# Random Sampling Assignment

Design of Experiments > Random Selection and Assignment

## What is Random Selection?

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**create your study sample randomly, by chance.**Random selection results in a representative sample; you can make generalizations and predictions about a population’s behavior based on your sample as long as you have used a probability sampling method.

The word “random” has a **precise meaning** in statistics. Random selection doesn’t just mean you can just randomly pick a few items to make up a sample. That method is actually something called *haphazard sampling*, where you try to create a random sample by haphazardly choosing items in order to try and recreate true randomness. That doesn’t usually work (because of something called selection bias). In order to create a true random selection, you need to use one of the tried and testing random selection methods, like simple random sampling.

**Example of random selection**: You are studying test taking behaviors at a college of 5,000 students. You choose every 50th student from a list (a random selection method called systematic sampling) to create a sample of 50 students to study.

**Example of non random selection**:

From the same list of 5,000 students, you randomly circle 50 names. This isn’t truly random as your biases (known or unknown) could affect who you circle. For example, you might unknowingly circle boys names over girls, or American-sounding names over foreign-sounding names.

## What is Random Assignment?

Random assignment is where study participants are randomly assigned to a study group (i.e. an experimental group or a control group). In a single blind study, the participant does not know whether they are in the experimental group or the control group. In a double blind study, neither the participant nor the researcher knows.

**Example of random assignment: **you have a study group of 50 people and you write their names on equal size balls. You then place the balls into an urn and mix them well (this is a classic ball and urn experiment). The first 25 balls you draw go into the experimental group. The rest go into the control group.

**Example of non-random assignment**: you have a list of 50 people to assign to control groups and experimental groups. You use your knowledge and experience to choose 25 people who you think would be better suited to the experimental group (a method called purposive sampling).

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**Random selection** is how you draw the sample of people for your study from a population.

**Random**is how you assign the sample that you draw to different groups or treatments in your study.

*assignment*It is possible to have *both* random selection and assignment in a study. Let's say you drew a random sample of 100 clients from a population list of 1000 current clients of your organization. That is random sampling. Now, let's say you randomly assign 50 of these clients to get some new additional treatment and the other 50 to be controls. That's random assignment.

It is also possible to have *only one of these* (random selection or random assignment) but not the other in a study. For instance, if you do not randomly draw the 100 cases from your list of 1000 but instead just take the first 100 on the list, you do not have random selection. But you could still randomly assign this nonrandom sample to treatment versus control. Or, you could randomly select 100 from your list of 1000 and then nonrandomly (haphazardly) assign them to treatment or control.

And, it's possible to have *neither* random selection nor random assignment. In a typical nonequivalent groups design in education you might nonrandomly choose two 5th grade classes to be in your study. This is nonrandom selection. Then, you could arbitrarily assign one to get the new educational program and the other to be the control. This is nonrandom (or nonequivalent) assignment.

Random selection is related to sampling. Therefore it is most related to the external validity (or generalizability) of your results. After all, we would randomly sample so that our research participants better represent the larger group from which they're drawn. Random assignment is most related to design. In fact, when we randomly assign participants to treatments we have, by definition, an experimental design. Therefore, random assignment is most related to internal validity. After all, we randomly assign in order to help assure that our treatment groups are similar to each other (i.e., equivalent) prior to the treatment.

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Copyright ©2006, William M.K. Trochim, All Rights Reserved

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Last Revised: 10/20/2006

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