post-hoc for non homogeneous data 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?
 A: 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))..
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A: There seems to be a little confusion.  
1) Levene's and SW are tests of homogeneity of variance which is one of the assumptions of ANOVA. One test showed non-homogenous variance and the other did not.
2) Games-Howell is a test of equality of means when the assumptions of ANOVA are rejected. I had not seen it used before, but it appears to be fairly widely used. So, you can probably use it. But you might want to do more research into it, particularly if this analysis is highly critical.
3) You didn't report an F test for the ANOVA itself. That would tell you whether there are differences among the means (but it makes those assumptions).  Some people think that you should not do post hoc tests if the ANOVA is not significant, particularly if particular differences were not specified a priori. 
3) Alternatives to using Games Howell include the methods in @Steven 's answer. However, it is hard to say which approach is best without a lot more information about both your study and your results. Even if you conclude that the variances of the residuals were different - why and how were they different?
My blog post "How to ask a statistics question" may be of help. 
