Question

What is a post-hoc test and why is it necessary to use one after a significant ANOVA?

Answer 1

Post-hoc test is a test which is use to test the significance of the difference of the means of two groups ( treatments means) simultaneously when the ANOVA test is significance.

It is necessary because of the following region.

If the level of significance is = 0.05

And suppose there are five groups.

Suppose ANOVA test is significance then we want to test difference of the means of the groups using two sample test using the level of significance = = 0.05.

We need to total test = 4 + 3 + 2 + 1 = 10

So level of significance become 1 - ( 1 - )^10 =1 - (1- 0.05)^10 = 1 - 0.5987 = 0.4013

Which is very large.

So we need to use Post-hoc test, it use 0.05 level of significance to compare all the pairs simultaneously.