What is the purpose of a paired sample t-test?

The purpose of a paired sample t-test is to compare means from the same group at different times or under different conditions. This statistical test is specifically designed to analyze data where the observations are not independent but rather related or paired.

For example, you might collect data from the same participants before and after a treatment to evaluate the effect of that treatment. The paired sample t-test accounts for the correlation between these paired observations, allowing researchers to assess whether the mean difference between them is statistically significant. This makes it a powerful tool for studies looking to understand changes within a single group, rather than comparing separate groups or conditions.

In contrast, the other options refer to different statistical concepts. Comparing variances of two independent groups pertains to tests like Levene's test or F-tests, determining linear relationships involves correlation analysis or regression, and assessing reliability of a measurement tool relates to tests like Cronbach's alpha or test-retest reliability measures. Each of these serves a distinct purpose in statistical research that does not align with the objectives of a paired sample t-test.