Completely Randomized Design — Definition, Formula & Examples
Completely randomized design is an experimental design in which all subjects are randomly assigned to treatment groups without any blocking or pairing. Every subject has an equal chance of receiving any treatment.
A completely randomized design is an experimental structure in which the entire pool of experimental units is allocated to treatments solely through random assignment, with no grouping based on characteristics of the subjects prior to assignment. It is the simplest of the three named AP Statistics experimental designs.
How It Works
Start with your full set of experimental units. Use a random process — such as a random number generator or drawing names from a hat — to assign each unit to one of the treatment groups. Because assignment is entirely random, any lurking variables should be roughly balanced across groups. After applying the treatments, measure the response variable and compare results across groups. This design works best when the experimental units are fairly similar to one another, since there is no blocking to reduce variability from known sources.
Example
Problem: A researcher wants to test whether a new fertilizer increases tomato yield. She has 30 identical tomato plants and two treatments: new fertilizer and standard fertilizer. Describe a completely randomized design for this experiment.
Step 1: Number the 30 plants from 1 to 30. Use a random number generator to select 15 numbers from 1 to 30 without replacement.
Step 2: Assign the 15 plants corresponding to the selected numbers to the new fertilizer group. The remaining 15 plants receive the standard fertilizer.
Step 3: Grow all 30 plants under the same conditions. After the growing period, measure the yield (in kg) of each plant and compare the mean yields of the two groups.
Answer: Randomly assign 15 of the 30 plants to the new fertilizer and 15 to the standard fertilizer, then compare mean tomato yields between the two groups.
Why It Matters
On the AP Statistics exam, you must identify or describe a completely randomized design and distinguish it from randomized block and matched pairs designs. In real research, this design is the default choice when there are no major known sources of variability to block on, making it the foundation for many clinical trials and agricultural experiments.
Common Mistakes
Mistake: Confusing random assignment with random sampling.
Correction: Random assignment places subjects into treatment groups to establish cause and effect. Random sampling selects subjects from a population to ensure generalizability. A completely randomized design requires random assignment but does not necessarily involve random sampling.