Discussion
Suppose n randomly chosen persons were enrolled to examine whether different skin creams A and B have different effects on the human body. Cream A was applied to one of the randomly chosen arm of each person, cream B to the other arm. Response is measured as a continuous variable. Which of the following tests is most appropriate to examine the difference ?
Answer: C
The appropriate test is the paired t-test, if normality can be assumed.
Each person receives both creams, one on each arm, so the observations come in matched pairs. The two responses from the same person share that person's skin type and other characteristics, so they are dependent. The right analysis works with the within-person differences \(d_{i} = A_{i} - B_{i}\) and tests whether their mean is zero, which is the paired t-test when the differences are approximately normal.
The two-sample t-test, the Mann-Whitney test and the two-sample Kolmogorov-Smirnov test all assume two independent samples. Using them here ignores the pairing, which both violates their assumptions and throws away the large reduction in variance that the design provides. (The nonparametric counterpart for paired data would be the Wilcoxon signed-rank test.)
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