Question

If there are significant main effects in a 2 x 2 ANOVA, one should conduct post hoc tests.

True or False?

Answer 1

In a two way anova you do post-hoc tests in two situations:

1. If you have an interaction between the two factors

2. If you have an overall effect and the group has more than 2 variables.

For example:

1. Treatment (A, B, C) versus sex (male, female):

If you have a treatment x sex interaction, you can follow with a post-hoc and compare whatever you want.

2. you dont have an interaction, but you have an overall sex effect: in this case you dont need a post hoc because you only have two groups and the anova is telling you that one sex is higher the the other.

3. you dont have an interaction, but you have a treatment effect: in this case you can do a posthoc to compare A, B, C. This will tell you that one or two treatments are higher than the other REGARDLESS of sex.

If there are 2 levels in each variable, then we don't need to run post-hoc test.