Question

Why do we run post hocs when calculating an ANOVA that is significant, but not for a T-test that is significant (be sure to discuss both parts of the question to get full points)?

Answer 1

To answer this question, first we have to understand the difference between t test and ANOVA

we use t test to find the difference between two means only, whereas we use ANOVA to test difference between three or more means, but not for two means.

In case of t test, we have only two means to test for difference. This means that if there is significant difference, then we can directly conclude that there is a significant difference between the given two means

In case of ANOVA, we can’t directly say that there is a significant difference between means because we have 3 or more means. So, ANOVA just tells us that there is a significant difference between at least one pair of means. That’s why we need post hocs to find out where the difference actually exists