When should you use a paired samples t-test instead of an independent samples t-test?

• A. When comparing two unrelated groups.
• B. When there are more than two related conditions.
• C. When you have two related observations from the same participants under different conditions.
• D. When the outcome is binary.

Answer: (C)

This is about when measurements come from the same people or from clearly matched pairs. A paired samples t-test (also called a dependent-samples t-test) is used when you have two related observations for each participant, such as a score before and after an intervention or measurements taken under two conditions for the same individuals. The test focuses on the differences within each pair and asks whether the average difference across all pairs is significantly different from zero. By analyzing the difference scores, it controls for individual differences, which typically increases statistical power when the two conditions are genuinely related.

The calculation centers on the difference for each pair (d), computing the mean of these differences and their standard deviation, then forming the t statistic as t = mean(d) / (sd(d) / sqrt(n)), with n being the number of pairs. Degrees of freedom are n−1, and the assumption is that the distribution of the differences is approximately normal.

This approach fits here rather than comparing two unrelated groups, which would ignore the pairing and use an independent-samples t-test. If there are more than two related conditions, you’d move beyond a simple t-test to methods like repeated-measures ANOVA. And if the outcome is binary, a t-test isn’t appropriate since it assumes a continuous outcome.