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I am running one-way ANOVA to determine whether several groups have differing means. I also run post-hoc multiple comparison to determine which means are different. The problem is that I need to have it showed which sets of groups are not different (like REGWQ test does). The problem is that Levene's test shows that the data I use do not have equal variances, thus, I cannot run REGWQ test.

Is there any alternative to REGWQ for cases when equal variances are not assumed (except for non-parametric K-W test)?

I use SPSS but can also try R.

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If I understand your question correctly, then yes SPSS has Unequal Sample Sizes and Unequal Variances (Post Hoc Tests algorithms): Games-Howell, Tamhane's T2, Dunnett's T3, and Dunnett's C. You would have to figure out yourself which one to use given your data, design and research objectives.

As for R, you can run the Games-Howell test in the userfriendlyscience R package (see also here for an example) and Dunnett's T3. For the other tests there don't seem to be packages/functions available for R.

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    $\begingroup$ Dear @Stefan, thanks for your answer. I am more interested, though, in a special REGWQ post-hoc test and its alternative. As far as I know, REGWQ can only be applied to situations, when equal variances are assumed. Then it groups variables with similar means (i.e. those that are not different) (egret.psychol.cam.ac.uk/statistics/…). My question is if there is an alternative to REGWQ in cases when equal variances are not assumed (because there is no such option in SPSS). $\endgroup$ – Tomas Jan 5 '17 at 7:31
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    $\begingroup$ @Tomas Oh I see, so the mean differences are first ordered from smallest to largest and then tested in a step-wise fashion. Sorry I don't know of any test that would do that for samples where the assumption of equal variances is not met. However, instead of testing this assumption with a formal test (e.g. Levene's test), you should inspect you data visually. Depending on your sample size these tests may or may not be very useful (e.g. here). $\endgroup$ – Stefan Jan 5 '17 at 15:21

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