Statistics · CED Unit 3: Collecting Data · 14 min read · Updated 2026-05-11
Inference and Experiments — AP Statistics
AP Statistics · CED Unit 3: Collecting Data · 14 min read
1. What Is Inference for Experiments?★★☆☆☆⏱ 3 min
Inference is the process of drawing general conclusions about treatment effects or population characteristics that go beyond raw observed data. For experiments, inference has two commonly tested goals: generalizing results to a broader population, and establishing that a treatment causes a change in the measured response variable. This topic makes up 10–15% of the total AP Statistics exam weight, appearing in both multiple-choice and free-response sections.
Unlike inference from observational studies, inference from experiments relies on random assignment of treatments to subjects, rather than only random sampling from a population. This key difference changes what types of inference are valid: random assignment allows causal inference, while random sampling allows generalization to a broader population. The AP exam heavily tests your ability to identify which inferences are appropriate based on study design, not just calculation.
2. Causal vs Associative Inference★★☆☆☆⏱ 4 min
The core rule tested on the exam is: random assignment balances all confounding variables (measured and unmeasured) across treatment groups on average, so any remaining difference between groups can be attributed to the treatment. Causal inference and generalization are independent: a study can have one, both, or neither, depending on design choices.
Exam tip: When asked about inference scope, always address both causation and generalization explicitly, even if the question only asks one. AP exam graders expect you to demonstrate you know the difference between the two requirements, so stating both will help you earn full credit.
3. Core Principles of Experimental Design★★★☆☆⏱ 4 min
For inference from an experiment to be valid, the experiment must follow four core design principles, each addressing a different threat to valid inference:
**Control**: Compare the treatment group to a control group that receives no treatment, a placebo, or the current standard treatment. This controls for confounding effects like the placebo effect, isolating the treatment effect.
**Replication**: Apply each treatment to multiple independent experimental units. Replication reduces the impact of random individual variation, leading to more precise inference and easier detection of true treatment effects.
**Randomization**: Randomly assign treatments to experimental units. This balances measured and unmeasured confounding variables across groups, enabling causal inference.
**Blocking**: Group experimental units similar on a known confounding variable into blocks, then randomly assign treatments within each block. Blocking removes variability from the known confounding variable, making it easier to detect a true treatment effect.
Exam tip: If the study groups units by a pre-existing variable before randomizing treatments, that is blocking, not confounding. Confounding is for uncontrolled variables; blocking is an intentional technique to improve inference.
4. Confounding and Threats to Valid Inference★★★☆☆⏱ 3 min
Confounding is the primary reason causal inference is not valid for observational studies, but it can also occur in poorly designed experiments. Common sources include selection bias (when subjects choose their own treatment), lack of blinding, and unmeasured lurking variables. AP questions frequently ask you to identify a possible confounding variable and explain how it threatens causal inference.
Exam tip: When asked to identify a confounding variable on an FRQ, you must explicitly explain how it is associated with both the treatment and the response to earn full credit. Naming the variable alone is not enough.
Common Pitfalls
Why: Students confuse random sampling and random assignment, mixing up which type of inference each supports.
Why: Students confuse controlled design choices with uncontrolled sources of bias.
Why: General science texts sometimes mention repeating experiments to confirm results, so students misapply the definition in AP Statistics experimental design.
Why: Students assume that one implies the other, but the two are independent based on different study design choices.
Why: Students think just naming the variable is enough for full credit on FRQ.
Why: Students learn blocking reduces variability, so they assume blocking is always better.