When the same subjects are measured under two conditions, which test should be used?

When the same subjects are measured under two conditions, which test should be used?

• A. 2-sample t-test
• B. Matched pairs t-test
• C. ANOVA
• D. Chi-square test

Answer: (B)

When the same subjects are measured under two conditions, the data are paired because each subject provides two related observations. The goal is to see if there is a nonzero average change from one condition to the other. The paired (matched) samples t-test does this by looking at the differences between the two conditions for each subject, then testing whether the average difference is zero. It uses the mean difference and the standard deviation of those differences, forming a t statistic as mean(diff) divided by (sd(diff) / sqrt(n)). This approach accounts for the inside-subject correlation, reducing variability due to individual differences and increasing statistical power. Two-sample t-test assumes the two groups are independent, which isn’t true here because measurements come from the same subjects. ANOVA handles more than two groups or conditions (and a repeated-measures version exists for related data), but with only two related measurements, the paired t-test is simpler and most appropriate. Chi-square tests apply to categorical data, not comparing means.

When the same subjects are measured under two conditions, the data are paired because each subject provides two related observations. The goal is to see if there is a nonzero average change from one condition to the other. The paired (matched) samples t-test does this by looking at the differences between the two conditions for each subject, then testing whether the average difference is zero. It uses the mean difference and the standard deviation of those differences, forming a t statistic as mean(diff) divided by (sd(diff) / sqrt(n)). This approach accounts for the inside-subject correlation, reducing variability due to individual differences and increasing statistical power.

Two-sample t-test assumes the two groups are independent, which isn’t true here because measurements come from the same subjects. ANOVA handles more than two groups or conditions (and a repeated-measures version exists for related data), but with only two related measurements, the paired t-test is simpler and most appropriate. Chi-square tests apply to categorical data, not comparing means.