I have a question regarding the appropriate use of comparisons for independent samples (3 factor levels) for various continuous variables.
Overall sample size is N=546, subsamples: 218 or 228 or 100), convenience sampling, stratified.
I use ANOVA with post hoc Tukey, if Levene indicates variance homogeneity.
My question:
If there no equal variance: What do do?
a) Using Kruskal-Wallis?
> For post hoc: Do I use Mann-Whitney for pairwise comparisons (if so: what about the alpha inflation?)?
b) Still using GLM but with non-parametric post hocs?
> If so: which one? Tamhane? Dunnett or Games-Howelll?
> What about F, can I still use it? isn’t H then the more appropriate statistic?
> Why gives GLM anyway the option of running on-parametric tests of homoscedasticity is an assumption.
Dear Anja
There is not a general rule for a situation like you describe. The GLM may tolerate some heteroscedasticity, but if it is very large you may be working with a very large type I error rate.
In option a) you may use Mann-Whitney for pairwise comparisons combined with the method of Bonferroni or Sidak that use an adjusted alpha for the posteriori comparisons.
You may also transform for each response looking for scales of measure where there are homoscedasticity.
You may also have an inference problem because the selection of the "convenience samples" of the three populations because the situation that produce the availability of the cases may be distorting the general characteristics of some of the populations. It is better to use a probabilistic sample.
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