents early progress toward the possible development of an ultra-secure communications network beamed from space.

The new experiment represents, however, the first time scientists have applied machine learning to “validation,” a further step toward confirming results that involves additional statistical calculation.

At first, the sites amounted to experiments on the outer edges of the crypto universe, but in 2020 they have started to attract real money.

To put it rather uncharitably, the USPHS practiced a major dental experiment on a city full of unconsenting subjects.

If the noble experiment of American democracy is to mean anything, it is fidelity to the principle of freedom.

A classroom experiment seeks to demonstrate what it looks like.

This video, courtesy of BuzzFeed, tries a bit of an experiment to get some answers.

In the fall of 1992, Booker became a vegetarian “as an experiment,” he said, “and I was surprised by how much my body took to it.”

With Bacon, experientia does not always mean observation; and may mean either experience or experiment.

I made the experiment two years ago, and all my experience since has corroborated the conclusion then arrived at.

But this is quite enough to justify the inconsiderable expense which the experiment I urge would involve.

He commenced to experiment in electro-pneumatics in the year 1860, and early in 1861 communicated his discoveries to Mr. Barker.

Readers will doubtless be familiar with the well-known experiment illustrating this point.

Related Words

• examination
• experimentation
• observation
• undertaking