Which test is designed for related samples such as repeated measures or matched pairs?

Which test is designed for related samples such as repeated measures or matched pairs?

• A. Related (paired) t test.
• B. Independent samples t test.
• C. One-sample t test.
• D. ANOVA.

Answer: (A)

When data come from related samples, like the same people measured before and after or matched pairs, the observations aren’t independent. The paired t test handles this by looking at the difference within each pair and asking whether the average difference is zero. By focusing on these within-pair differences, it controls for individual differences and increases power to detect an effect. You compute the difference for each pair, find the mean and standard deviation of those differences, and then form the t statistic from the mean difference divided by the standard error of the differences (with n−1 degrees of freedom). The method assumes those differences are approximately normally distributed and that the data are measured on an interval or ratio scale. Independent samples t test is for two unrelated groups, so it would violate the related-samples assumption. A one-sample t test compares a single sample to a known value. ANOVA compares means across three or more groups; for related samples with more than two conditions, repeated-measures ANOVA is used, but for two related samples, the paired t test is the standard approach.

When data come from related samples, like the same people measured before and after or matched pairs, the observations aren’t independent. The paired t test handles this by looking at the difference within each pair and asking whether the average difference is zero. By focusing on these within-pair differences, it controls for individual differences and increases power to detect an effect. You compute the difference for each pair, find the mean and standard deviation of those differences, and then form the t statistic from the mean difference divided by the standard error of the differences (with n−1 degrees of freedom). The method assumes those differences are approximately normally distributed and that the data are measured on an interval or ratio scale.

Independent samples t test is for two unrelated groups, so it would violate the related-samples assumption. A one-sample t test compares a single sample to a known value. ANOVA compares means across three or more groups; for related samples with more than two conditions, repeated-measures ANOVA is used, but for two related samples, the paired t test is the standard approach.