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I have run a repeated measures ANOVA using 3 groups and one factor with two levels.

I have discovered that the data are not normally distributed (but not badly), nor is the variance homogeneous in either of the factor's conditions across groups.

If the data are not normal, I would use a Kruskal-Wallis and post-hoc Mann Whitney; if the data are not homogeneous with respect to variance, I would use a Welch Test and post-hoc Games-Howell test.

Can anyone tell which test(s) should be used if the data are not normal, and it does not have homogeneous variance?

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I don't believe the Kruskal-Wallis test is appropriate for clustered (repeated measures) data. Note that non-normality isn't generally a big deal if your data are continuous & interval, but you just have small but non-0 skew or kurtosis. If you have heterogeneity, would a transformation help to stabilize the variances? What software are you using? Would you be able to code up a bootstrap analysis? – gung Jul 23 '12 at 16:50
@gung you stold my thunder. I was going to mention that the F test works okay when comparing means if the normality and homoskedasity assumptions were violated only mildly. Also the bootstrap does work in this situation so I was going to suggest it. I think you should turn your comment to an answer. I would have made it an answer but you beat me on this one and my advice is the same. – Michael Chernick Jul 23 '12 at 17:34
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One note - OLS regression does not require that the data be normally distributed, only that the error, as estimated by the residuals, are. – Peter Flom Jul 23 '12 at 18:06

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