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experimental unit

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experimental unit , in an experimental study, a physical entity that is the primary unit of interest in a specific research objective. Generally, the experimental unit is the person, animal, or object that is the subject of the experiment. Experimental units receive different treatments from one another in an experiment.

As a case in point, consider an experiment designed to determine the effect of three different exercise programs on the cholesterol level of patients with elevated cholesterol. Each patient is referred to as an experimental unit, the response variable is the cholesterol level of the patient at the completion of the program, and the exercise program is the factor whose effect on cholesterol level is being investigated. Each of the three exercise programs is referred to as a treatment .

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1.1 - cases & variables.

Throughout the course, we will be using many of the terms introduced in this lesson. Let's start by defining some of the most frequently used terms: case, variable, and constant.

A  case  is an experimental unit. These are the individuals from which data are collected. When data are collected from humans, we sometimes call them  participants . When data are collected from animals, the term  subjects  is often used. Another synonym is  experimental unit . 

A  variable  is a characteristic that is measured and can take on different values. In other words, something that varies between cases. This is in contrast to a constant  which is the same for all cases in a research study.

Let's look at a few examples.

Example: Study Time & Grades Section  

A teacher wants to know if third grade students who spend more time reading at home get higher homework and exam grades.

The students are the  cases . There are three  variables : amount of time spent reading at home, homework grades, and exam grades. The grade-level of the students is a  constant  because all students are in the third grade.

Example: Dog Food Section  

A researcher wants to know if dogs who are fed only canned food have different body mass indexes (BMI) than dogs who are fed only hard food. They collect BMI data from 50 dogs who eat only canned food and 50 dogs who eat only hard food.

The  cases  are the dogs. There are two  variables : type of food and BMI. A  constant  would be subspecies, because all cases are domestic dogs.

Example: Age & Weight of Sea Otters Section  

Researchers are studying the relationship between age and weight in a sample of 100 male sea otters ( Enhydra lutris ).

The 100 otters are the  cases . There are two  variables : age and weight. Biological sex is a  constant  because all subjects are male. Species is also a  constant . 

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AP Statistics : How to define experimental units

Study concepts, example questions & explanations for ap statistics, all ap statistics resources, example questions, example question #1 : how to define experimental units.

Of the following examples, which best describes quantitative data?

A child's gender.

Temperature measurements of water in degrees Fahrenheit.

The softness of a chair.

College grade level-freshman, sophomore, junior, or senior.

A student's least favorite sport.

Quantitative data describes a certain type of information that can be counted or expressed numerically and can be used in meaningful computations. Quantitative data is different from qualitative data, which is primarily involved in describing things in terms of categorizations or specific qualities. Looking at the answer choices, it is clear that measuring the temperature of water in degrees Fahrenheit is a numerical piece of information, and is thus quantitative.

Example Question #2 : How To Define Experimental Units

When designing an experiment, what is the purpose of blocking?

To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments

To use chance to randomly assign experimental units to treatment groups (or vice versa)

To increase the number of experimental units

To hold an extraneous variable constant

None of the other answers

The purpose of blocking, by definition, is to separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments. The other choices pertain to control (keeping an extraneous variable constant), randomization (using random chance to assign experimental units to treatments), and replication (increasing the number of experimental units to reduce chance variation) in an experiment.

Example Question #1 : Data Collection

Which of the following is an example of qualitative data? 

The average SAT score of students at a particular high school 

The speed at which a car is traveling

The gender of a high school student

The temperature of a glass of water

The amount of carbon monoxide emissions in the air

The only example of qualitative data here is the gender of a high school student (i.e. male or female). This cannot be quantified, unlike the other answer choices which all have numbers, quantities, and amounts associated with them.

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Experimental Units

Experimental units are the individuals or objects on which we collect data in an experiment. They can be people, animals, plants, or any other entities that are being studied.

Related terms

Treatment Conditions : These are different levels or variations of the independent variable that experimental units are exposed to during an experiment.

Extraneous Variables : These are variables other than the independent variable that may affect the response variable and need to be controlled or accounted for in an experiment.

Control Group : A group of experimental units that does not receive any treatment and serves as a baseline for comparison with groups receiving treatments.

" Experimental Units " appears in:

Study guides ( 2 ).

• AP Statistics - 1.1 Introducing Statistics: What Can We Learn from Data?
• AP Statistics - 3.7 Inference and Experiments

Subjects ( 1 )

• Business Process Optimization

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5.2 – Experimental units, Sampling units

Introduction, experimental units, experimental and sampling units often, but not always the same, replication: groups and individuals as sampling units, chapter 5 contents.

Sampling units  refer to the measured items, the focus of data collection; samples are selected from populations. Often, sampling units are the same thing as individuals. For example, if we are interested in the knowing whether men are more obese than women in Hawai’i, we would select individuals from the population; we would measure individuals. Thus, the sampling unit would be individuals, and the measurement unit would be percent body fat recorded for each individual. The data set would be the collection of all body fat measures for all individuals in the study, and we would then make inferences (draw conclusions) about the differences, if any, between adult males and females for body fat.

But sampling units can also refer to something more restrictive than the individual. For example, we may be interested in how stable, or consistent, is a person’s body fat over time. If we take a body fat measure once per year over a decade on the same group of adults, then the sampling unit refers to each observation of body fat recorded (once per year, ten times for an individual), and the population we are most likely to be referring to is the collection of all such readings (ten is arbitrary — we could have potentially measured the same individual thousands of times).

In some cases the researcher may wish to compare groups of individuals and not the individuals themselves. For example, a 2001 study sought to see if family structure influenced the metabolic (glycemic) control of children with diabetes (Thompson et al 2001). The researchers compared how well metabolic control was achieved in children of single parents and two-parent families. Thus, the sampling units would be families and not the individual children.

Experimental units  refers to the level at which treatments are independently applied in a study. Often, but not always, treatments are applied directly to individuals and therefore the sampling units and experimental units in these cases would be the same.

Question 1 : What is the sampling unit in the following cell experiment?

A technician thaws a cryo tube containing about ½ million A549 cells (Foster et al 1998) and grows the cells in a T-75 culture flask (the 75 corresponds to 75 cm 2  growing area) in a CO 2  incubator at 37 °C. After the cells reach about 70% confluency, which may represent hundreds of thousands of cells, the technician aliquots 1000 cells into twelve wells of a plate for a total of 12000 cells. To three wells the technician adds a cytokine, to another three wells he adds a cytokine inhibitor, and to another three wells he adds both the cytokine and it’s inhibitor, and to the last three wells he adds DMSO, which was the solvent for both the cytokine and the inhibitor. He then returns the plate to the incubator and 24 hours later extracts all of the cells and performs a multiplex quantitative PCR to determine gene expression of several target genes known to be relevant to cell proliferation.

The described experiment would be an example of a routine, but not trivial procedure the technician would do in the course of working on the project in a molecular biology laboratory.

The choices for numbers provided in the description we may consider for the number of sampling units are:

• 12,000 cells
• ½ million cells
• The target genes
• None of the above

The correct answer is G, None of the above.

“None of the above” because the correct answer is … there was just one sampling unit! All cells trace back to that single cryo tube.

To answer the question, start from the end and work your way back. What we are looking for is independence of samples and at what level in the experiment we find independence. Our basic choice is between numbers of cells and numbers of wells. Clearly, cells are contained in the wells, so all of the cells in one well share the same medium, being treated the same way, including all the way back to the cryo tube — all of the cells came from that one tube so this lack of independence traces all the way back to the source of the cells. Thus, the answer can’t be related to cell number. How many wells did the technician set up? Twelve total. So, the maximum number of sampling units would be twelve, unless the samples are not independent. And clearly the wells (samples) are not independent because, again, all cells in the twelve wells trace back to a single cryo tube. Thus, from both perspectives, wells and cells, the answer is actually just one sampling unit! (Cumming et al 2007; Lazic 2010). Finally, the genes themselves are the targets of our study — they are the variables, not the samples. Moreover, the same logic applies — all copies of the genes are in effect descended from the few cells used to start the population.

Question 2 : What is the experimental unit in the described cell experiment?

The correct answer is E, 12 wells. Noted above, the technician applied treatments to 12 wells. There were two treatments, cytokine and cytokine-inhibitor (Table 1).

Table 1. Translate experiment description to a table to better visualize the design

The correct identification of levels at which sampling independence occurs is crucial to successful interpretation of inferential statistics. Note replication in Table 1: three cytokine, three cytokine-inhibitor, three with both.  Sampling error rate is evaluated at the level of the sampling units. Technical replication of sampling units allows one to evaluate errors of measurement (e.g., instrument noise) (Blainey et al 2014). Replication of sampling units increases statistical power, the ability to correctly reject hypotheses. If the correct design reflects sampling units are groups and not individuals, then by counting the individuals as the independent sampling units would lead the researcher to think his design has more replication than it actually does. The consequence on the inferential statistics is that he will more likely reject a correct null hypothesis, in other words, the risk of elevated type I error occurs ( Chapter 8 – Inferential statistics ). This error, confusing individual and group sampling units, is called pseudoreplication  (Lazic 2010).

Consider a simpler experimental design scenario depicted in Figure 2: Three different water treatments (e.g., concentrations of synthetic progestins, Zeilinger et al. 2009) in bowls A, B, and C; three fish in bowl A, three fish in bowl B, and three fish in bowl C. The outcome variable might be a stress indicator, e.g., plasma cortisol (Luz et al 2008).

Figure 2. Three aquariums, three fish. Image modified from https://www.pngrepo.com/svg/153528/aquarium

Question 3 : What were the experimental units for the fish in the bowl experiment (Fig. 2)?

• Three bowls
• Three water treatments

The correct answer is A, 3 bowls. The treatments were allocated to the bowls, not to individual fish. The three fish in each bowl provides technical replication for the effects of bowl A, bowl B, and bowl C, but does not provide replication for the effects of the water treatments.  Adding three bowls for each water treatment, each with three fish, would be the simplest correction of the design, but may not be available to the researcher because of space or cost limitations. The design would then include nine bowls and 27 fish.  If resources are not available to simply scale up the design, then the researcher could repeat the study several times, taking care to control nuisance variables . Alternatively, if the treatments were applied to the individual fish, then the experimental units become the individual fish and the bowls reduced to a blocking effect ( Chapter 14.4 ), where differences may exist among the bowls, but they are no longer the level by which measurements are made. Note that if pseudoreplication is present in a study, this may be accounted for by specifying the error structure in a linear mixed model (e.g., random effects, blocking effects, etc., see Chapter 14 and Chapter 18 ).

Question 4 : What were the sampling units for the fish in the bowl experiment (Fig. 2)?

The correct answer is B, the individual fish. If instead of aqueous application of synthetic progestin, treatments were applied directly to each fish via injection, what would be the answers to Question 3 and Question 4?

Choices like these clearly involve additional compromises and assumptions about experimental design and inference about hypotheses.

Sampling units, experimental units, and the concept of level at which units are independent within an experiment were introduced. Lack of independence yields the problem of pseudoreplication in an experiment, which will increase the chance that we will detect differences between our treatment groups, when no such difference exists!

Figure 3. Three Miracle-Grow AeroGarden planters, each with nine seedlings of an Arabidopsis thaliana strain.

1. Nine seeds each of three strains of Arabidopsis thaliana were germinated in three Miracle-Grow AeroGarden ® hydroponic planters (Fig. 2). Each planter had nine or ten vials with sphagnum peat. All seeds from a strain were planted in the same apparatus, one seed per vial. What were the experimental units?

• strains of Arabidopsis
• vials in the planters

2. This experimental design is an example of pseudoreplication, but at what level?

3. How would you re-do this experiment to avoid pseudoreplication? (Hint: you can’t add more planters!)

• The basics explained
• Experiments
• Experimental and Sampling units
• Replication, Bias, and Nuisance Variables
• Clinical trials
• Importance of randomization in experimental design
• Sampling from Populations
• References and suggested readings

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

1.4 Designed Experiments

Observational studies vs. experiments.

Ignoring anecdotal evidence, there are two primary types of data collection: observational studies and controlled (designed) experiments .  Remember, we typically cannot make claims of causality from observation studies because of the potential presence of confounding factors.  However, making causal conclusions based on experiments is often reasonable by controlling for those factors. Consider the following example:

Suppose you want to investigate the effectiveness of vitamin D in preventing disease. You recruit a group of subjects and ask them if they regularly take vitamin D. You notice that the subjects who take vitamin D exhibit better health on average than those who do not. Does this prove that vitamin D is effective in disease prevention? It does not. There are many differences between the two groups compared in addition to vitamin D consumption. People who take vitamin D regularly often take other steps to improve their health: exercise, diet, other vitamin supplements, choosing not to smoke. Any one of these factors could be influencing health. As described, this study does not necessarily prove that vitamin D is the key to disease prevention.

Experiments ultimately provide evidence to make decisions, so how could we narrow our focus and make claims of causality? In this section, you will learn important aspects of experimental design.

Designed Experiments

The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory variable . The affected variable is called the response variable . In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different values of the explanatory variable may be called treatments . An experimental unit is a single object or individual to be measured. 

The main principles we want to follow in experimental design are:

Randomization

Replication.

In order to provide evidence that the explanatory variable is indeed causing the changes in the response variable, it is necessary to isolate the explanatory variable. The researcher must design their experiment in such a way that there is only one difference between groups being compared: the planned treatments. This is accomplished by randomization of experimental units to treatment groups. When subjects are assigned treatments randomly, all of the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can show an apparent cause-and-effect connection between the explanatory and response variables.

Recall our previous example of investigating the effectiveness of vitamin D in preventing disease. Individuals in our trial could be randomly assigned, perhaps by flipping a coin, into one of two groups:  The control group (no treatment) and the second group receives extra doses of Vitamin D.

The more cases researchers observe, the more accurately they can estimate the effect of the explanatory variable on the response. In a single study, we replicate by collecting a sufficiently large sample. Additionally, a group of scientists may replicate an entire study to verify an earlier finding.  Having individuals experience a treatment more than once, called repeated measures is often helpful as well.

The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing drugs, researchers noted:

Results showed that believing one had taken the substance resulted in [ performance ] times almost as fast as those associated with consuming the drug itself. In contrast, taking the drug without knowledge yielded no significant performance increment. [1]

It is often difficult to isolate the effects of the explanatory variable. To counter the power of suggestion, researchers set aside one treatment group as a control group . This group is given a placebo treatment–a treatment that cannot influence the response variable. The control group helps researchers balance the effects of being in an experiment with the effects of the active treatments. Of course, if you are participating in a study and you know that you are receiving a pill which contains no actual medication, then the power of suggestion is no longer a factor. Blinding in a randomized experiment preserves the power of suggestion. When a person involved in a research study is blinded, he does not know who is receiving the active treatment(s) and who is receiving the placebo treatment. A double-blind experiment is one in which both the subjects and the researchers involved with the subjects are blinded.

Randomized experiments are an essential tool in research. The US Food and Drug Administration typically requires that a new drug can only be marketed after two independently conducted randomized trials confirm its safety and efficacy; the European Medicines Agency has a similar policy. Large randomized experiments in medicine have provided the basis for major public health initiatives. In 1954 approximately 750,000 children participated in a randomized study comparing the polio vaccine with a placebo. In the United States, the results of the study quickly led to the widespread and successful use of the vaccine for polio prevention.

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

The Smell & Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper mazes three times wearing floral-scented masks, and three times with unscented masks. Participants were assigned at random to wear the floral mask during the first three trials or during the last three trials. For each trial, researchers recorded the time it took to complete the maze and the subject’s impression of the mask’s scent: positive, negative, or neutral.

More Experimental Design

There are many different experimental designs from the most basic, a single treatment and control group, to some very complicated designs.  In an experimental design setting, when working with more than one variable, or treatment, they are often called factors , especially if it is categorical .  The values of factors are are often called levels .  When there are multiple factors, the combinations of each of the levels are called treatment combinations , or interactions.  Some basic ones you may see are:

• Completely randomized
• Block design
• Matched pairs design

Completely Randomized

While very important and an essential research tool, not much explanation is needed for this design.  It involves figuring out how many treatments will be administered and randomly assigning participants to their respective groups.

Block Design 

Researchers sometimes know or suspect that variables, other than the treatment, influence the response. Under these circumstances, they may first group individuals based on this variable into blocks and then randomize cases within each block to the treatment groups. This strategy is often referred to as blocking. For instance, if we are looking at the effect of a drug on heart attacks, we might first split patients in the study into low-risk and high-risk blocks, then randomly assign half the patients from each block to the control group and the other half to the treatment group, as shown in the figure below. This strategy ensures each treatment group has an equal number of low-risk and high-risk patients.

Matched Pairs

A matched pairs design is one where we have very similar individuals (or even the same individual) receiving different two treatments (or treatment vs. control), then comparing their results.  This design is very powerful, however, it can be hard to find many like individuals to match up.  Some common ways of creating a matched pairs design are twin studies, before and after measurements,  pre and post test situations, or crossover studies.  Consider the following example:

In the 2000 Olympics, was the use of a new wetsuit design responsible for an observed increase in swim velocities? In a matched pairs study designed to investigate this question, twelve competitive swimmers swam 1500 meters at maximal speed, once wearing a wetsuit and once wearing a regular swimsuit. The order of wetsuit versus swimsuit was randomized for each of the 12 swimmers. Figure 1.6 shows the average velocity recorded for each swimmer, measured in meters per second (m/s).

Notice in this data, two sets of observations are uniquely paired so that an observation in one set matches an observation in the other; in this case, each swimmer has two measured velocities, one with a wetsuit and one with a swimsuit. A natural measure of the effect of the wetsuit on swim velocity is the difference between the measured maximum velocities (velocity.diff = wet.suit.velocity- swim.suit.velocity).  Even though there are two measurements per individual, using the difference in observations as the variable of interest allows for the problem to be analyzed.

A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again.  What experiment design is being implemented here?

A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means hours slept for each person were recorded before starting the medication and after. What experiment design is being implemented here?

Image References

Figure 1.5: Kindred Grey (2020). “Block Design.” CC BY-SA 4.0. Retrieved from https://commons.wikimedia.org/wiki/File:Block_Design.png

• McClung, M. Collins, D. “Because I know it will!”: placebo effects of an ergogenic aid on athletic performance. Journal of Sport & Exercise Psychology. 2007 Jun. 29(3):382-94. Web. April 30, 2013. ↵

Data collection where no variables are manipulated

Type of experiment where variables are manipulated; data is collected in a controlled setting

The independent variable in an experiment; the value controlled by researchers

The dependent variable in an experiment; the value that is measured for change at the end of an experiment

Different values or components of the explanatory variable applied in an experiment

Any individual or object to be measured

When an individual goes through a single treatment more than once

A group in a randomized experiment that receives no (or an inactive) treatment but is otherwise managed exactly as the other groups

An inactive treatment that has no real effect on the explanatory variable

Not telling participants which treatment they are receiving

The act of blinding both the subjects of an experiment and the researchers who work with the subjects

Variables in an experiment

Certain values of variables in an experiment

Combinations of levels of variables in an experiment

Dividing participants into treatment groups randomly

Grouping individuals based on a variable into "blocks" and then randomizing cases within each block to the treatment groups

Very similar individuals (or even the same individual) receive two different two treatments (or treatment vs. control) then the difference in results are compared

Significant Statistics Copyright © 2020 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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Calcworkshop

Experimental Design in Statistics w/ 11 Examples!

// Last Updated: September 20, 2020 - Watch Video //

A proper experimental design is a critical skill in statistics.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Without proper controls and safeguards, unintended consequences can ruin our study and lead to wrong conclusions.

So let’s dive in to see what’s this is all about!

What’s the difference between an observational study and an experimental study?

An observational study is one in which investigators merely measure variables of interest without influencing the subjects.

And an experiment is a study in which investigators administer some form of treatment on one or more groups?

In other words, an observation is hands-off, whereas an experiment is hands-on.

So what’s the purpose of an experiment?

To establish causation (i.e., cause and effect).

All this means is that we wish to determine the effect an independent explanatory variable has on a dependent response variable.

The explanatory variable explains a response, similar to a child falling and skins their knee and starting to cry. The child is crying in response to falling and skinning their knee. So the explanatory variable is the fall, and the response variable is crying.

Explanatory Vs Response Variable In Everyday Life

Let’s look at another example. Suppose a medical journal describes two studies in which subjects who had a seizure were randomly assigned to two different treatments:

• No treatment.
• A high dose of vitamin C.

The subjects were observed for a year, and the number of seizures for each subject was recorded. Identify the explanatory variable (independent variable), response variable (dependent variable), and include the experimental units.

The explanatory variable is whether the subject received either no treatment or a high dose of vitamin C. The response variable is whether the subject had a seizure during the time of the study. The experimental units in this study are the subjects who recently had a seizure.

Okay, so using the example above, notice that one of the groups did not receive treatment. This group is called a control group and acts as a baseline to see how a new treatment differs from those who don’t receive treatment. Typically, the control group is given something called a placebo, a substance designed to resemble medicine but does not contain an active drug component. A placebo is a dummy treatment, and should not have a physical effect on a person.

Before we talk about the characteristics of a well-designed experiment, we need to discuss some things to look out for:

• Confounding
• Lurking variables

Confounding happens when two explanatory variables are both associated with a response variable and also associated with each other, causing the investigator not to be able to identify their effects and the response variable separately.

A lurking variable is usually unobserved at the time of the study, which influences the association between the two variables of interest. In essence, a lurking variable is a third variable that is not measured in the study but may change the response variable.

For example, a study reported a relationship between smoking and health. A study of 1430 women were asked whether they smoked. Ten years later, a follow-up survey observed whether each woman was still alive or deceased. The researchers studied the possible link between whether a woman smoked and whether she survived the 10-year study period. They reported that:

• 21% of the smokers died
• 32% of the nonsmokers died

So, is smoking beneficial to your health, or is there something that could explain how this happened?

Older women are less likely to be smokers, and older women are more likely to die. Because age is a variable that influences the explanatory and response variable, it is considered a confounding variable.

But does smoking cause death?

Notice that the lurking variable, age, can also be a contributing factor. While there is a correlation between smoking and mortality, and also a correlation between smoking and age, we aren’t 100% sure that they are the cause of the mortality rate in women.

Lurking – Confounding – Correlation – Causation Diagram

Now, something important to point out is that a lurking variable is one that is not measured in the study that could influence the results. Using the example above, some other possible lurking variables are:

• Stress Level.

These variables were not measured in the study but could influence smoking habits as well as mortality rates.

What is important to note about the difference between confounding and lurking variables is that a confounding variable is measured in a study, while a lurking variable is not.

Additionally, correlation does not imply causation!

Alright, so now it’s time to talk about blinding: single-blind, double-blind experiments, as well as the placebo effect.

A single-blind experiment is when the subjects are unaware of which treatment they are receiving, but the investigator measuring the responses knows what treatments are going to which subject. In other words, the researcher knows which individual gets the placebo and which ones receive the experimental treatment. One major pitfall for this type of design is that the researcher may consciously or unconsciously influence the subject since they know who is receiving treatment and who isn’t.

A double-blind experiment is when both the subjects and investigator do not know who receives the placebo and who receives the treatment. A double-blind model is considered the best model for clinical trials as it eliminates the possibility of bias on the part of the researcher and the possibility of producing a placebo effect from the subject.

The placebo effect is when a subject has an effect or response to a fake treatment because they “believe” that the result should occur as noted by Yale . For example, a person struggling with insomnia takes a placebo (sugar pill) but instantly falls asleep because they believe they are receiving a sleep aid like Ambien or Lunesta.

Placebo Effect – Real Life Example

So, what are the three primary requirements for a well-designed experiment?

• Randomization

In a controlled experiment , the researchers, or investigators, decide which subjects are assigned to a control group and which subjects are assigned to a treatment group. In doing so, we ensure that the control and treatment groups are as similar as possible, and limit possible confounding influences such as lurking variables. A replicated experiment that is repeated on many different subjects helps reduce the chance of variation on the results. And randomization means we randomly assign subjects into control and treatment groups.

When subjects are divided into control groups and treatment groups randomly, we can use probability to predict the differences we expect to observe. If the differences between the two groups are higher than what we would expect to see naturally (by chance), we say that the results are statistically significant.

For example, if it is surmised that a new medicine reduces the effects of illness from 72 hours to 71 hours, this would not be considered statistically significant. The difference from 72 hours to 71 hours is not substantial enough to support that the observed effect was due to something other than normal random variation.

Now there are two major types of designs:

• Completely-Randomized Design (CRD)
• Block Design

A completely randomized design is the process of assigning subjects to control and treatment groups using probability, as seen in the flow diagram below.

Completely Randomized Design Example

A block design is a research method that places subjects into groups of similar experimental units or conditions, like age or gender, and then assign subjects to control and treatment groups using probability, as shown below.

Randomized Block Design Example

Additionally, a useful and particular case of a blocking strategy is something called a matched-pair design . This is when two variables are paired to control for lurking variables.

For example, imagine we want to study if walking daily improved blood pressure. If the blood pressure for five subjects is measured at the beginning of the study and then again after participating in a walking program for one month, then the observations would be considered dependent samples because the same five subjects are used in the before and after observations; thus, a matched-pair design.

Please note that our video lesson will not focus on quasi-experiments. A quasi experimental design lacks random assignments; therefore, the independent variable can be manipulated prior to measuring the dependent variable, which may lead to confounding. For the sake of our lesson, and all future lessons, we will be using research methods where random sampling and experimental designs are used.

Together we will learn how to identify explanatory variables (independent variable) and response variables (dependent variables), understand and define confounding and lurking variables, see the effects of single-blind and double-blind experiments, and design randomized and block experiments.

Experimental Designs – Lesson & Examples (Video)

1 hr 06 min

• Introduction to Video: Experiments
• 00:00:29 – Observational Study vs Experimental Study and Response and Explanatory Variables (Examples #1-4)
• Exclusive Content for Members Only
• 00:09:15 – Identify the response and explanatory variables and the experimental units and treatment (Examples #5-6)
• 00:14:47 – Introduction of lurking variables and confounding with ice cream and homicide example
• 00:18:57 – Lurking variables, Confounding, Placebo Effect, Single Blind and Double Blind Experiments (Example #7)
• 00:27:20 – What was the placebo effect and was the experiment single or double blind? (Example #8)
• 00:30:36 – Characteristics of a well designed and constructed experiment that is statistically significant
• 00:35:08 – Overview of Complete Randomized Design, Block Design and Matched Pair Design
• 00:44:23 – Design and experiment using complete randomized design or a block design (Examples #9-10)
• 00:56:09 – Identify the response and explanatory variables, experimental units, lurking variables, and design an experiment to test a new drug (Example #11)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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• Animal characteristics
• Independent variables
• Group and sample size

Experimental unit

• Inclusion and exclusion
• Intervention
• Measurement
• Overview and demonstration of the EDA
• Getting the most out of the EDA
• What is the experiment diagram?
• Troubleshooting

How to identify the experimental unit in an in vivo experiment.

Why is the experimental unit important, the individual animal.

• A breeding female and litter
• The cage of animals

A part of an animal

An animal for a period of time, experiments with more than one experimental unit, representing the experimental unit in the eda.

The experimental unit is the entity you want to make inferences about (in the population) based on the sample (in your experiment).

The experimental unit is the entity subjected to an intervention independently of all other units. It must be possible to assign any two experimental units to different treatment groups. 

The sample size is the number of experimental units per group. You need enough experimental units in your experiment for reliable results. But, if you do not correctly identify the experimental unit, there is a risk you overestimate your sample size which could invalidate the results of your statistical analysis and conclusions.

The British Pharmacological Society have created an animated video to introduce the concept of experimental units and how correctly identifying them is important to interpret your results.

Back to top

Know your experimental unit

In animal experiments the experimental unit is often the individual animal. In this case, each animal is allocated to a particular treatment group independently of other animals. But this is not always the case. Depending on the treatment administered, the experimental unit may be bigger than the animal (e.g. a litter or a cage) or smaller than the animal (e.g. part of the animal or an animal for a period of time). You can learn more about how to identify your experimental unit using the examples in this section. 

Note that if you take multiple measurements from the same animal it does not mean that each animal provides multiple experimental units. The experimental unit is defined as the entity which receives an intervention or treatment, regardless of how many times you take measurements from it.

This is the most common situation and individual animals are independently assigned to distinct categories of the variable(s) of interest. It must be possible for any two individual animals to receive different treatments. 

An example could be an experiment with four groups defined by two variables of interest, sex and exercise. The categories of the variables of interest are 'female with exercise', 'female no exercise', 'male with exercise', and 'male no exercise'. Animals are either male or female independently of other animals, and each animal is allocated to different activity levels independently of the other animals. Thus, the experimental unit is the individual animal.  

A breeding female and litter 

Consider a teratogenesis experiment where the pregnant female receives a treatment and measurements are made on the individual pups after birth. Animals within a litter are all exposed to the same treatment – the experimental unit is therefore the whole litter. In this case, the variable  ‘individual pups’ is nested into the experimental unit ‘litter’.

The cage of animals 

If animals are group housed in a cage and all animals within that cage receive the same treatment, for example in the drinking water or diet, then the experimental unit is the cage of animals. 

However, if animals are group housed but can each receive a different treatment, for example by injection (and the treatment will not contaminate cage mates), then the experimental unit would be the individual animal.

If animals are exposed to a treatment via topical application, it may be possible to divide an area of skin into a number of different patches which can each receive distinct treatments. In this situation, the patch of skin on the animal is the experimental unit.

If individual cells can be stimulated independently and recording of the responses is made at the individual cell level, the experimental unit for the stimulation is the individual cell. Provided the experiment does not include another treatment which the whole animal is exposed to (e.g. drug injection or genotype), the individual cell can be the experimental unit for the whole experiment and a single animal provides many experimental units. It is important to note that if just a single animal is used, then the results hold true for that animal alone and cannot be generalised to the population.

When a single animal provides multiple experimental units, to avoid the confounding effect of between-animal variability, the individual animal should be used as a blocking factor and more than one animal should be used to improve generalisability. The number of animals needed depends on the between-animal variability.

Another scenario where a single animal can provide several experiment units is in a crossover experiment. In this experimental design, each animal is used as its own control and receives distinct treatments, separated by wash out periods. As animals can be exposed to different treatments in different test periods, the experimental unit is the animal for period of time.

Occasionally, there may be multiple experimental units in a single experiment, for example in a so-called split plot experiment.

Consider a situation where the effects of two different treatments (diet and vitamin supplements) on growth rate are investigated in mice. Diet is administered at the cage level and all mice housed in the same cage receive the same diet – the experimental unit for the diet treatment is therefore the cage. However, the vitamin supplement is administered by gavage meaning animals within the same cage can receive different supplements – the experimental unit for the vitamin supplement is the individual mouse.

This type of design is powerful as it enables researchers to investigate whether the effect of the vitamin is related to the diet administered. However the statistical analysis can be complicated and expert statistical advice should be sought before conducting such an experiment.

On your EDA diagram, the experimental unit is represented by the experimental unit node . This node is connected from one of the group nodes as shown in the image below.

If the experimental unit is the same throughout your experiment you only need one experimental unit node in your diagram. If there are multiple experimental units, multiple nodes may be necessary to clarify which unit different interventions are applied to.

Festing, MFW, et al. (2002). The design of animal experiments: reducing the use of animals in research through better experimental design . Royal Society of Medicine.

Lazic, SE (2010). The problem of pseudoreplication in neuroscientific studies: is it affecting your analysis? BMC Neurosci 11:5. doi: 10.1186/1471-2202-11-5

Lazic, SE, Clarke-Williams, CJ and Munafo, MR (2018). What exactly is 'N' in cell culture and animal experiments? PLOS Biol 16(4):e2005282. doi: 10.1371/journal.pbio.2005282

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Identifying the experimental unit

I have included a diagram of an experiment where cells are pooled from multiple animals, cells from the pool are then allocated to different treatments and a measurement is taken from each individual cell in each treatment. The aim of this experiment is to determine how doses of a drug (treatments) affect cell size. I have previously received different opinions on what constitutes the experimental unit in this case. I would say the experimental unit is the pool so n=1 but when looking at the definition of experimental unit it states: “The smallest division of the experimental material such that any two experimental units can receive different treatments” - surely two individual cells could theoretically receive different treatments since they are separate entities?

Most examples I have found are more straight forward, for example had the snails themselves been exposed to the treatment I could see how the cells within each snail would no longer be independent and thus the snail would be the experimental unit.

• experiment-design
• biostatistics

• $\begingroup$ Welcome to CrossValidated. I think the EUs are the pools, because it is those that are assigned to treatments. I think you must be using the word "treatment" in a different sense in the last sentence of your 1st paragraph. It is what is assigned to treatments that matters. $\endgroup$ –  Russ Lenth Commented Aug 20, 2014 at 15:16
• $\begingroup$ About how many individual cells are subjected to each of the 6 treatments? $\endgroup$ –  half-pass Commented Aug 20, 2014 at 19:00
• $\begingroup$ Why are you grouping the cells from different individuals? Isn't it possible that the cells from different animals react differently to each treatment? $\endgroup$ –  Rodrigo Commented Aug 20, 2014 at 19:31
• $\begingroup$ Hi, the cells from different individuals are pooled because a single snail doesn't produce a large enough volume to use $\endgroup$ –  John Smith Commented Aug 21, 2014 at 10:05

Since you're assigning individual cells to treatments and measuring sizes of individual cells, the experimental unit is individual cells .

You're not keeping track of which snail contributed each cell, so the number of snails is only relevant to generalizability, not sample size. In other words, although you may have a very large sample of cells, they are coming from a small population. If you knew which snail contributed each cell, you could account for inter-snail variability by treating each snail as a cluster from which you draw individual units (cells). But when it comes to cell size, this would probably not accomplish much anyway.

• $\begingroup$ Thanks, I've gone back and forth between the pool and the cell. I suppose it depends on the question being asked i.e are we looking at difference between snails or between cells and in my case I'm interested in difference between cells. $\endgroup$ –  John Smith Commented Aug 21, 2014 at 10:07
• 1 $\begingroup$ I disagree. To me the UE is each well receiving a treatment and the cells are sample units. The pool receive the same treatment. $\endgroup$ –  Emilie Commented Aug 21, 2014 at 12:26
• 1 $\begingroup$ I found this quote: "There is controversy amongst statisticians and biologists as to the most appropriate experimental unit when, for example, several animals are fed together within a pen or paddock. Broadly speaking, these positions can be divided into a view that the most appropriate experimental unit is the smallest unit upon which a treatment can be applied (generally the group of animals) versus a view that the most appropriate experimental unit is the smallest unit upon which a measurement can be made (generally the animal)." $\endgroup$ –  John Smith Commented Aug 21, 2014 at 13:08
• 1 $\begingroup$ Perhaps the seminal paper of Hulbert would help you : Hurlbert, S. H. 1984. Pseudoreplication and the design of ecological field experiments. — Ecol. Monogr. 54: 187-211. As it's made for ecologist, it will probably be better than statisticians definitions. But in your case, all the cell in your treatment "wells" receive the same treatment. It seems quite clear they are sample units. $\endgroup$ –  Emilie Commented Aug 21, 2014 at 19:08
• 2 $\begingroup$ Ah, I didn't realize there were multiple wells for each dose. In that case, I would consider this a cluster design that could be analyzed with, e.g., a multilevel model. The clusters are the wells and the individuals within each cluster are the cells. $\endgroup$ –  half-pass Commented Aug 21, 2014 at 19:41

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