Paired or two-sample?

Topic: Hypothesis tests · more questions on this topic
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For each study, say whether a paired or a two-sample test is appropriate, and why. (a) Blood pressure of 20 patients before and after a drug. (b) Yields of 12 plots given fertiliser A and 12 other plots given fertiliser B. (c) Reaction times of each of 15 drivers, sober and after one drink. (d) Exam scores of twins, one taught by each of two methods.

Worked answer (click to show)

1. Paired: each patient gives a before and an after reading, and patients differ greatly in baseline blood pressure.

2. Two-sample: the 24 plots are distinct, and no plot of A is matched with a plot of B.

3. Paired: each driver is measured in both conditions.

4. Paired: twins share genes and upbringing, so the two scores in a pair are dependent, and the pair is the natural block.

In each paired case the analysis is a one-sample test on the within-pair differences.