Question

when would a tukey test or other follow up test be needed in a study using ANOVA? explain why

Answer 1

When we do an ANOVA, for 2 or more different groups, the null hypothesis is that

H0: The means of all the treatments are the same

Ha: The means are all different or the mean at least one treatment is different from the others.

If the Analysis of Variance (ANOVA), rejects the Null hypothesis (F stat > F critical), it means at least one pair of groups are different in each other

A Tukeys test or any other Post Hoc test (Scheffes Test, Bonferronis Test etc) would be required to find which means are different from each other.

By using the post hoc tests (either by simple calculations in terms of an equation of by using confidence intervals), we get to know the means of which 2 groups are significantly different from each other. This is actually much faster and easier than having to do pairwise 2 independent sample t tests for every 2 means where there is a chance of making a Type I or a Type II error.