Which post-hoc test is used for non homogeneous data.
I have checked my data set and they are normally distributes. I used Anova with Levene's test and it showed that my data is not homogeneous, and my p value is 0.005.
SO I want to check whether between groups I have significance, and for this need to do a post-hoc test.
Which post-hoc is used?
So if I understand correctly you ran a Kolmogorov Smirnov test (or Shapiro Wilk) and it was ok (p bigger than .05) but your Levene's test ran significant (p smaller than .05).. (you didn't add the '… of variance' part, that might be why there is some misunderstanding in answers before..) Also, the post-hoc tests (bonferroni, tukey's HSD etc) are not to correct for your data having heterogenuous (or nonhomogenous) variances. They are used to lower the familywise error rate when running multiple comparisons (cumulating alpha (p values)). What you meant to do is either correct your data (transfomring, windsorizing, trimming or bootstrapping) or use a non-parametric test. But if you just want to use a post-hoc; it depends on the amount of comparisons (and the size of your sample (so not enough information in your question)).. 1