Random Assignment — Definition, Formula & Examples
Random assignment is the process of using chance (such as a coin flip or random number generator) to decide which treatment each subject receives in an experiment. It ensures that treatment groups are roughly equivalent before the experiment begins, so any observed differences in outcomes can be attributed to the treatment itself.
In experimental design, random assignment is the allocation of experimental units to treatment conditions via a randomization mechanism, such that each unit has a known, nonzero probability of being assigned to any given group. This procedure controls for both known and unknown confounding variables by distributing them approximately equally across groups, thereby supporting valid causal inference.
How It Works
After you recruit your subjects, you use a chance-based method—a random number table, a coin flip, or software—to sort each subject into one of the treatment groups. Because the sorting is random, characteristics like age, health, motivation, and other lurking variables get spread roughly evenly across all groups. This means the groups are comparable at the start, so if one group ends up with a significantly different outcome, you can reasonably conclude the treatment caused it rather than some pre-existing difference. Random assignment is the key feature that distinguishes a true experiment from an observational study.
Example
Problem: A researcher wants to test whether a new study app improves test scores. She has 40 student volunteers. Describe how to use random assignment and identify the resulting groups.
Step 1: Label each of the 40 students with a number from 01 to 40.
Step 2: Use a random number generator to produce 20 distinct numbers between 01 and 40. The students with those numbers are placed in the treatment group (they use the new app).
Step 3: The remaining 20 students form the control group (they study without the app).
Step 4: After the study period, compare the mean test scores of the two groups. Because random assignment was used, any statistically significant difference in means can be attributed to the app rather than to pre-existing differences between students.
Answer: Random assignment produces two groups of 20 students each, balanced on lurking variables, allowing a valid causal comparison of the app's effect on test scores.
Why It Matters
Random assignment is tested heavily on the AP Statistics exam, particularly in free-response questions about experimental design. Beyond the classroom, clinical trials in medicine rely on it to determine whether a new drug actually works or whether observed improvements are due to other factors. Understanding this principle is also essential in psychology, education research, and any field that draws causal conclusions from data.
Common Mistakes
Mistake: Confusing random assignment with random sampling.
Correction: Random sampling selects who enters the study (for generalizability). Random assignment decides which treatment each participant receives (for causation). They answer different questions and can be used independently.
Mistake: Believing random assignment guarantees perfectly equal groups.
Correction: Random assignment makes groups approximately equivalent on average, especially with large sample sizes. With small samples, imbalances can still occur by chance, which is why statistical tests are used to assess whether observed differences are likely due to the treatment.