appropiate post hoc test

May someone help me with this?
I have done a 2 factor univariate ANOVA, although some of my data is not still normally distributed (Kolmogorov and Smirnoff Test).
Although ANOVA is quite robust against violation and homogeneity of variances is always been observed (Levene Test) in my data - I am not quite sure which post hoc methode to select.

First of all I thought about Bonferroni - but the multiple t tests assume normally distributed data or not?

So what about Tukey or something else?:confused: Thanks


TS Contributor
Don't worry about normality - the biggest thing to consider on post-hoc tests is how conservative you want to be....

Bonferroni is the most conservative (lowest power) since it divides the Type I error probability by the number of comparisons to be made.

On the other end of the spectrum, Fisher's LSD tests are the most powerful (but the least conservative) because it maintains Type I error at the original value from the ANOVA.

Tukey is basically in the middle, and therefore it is the most popular.