Completely Randomized Design (College Board AP® Statistics)
Revision Note
Completely randomized design
What is a completely randomized design?
An experiment that has a completely randomized design is one in which all the experimental units are randomly assigned the different treatments
This creates treatment groups that are as similar as possible
This can also help to balance out any effects of confounding variables across the groups
Completely randomized designs can be used for two or more treatment groups
How do I randomly assign treatments?
To randomly assign two different treatments to, say, 100 experimental units
Label the experimental units from 1 to 100
Use a random number generator to generate random numbers between 1 and 100 until 50 unique numbers are obtained
Note how this is half of the sample size
Unique means no duplicate numbers (repeats)
Assign the experimental units who have those 50 unique numbers the first treatment and the remaining 50 receive the second treatment
Exam Tip
When describing how to randomly assign treatments to experimental units in the exam, it is important to highlight that you want unique numbers from a random number generator (no duplicates)!
How do I randomly assign treatments when there are more than two treatments?
This is most easily shown through an example
To randomly assign four different treatments to, say, 100 experimental units
Label the experimental units from 1 to 100
Use a random number generator to generate random numbers between 1 and 100 until 75 unique numbers are obtained
Note how this is three-quarters of the sample size
Assign the experimental units who have
the first 25 unique numbers the first treatment
the second 25 unique numbers the second treatment
the third 25 unique numbers the third treatment
then the remaining 25 the fourth treatment
Exam Tip
Whilst there are other methods for generating random numbers, it is easy to lose points in the exam when trying to describe them. It is often safer to talk about random number generators instead!
Worked Example
A medical researcher is conducting an experiment using a completely randomized design with 50 patients. The patients will be split into two equal groups, with one group taking a new medical drug and the other group taking a placebo.
Describe a method that the medical researcher can use to randomly assign the new medical drug and the placebo to all fifty patients.
Answer:
Number the patients from 1 to 50
Use a random number generator to generate random numbers between 1 and 50 until 25 unique numbers are obtained
Assign the patients who have those 25 unique numbers the new medical drug and assign the remaining patients the placebo
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