What is a Completely Randomized Design?

Stage 2The most basic experimental design is the completely randomized design. It is simple and straightforward when plenty of unrelated subjects are available for an experiment. It’s so simple, it almost seems obvious. But there are important principles in this simple design that are important for tackling more complex experimental designs.

Let’s take a look.

How It Works

The basic idea of any experiment is to learn how different conditions or versions of a treatment affect an outcome. To do this, you assign subjects to different treatment groups. You then run the experiment and record the results for each subject.

Afterward, you use statistical methods to determine whether the different treatment groups have different outcomes.

Key principles for any experimental design are randomization, replication, and reduction of variance. Randomization means assigning the subjects to the different groups in a random way.

Replication means ensuring there are multiple subjects in each group.

Reduction of variance refers to removing or accounting for systematic differences among subjects. Completely randomized designs address the first two principles in a simple way.

To execute a completely randomized design, first determine how many versions of the treatment there are. Next determine how many subjects are available. Divide the number of subjects by the number of treatments to get the number of subjects in each group.

The final design step is to randomly assign individual subjects to fill the spots in each group.


Suppose you are running an experiment. You want to compare three training regimens that may affect the time it takes to run one mile. You also have 12 human subjects who are willing to participate in the experiment. Because you have three training regimens, you will have 12/3 = 4 subjects in each group.

Statistical software (or even Excel) can do the actual assignment. You only need to start by numbering the subjects from 1 to 12 in any way that is convenient. The following table shows one possible random assignment of 12 subjects to three groups.

It’s okay if the number of replicates in each group isn’t exactly the same. Make them as even as possible and assign more to groups that are more interesting to you. Modern statistical software has no trouble adjusting for different sample sizes.

When there is more than one treatment variable, not much changes. Use the combination of treatments when performing random assignment.

For example, say that you add a diet treatment with two conditions in addition to the training. Combined with the three versions of training, there are six possible treatment groups. Assign the subjects in the exact way already described, but with six groups instead of three.

Do not skip randomization! Randomization is the only way to ensure your groups are similar except for the treatment. This is important to ensuring you can attribute group differences to the treatment.

When This Design DOESN’T Work

The completely randomized design is excellent when plenty of unrelated subjects are available to sample.  But some situations call for more advanced designs.

This design doesn’t address the third principle of experimental design, reduction of variance.

Sure, you may be able to address this by adding covariates to the analysis. These are variables that are not experimentally assigned but you can measure them. But if reduction of variance is important, other designs do this better.

If some of the subjects are related to each other or a single subject is exposed to multiple conditions of a treatment, you’re going to need another design.

Sometimes it is important to measure outcomes more than once during experimental treatment. For example, you might want to know how quickly the subjects make progress in their training. Again, any repeated measures of outcomes constitute a more complicated design.

Strengths of the Completely Randomized Design

When it works, it has many strengths.

It’s not only easy to create, it’s straightforward to analyze. The results are relatively easy to explain to a non-statistical audience.

Finally, familiarity with this design will help you recognize when it isn’t appropriate. Understanding the ways in which it is not appropriate can help you choose a more advanced design.

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