define random assignment in statistics

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AP®︎/College Statistics

Course: ap®︎/college statistics > unit 6.

Statistical significance of experiment

Random sampling vs. random assignment (scope of inference)

Conclusions in observational studies versus experiments
Finding errors in study conclusions
(Choice A) Just the residents involved in Hilary's study. A Just the residents involved in Hilary's study.
(Choice B) All residents in Hilary's town. B All residents in Hilary's town.
(Choice C) All residents in Hilary's country. C All residents in Hilary's country.
(Choice A) Yes A Yes
(Choice B) No B No
(Choice A) Just the residents in Hilary's study. A Just the residents in Hilary's study.

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Statistics Made Easy

Random Selection vs. Random Assignment

Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.

Random selection refers to the process of randomly selecting individuals from a population to be involved in a study.

Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group.

You can think of random selection as the process you use to “get” the individuals in a study and you can think of random assignment as what you “do” with those individuals once they’re selected to be part of the study.

The Importance of Random Selection and Random Assignment

When a study uses random selection , it selects individuals from a population using some random process. For example, if some population has 1,000 individuals then we might use a computer to randomly select 100 of those individuals from a database. This means that each individual is equally likely to be selected to be part of the study, which increases the chances that we will obtain a representative sample – a sample that has similar characteristics to the overall population.

By using a representative sample in our study, we’re able to generalize the findings of our study to the population. In statistical terms, this is referred to as having external validity – it’s valid to externalize our findings to the overall population.

When a study uses random assignment , it randomly assigns individuals to either a treatment group or a control group. For example, if we have 100 individuals in a study then we might use a random number generator to randomly assign 50 individuals to a control group and 50 individuals to a treatment group.

By using random assignment, we increase the chances that the two groups will have roughly similar characteristics, which means that any difference we observe between the two groups can be attributed to the treatment. This means the study has internal validity – it’s valid to attribute any differences between the groups to the treatment itself as opposed to differences between the individuals in the groups.

Examples of Random Selection and Random Assignment

It’s possible for a study to use both random selection and random assignment, or just one of these techniques, or neither technique. A strong study is one that uses both techniques.

The following examples show how a study could use both, one, or neither of these techniques, along with the effects of doing so.

Example 1: Using both Random Selection and Random Assignment

Study: Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. Once they have the 100 individuals, they once again use a computer to randomly assign 50 of the individuals to a control group (e.g. stick with their standard diet) and 50 individuals to a treatment group (e.g. follow the new diet). They record the total weight loss of each individual after one month.

Results: The researchers used random selection to obtain their sample and random assignment when putting individuals in either a treatment or control group. By doing so, they’re able to generalize the findings from the study to the overall population and they’re able to attribute any differences in average weight loss between the two groups to the new diet.

Example 2: Using only Random Selection

Study: Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. However, they decide to assign individuals to groups based solely on gender. Females are assigned to the control group and males are assigned to the treatment group. They record the total weight loss of each individual after one month.

Random assignment vs. random selection in statistics

Results: The researchers used random selection to obtain their sample, but they did not use random assignment when putting individuals in either a treatment or control group. Instead, they used a specific factor – gender – to decide which group to assign individuals to. By doing this, they’re able to generalize the findings from the study to the overall population but they are not able to attribute any differences in average weight loss between the two groups to the new diet. The internal validity of the study has been compromised because the difference in weight loss could actually just be due to gender, rather than the new diet.

Example 3: Using only Random Assignment

Study: Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 males athletes to be in the study. Then, they use a computer program to randomly assign 50 of the male athletes to a control group and 50 to the treatment group. They record the total weight loss of each individual after one month.

Random assignment vs. random selection example

Results: The researchers did not use random selection to obtain their sample since they specifically chose 100 male athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. However, they did use random assignment, which means they can attribute any difference in weight loss to the new diet.

Example 4: Using Neither Technique

Study: Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 50 males athletes and 50 female athletes to be in the study. Then, they assign all of the female athletes to the control group and all of the male athletes to the treatment group. They record the total weight loss of each individual after one month.

Results: The researchers did not use random selection to obtain their sample since they specifically chose 100 athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. Also, they split individuals into groups based on gender rather than using random assignment, which means their internal validity is also compromised – differences in weight loss might be due to gender rather than the diet.

Published by Zach

Random Selection vs. Random Assignment

Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.

Random selection refers to the process of randomly selecting individuals from a population to be involved in a study.

Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group.

The Importance of Random Selection and Random Assignment

Examples of Random Selection and Random Assignment

It’s possible for a study to use both random selection and random assignment, or just one of these techniques, or neither technique. A strong study is one that uses both techniques.

The following examples show how a study could use both, one, or neither of these techniques, along with the effects of doing so.

Example 1: Using both Random Selection and Random Assignment

Example 2: Using only Random Selection

Study: Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. However, they decide to assign individuals to groups based solely on gender. Females are assigned to the control group and males are assigned to the treatment group. They record the total weight loss of each individual after one month.

Example 3: Using only Random Assignment

Example 4: Using Neither Technique

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Random Assignment in Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

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In psychology, random assignment refers to the practice of allocating participants to different experimental groups in a study in a completely unbiased way, ensuring each participant has an equal chance of being assigned to any group.

In experimental research, random assignment, or random placement, organizes participants from your sample into different groups using randomization.

Random assignment uses chance procedures to ensure that each participant has an equal opportunity of being assigned to either a control or experimental group.

The control group does not receive the treatment in question, whereas the experimental group does receive the treatment.

When using random assignment, neither the researcher nor the participant can choose the group to which the participant is assigned. This ensures that any differences between and within the groups are not systematic at the onset of the study.

In a study to test the success of a weight-loss program, investigators randomly assigned a pool of participants to one of two groups.

Group A participants participated in the weight-loss program for 10 weeks and took a class where they learned about the benefits of healthy eating and exercise.

Group B participants read a 200-page book that explains the benefits of weight loss. The investigator randomly assigned participants to one of the two groups.

The researchers found that those who participated in the program and took the class were more likely to lose weight than those in the other group that received only the book.

Importance

Random assignment ensures that each group in the experiment is identical before applying the independent variable.

In experiments , researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. Random assignment increases the likelihood that the treatment groups are the same at the onset of a study.

Thus, any changes that result from the independent variable can be assumed to be a result of the treatment of interest. This is particularly important for eliminating sources of bias and strengthening the internal validity of an experiment.

Random assignment is the best method for inferring a causal relationship between a treatment and an outcome.

Random Selection vs. Random Assignment

Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study.

On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups.

Random selection ensures that everyone in the population has an equal chance of being selected for the study. Once the pool of participants has been chosen, experimenters use random assignment to assign participants into groups.

Random assignment is only used in between-subjects experimental designs, while random selection can be used in a variety of study designs.

Random Assignment vs Random Sampling

Random sampling refers to selecting participants from a population so that each individual has an equal chance of being chosen. This method enhances the representativeness of the sample.

Random assignment, on the other hand, is used in experimental designs once participants are selected. It involves allocating these participants to different experimental groups or conditions randomly.

This helps ensure that any differences in results across groups are due to manipulating the independent variable, not preexisting differences among participants.

When to Use Random Assignment

Random assignment is used in experiments with a between-groups or independent measures design.

In these research designs, researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables.

There is usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable at the onset of the study.

How to Use Random Assignment

There are a variety of ways to assign participants into study groups randomly. Here are a handful of popular methods:

Random Number Generator : Give each member of the sample a unique number; use a computer program to randomly generate a number from the list for each group.
Lottery : Give each member of the sample a unique number. Place all numbers in a hat or bucket and draw numbers at random for each group.
Flipping a Coin : Flip a coin for each participant to decide if they will be in the control group or experimental group (this method can only be used when you have just two groups)
Roll a Die : For each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1, 2, or 3 places them in a control group and rolling 3, 4, 5 lands them in an experimental group.

When is Random Assignment not used?

When it is not ethically permissible: Randomization is only ethical if the researcher has no evidence that one treatment is superior to the other or that one treatment might have harmful side effects.
When answering non-causal questions : If the researcher is just interested in predicting the probability of an event, the causal relationship between the variables is not important and observational designs would be more suitable than random assignment.
When studying the effect of variables that cannot be manipulated: Some risk factors cannot be manipulated and so it would not make any sense to study them in a randomized trial. For example, we cannot randomly assign participants into categories based on age, gender, or genetic factors.

Drawbacks of Random Assignment

While randomization assures an unbiased assignment of participants to groups, it does not guarantee the equality of these groups. There could still be extraneous variables that differ between groups or group differences that arise from chance. Additionally, there is still an element of luck with random assignments.

Thus, researchers can not produce perfectly equal groups for each specific study. Differences between the treatment group and control group might still exist, and the results of a randomized trial may sometimes be wrong, but this is absolutely okay.

Scientific evidence is a long and continuous process, and the groups will tend to be equal in the long run when data is aggregated in a meta-analysis.

Additionally, external validity (i.e., the extent to which the researcher can use the results of the study to generalize to the larger population) is compromised with random assignment.

Random assignment is challenging to implement outside of controlled laboratory conditions and might not represent what would happen in the real world at the population level.

Random assignment can also be more costly than simple observational studies, where an investigator is just observing events without intervening with the population.

Randomization also can be time-consuming and challenging, especially when participants refuse to receive the assigned treatment or do not adhere to recommendations.

What is the difference between random sampling and random assignment?

Random sampling refers to randomly selecting a sample of participants from a population. Random assignment refers to randomly assigning participants to treatment groups from the selected sample.

Does random assignment increase internal validity?

Yes, random assignment ensures that there are no systematic differences between the participants in each group, enhancing the study’s internal validity .

Does random assignment reduce sampling error?

Yes, with random assignment, participants have an equal chance of being assigned to either a control group or an experimental group, resulting in a sample that is, in theory, representative of the population.

Random assignment does not completely eliminate sampling error because a sample only approximates the population from which it is drawn. However, random sampling is a way to minimize sampling errors.

When is random assignment not possible?

Random assignment is not possible when the experimenters cannot control the treatment or independent variable.

For example, if you want to compare how men and women perform on a test, you cannot randomly assign subjects to these groups.

Participants are not randomly assigned to different groups in this study, but instead assigned based on their characteristics.

Does random assignment eliminate confounding variables?

Yes, random assignment eliminates the influence of any confounding variables on the treatment because it distributes them at random among the study groups. Randomization invalidates any relationship between a confounding variable and the treatment.

Why is random assignment of participants to treatment conditions in an experiment used?

Random assignment is used to ensure that all groups are comparable at the start of a study. This allows researchers to conclude that the outcomes of the study can be attributed to the intervention at hand and to rule out alternative explanations for study results.

MA121: Introduction to Statistics

Descriptive and Inferential Statistics

Read these sections and complete the questions at the end of each section. Here, we introduce descriptive statistics using examples and discuss the difference between descriptive and inferential statistics. We also talk about samples and populations, explain how you can identify biased samples, and define differential statistics.

Inferential Statistics

Random assignment.

In experimental research, populations are often hypothetical. For example, in an experiment comparing the effectiveness of a new anti-depressant drug with a placebo, there is no actual population of individuals taking the drug. In this case, a specified population of people with some degree of depression is defined and a random sample is taken from this population. The sample is then randomly divided into two groups; one group is assigned to the treatment condition (drug) and the other group is assigned to the control condition (placebo). This random division of the sample into two groups is called random assignment . Random assignment is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first 20 subjects to show up at the experiment were assigned to the experimental group and the second 20 subjects were assigned to the control group. It is possible that subjects who show up late tend to be more depressed than those who show up early, thus making the experimental group less depressed than the control group even before the treatment was administered.

In experimental research of this kind, failure to assign subjects randomly to groups is generally more serious than having a non-random sample. Failure to randomize (the former error) invalidates the experimental findings. A non-random sample (the latter error) simply restricts the generalizability of the results.

Random Assignment

Random assignment refers to assigning participants or subjects into different groups (e.g., control group vs. treatment group) randomly. This helps ensure that any differences observed between groups are due to treatment effects rather than pre-existing differences.

Imagine you are organizing a basketball tournament. To ensure fairness, you randomly assign players to different teams rather than letting them choose their own teams. This way, any differences in team performance can be attributed to the skills and strategies of the players, not the initial composition of the teams.

Related terms

Experimental Design : Experimental design involves planning and structuring an experiment to minimize bias and maximize the ability to draw valid conclusions.

Control Group : A control group is a group that does not receive the experimental treatment and serves as a baseline for comparison.

Treatment Group : A treatment group is a group that receives the experimental treatment or intervention being studied.

" Random Assignment " appears in:

Subjects ( 1 ).

AP Psychology

Study guides ( 4 )

AP Statistics - 3.1 Introducing Statistics: Do the Data We Collected Tell the Truth?

AP Statistics - 3.2 Introduction to Planning a Study

AP Statistics - 3.5 Introduction to Experimental Design

AP Statistics - 3.7 Inference and Experiments

Practice Questions ( 2 )

What is random assignment in experimental research design?
What does random assignment allow researchers to conclude about observed changes?

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Methodology

Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on August 28, 2020 by Lauren Thomas . Revised on December 18, 2023.

A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected.

This method is the most straightforward of all the probability sampling methods , since it only involves a single random selection and requires little advance knowledge about the population. Because it uses randomization, any research performed on this sample should have high internal and external validity, and be at a lower risk for research biases like sampling bias and selection bias .

When to use simple random sampling, how to perform simple random sampling, other interesting articles, frequently asked questions about simple random sampling.

Simple random sampling is used to make statistical inferences about a population. It helps ensure high internal validity : randomization is the best method to reduce the impact of potential confounding variables .

In addition, with a large enough sample size, a simple random sample has high external validity : it represents the characteristics of the larger population.

However, simple random sampling can be challenging to implement in practice. To use this method, there are some prerequisites:

You have a complete list of every member of the population .
You can contact or access each member of the population if they are selected.
You have the time and resources to collect data from the necessary sample size.

Simple random sampling works best if you have a lot of time and resources to conduct your study, or if you are studying a limited population that can easily be sampled.

In some cases, it might be more appropriate to use a different type of probability sampling:

Systematic sampling involves choosing your sample based on a regular interval, rather than a fully random selection. It can also be used when you don’t have a complete list of the population.
Stratified sampling is appropriate when you want to ensure that specific characteristics are proportionally represented in the sample. You split your population into strata (for example, divided by gender or race), and then randomly select from each of these subgroups.
Cluster sampling is appropriate when you are unable to sample from the entire population. You divide the sample into clusters that approximately reflect the whole population, and then choose your sample from a random selection of these clusters.

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There are 4 key steps to select a simple random sample.

Step 1: Define the population

Start by deciding on the population that you want to study.

It’s important to ensure that you have access to every individual member of the population, so that you can collect data from all those who are selected for the sample.

Step 2: Decide on the sample size

Next, you need to decide how large your sample size will be. Although larger samples provide more statistical certainty, they also cost more and require far more work.

There are several potential ways to decide upon the size of your sample, but one of the simplest involves using a formula with your desired confidence interval and confidence level , estimated size of the population you are working with, and the standard deviation of whatever you want to measure in your population.

The most common confidence interval and levels used are 0.05 and 0.95, respectively. Since you may not know the standard deviation of the population you are studying, you should choose a number high enough to account for a variety of possibilities (such as 0.5).

You can then use a sample size calculator to estimate the necessary sample size.

Step 3: Randomly select your sample

This can be done in one of two ways: the lottery or random number method.

In the lottery method , you choose the sample at random by “drawing from a hat” or by using a computer program that will simulate the same action.

In the random number method , you assign every individual a number. By using a random number generator or random number tables, you then randomly pick a subset of the population. You can also use the random number function (RAND) in Microsoft Excel to generate random numbers.

Step 4: Collect data from your sample

Finally, you should collect data from your sample.

To ensure the validity of your findings, you need to make sure every individual selected actually participates in your study. If some drop out or do not participate for reasons associated with the question that you’re studying, this could bias your findings.

For example, if young participants are systematically less likely to participate in your study, your findings might not be valid due to the underrepresentation of this group.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Student’s t -distribution
Normal distribution
Null and Alternative Hypotheses
Chi square tests
Confidence interval
Quartiles & Quantiles
Cluster sampling
Stratified sampling
Data cleansing
Reproducibility vs Replicability
Peer review
Prospective cohort study

Research bias

Implicit bias
Cognitive bias
Placebo effect
Hawthorne effect
Hindsight bias
Affect heuristic
Social desirability bias

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 .

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.

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.

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.

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

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

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Encyclopedia of Personality and Individual Differences pp 1–3 Cite as

Random Assignment

Sven Hilbert 3
Living reference work entry
First Online: 25 January 2017

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Random assignment defines the assignment of participants of a study to their respective group strictly by chance.

Introduction

Statistical inference is based on the theory of probability, and effects investigated in psychological studies are defined by measures that are treated as random variables. The inference about the probability of a given result with regard to an assumed population and the popular term “significance” are only meaningful and without bias if the measure of interest is really a random variable. To achieve the creation of a random variable in form of a measure derived from a sample of participants, these participants have to be randomly drawn. In an experimental study involving different groups of participants, these participants have to additionally be randomly assigned to one of the groups.

Why Is Random Assignment Crucial for Statistical Inference?

Many psychological investigations, such as clinical treatment studies or neuropsychological training...

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Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J., & Kruger, L. (1989). The empire of chance: How probability changed science and everyday-life . Cambridge: New York.

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Hilbert, S. (2017). Random Assignment. In: Zeigler-Hill, V., Shackelford, T. (eds) Encyclopedia of Personality and Individual Differences. Springer, Cham. https://doi.org/10.1007/978-3-319-28099-8_1343-1

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15.1: Random Selection

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Paul Pfeiffer
Rice University

Introduction

The usual treatments deal with a single random variable or a fixed, finite number of random variables, considered jointly. However, there are many common applications in which we select at random a member of a class of random variables and observe its value, or select a random number of random variables and obtain some function of those selected. This is formulated with the aid of a counting or selecting random variable $N$, which is nonegative, integer valued. It may be independent of the class selected, or may be related in some sequential way to members of the class. We consider only the independent case. Many important problems require optional random variables, sometimes called Markov times . These involve more theory than we develop in this treatment.

Some common examples:

Total demand of $N$ customers— $N$ independent of the individual demands. Total service time for $N$ units— $N$ independent of the individual service times. Net gain in $N$ plays of a game— $N$ independent of the individual gains. Extreme values of $N$ random variables— $N$ independent of the individual values. Random sample of size $N$— $N$ is usually determined by propereties of the sample observed. Decide when to play on the basis of past results— $N$ dependent on past

A useful model—random sums

As a basic model, we consider the sum of a random number of members of an iid class. In order to have a concrete interpretation to help visualize the formal patterns, we think of the demand of a random number of customers. We suppose the number of customers N is independent of the individual demands. We formulate a model to be used for a variety of applications.

A basic sequence $\{X_n: 0 \le n\}$ [Demand of $n$ customers] An incremental sequence $\{Y_n:0 \le n\}$ [Individual demands] These are related as follows:

$X_n = \sum_{k = 0}^{n} Y_k$ for $n \ge 0$ and $X_n = 0$ for $n < 0$ $Y_n = X_n - X_{n - 1}$ for all $n$

A counting random variable $N$. If $N = n$ then $n$ of the $Y_k$ are added to give the compound demand $D$ (the random sum)

$D = \sum_{k = 0}^{N} Y_k = \sum_{k = 0}^{\infty} I_{[N = k]} X_k = \sum_{k = 0}^{\infty} I_{\{k\}} (N) X_k$

Note . In some applications the counting random variable may take on the idealized value $\infty$. For example, in a game that is played until some specified result occurs, this may never happen, so that no finite value can be assigned to $N$. In such a case, it is necessary to decide what value $X_{\infty}$ is to be assigned. For $N$ independent of the $Y_n$ (hence of the $X_n$), we rarely need to consider this possibility.

Independent selection from an iid incremental sequence

We assume throughout , unless specifically stated otherwise, that: $X_0 = Y_0 = 0$ $\{Y_k: 1 \le k\}$ is iid $\{N, Y_k: 0 \le k\}$ is an independent class

We utilize repeatedly two important propositions: $E[h(D)|N = n] = E[h(X_n)]$, $n \ge 0$ $M_D (s) = g_N [M_Y (s)]$. If the $Y_n$ are nonnegative integer valued, then so is $D$ and $g_D (s) = g_N[g_Y (s)]$

We utilize properties of generating functions, moment generating functions, and conditional expectation. $E[I_{\{n\}} (N) h(D)] = E[h(D)|N = n] P(N = n)$ by definition of conditional expectation, given an event, Now, $I_{\{n\}} (N) h(D) = I_{\{n\}} (N) h(X_n)$ and $E[I_{\{n\}} (N) h(X_n)] = P(N = n) E[h(X_n)]$. Hence $E[h(D) |N = n] P(N = n) = P(N = n) E[h(X_n)]$. Division by $P(N = n)$ gives the desired result. By the law of total probability (CE1b), $M_D(s)= E[e^{sD}] = E\{E[e^{sD} |N]\}$. By proposition 1 and the product rule for moment generating functions,

$E[e^{sD}|N = n] = E[e^{sX_n}] = \prod_{k = 1}^{n} E[e^{sY_k}] = M_Y^n (s)$

$M_D(s) = \sum_{n = 0}^{\infty} M_Y^n (s) P(N = n) = g_N[M_Y (s)]$

A parallel argument holds for $g_D$

— □

Remark . The result on $M_D$ and $g_D$ may be developed without use of conditional expectation.

in the integer-valued case.

$M_D(s) = E[e^{sD}] = \sum_{k = 0}^{\infty} E[I_{\{N = n\}} e^{sX_n}] = \sum_{k = 0}^{\infty} P(N = n) E[e^{sX_n}]$

$= \sum_{k = 0}^{\infty} P(N = n) M_Y^n (s) = g_N [M_Y (s)]$

Example $\PageIndex{1}$ A service shop

Suppose the number $N$ of jobs brought to a service shop in a day is Poisson (8). One fourth of these are items under warranty for which no charge is made. Others fall in one of two categories. One half of the arriving jobs are charged for one hour of shop time; the remaining one fourth are charged for two hours of shop time. Thus, the individual shop hour charges $Y_k$ have the common distribution

$Y =$ [0 1 2] with probabilities $PY =$ [1/4 1/2 1/4]

Make the basic assumptions of our model. Determine $P(D \le 4)$.

$g_N(s) = e^{8(s - 1)} g_Y (s) = \dfrac{1}{4} (1 + 2s + s^2)$

According to the formula developed above,

$g_D (s) = g_N [g_Y (s)] = \text{exp} ((8/4) (1 + 2s + s^2) - 8) = e^{4s} e^{2s^2} e^{-6}$

Expand the exponentials in power series about the origin, multiply out to get enough terms. The result of straightforward but somewhat tedious calculations is

$g_D (s) = e^{-6} ( 1 + 4s + 10s^2 + \dfrac{56}{3} s^3 + \dfrac{86}{3} s^4 + \cdot\cdot\cdot)$

Taking the coefficients of the generating function, we get

$P(D \le 4) \approx e^{-6} (1 + 4 + 10 + \dfrac{56}{3} + \dfrac{86}{3}) = e^{-6} \dfrac{187}{3} \approx 0.1545$

Example $\PageIndex{2}$ A result on Bernoulli trials

Suppose the counting random variable $N$ ~ binomial $(n, p)$ and $Y_i = I_{E_i}$, with $P(E_i) = p_0$. Then

$g_N = (q + ps)^n$ and $g_Y (s) = q_0 + p_0 s$

By the basic result on random selection, we have

$g_D (s) = g_N [g_Y(s)] = [q + p(q_0 + p_0 s)]^n = [(1 - pp_0) + pp_0 s]^n$

so that $D$ ~ binomial $(n, pp_0)$.

In the next section we establish useful m-procedures for determining the generating function g D and the moment generating function $M_D$ for the compound demand for simple random variables, hence for determining the complete distribution. Obviously, these will not work for all problems. It may helpful, if not entirely sufficient, in such cases to be able to determine the mean value $E[D]$ and variance $\text{Var} [D]$. To this end, we establish the following expressions for the mean and variance.

Example $\PageIndex{3}$ Mean and variance of the compound demand

$E[D] = E[N]E[Y]$ and $\text{Var} [D] = E[N] \text{Var} [Y] + \text{Var} [N] E^2 [Y]$

$E[D] = E[\sum_{n = 0}^{\infty} I_{\{N = n\}} X_n] = \sum_{n = 0}^{\infty} P(N = n) E[X_n]$

$= E[Y] \sum_{n = 0}^{\infty} n P(N = n) = E[Y] E[N]$

$E[D^2] = \sum_{n = 0}^{\infty} P(N = n) E[X_n^2] = \sum_{n = 0}^{\infty} P(N = n) \{\text{Var} [X_n] + E^2 [X_n]\}$

$= \sum_{n = 0}^{\infty} P(N = n) \{n \text{Var} [Y] = n^2 E^2 [Y]\} = E[N] \text{Var} [Y] + E[N^2] E^2[Y]$

$\text{Var} [D] = E[N] \text{Var} [Y] + E[N^2] E^2 [Y] - E[N]^2 E^2[Y] = E[N] \text{Var} [Y] + \text{Var} [N] E^2[Y]$

Example $\PageIndex{4}$ Mean and variance for Example 15.1.1

$E[N] = \text{Var} [N] = 9$. By symmetry $E[Y] = 1$. $\text{Var} [Y] = 0.25(0 + 2 + 4) - 1 = 0.5$. Hence,

$E[D] = 8 \cdot 1 = 8$, $\text{Var} [D] = 8 \cdot 0.5 + 8 \cdot 1 = 12$

Calculations for the compound demand

We have m-procedures for performing the calculations necessary to determine the distribution for a composite demand $D$ when the counting random variable $N$ and the individual demands $Y_k$ are simple random variables with not too many values. In some cases, such as for a Poisson counting random variable, we are able to approximate by a simple random variable.

The procedure gend

If the $Y_i$ are nonnegative, integer valued, then so is $D$, and there is a generating function. We examine a strategy for computation which is implemented in the m-procedure gend . Suppose

$g_N (s) = p_0 + p_1 s + p_2 s^2 + \cdot\cdot\cdot p_n s^n$

$g_Y (s) = \pi_0 + \pi_1 s + \pi_2 s^2 + \cdot\cdot\cdot \pi_m s^m$

The coefficients of $g_N$ and $g_Y$ are the probabilities of the values of $N$ and $Y$, respectively. We enter these and calculate the coefficients for powers of $g_Y$:

$\begin{array} {lcr} {gN = [p_0\ p_1\ \cdot\cdot\cdot\ p_n]} & {1 \times (n + 1)} & {\text{Coefficients of } g_N} \\ {y = [\pi_0\ \pi_1\ \cdot\cdot\cdot\ \pi_n]} & {1 \times (m + 1)} & {\text{Coefficients of } g_Y} \\ {\ \ \ \ \ \cdot\cdot\cdot} & { } & { } \\ {y2 = \text{conv}(y,y)} & {1 \times (2m + 1)} & {\text{Coefficients of } g_Y^2} \\ {y3 = \text{conv}(y,y2)} & {1 \times (3m + 1)} & {\text{Coefficients of } g_Y^3} \\ {\ \ \ \ \ \cdot\cdot\cdot} & { } & { } \\ {yn = \text{conv}(y,y(n - 1))} & {1 \times (nm + 1)} & {\text{Coefficients of } g_Y^n}\end{array}$

We wish to generate a matrix $P$ whose rows contain the joint probabilities. The probabilities in the $i$th row consist of the coefficients for the appropriate power of $g_Y$ multiplied by the probability $N$ has that value. To achieve this, we need a matrix, each of whose $n + 1$ rows has $nm + 1$ elements, the length of $yn$. We begin by “preallocating” zeros to the rows. That is, we set $P = \text{zeros}(n + 1, n\ ^*\ m + 1)$. We then replace the appropriate elements of the successive rows. The replacement probabilities for the $i$th row are obtained by the convolution of $g_Y$ and the power of $g_Y$ for the previous row. When the matrix $P$ is completed, we remove zero rows and columns, corresponding to missing values of $N$ and $D$ (i.e., values with zero probability). To orient the joint probabilities as on the plane, we rotate $P$ ninety degrees counterclockwise. With the joint distribution, we may then calculate any desired quantities.

Example $\PageIndex{5}$ A compound demand

The number of customers in a major appliance store is equally likely to be 1, 2, or 3. Each customer buys 0, 1, or 2 items with respective probabilities 0.5, 0.4, 0.1. Customers buy independently, regardless of the number of customers. First we determine the matrices representing $g_N$ and $g_Y$. The coefficients are the probabilities that each integer value is observed. Note that the zero coefficients for any missing powers must be included.

Example $\PageIndex{6}$ A numerical example

$g_N (s) = \dfrac{1}{5} (1 + s + s^2 + s^3 + s^4)$ $g_Y (s) = 0.1 (5s + 3s^2 + 2s^3$

Note that the zero power is missing from $gY$. corresponding to the fact that $P(Y = 0) = 0$.

Example $\PageIndex{7}$ Number of successes for random number $N$ of trials.

We are interested in the number of successes in $N$ trials for a general counting random variable. This is a generalization of the Bernoulli case in Example 15.1.2 . Suppose, as in Example 15.1.2 , the number of customers in a major appliance store is equally likely to be 1, 2, or 3, and each buys at least one item with probability $p = 0.6$. Determine the distribution for the number $D$ of buying customers.

We use $gN$, $gY$, and gend.

The procedure gend is limited to simple $N$ and $Y_k$, with nonnegative integer values. Sometimes, a random variable with unbounded range may be approximated by a simple random variable. The solution in the following example utilizes such an approximation procedure for the counting random variable $N$.

Example $\PageIndex{8}$ Solution of the shop time Example 15.1.1

The number $N$ of jobs brought to a service shop in a day is Poisson (8). The individual shop hour charges $Y_k$ have the common distribution $Y =$ [0 1 2] with probabilities $PY =$ [1/4 1/2 1/4].

Under the basic assumptions of our model, determine $P(D \le 4)$.

Since Poisson $N$ is unbounded, we need to check for a sufficient number of terms in a simple approximation. Then we proceed as in the simple case.

The m-procedures mgd and jmgd

The next example shows a fundamental limitation of the gend procedure. The values for the individual demands are not limited to integers, and there are considerable gaps between the values. In this case, we need to implement the moment generating function $M_D$ rather than the generating function $g_D$.

In the generating function case, it is as easy to develop the joint distribution for $\{N, D\}$ as to develop the marginal distribution for $D$. For the moment generating function, the joint distribution requires considerably more computation. As a consequence, we find it convenient to have two m-procedures: mgd for the marginal distribution and jmgd for the joint distribution.

Instead of the convolution procedure used in gend to determine the distribution for the sums of the individual demands, the m-procedure mgd utilizes the m-function mgsum to obtain these distributions. The distributions for the various sums are concatenated into two row vectors, to which csort is applied to obtain the distribution for the compound demand. The procedure requires as input the generating function for $N$ and the actual distribution, $Y$ and $PY$, for the individual demands. For $gN$, it is necessary to treat the coefficients as in gend. However, the actual values and probabilities in the distribution for Y are put into a pair of row matrices. If $Y$ is integer valued, there are no zeros in the probability matrix for missing values.

Example $\PageIndex{9}$ Noninteger values

A service shop has three standard charges for a certain class of warranty services it performs: $10, $12.50, and $15. The number of jobs received in a normal work day can be considered a random variable $N$ which takes on values 0, 1, 2, 3, 4 with equal probabilities 0.2. The job types for arrivals may be represented by an iid class $\{Y_i: 1 \le i \le 4\}$, independent of the arrival process. The $Y_i$ take on values 10, 12.5, 15 with respective probabilities 0.5, 0.3, 0.2. Let $C$ be the total amount of services rendered in a day. Determine the distribution for $C$.

We next recalculate Example 15.1.6 , above, using mgd rather than gend.

Example $\PageIndex{10}$ Recalculation of Example 15.1.6

In Example 15.1.6, we have

$g_N (s) = \dfrac{1}{5} (1 + s + s^2 + s^3 + s^4)$ $g_Y (s) = 0.1 (5s + 3s^2 + 2s^3)$

The means that the distribution for $Y$ is $Y =$ [1 2 3] and $PY =$ 0.1 * [5 3 2].

We use the same expression for $gN$ as in Example 15.1.6.

As expected, the results are the same as those obtained with gend.

If it is desired to obtain the joint distribution for $\{N, D\}$, we use a modification of mgd called jmgd . The complications come in placing the probabilities in the $P$ matrix in the desired positions. This requires some calculations to determine the appropriate size of the matrices used as well as a procedure to put each probability in the position corresponding to its $D$ value. Actual operation is quite similar to the operation of mgd, and requires the same data format.

A principle use of the joint distribution is to demonstrate features of the model, such as $E[D|N = n] = nE[Y]$, etc. This, of course, is utilized in obtaining the expressions for $M_D (s)$ in terms of $g_N (s)$ and $M_Y (s)$. This result guides the development of the computational procedures, but these do not depend upon this result. However, it is usually helpful to demonstrate the validity of the assumptions in typical examples.

Remark . In general, if the use of gend is appropriate, it is faster and more efficient than mgd (or jmgd). And it will handle somewhat larger problems. But both m-procedures work quite well for problems of moderate size, and are convenient tools for solving various “compound demand” type problems.

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Random Assignment – A Simple Introduction with Examples

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Completing a research or thesis paper is more work than most students imagine. For instance, you must conduct experiments before coming up with conclusions. Random assignment, a key methodology in academic research, ensures every participant has an equal chance of being placed in any group within an experiment. In experimental studies, the random assignment of participants is a vital element, which this article will discuss.

Inhaltsverzeichnis

1 Random Assignment – In a Nutshell
2 Definition: Random assignment
3 Importance of random assignment
4 Random assignment vs. random sampling
5 How to use random assignment
6 When random assignment is not used

Random Assignment – In a Nutshell

Random assignment is where you randomly place research participants into specific groups.
This method eliminates bias in the results by ensuring that all participants have an equal chance of getting into either group.
Random assignment is usually used in independent measures or between-group experiment designs.

Definition: Random assignment

Pearson Correlation is a descriptive statistical procedure that describes the measure of linear dependence between two variables. It entails a sample, control group , experimental design , and randomized design. In this statistical procedure, random assignment is used. Random assignment is the random placement of participants into different groups in experimental research.

Importance of random assignment

Random assessment is essential for strengthening the internal validity of experimental research. Internal validity helps make a casual relationship’s conclusions reliable and trustworthy.

In experimental research, researchers isolate independent variables and manipulate them as they assess the impact while managing other variables. To achieve this, an independent variable for diverse member groups is vital. This experimental design is called an independent or between-group design.

Example: Different levels of independent variables

In a medical study, you can research the impact of nutrient supplements on the immune (nutrient supplements = independent variable, immune = dependent variable)

Three independent participant levels are applicable here:

Control group (given 0 dosages of iron supplements)
The experimental group (low dosage)
The second experimental group (high dosage)

This assignment technique in experiments ensures no bias in the treatment sets at the beginning of the trials. Therefore, if you do not use this technique, you won’t be able to exclude any alternate clarifications for your findings.

In the research experiment above, you can recruit participants randomly by handing out flyers at public spaces like gyms, cafés, and community centers. Then:

Place the group from cafés in the control group
Community center group in the low prescription trial group
Gym group in the high-prescription group

Even with random participant assignment, other extraneous variables may still create bias in experiment results. However, these variations are usually low, hence should not hinder your research. Therefore, using random placement in experiments is highly necessary, especially where it is ethically required or makes sense for your research subject.

Random assignment vs. random sampling

Simple random sampling is a method of choosing the participants for a study. On the other hand, the random assignment involves sorting the participants selected through random sampling. Another difference between random sampling and random assignment is that the former is used in several types of studies, while the latter is only applied in between-subject experimental designs.

Your study researches the impact of technology on productivity in a specific company.

In such a case, you have contact with the entire staff. So, you can assign each employee a quantity and apply a random number generator to pick a specific sample.

For instance, from 500 employees, you can pick 200. So, the full sample is 200.

Random sampling enhances external validity, as it guarantees that the study sample is unbiased, and that an entire population is represented. This way, you can conclude that the results of your studies can be accredited to the autonomous variable.

After determining the full sample, you can break it down into two groups using random assignment. In this case, the groups are:

The control group (does get access to technology)
The experimental group (gets access to technology)

Using random assignment assures you that any differences in the productivity results for each group are not biased and will help the company make a decision.

How to use random assignment

Firstly, give each participant a unique number as an identifier. Then, use a specific tool to simplify assigning the participants to the sample groups. Some tools you can use are:

Random member assignment is a prevailing technique for placing participants in specific groups because each person has a fair opportunity of being put in either group.

Random assignment in block experimental designs

In complex experimental designs , you must group your participants into blocks before using the random assignment technique.

You can create participant blocks depending on demographic variables, working hours, or scores. However, the blocks imply that you will require a bigger sample to attain high statistical power.

After grouping the participants in blocks, you can use random assignments inside each block to allocate the members to a specific treatment condition. Doing this will help you examine if quality impacts the result of the treatment.

Depending on their unique characteristics, you can also use blocking in experimental matched designs before matching the participants in each block. Then, you can randomly allot each partaker to one of the treatments in the research and examine the results.

When random assignment is not used

As powerful a tool as it is, random assignment does not apply in all situations. Like the following:

Comparing different groups

When the purpose of your study is to assess the differences between the participants, random member assignment may not work.

If you want to compare teens and the elderly with and without specific health conditions, you must ensure that the participants have specific characteristics. Therefore, you cannot pick them randomly.

In such a study, the medical condition (quality of interest) is the independent variable, and the participants are grouped based on their ages (different levels). Also, all partakers are tried similarly to ensure they have the medical condition, and their outcomes are tested per group level.

No ethical justifiability

Another situation where you cannot use random assignment is if it is ethically not permitted.

If your study involves unhealthy or dangerous behaviors or subjects, such as drug use. Instead of assigning random partakers to sets, you can conduct quasi-experimental research.

When using a quasi-experimental design , you examine the conclusions of pre-existing groups you have no control over, such as existing drug users. While you cannot randomly assign them to groups, you can use variables like their age, years of drug use, or socioeconomic status to group the participants.

What is the definition of random assignment?

It is an experimental research technique that involves randomly placing participants from your samples into different groups. It ensures that every sample member has the same opportunity of being in whichever group (control or experimental group).

When is random assignment applicable?

You can use this placement technique in experiments featuring an independent measures design. It helps ensure that all your sample groups are comparable.

What is the importance of random assignment?

It can help you enhance your study’s validity . This technique also helps ensure that every sample has an equal opportunity of being assigned to a control or trial group.

When should you NOT use random assignment

You should not use this technique if your study focuses on group comparisons or if it is not legally ethical.

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Statistical Thinking: A Simulation Approach to Modeling Uncertainty (UM STAT 216 edition)

3.6 causation and random assignment.

Medical researchers may be interested in showing that a drug helps improve people’s health (the cause of improvement is the drug), while educational researchers may be interested in showing a curricular innovation improves students’ learning (the curricular innovation causes improved learning).

To attribute a causal relationship, there are three criteria a researcher needs to establish:

Association of the Cause and Effect: There needs to be a association between the cause and effect.
Timing: The cause needs to happen BEFORE the effect.
No Plausible Alternative Explanations: ALL other possible explanations for the effect need to be ruled out.

Please read more about each of these criteria at the Web Center for Social Research Methods .

The third criterion can be quite difficult to meet. To rule out ALL other possible explanations for the effect, we want to compare the world with the cause applied to the world without the cause. In practice, we do this by comparing two different groups: a “treatment” group that gets the cause applied to them, and a “control” group that does not. To rule out alternative explanations, the groups need to be “identical” with respect to every possible characteristic (aside from the treatment) that could explain differences. This way the only characteristic that will be different is that the treatment group gets the treatment and the control group doesn’t. If there are differences in the outcome, then it must be attributable to the treatment, because the other possible explanations are ruled out.

So, the key is to make the control and treatment groups “identical” when you are forming them. One thing that makes this task (slightly) easier is that they don’t have to be exactly identical, only probabilistically equivalent . This means, for example, that if you were matching groups on age that you don’t need the two groups to have identical age distributions; they would only need to have roughly the same AVERAGE age. Here roughly means “the average ages should be the same within what we expect because of sampling error.”

Now we just need to create the groups so that they have, on average, the same characteristics … for EVERY POSSIBLE CHARCTERISTIC that could explain differences in the outcome.

It turns out that creating probabilistically equivalent groups is a really difficult problem. One method that works pretty well for doing this is to randomly assign participants to the groups. This works best when you have large sample sizes, but even with small sample sizes random assignment has the advantage of at least removing the systematic bias between the two groups (any differences are due to chance and will probably even out between the groups). As Wikipedia’s page on random assignment points out,

Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment. … Random assignment does not guarantee that the groups are matched or equivalent. The groups may still differ on some preexisting attribute due to chance. The use of random assignment cannot eliminate this possibility, but it greatly reduces it.

We use the term internal validity to describe the degree to which cause-and-effect inferences are accurate and meaningful. Causal attribution is the goal for many researchers. Thus, by using random assignment we have a pretty high degree of evidence for internal validity; we have a much higher belief in causal inferences. Much like evidence used in a court of law, it is useful to think about validity evidence on a continuum. For example, a visualization of the internal validity evidence for a study that employed random assignment in the design might be:

The degree of internal validity evidence is high (in the upper-third). How high depends on other factors such as sample size.

To learn more about random assignment, you can read the following:

The research report, Random Assignment Evaluation Studies: A Guide for Out-of-School Time Program Practitioners

3.6.1 Example: Does sleep deprivation cause an decrease in performance?

Let’s consider the criteria with respect to the sleep deprivation study we explored in class.

3.6.1.1 Association of cause and effect

First, we ask, Is there an association between the cause and the effect? In the sleep deprivation study, we would ask, “Is sleep deprivation associated with an decrease in performance?”

This is what a hypothesis test helps us answer! If the result is statistically significant , then we have an association between the cause and the effect. If the result is not statistically significant, then there is not sufficient evidence for an association between cause and effect.

In the case of the sleep deprivation experiment, the result was statistically significant, so we can say that sleep deprivation is associated with a decrease in performance.

3.6.1.2 Timing

Second, we ask, Did the cause come before the effect? In the sleep deprivation study, the answer is yes. The participants were sleep deprived before their performance was tested. It may seem like this is a silly question to ask, but as the link above describes, it is not always so clear to establish the timing. Thus, it is important to consider this question any time we are interested in establishing causality.

3.6.1.3 No plausible alternative explanations

Finally, we ask Are there any plausible alternative explanations for the observed effect? In the sleep deprivation study, we would ask, “Are there plausible alternative explanations for the observed difference between the groups, other than sleep deprivation?” Because this is a question about plausibility, human judgment comes into play. Researchers must make an argument about why there are no plausible alternatives. As described above, a strong study design can help to strengthen the argument.

At first, it may seem like there are a lot of plausible alternative explanations for the difference in performance. There are a lot of things that might affect someone’s performance on a visual task! Sleep deprivation is just one of them! For example, artists may be more adept at visual discrimination than other people. This is an example of a potential confounding variable. A confounding variable is a variable that might affect the results, other than the causal variable that we are interested in.

Here’s the thing though. We are not interested in figuring out why any particular person got the score that they did. Instead, we are interested in determining why one group was different from another group. In the sleep deprivation study, the participants were randomly assigned. This means that the there is no systematic difference between the groups, with respect to any confounding variables. Yes—artistic experience is a possible confounding variable, and it may be the reason why two people score differently. BUT: There is no systematic difference between the groups with respect to artistic experience, and so artistic experience is not a plausible explanation as to why the groups would be different. The same can be said for any possible confounding variable. Because the groups were randomly assigned, it is not plausible to say that the groups are different with respect to any confounding variable. Random assignment helps us rule out plausible alternatives.

3.6.1.4 Making a causal claim

Now, let’s see about make a causal claim for the sleep deprivation study:

Association: There is a statistically significant result, so the cause is associated with the effect
Timing: The participants were sleep deprived before their performance was measured, so the cause came before the effect
Plausible alternative explanations: The participants were randomly assigned, so the groups are not systematically different on any confounding variable. The only systematic difference between the groups was sleep deprivation. Thus, there are no plausible alternative explanations for the difference between the groups, other than sleep deprivation

Thus, the internal validity evidence for this study is high, and we can make a causal claim. For the participants in this study, we can say that sleep deprivation caused a decrease in performance.

Key points: Causation and internal validity

To make a cause-and-effect inference, you need to consider three criteria:

Association of the Cause and Effect: There needs to be a association between the cause and effect. This can be established by a hypothesis test.

Random assignment removes any systematic differences between the groups (other than the treatment), and thus helps to rule out plausible alternative explanations.

Internal validity describes the degree to which cause-and-effect inferences are accurate and meaningful.

Confounding variables are variables that might affect the results, other than the causal variable that we are interested in.

Probabilistic equivalence means that there is not a systematic difference between groups. The groups are the same on average.

How can we make "equivalent" experimental groups?

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6.2 Experimental Design

Learning objectives.

Explain the difference between between-subjects and within-subjects experiments, list some of the pros and cons of each approach, and decide which approach to use to answer a particular research question.
Define random assignment, distinguish it from random sampling, explain its purpose in experimental research, and use some simple strategies to implement it.
Define what a control condition is, explain its purpose in research on treatment effectiveness, and describe some alternative types of control conditions.
Define several types of carryover effect, give examples of each, and explain how counterbalancing helps to deal with them.

In this section, we look at some different ways to design an experiment. The primary distinction we will make is between approaches in which each participant experiences one level of the independent variable and approaches in which each participant experiences all levels of the independent variable. The former are called between-subjects experiments and the latter are called within-subjects experiments.

Between-Subjects Experiments

In a between-subjects experiment , each participant is tested in only one condition. For example, a researcher with a sample of 100 college students might assign half of them to write about a traumatic event and the other half write about a neutral event. Or a researcher with a sample of 60 people with severe agoraphobia (fear of open spaces) might assign 20 of them to receive each of three different treatments for that disorder. It is essential in a between-subjects experiment that the researcher assign participants to conditions so that the different groups are, on average, highly similar to each other. Those in a trauma condition and a neutral condition, for example, should include a similar proportion of men and women, and they should have similar average intelligence quotients (IQs), similar average levels of motivation, similar average numbers of health problems, and so on. This is a matter of controlling these extraneous participant variables across conditions so that they do not become confounding variables.

Random Assignment

The primary way that researchers accomplish this kind of control of extraneous variables across conditions is called random assignment , which means using a random process to decide which participants are tested in which conditions. Do not confuse random assignment with random sampling. Random sampling is a method for selecting a sample from a population, and it is rarely used in psychological research. Random assignment is a method for assigning participants in a sample to the different conditions, and it is an important element of all experimental research in psychology and other fields too.

In its strictest sense, random assignment should meet two criteria. One is that each participant has an equal chance of being assigned to each condition (e.g., a 50% chance of being assigned to each of two conditions). The second is that each participant is assigned to a condition independently of other participants. Thus one way to assign participants to two conditions would be to flip a coin for each one. If the coin lands heads, the participant is assigned to Condition A, and if it lands tails, the participant is assigned to Condition B. For three conditions, one could use a computer to generate a random integer from 1 to 3 for each participant. If the integer is 1, the participant is assigned to Condition A; if it is 2, the participant is assigned to Condition B; and if it is 3, the participant is assigned to Condition C. In practice, a full sequence of conditions—one for each participant expected to be in the experiment—is usually created ahead of time, and each new participant is assigned to the next condition in the sequence as he or she is tested. When the procedure is computerized, the computer program often handles the random assignment.

One problem with coin flipping and other strict procedures for random assignment is that they are likely to result in unequal sample sizes in the different conditions. Unequal sample sizes are generally not a serious problem, and you should never throw away data you have already collected to achieve equal sample sizes. However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups. It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible. One approach is block randomization . In block randomization, all the conditions occur once in the sequence before any of them is repeated. Then they all occur again before any of them is repeated again. Within each of these “blocks,” the conditions occur in a random order. Again, the sequence of conditions is usually generated before any participants are tested, and each new participant is assigned to the next condition in the sequence. Table 6.2 “Block Randomization Sequence for Assigning Nine Participants to Three Conditions” shows such a sequence for assigning nine participants to three conditions. The Research Randomizer website ( http://www.randomizer.org ) will generate block randomization sequences for any number of participants and conditions. Again, when the procedure is computerized, the computer program often handles the block randomization.

Table 6.2 Block Randomization Sequence for Assigning Nine Participants to Three Conditions

Random assignment is not guaranteed to control all extraneous variables across conditions. It is always possible that just by chance, the participants in one condition might turn out to be substantially older, less tired, more motivated, or less depressed on average than the participants in another condition. However, there are some reasons that this is not a major concern. One is that random assignment works better than one might expect, especially for large samples. Another is that the inferential statistics that researchers use to decide whether a difference between groups reflects a difference in the population takes the “fallibility” of random assignment into account. Yet another reason is that even if random assignment does result in a confounding variable and therefore produces misleading results, this is likely to be detected when the experiment is replicated. The upshot is that random assignment to conditions—although not infallible in terms of controlling extraneous variables—is always considered a strength of a research design.

Treatment and Control Conditions

Between-subjects experiments are often used to determine whether a treatment works. In psychological research, a treatment is any intervention meant to change people’s behavior for the better. This includes psychotherapies and medical treatments for psychological disorders but also interventions designed to improve learning, promote conservation, reduce prejudice, and so on. To determine whether a treatment works, participants are randomly assigned to either a treatment condition , in which they receive the treatment, or a control condition , in which they do not receive the treatment. If participants in the treatment condition end up better off than participants in the control condition—for example, they are less depressed, learn faster, conserve more, express less prejudice—then the researcher can conclude that the treatment works. In research on the effectiveness of psychotherapies and medical treatments, this type of experiment is often called a randomized clinical trial .

There are different types of control conditions. In a no-treatment control condition , participants receive no treatment whatsoever. One problem with this approach, however, is the existence of placebo effects. A placebo is a simulated treatment that lacks any active ingredient or element that should make it effective, and a placebo effect is a positive effect of such a treatment. Many folk remedies that seem to work—such as eating chicken soup for a cold or placing soap under the bedsheets to stop nighttime leg cramps—are probably nothing more than placebos. Although placebo effects are not well understood, they are probably driven primarily by people’s expectations that they will improve. Having the expectation to improve can result in reduced stress, anxiety, and depression, which can alter perceptions and even improve immune system functioning (Price, Finniss, & Benedetti, 2008).

Placebo effects are interesting in their own right (see Note 6.28 “The Powerful Placebo” ), but they also pose a serious problem for researchers who want to determine whether a treatment works. Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” shows some hypothetical results in which participants in a treatment condition improved more on average than participants in a no-treatment control condition. If these conditions (the two leftmost bars in Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” ) were the only conditions in this experiment, however, one could not conclude that the treatment worked. It could be instead that participants in the treatment group improved more because they expected to improve, while those in the no-treatment control condition did not.

Figure 6.2 Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions

Fortunately, there are several solutions to this problem. One is to include a placebo control condition , in which participants receive a placebo that looks much like the treatment but lacks the active ingredient or element thought to be responsible for the treatment’s effectiveness. When participants in a treatment condition take a pill, for example, then those in a placebo control condition would take an identical-looking pill that lacks the active ingredient in the treatment (a “sugar pill”). In research on psychotherapy effectiveness, the placebo might involve going to a psychotherapist and talking in an unstructured way about one’s problems. The idea is that if participants in both the treatment and the placebo control groups expect to improve, then any improvement in the treatment group over and above that in the placebo control group must have been caused by the treatment and not by participants’ expectations. This is what is shown by a comparison of the two outer bars in Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” .

Of course, the principle of informed consent requires that participants be told that they will be assigned to either a treatment or a placebo control condition—even though they cannot be told which until the experiment ends. In many cases the participants who had been in the control condition are then offered an opportunity to have the real treatment. An alternative approach is to use a waitlist control condition , in which participants are told that they will receive the treatment but must wait until the participants in the treatment condition have already received it. This allows researchers to compare participants who have received the treatment with participants who are not currently receiving it but who still expect to improve (eventually). A final solution to the problem of placebo effects is to leave out the control condition completely and compare any new treatment with the best available alternative treatment. For example, a new treatment for simple phobia could be compared with standard exposure therapy. Because participants in both conditions receive a treatment, their expectations about improvement should be similar. This approach also makes sense because once there is an effective treatment, the interesting question about a new treatment is not simply “Does it work?” but “Does it work better than what is already available?”

The Powerful Placebo

Many people are not surprised that placebos can have a positive effect on disorders that seem fundamentally psychological, including depression, anxiety, and insomnia. However, placebos can also have a positive effect on disorders that most people think of as fundamentally physiological. These include asthma, ulcers, and warts (Shapiro & Shapiro, 1999). There is even evidence that placebo surgery—also called “sham surgery”—can be as effective as actual surgery.

Medical researcher J. Bruce Moseley and his colleagues conducted a study on the effectiveness of two arthroscopic surgery procedures for osteoarthritis of the knee (Moseley et al., 2002). The control participants in this study were prepped for surgery, received a tranquilizer, and even received three small incisions in their knees. But they did not receive the actual arthroscopic surgical procedure. The surprising result was that all participants improved in terms of both knee pain and function, and the sham surgery group improved just as much as the treatment groups. According to the researchers, “This study provides strong evidence that arthroscopic lavage with or without débridement [the surgical procedures used] is not better than and appears to be equivalent to a placebo procedure in improving knee pain and self-reported function” (p. 85).

Research has shown that patients with osteoarthritis of the knee who receive a “sham surgery” experience reductions in pain and improvement in knee function similar to those of patients who receive a real surgery.

Army Medicine – Surgery – CC BY 2.0.

Within-Subjects Experiments

In a within-subjects experiment , each participant is tested under all conditions. Consider an experiment on the effect of a defendant’s physical attractiveness on judgments of his guilt. Again, in a between-subjects experiment, one group of participants would be shown an attractive defendant and asked to judge his guilt, and another group of participants would be shown an unattractive defendant and asked to judge his guilt. In a within-subjects experiment, however, the same group of participants would judge the guilt of both an attractive and an unattractive defendant.

The primary advantage of this approach is that it provides maximum control of extraneous participant variables. Participants in all conditions have the same mean IQ, same socioeconomic status, same number of siblings, and so on—because they are the very same people. Within-subjects experiments also make it possible to use statistical procedures that remove the effect of these extraneous participant variables on the dependent variable and therefore make the data less “noisy” and the effect of the independent variable easier to detect. We will look more closely at this idea later in the book.

Carryover Effects and Counterbalancing

The primary disadvantage of within-subjects designs is that they can result in carryover effects. A carryover effect is an effect of being tested in one condition on participants’ behavior in later conditions. One type of carryover effect is a practice effect , where participants perform a task better in later conditions because they have had a chance to practice it. Another type is a fatigue effect , where participants perform a task worse in later conditions because they become tired or bored. Being tested in one condition can also change how participants perceive stimuli or interpret their task in later conditions. This is called a context effect . For example, an average-looking defendant might be judged more harshly when participants have just judged an attractive defendant than when they have just judged an unattractive defendant. Within-subjects experiments also make it easier for participants to guess the hypothesis. For example, a participant who is asked to judge the guilt of an attractive defendant and then is asked to judge the guilt of an unattractive defendant is likely to guess that the hypothesis is that defendant attractiveness affects judgments of guilt. This could lead the participant to judge the unattractive defendant more harshly because he thinks this is what he is expected to do. Or it could make participants judge the two defendants similarly in an effort to be “fair.”

Carryover effects can be interesting in their own right. (Does the attractiveness of one person depend on the attractiveness of other people that we have seen recently?) But when they are not the focus of the research, carryover effects can be problematic. Imagine, for example, that participants judge the guilt of an attractive defendant and then judge the guilt of an unattractive defendant. If they judge the unattractive defendant more harshly, this might be because of his unattractiveness. But it could be instead that they judge him more harshly because they are becoming bored or tired. In other words, the order of the conditions is a confounding variable. The attractive condition is always the first condition and the unattractive condition the second. Thus any difference between the conditions in terms of the dependent variable could be caused by the order of the conditions and not the independent variable itself.

There is a solution to the problem of order effects, however, that can be used in many situations. It is counterbalancing , which means testing different participants in different orders. For example, some participants would be tested in the attractive defendant condition followed by the unattractive defendant condition, and others would be tested in the unattractive condition followed by the attractive condition. With three conditions, there would be six different orders (ABC, ACB, BAC, BCA, CAB, and CBA), so some participants would be tested in each of the six orders. With counterbalancing, participants are assigned to orders randomly, using the techniques we have already discussed. Thus random assignment plays an important role in within-subjects designs just as in between-subjects designs. Here, instead of randomly assigning to conditions, they are randomly assigned to different orders of conditions. In fact, it can safely be said that if a study does not involve random assignment in one form or another, it is not an experiment.

There are two ways to think about what counterbalancing accomplishes. One is that it controls the order of conditions so that it is no longer a confounding variable. Instead of the attractive condition always being first and the unattractive condition always being second, the attractive condition comes first for some participants and second for others. Likewise, the unattractive condition comes first for some participants and second for others. Thus any overall difference in the dependent variable between the two conditions cannot have been caused by the order of conditions. A second way to think about what counterbalancing accomplishes is that if there are carryover effects, it makes it possible to detect them. One can analyze the data separately for each order to see whether it had an effect.

When 9 Is “Larger” Than 221

Researcher Michael Birnbaum has argued that the lack of context provided by between-subjects designs is often a bigger problem than the context effects created by within-subjects designs. To demonstrate this, he asked one group of participants to rate how large the number 9 was on a 1-to-10 rating scale and another group to rate how large the number 221 was on the same 1-to-10 rating scale (Birnbaum, 1999). Participants in this between-subjects design gave the number 9 a mean rating of 5.13 and the number 221 a mean rating of 3.10. In other words, they rated 9 as larger than 221! According to Birnbaum, this is because participants spontaneously compared 9 with other one-digit numbers (in which case it is relatively large) and compared 221 with other three-digit numbers (in which case it is relatively small).

Simultaneous Within-Subjects Designs

So far, we have discussed an approach to within-subjects designs in which participants are tested in one condition at a time. There is another approach, however, that is often used when participants make multiple responses in each condition. Imagine, for example, that participants judge the guilt of 10 attractive defendants and 10 unattractive defendants. Instead of having people make judgments about all 10 defendants of one type followed by all 10 defendants of the other type, the researcher could present all 20 defendants in a sequence that mixed the two types. The researcher could then compute each participant’s mean rating for each type of defendant. Or imagine an experiment designed to see whether people with social anxiety disorder remember negative adjectives (e.g., “stupid,” “incompetent”) better than positive ones (e.g., “happy,” “productive”). The researcher could have participants study a single list that includes both kinds of words and then have them try to recall as many words as possible. The researcher could then count the number of each type of word that was recalled. There are many ways to determine the order in which the stimuli are presented, but one common way is to generate a different random order for each participant.

Between-Subjects or Within-Subjects?

Almost every experiment can be conducted using either a between-subjects design or a within-subjects design. This means that researchers must choose between the two approaches based on their relative merits for the particular situation.

Between-subjects experiments have the advantage of being conceptually simpler and requiring less testing time per participant. They also avoid carryover effects without the need for counterbalancing. Within-subjects experiments have the advantage of controlling extraneous participant variables, which generally reduces noise in the data and makes it easier to detect a relationship between the independent and dependent variables.

A good rule of thumb, then, is that if it is possible to conduct a within-subjects experiment (with proper counterbalancing) in the time that is available per participant—and you have no serious concerns about carryover effects—this is probably the best option. If a within-subjects design would be difficult or impossible to carry out, then you should consider a between-subjects design instead. For example, if you were testing participants in a doctor’s waiting room or shoppers in line at a grocery store, you might not have enough time to test each participant in all conditions and therefore would opt for a between-subjects design. Or imagine you were trying to reduce people’s level of prejudice by having them interact with someone of another race. A within-subjects design with counterbalancing would require testing some participants in the treatment condition first and then in a control condition. But if the treatment works and reduces people’s level of prejudice, then they would no longer be suitable for testing in the control condition. This is true for many designs that involve a treatment meant to produce long-term change in participants’ behavior (e.g., studies testing the effectiveness of psychotherapy). Clearly, a between-subjects design would be necessary here.

Remember also that using one type of design does not preclude using the other type in a different study. There is no reason that a researcher could not use both a between-subjects design and a within-subjects design to answer the same research question. In fact, professional researchers often do exactly this.

Key Takeaways

Experiments can be conducted using either between-subjects or within-subjects designs. Deciding which to use in a particular situation requires careful consideration of the pros and cons of each approach.
Random assignment to conditions in between-subjects experiments or to orders of conditions in within-subjects experiments is a fundamental element of experimental research. Its purpose is to control extraneous variables so that they do not become confounding variables.
Experimental research on the effectiveness of a treatment requires both a treatment condition and a control condition, which can be a no-treatment control condition, a placebo control condition, or a waitlist control condition. Experimental treatments can also be compared with the best available alternative.

Discussion: For each of the following topics, list the pros and cons of a between-subjects and within-subjects design and decide which would be better.

You want to test the relative effectiveness of two training programs for running a marathon.
Using photographs of people as stimuli, you want to see if smiling people are perceived as more intelligent than people who are not smiling.
In a field experiment, you want to see if the way a panhandler is dressed (neatly vs. sloppily) affects whether or not passersby give him any money.
You want to see if concrete nouns (e.g., dog ) are recalled better than abstract nouns (e.g., truth ).
Discussion: Imagine that an experiment shows that participants who receive psychodynamic therapy for a dog phobia improve more than participants in a no-treatment control group. Explain a fundamental problem with this research design and at least two ways that it might be corrected.

Birnbaum, M. H. (1999). How to show that 9 > 221: Collect judgments in a between-subjects design. Psychological Methods, 4 , 243–249.

Moseley, J. B., O’Malley, K., Petersen, N. J., Menke, T. J., Brody, B. A., Kuykendall, D. H., … Wray, N. P. (2002). A controlled trial of arthroscopic surgery for osteoarthritis of the knee. The New England Journal of Medicine, 347 , 81–88.

Price, D. D., Finniss, D. G., & Benedetti, F. (2008). A comprehensive review of the placebo effect: Recent advances and current thought. Annual Review of Psychology, 59 , 565–590.

Shapiro, A. K., & Shapiro, E. (1999). The powerful placebo: From ancient priest to modern physician . Baltimore, MD: Johns Hopkins University Press.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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The Definition of Random Assignment According to Psychology

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

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

Materio / Getty Images

Random assignment refers to the use of chance procedures in psychology experiments to ensure that each participant has the same opportunity to be assigned to any given group in a study to eliminate any potential bias in the experiment at the outset. Participants are randomly assigned to different groups, such as the treatment group versus the control group. In clinical research, randomized clinical trials are known as the gold standard for meaningful results.

Simple random assignment techniques might involve tactics such as flipping a coin, drawing names out of a hat, rolling dice, or assigning random numbers to a list of participants. It is important to note that random assignment differs from random selection .

While random selection refers to how participants are randomly chosen from a target population as representatives of that population, random assignment refers to how those chosen participants are then assigned to experimental groups.

Random Assignment In Research

To determine if changes in one variable will cause changes in another variable, psychologists must perform an experiment. Random assignment is a critical part of the experimental design that helps ensure the reliability of the study outcomes.

Researchers often begin by forming a testable hypothesis predicting that one variable of interest will have some predictable impact on another variable.

The variable that the experimenters will manipulate in the experiment is known as the independent variable , while the variable that they will then measure for different outcomes is known as the dependent variable. While there are different ways to look at relationships between variables, an experiment is the best way to get a clear idea if there is a cause-and-effect relationship between two or more variables.

Once researchers have formulated a hypothesis, conducted background research, and chosen an experimental design, it is time to find participants for their experiment. How exactly do researchers decide who will be part of an experiment? As mentioned previously, this is often accomplished through something known as random selection.

Random Selection

In order to generalize the results of an experiment to a larger group, it is important to choose a sample that is representative of the qualities found in that population. For example, if the total population is 60% female and 40% male, then the sample should reflect those same percentages.

Choosing a representative sample is often accomplished by randomly picking people from the population to be participants in a study. Random selection means that everyone in the group stands an equal chance of being chosen to minimize any bias. Once a pool of participants has been selected, it is time to assign them to groups.

By randomly assigning the participants into groups, the experimenters can be fairly sure that each group will have the same characteristics before the independent variable is applied.

Participants might be randomly assigned to the control group , which does not receive the treatment in question. The control group may receive a placebo or receive the standard treatment. Participants may also be randomly assigned to the experimental group , which receives the treatment of interest. In larger studies, there can be multiple treatment groups for comparison.

There are simple methods of random assignment, like rolling the die. However, there are more complex techniques that involve random number generators to remove any human error.

There can also be random assignment to groups with pre-established rules or parameters. For example, if you want to have an equal number of men and women in each of your study groups, you might separate your sample into two groups (by sex) before randomly assigning each of those groups into the treatment group and control group.

Random assignment is essential because it increases the likelihood that the groups are the same at the outset. With all characteristics being equal between groups, other than the application of the independent variable, any differences found between group outcomes can be more confidently attributed to the effect of the intervention.

Example of Random Assignment

Imagine that a researcher is interested in learning whether or not drinking caffeinated beverages prior to an exam will improve test performance. After randomly selecting a pool of participants, each person is randomly assigned to either the control group or the experimental group.

The participants in the control group consume a placebo drink prior to the exam that does not contain any caffeine. Those in the experimental group, on the other hand, consume a caffeinated beverage before taking the test.

Participants in both groups then take the test, and the researcher compares the results to determine if the caffeinated beverage had any impact on test performance.

A Word From Verywell

Random assignment plays an important role in the psychology research process. Not only does this process help eliminate possible sources of bias, but it also makes it easier to generalize the results of a tested sample of participants to a larger population.

Random assignment helps ensure that members of each group in the experiment are the same, which means that the groups are also likely more representative of what is present in the larger population of interest. Through the use of this technique, psychology researchers are able to study complex phenomena and contribute to our understanding of the human mind and behavior.

Lin Y, Zhu M, Su Z. The pursuit of balance: An overview of covariate-adaptive randomization techniques in clinical trials . Contemp Clin Trials. 2015;45(Pt A):21-25. doi:10.1016/j.cct.2015.07.011

Sullivan L. Random assignment versus random selection . In: The SAGE Glossary of the Social and Behavioral Sciences. SAGE Publications, Inc.; 2009. doi:10.4135/9781412972024.n2108

Alferes VR. Methods of Randomization in Experimental Design . SAGE Publications, Inc.; 2012. doi:10.4135/9781452270012

Nestor PG, Schutt RK. Research Methods in Psychology: Investigating Human Behavior. (2nd Ed.). SAGE Publications, Inc.; 2015.

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

Random Assignment in Psychology (Definition + 40 Examples)

Have you ever wondered how researchers discover new ways to help people learn, make decisions, or overcome challenges? A hidden hero in this adventure of discovery is a method called random assignment, a cornerstone in psychological research that helps scientists uncover the truths about the human mind and behavior.

Random Assignment is a process used in research where each participant has an equal chance of being placed in any group within the study. This technique is essential in experiments as it helps to eliminate biases, ensuring that the different groups being compared are similar in all important aspects.

By doing so, researchers can be confident that any differences observed are likely due to the variable being tested, rather than other factors.

In this article, we’ll explore the intriguing world of random assignment, diving into its history, principles, real-world examples, and the impact it has had on the field of psychology.

History of Random Assignment

Stepping back in time, we delve into the origins of random assignment, which finds its roots in the early 20th century.

The pioneering mind behind this innovative technique was Sir Ronald A. Fisher , a British statistician and biologist. Fisher introduced the concept of random assignment in the 1920s, aiming to improve the quality and reliability of experimental research .

His contributions laid the groundwork for the method's evolution and its widespread adoption in various fields, particularly in psychology.

Fisher’s groundbreaking work on random assignment was motivated by his desire to control for confounding variables – those pesky factors that could muddy the waters of research findings.

By assigning participants to different groups purely by chance, he realized that the influence of these confounding variables could be minimized, paving the way for more accurate and trustworthy results.

Early Studies Utilizing Random Assignment

Following Fisher's initial development, random assignment started to gain traction in the research community. Early studies adopting this methodology focused on a variety of topics, from agriculture (which was Fisher’s primary field of interest) to medicine and psychology.

The approach allowed researchers to draw stronger conclusions from their experiments, bolstering the development of new theories and practices.

One notable early study utilizing random assignment was conducted in the field of educational psychology. Researchers were keen to understand the impact of different teaching methods on student outcomes.

By randomly assigning students to various instructional approaches, they were able to isolate the effects of the teaching methods, leading to valuable insights and recommendations for educators.

Evolution of the Methodology

As the decades rolled on, random assignment continued to evolve and adapt to the changing landscape of research.

Advances in technology introduced new tools and techniques for implementing randomization, such as computerized random number generators, which offered greater precision and ease of use.

The application of random assignment expanded beyond the confines of the laboratory, finding its way into field studies and large-scale surveys.

Researchers across diverse disciplines embraced the methodology, recognizing its potential to enhance the validity of their findings and contribute to the advancement of knowledge.

From its humble beginnings in the early 20th century to its widespread use today, random assignment has proven to be a cornerstone of scientific inquiry.

Its development and evolution have played a pivotal role in shaping the landscape of psychological research, driving discoveries that have improved lives and deepened our understanding of the human experience.

Principles of Random Assignment

Delving into the heart of random assignment, we uncover the theories and principles that form its foundation.

The method is steeped in the basics of probability theory and statistical inference, ensuring that each participant has an equal chance of being placed in any group, thus fostering fair and unbiased results.

Basic Principles of Random Assignment

Understanding the core principles of random assignment is key to grasping its significance in research. There are three principles: equal probability of selection, reduction of bias, and ensuring representativeness.

The first principle, equal probability of selection , ensures that every participant has an identical chance of being assigned to any group in the study. This randomness is crucial as it mitigates the risk of bias and establishes a level playing field.

The second principle focuses on the reduction of bias . Random assignment acts as a safeguard, ensuring that the groups being compared are alike in all essential aspects before the experiment begins.

This similarity between groups allows researchers to attribute any differences observed in the outcomes directly to the independent variable being studied.

Lastly, ensuring representativeness is a vital principle. When participants are assigned randomly, the resulting groups are more likely to be representative of the larger population.

This characteristic is crucial for the generalizability of the study’s findings, allowing researchers to apply their insights broadly.

Theoretical Foundation

The theoretical foundation of random assignment lies in probability theory and statistical inference .

Probability theory deals with the likelihood of different outcomes, providing a mathematical framework for analyzing random phenomena. In the context of random assignment, it helps in ensuring that each participant has an equal chance of being placed in any group.

Statistical inference, on the other hand, allows researchers to draw conclusions about a population based on a sample of data drawn from that population. It is the mechanism through which the results of a study can be generalized to a broader context.

Random assignment enhances the reliability of statistical inferences by reducing biases and ensuring that the sample is representative.

Differentiating Random Assignment from Random Selection

It’s essential to distinguish between random assignment and random selection, as the two terms, while related, have distinct meanings in the realm of research.

Random assignment refers to how participants are placed into different groups in an experiment, aiming to control for confounding variables and help determine causes.

In contrast, random selection pertains to how individuals are chosen to participate in a study. This method is used to ensure that the sample of participants is representative of the larger population, which is vital for the external validity of the research.

While both methods are rooted in randomness and probability, they serve different purposes in the research process.

Understanding the theories, principles, and distinctions of random assignment illuminates its pivotal role in psychological research.

This method, anchored in probability theory and statistical inference, serves as a beacon of reliability, guiding researchers in their quest for knowledge and ensuring that their findings stand the test of validity and applicability.

Methodology of Random Assignment

Implementing random assignment in a study is a meticulous process that involves several crucial steps.

The initial step is participant selection, where individuals are chosen to partake in the study. This stage is critical to ensure that the pool of participants is diverse and representative of the population the study aims to generalize to.

Once the pool of participants has been established, the actual assignment process begins. In this step, each participant is allocated randomly to one of the groups in the study.

Researchers use various tools, such as random number generators or computerized methods, to ensure that this assignment is genuinely random and free from biases.

Monitoring and adjusting form the final step in the implementation of random assignment. Researchers need to continuously observe the groups to ensure that they remain comparable in all essential aspects throughout the study.

If any significant discrepancies arise, adjustments might be necessary to maintain the study’s integrity and validity.

Tools and Techniques Used

The evolution of technology has introduced a variety of tools and techniques to facilitate random assignment.

Random number generators, both manual and computerized, are commonly used to assign participants to different groups. These generators ensure that each individual has an equal chance of being placed in any group, upholding the principle of equal probability of selection.

In addition to random number generators, researchers often use specialized computer software designed for statistical analysis and experimental design.

These software programs offer advanced features that allow for precise and efficient random assignment, minimizing the risk of human error and enhancing the study’s reliability.

Ethical Considerations

The implementation of random assignment is not devoid of ethical considerations. Informed consent is a fundamental ethical principle that researchers must uphold.

Informed consent means that every participant should be fully informed about the nature of the study, the procedures involved, and any potential risks or benefits, ensuring that they voluntarily agree to participate.

Beyond informed consent, researchers must conduct a thorough risk and benefit analysis. The potential benefits of the study should outweigh any risks or harms to the participants.

Safeguarding the well-being of participants is paramount, and any study employing random assignment must adhere to established ethical guidelines and standards.

Conclusion of Methodology

The methodology of random assignment, while seemingly straightforward, is a multifaceted process that demands precision, fairness, and ethical integrity. From participant selection to assignment and monitoring, each step is crucial to ensure the validity of the study’s findings.

The tools and techniques employed, coupled with a steadfast commitment to ethical principles, underscore the significance of random assignment as a cornerstone of robust psychological research.

Benefits of Random Assignment in Psychological Research

The impact and importance of random assignment in psychological research cannot be overstated. It is fundamental for ensuring the study is accurate, allowing the researchers to determine if their study actually caused the results they saw, and making sure the findings can be applied to the real world.

Facilitating Causal Inferences

When participants are randomly assigned to different groups, researchers can be more confident that the observed effects are due to the independent variable being changed, and not other factors.

This ability to determine the cause is called causal inference .

This confidence allows for the drawing of causal relationships, which are foundational for theory development and application in psychology.

Ensuring Internal Validity

One of the foremost impacts of random assignment is its ability to enhance the internal validity of an experiment.

Internal validity refers to the extent to which a researcher can assert that changes in the dependent variable are solely due to manipulations of the independent variable , and not due to confounding variables.

By ensuring that each participant has an equal chance of being in any condition of the experiment, random assignment helps control for participant characteristics that could otherwise complicate the results.

Enhancing Generalizability

Beyond internal validity, random assignment also plays a crucial role in enhancing the generalizability of research findings.

When done correctly, it ensures that the sample groups are representative of the larger population, so can allow researchers to apply their findings more broadly.

This representative nature is essential for the practical application of research, impacting policy, interventions, and psychological therapies.

Limitations of Random Assignment

Potential for implementation issues.

While the principles of random assignment are robust, the method can face implementation issues.

One of the most common problems is logistical constraints. Some studies, due to their nature or the specific population being studied, find it challenging to implement random assignment effectively.

For instance, in educational settings, logistical issues such as class schedules and school policies might stop the random allocation of students to different teaching methods .

Ethical Dilemmas

Random assignment, while methodologically sound, can also present ethical dilemmas.

In some cases, withholding a potentially beneficial treatment from one of the groups of participants can raise serious ethical questions, especially in medical or clinical research where participants' well-being might be directly affected.

Researchers must navigate these ethical waters carefully, balancing the pursuit of knowledge with the well-being of participants.

Generalizability Concerns

Even when implemented correctly, random assignment does not always guarantee generalizable results.

The types of people in the participant pool, the specific context of the study, and the nature of the variables being studied can all influence the extent to which the findings can be applied to the broader population.

Researchers must be cautious in making broad generalizations from studies, even those employing strict random assignment.

Practical and Real-World Limitations

In the real world, many variables cannot be manipulated for ethical or practical reasons, limiting the applicability of random assignment.

For instance, researchers cannot randomly assign individuals to different levels of intelligence, socioeconomic status, or cultural backgrounds.

This limitation necessitates the use of other research designs, such as correlational or observational studies , when exploring relationships involving such variables.

Response to Critiques

In response to these critiques, people in favor of random assignment argue that the method, despite its limitations, remains one of the most reliable ways to establish cause and effect in experimental research.

They acknowledge the challenges and ethical considerations but emphasize the rigorous frameworks in place to address them.

The ongoing discussion around the limitations and critiques of random assignment contributes to the evolution of the method, making sure it is continuously relevant and applicable in psychological research.

While random assignment is a powerful tool in experimental research, it is not without its critiques and limitations. Implementation issues, ethical dilemmas, generalizability concerns, and real-world limitations can pose significant challenges.

However, the continued discourse and refinement around these issues underline the method's enduring significance in the pursuit of knowledge in psychology.

By being careful with how we do things and doing what's right, random assignment stays a really important part of studying how people act and think.

Real-World Applications and Examples

Random assignment has been employed in many studies across various fields of psychology, leading to significant discoveries and advancements.

Here are some real-world applications and examples illustrating the diversity and impact of this method:

Medicine and Health Psychology: Randomized Controlled Trials (RCTs) are the gold standard in medical research. In these studies, participants are randomly assigned to either the treatment or control group to test the efficacy of new medications or interventions.
Educational Psychology: Studies in this field have used random assignment to explore the effects of different teaching methods, classroom environments, and educational technologies on student learning and outcomes.
Cognitive Psychology: Researchers have employed random assignment to investigate various aspects of human cognition, including memory, attention, and problem-solving, leading to a deeper understanding of how the mind works.
Social Psychology: Random assignment has been instrumental in studying social phenomena, such as conformity, aggression, and prosocial behavior, shedding light on the intricate dynamics of human interaction.

Let's get into some specific examples. You'll need to know one term though, and that is "control group." A control group is a set of participants in a study who do not receive the treatment or intervention being tested , serving as a baseline to compare with the group that does, in order to assess the effectiveness of the treatment.

Smoking Cessation Study: Researchers used random assignment to put participants into two groups. One group received a new anti-smoking program, while the other did not. This helped determine if the program was effective in helping people quit smoking.
Math Tutoring Program: A study on students used random assignment to place them into two groups. One group received additional math tutoring, while the other continued with regular classes, to see if the extra help improved their grades.
Exercise and Mental Health: Adults were randomly assigned to either an exercise group or a control group to study the impact of physical activity on mental health and mood.
Diet and Weight Loss: A study randomly assigned participants to different diet plans to compare their effectiveness in promoting weight loss and improving health markers.
Sleep and Learning: Researchers randomly assigned students to either a sleep extension group or a regular sleep group to study the impact of sleep on learning and memory.
Classroom Seating Arrangement: Teachers used random assignment to place students in different seating arrangements to examine the effect on focus and academic performance.
Music and Productivity: Employees were randomly assigned to listen to music or work in silence to investigate the effect of music on workplace productivity.
Medication for ADHD: Children with ADHD were randomly assigned to receive either medication, behavioral therapy, or a placebo to compare treatment effectiveness.
Mindfulness Meditation for Stress: Adults were randomly assigned to a mindfulness meditation group or a waitlist control group to study the impact on stress levels.
Video Games and Aggression: A study randomly assigned participants to play either violent or non-violent video games and then measured their aggression levels.
Online Learning Platforms: Students were randomly assigned to use different online learning platforms to evaluate their effectiveness in enhancing learning outcomes.
Hand Sanitizers in Schools: Schools were randomly assigned to use hand sanitizers or not to study the impact on student illness and absenteeism.
Caffeine and Alertness: Participants were randomly assigned to consume caffeinated or decaffeinated beverages to measure the effects on alertness and cognitive performance.
Green Spaces and Well-being: Neighborhoods were randomly assigned to receive green space interventions to study the impact on residents’ well-being and community connections.
Pet Therapy for Hospital Patients: Patients were randomly assigned to receive pet therapy or standard care to assess the impact on recovery and mood.
Yoga for Chronic Pain: Individuals with chronic pain were randomly assigned to a yoga intervention group or a control group to study the effect on pain levels and quality of life.
Flu Vaccines Effectiveness: Different groups of people were randomly assigned to receive either the flu vaccine or a placebo to determine the vaccine’s effectiveness.
Reading Strategies for Dyslexia: Children with dyslexia were randomly assigned to different reading intervention strategies to compare their effectiveness.
Physical Environment and Creativity: Participants were randomly assigned to different room setups to study the impact of physical environment on creative thinking.
Laughter Therapy for Depression: Individuals with depression were randomly assigned to laughter therapy sessions or control groups to assess the impact on mood.
Financial Incentives for Exercise: Participants were randomly assigned to receive financial incentives for exercising to study the impact on physical activity levels.
Art Therapy for Anxiety: Individuals with anxiety were randomly assigned to art therapy sessions or a waitlist control group to measure the effect on anxiety levels.
Natural Light in Offices: Employees were randomly assigned to workspaces with natural or artificial light to study the impact on productivity and job satisfaction.
School Start Times and Academic Performance: Schools were randomly assigned different start times to study the effect on student academic performance and well-being.
Horticulture Therapy for Seniors: Older adults were randomly assigned to participate in horticulture therapy or traditional activities to study the impact on cognitive function and life satisfaction.
Hydration and Cognitive Function: Participants were randomly assigned to different hydration levels to measure the impact on cognitive function and alertness.
Intergenerational Programs: Seniors and young people were randomly assigned to intergenerational programs to study the effects on well-being and cross-generational understanding.
Therapeutic Horseback Riding for Autism: Children with autism were randomly assigned to therapeutic horseback riding or traditional therapy to study the impact on social communication skills.
Active Commuting and Health: Employees were randomly assigned to active commuting (cycling, walking) or passive commuting to study the effect on physical health.
Mindful Eating for Weight Management: Individuals were randomly assigned to mindful eating workshops or control groups to study the impact on weight management and eating habits.
Noise Levels and Learning: Students were randomly assigned to classrooms with different noise levels to study the effect on learning and concentration.
Bilingual Education Methods: Schools were randomly assigned different bilingual education methods to compare their effectiveness in language acquisition.
Outdoor Play and Child Development: Children were randomly assigned to different amounts of outdoor playtime to study the impact on physical and cognitive development.
Social Media Detox: Participants were randomly assigned to a social media detox or regular usage to study the impact on mental health and well-being.
Therapeutic Writing for Trauma Survivors: Individuals who experienced trauma were randomly assigned to therapeutic writing sessions or control groups to study the impact on psychological well-being.
Mentoring Programs for At-risk Youth: At-risk youth were randomly assigned to mentoring programs or control groups to assess the impact on academic achievement and behavior.
Dance Therapy for Parkinson’s Disease: Individuals with Parkinson’s disease were randomly assigned to dance therapy or traditional exercise to study the effect on motor function and quality of life.
Aquaponics in Schools: Schools were randomly assigned to implement aquaponics programs to study the impact on student engagement and environmental awareness.
Virtual Reality for Phobia Treatment: Individuals with phobias were randomly assigned to virtual reality exposure therapy or traditional therapy to compare effectiveness.
Gardening and Mental Health: Participants were randomly assigned to engage in gardening or other leisure activities to study the impact on mental health and stress reduction.

Each of these studies exemplifies how random assignment is utilized in various fields and settings, shedding light on the multitude of ways it can be applied to glean valuable insights and knowledge.

Real-world Impact of Random Assignment

Random assignment is like a key tool in the world of learning about people's minds and behaviors. It’s super important and helps in many different areas of our everyday lives. It helps make better rules, creates new ways to help people, and is used in lots of different fields.

Health and Medicine

In health and medicine, random assignment has helped doctors and scientists make lots of discoveries. It’s a big part of tests that help create new medicines and treatments.

By putting people into different groups by chance, scientists can really see if a medicine works.

This has led to new ways to help people with all sorts of health problems, like diabetes, heart disease, and mental health issues like depression and anxiety.

Schools and education have also learned a lot from random assignment. Researchers have used it to look at different ways of teaching, what kind of classrooms are best, and how technology can help learning.

This knowledge has helped make better school rules, develop what we learn in school, and find the best ways to teach students of all ages and backgrounds.

Workplace and Organizational Behavior

Random assignment helps us understand how people act at work and what makes a workplace good or bad.

Studies have looked at different kinds of workplaces, how bosses should act, and how teams should be put together. This has helped companies make better rules and create places to work that are helpful and make people happy.

Environmental and Social Changes

Random assignment is also used to see how changes in the community and environment affect people. Studies have looked at community projects, changes to the environment, and social programs to see how they help or hurt people’s well-being.

This has led to better community projects, efforts to protect the environment, and programs to help people in society.

Technology and Human Interaction

In our world where technology is always changing, studies with random assignment help us see how tech like social media, virtual reality, and online stuff affect how we act and feel.

This has helped make better and safer technology and rules about using it so that everyone can benefit.

The effects of random assignment go far and wide, way beyond just a science lab. It helps us understand lots of different things, leads to new and improved ways to do things, and really makes a difference in the world around us.

From making healthcare and schools better to creating positive changes in communities and the environment, the real-world impact of random assignment shows just how important it is in helping us learn and make the world a better place.

So, what have we learned? Random assignment is like a super tool in learning about how people think and act. It's like a detective helping us find clues and solve mysteries in many parts of our lives.

From creating new medicines to helping kids learn better in school, and from making workplaces happier to protecting the environment, it’s got a big job!

This method isn’t just something scientists use in labs; it reaches out and touches our everyday lives. It helps make positive changes and teaches us valuable lessons.

Whether we are talking about technology, health, education, or the environment, random assignment is there, working behind the scenes, making things better and safer for all of us.

In the end, the simple act of putting people into groups by chance helps us make big discoveries and improvements. It’s like throwing a small stone into a pond and watching the ripples spread out far and wide.

Thanks to random assignment, we are always learning, growing, and finding new ways to make our world a happier and healthier place for everyone!

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COMMENTS

Random Assignment in Experiments
Random Assignment in Experiments | Introduction & Examples. Published on March 8, 2021 by Pritha Bhandari.Revised on June 22, 2023. In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomization. With simple random assignment, every member of the sample has a known or equal chance of being placed in a control ...
Random Assignment in Experiments
Random sampling is a process for obtaining a sample that accurately represents a population. Random assignment uses a chance process to assign subjects to experimental groups. Using random assignment requires that the experimenters can control the group assignment for all study subjects. For our study, we must be able to assign our participants ...
Random sampling vs. random assignment (scope of inference)
Random sampling Not random sampling; Random assignment: Can determine causal relationship in population. This design is relatively rare in the real world. Can determine causal relationship in that sample only. This design is where most experiments would fit. No random assignment: Can detect relationships in population, but cannot determine ...
Random Selection vs. Random Assignment
Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.. Random selection refers to the process of randomly selecting individuals from a population to be involved in a study.. Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group.
Random Sampling vs. Random Assignment
Random assignment is a fundamental part of a "true" experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable. So, to summarize, random sampling refers to how you select individuals from the population to participate in your study.
Random Selection vs. Random Assignment
Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.. Random selection refers to the process of randomly selecting individuals from a population to be involved in a study. Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group.
Random Assignment in Psychology: Definition & Examples
Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study. On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups. Random selection ensures that everyone in the population has an equal ...
Difference between Random Selection and Random Assignment
Random selection is thus essential to external validity, or the extent to which the researcher can use the results of the study to generalize to the larger population. Random assignment is central to internal validity, which allows the researcher to make causal claims about the effect of the treatment. Nonrandom assignment often leads to non ...
1.4: Inferential Statistics
Define inferential statistics; Identify biased samples; Distinguish between simple random sampling and stratified sampling; ... Random assignment is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first $20$ subjects to show up at the experiment were assigned to the experimental group ...
Descriptive and Inferential Statistics: Random Assignment
Random assignment is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first 20 subjects to show up at the experiment were assigned to the experimental group and the second 20 subjects were assigned to the control group. It is possible that subjects who show up late tend to be more ...
Random Allocation & Random Selection
Random allocation, or random assignment, is useful in experimental situations in which different people will be administered different treatments or conditions. By using randomization to choose ...
Random Assignment
AP Statistics. Random Assignment. Random Assignment. Definition. Random assignment refers to assigning participants or subjects into different groups (e.g., control group vs. treatment group) randomly. This helps ensure that any differences observed between groups are due to treatment effects rather than pre-existing differences.
14.2: Randomness in Statistics
14.2: Randomness in Statistics. The term "random" is often used colloquially to refer to things that are bizarre or unexpected, but in statistics the term has a very specific meaning: A process is random if it is unpredictable. For example, if I flip a fair coin 10 times, the value of the outcome on one flip does not provide me with any ...
Random assignment
Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. This ensures that each participant or subject has an equal chance of being placed in ...
Simple Random Sampling
Revised on December 18, 2023. A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected. This method is the most straightforward of all the probability sampling methods, since it only involves a single random selection and requires ...
Random Assignment
Definition. Random assignment defines the assignment of participants of a study to their respective group strictly by chance. Introduction. Statistical inference is based on the theory of probability, and effects investigated in psychological studies are defined by measures that are treated as random variables. The inference about the ...
15.1: Random Selection
A useful model—random sums. As a basic model, we consider the sum of a random number of members of an iid class. In order to have a concrete interpretation to help visualize the formal patterns, we think of the demand of a random number of customers. We suppose the number of customers Nis independent of the individual demands. We formulate a ...
Random Assignment ~ A Simple Introduction with Examples
Random Assignment - In a Nutshell. Random assignment is where you randomly place research participants into specific groups. This method eliminates bias in the results by ensuring that all participants have an equal chance of getting into either group. Random assignment is usually used in independent measures or between-group experiment designs.
3.6 Causation and Random Assignment
Random assignment helps us rule out plausible alternatives. 3.6.1.4 Making a causal claim. Now, let's see about make a causal claim for the sleep deprivation study: Association: There is a statistically significant result, so the cause is associated with the effect;
6.2 Experimental Design
Define random assignment, distinguish it from random sampling, explain its purpose in experimental research, and use some simple strategies to implement it. ... Another is that the inferential statistics that researchers use to decide whether a difference between groups reflects a difference in the population takes the "fallibility" of ...
Randomized Controlled Trial (RCT) Overview
In this design, random assignment tends to equally distribute all subject characteristics that affect the outcome. In short, randomization balances the treatment and control groups at the beginning of a randomized controlled trial. The only difference between groups is the treatment condition itself.
The Definition of Random Assignment In Psychology
Random assignment refers to the use of chance procedures in psychology experiments to ensure that each participant has the same opportunity to be assigned to any given group in a study to eliminate any potential bias in the experiment at the outset. Participants are randomly assigned to different groups, such as the treatment group versus the ...
Random Assignment in Psychology (Definition + 40 Examples)
Random Assignment is a process used in research where each participant has an equal chance of being placed in any group within the study. This technique is essential in experiments as it helps to eliminate biases, ensuring that the different groups being compared are similar in all important aspects.

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15.1: Random Selection

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