# 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?

• Did you look at the normality of the data, or of the residuals? You might get a different story from the residuals Sep 28, 2014 at 21:44
• I doubt you can assert your data to be normal. In particular, failure to reject normality doesn't imply normality. When you say your data are "not homogeneous" are you talking about changing means (which is fine) or changing variances (for which you'll presumably want something like Welch-Satterthwaite type approaches)? Sep 29, 2014 at 0:27

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

• Yes I used Shapiro Wilk and it was ok, but Levene's test showed a p<0.05. I use Games Howell test as post-hoc but this is not showing a significance either, and I am not sure whether I can believe to it. You said that I can transform my data. Can I use log to transform them? Sep 29, 2014 at 12:42
• Yes you can, (but if you have data with zero's or negative values you have to add up until positive (log(xi+1))). If it's for a bachelor/master thesis a non parametric test (e.g. kruskal wallis) would usually suffice though.. good luck! Sep 29, 2014 at 13:29
• *the 'post hoc' you might have meant before could also actually be the alternative F-ratio's SPSS can provide: 'Welch's F' and 'Brown-Forsythe's F'. But I am not sure that is what you meant.. I would go with the non-parametric tests or log transformation.. Sep 29, 2014 at 14:24

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.