AP® Statistics · Unit 1 · Topic 1.13
Control, Randomization, and Replication
Control, randomization, and replication are the three design principles that let an experiment show cause and effect: they rule out confounding variables, bias, and plain luck as explanations for a result.
Control means holding conditions steady so the only real difference between groups is the treatment itself. That's why experiments need a control group, one that gets no treatment, a placebo, or the current standard, as a baseline. Without it, you can't tell whether a change in the response was caused by the treatment or would have happened anyway. Randomization is how you decide who lands in which group: use a random process, like numbering 40 volunteers 1 to 40 and using a random number generator to assign the first 20 numbers drawn to Group A and the rest to Group B. Random assignment spreads out confounding variables, like age, fitness, or diet, roughly evenly between groups, so any leftover difference in outcomes is plausibly due to the treatment, not some lurking variable.
Replication means using enough subjects that a real treatment effect stands out from ordinary chance variation. One person responding well to a drug could be a fluke; forty people split into two groups showing a consistent gap is much harder to explain by luck alone. More subjects per group shrink the natural noise in the data, making a genuine effect easier to detect.
A common mix-up: random assignment and random sampling are different tools. Random sampling selects who gets studied at all, and supports generalizing results to a larger population. Random assignment decides who gets which treatment among the people already in the study, and supports claiming cause and effect. An experiment can have one, both, or neither, and each weakness limits a different kind of conclusion.
Key terms
- Control group
- The group that receives no treatment, a placebo, or the standard treatment, used as a baseline for comparison.
- Random assignment
- Using a chance process to place subjects already in a study into treatment groups.
- Random sampling
- Using a chance process to select which individuals from a population are included in a study.
- Replication
- Applying each treatment to enough subjects that a real effect can be distinguished from chance variation.
- Confounding variable
- An outside factor linked to both the treatment and the outcome that can distort or explain an observed effect.
Watch it explained
- How it worksWalk me through randomly assigning 40 volunteers to two treatment groups.
- How it worksHow does replication in an experiment separate a real effect from plain luck?
- Common mistakeWhy isn't random assignment the same thing as random sampling?
- Going furtherWhat happens to an experiment when the two groups end up different sizes?
Check yourself
End of topic.