Experiment Design

Unit 3 · Collecting Data

What AP Stats asks here

An experiment assigns treatments; an observational study only records what happened. The watershed: random assignment is what licenses a causal claim. AP examiners test whether you can name the experiment's parts (subjects, factor, levels, treatments, response), distinguish the two study types, and pick the right blinding when the response is subjective.

Three principles

Control

\text{hold other variables constant; use a control group}

Randomization

\text{random assignment balances confounders}

Replication

\text{enough subjects to detect a real effect}

Vocabulary

Factor / Level / Treatment

\text{factor = manipulated variable; level = setting; treatment = combination}

Single-blind

\text{subjects don't know assignment}

Double-blind

\text{neither subjects nor evaluators know}

AP Tip: Random assignment is what makes an experiment an experiment. Without it, you have an observational study and you cannot conclude causation no matter how clean the comparison looks.

Caution: Subjective responses (pain, taste, mood) demand double-blinding. Otherwise expectations on both sides distort the measurement.

Type 1

Identify experiment components

The factor is the manipulated variable. Levels are its settings. A treatment is a combination of one level from each factor. The response is what you measure.

Example 1

A study tests two doses of a drug (50 mg and 100 mg) and a placebo on 90 patients with high blood pressure; the outcome is change in blood pressure. Which assignment is correct? (A) Subjects = 90 patients; factor = blood pressure; levels = mg; treatments = placebo; response = drug dose. (B) Subjects = 90 patients; factor = drug dosage; levels = placebo / 50 mg / 100 mg; treatments = the same three; response = change in blood pressure. (C) Subjects = drug dosage; factor = patients; levels = 90; treatments = high BP; response = mg. (D) Subjects = the three doses; factor = patients; levels = blood pressure; treatments = patients; response = dose.

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Type 2

Experiment vs observational study

Random assignment ⇒ experiment ⇒ causation valid within the assigned group. No random assignment ⇒ observational ⇒ association only.

Example 2

Researchers track 5000 people's coffee consumption and heart disease for 10 years without intervening. Which conclusion is valid? (A) Coffee causes heart disease (or prevents it). (B) The study can establish an association between coffee consumption and heart disease but cannot establish causation, because participants were not randomly assigned to drink coffee. (C) Coffee and heart disease are statistically independent. (D) The study is an experiment because subjects were measured.

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Type 3

Blinding choices

When the response is subjective, both subjects and evaluators must be blinded. Otherwise expectations distort the measurement.

Example 3

A pain-medication trial compares a new drug to a placebo. Subjects rate their pain after taking the pill. Which blinding is most appropriate? (A) No blinding — subjects deserve to know what they took. (B) Single-blind — only subjects are blinded. (C) Double-blind — both subjects and the experimenters administering the pill or recording pain are blinded. (D) Triple-blind — even the statistician doing the analysis is blinded to which group is which.

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