Which type of t-test is appropriate for comparing means of two related groups?

The paired samples t-test is the appropriate choice for comparing means of two related groups because this test is specifically designed to analyze situations where two measurements are taken from the same subjects. For example, if you were measuring the same individuals' performance before and after a treatment, the measurements are naturally related since they come from the same source.

The paired samples t-test works by assessing whether the average difference between these two sets of related scores is statistically significant. It takes into account the paired nature of the data, which helps to control for individual variability and provides a more powerful test compared to analyzing these data independently.

In contrast, independent samples t-tests are used when comparing means from two different groups that do not influence each other. ANOVA is a method used for comparing means among three or more groups, rather than just two, and nonparametric tests are alternative methods that can be applied when certain assumptions of parametric tests are violated, but they do not specifically focus on the paired nature of related groups. Hence, the paired samples t-test is the correct option for this particular scenario.