Planned comparisons after an ANOVA using the t-test procedure tend to have higher precisions than regular two-sample t-tests. Why is that?

Question

Quizplus · Accepted Answer

The degrees of freedom for the error term in an ANOVA are typically larger than those for a two-sample t-test because they are based on the variance estimated from all groups combined, not just two. This larger degrees of freedom value generally leads to narrower confidence intervals and thus higher precision in the planned comparisons.

Planned Comparisons After an ANOVA Using the T-Test Procedure Tend