AP Statistics Unit 3 Experimental Design: How to Collect Data for Causal Conclusions

Variable

Any characteristic recorded on individuals (e.g., height, test score, blood pressure).

Explanatory variable

The variable you suspect may help explain differences in another variable; may be the cause or predictor.

Response variable

The outcome measured to assess the effect of the explanatory variable.

Observational study

Records values of variables on individuals without assigning treatments; can show association but typically not causation due to possible confounding.

Experiment

Deliberately imposes one or more treatments on individuals and measures a response; with random assignment, can support cause-and-effect conclusions.

Factor

In an experiment, an explanatory variable that the experimenter controls.

Level

A specific value of a factor (e.g., “caffeinated” vs “decaf”).

Treatment

A specific combination of factor levels imposed on experimental units.

Experimental unit

The individuals/objects to which treatments are applied (called subjects if human).

Association

A relationship in which two variables tend to vary together (positive, negative, or none) in observed data.

Causation

A relationship where changing one variable produces a change in another; typically requires a randomized experiment for support.

Random assignment

Using a chance process to assign experimental units to treatment groups; supports causal conclusions by balancing other variables in expectation.

Random sampling

Using a chance process to select individuals from a population; supports generalizing results to that population.

Confounding variable

A variable related to both the explanatory and response variables such that its effects on the response cannot be separated from the explanatory variable’s effect.

Control group

A group receiving standard treatment, no treatment, or a placebo to provide a baseline comparison for the treatment group.

Placebo

A treatment that looks like a real treatment but has no active ingredient/mechanism expected to affect the response.

Placebo effect

A change in subjects’ responses caused by the belief they are receiving treatment rather than the treatment itself.

Blinding

When subjects do not know which treatment they received, reducing behavior changes and bias due to expectations.

Double-blind

When neither subjects nor those measuring/evaluating the response know which treatment each subject received, reducing measurement/evaluation bias.

Randomization

Using chance to assign experimental units to treatments; helps create comparable groups by balancing known and unknown variables.

Replication

Applying each treatment to many experimental units; reduces chance variation and makes group comparisons more reliable.

Completely randomized design

All experimental units are assigned to treatments entirely by chance, with no blocking or pairing.

Randomized block design

Groups units into blocks based on a variable expected to affect the response, then randomly assigns treatments within each block to reduce variability.

Block

A group of experimental units that are similar with respect to a variable expected to influence the response (blocks are not treatments).

Matched pairs design

A special blocking design with pairs (or repeated measures on the same individual); treatments are compared within each pair to reduce variability.