Control Group — Definition, Formula & Examples
A control group is the group of subjects in an experiment that does not receive the treatment or intervention being tested, serving as a baseline for comparison against the treatment group.
In a controlled experiment, the control group consists of experimental units assigned to a condition that omits the independent variable (or receives a placebo), so that any observed difference in the response variable between the control and treatment groups can be attributed to the effect of the treatment rather than to confounding variables.
How It Works
When you design an experiment, you split your subjects into at least two groups: one or more treatment groups and a control group. The treatment group receives the intervention you want to test, while the control group receives either no intervention or a placebo. After the experiment, you compare the response variable across groups. Because the control group experienced the same conditions minus the treatment, any statistically significant difference in outcomes provides evidence that the treatment itself caused the change. Random assignment of subjects to groups is essential — it helps ensure that pre-existing differences between individuals do not bias the comparison.
Example
Problem: A researcher wants to test whether a new fertilizer increases tomato yield. She has 40 tomato plants available. Describe how to set up a control group and determine whether the fertilizer had an effect, given that the treatment group averaged 12.4 kg per plant and the control group averaged 9.1 kg per plant.
Step 1 — Random Assignment: Randomly assign the 40 plants into two groups of 20. Group A (treatment) receives the new fertilizer. Group B (control) receives the same amount of water and standard soil but no fertilizer.
Step 2 — Keep Conditions Equal: Both groups are grown in the same greenhouse, with identical sunlight, watering schedules, and pot sizes. The only difference is the fertilizer.
Step 3 — Measure the Response: After the growing season, record the tomato yield (kg) for every plant in both groups and compute the group means.
Step 4 — Compare to Control: The difference in means is 3.3 kg per plant. A hypothesis test (e.g., a two-sample t-test) can determine whether this difference is statistically significant or could be due to chance.
Answer: The control group (no fertilizer) yielded an average of 9.1 kg per plant, while the treatment group yielded 12.4 kg. The 3.3 kg difference, if statistically significant, provides evidence that the fertilizer increases tomato yield.
Visualization
Why It Matters
In AP Statistics, nearly every free-response question on experimental design asks you to identify or describe a control group. Beyond the exam, control groups are the backbone of clinical trials in medicine — the FDA requires them before approving new drugs. Understanding this concept is also critical in fields like agriculture, psychology, and engineering, where researchers must isolate the effect of a single variable.
Common Mistakes
Mistake: Confusing a control group with a controlled variable.
Correction: A control group is a set of subjects that does not receive the treatment. A controlled variable (also called a constant) is any factor the experimenter keeps the same across all groups, such as temperature or light exposure. They serve different purposes.
Mistake: Skipping random assignment and letting subjects choose their own group.
Correction: Without random assignment, pre-existing differences between groups (confounding variables) can explain the results instead of the treatment. Always use a random process — like a random number generator — to assign subjects to the control and treatment groups.