Question

# Why do we run post hocs when calculating an ANOVA that is significant, but not for...

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)?

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