Post hoc test for 1-way Anova with heteroscedasticity

Question

I understand that post-hoc Tukey contrasts are inadequate on a 1-way ANOVA that violates the homoscedastiscity assumption, and that Games Howell or Dunnet contrasts are among the recommended alternatives. Does anyone know if this holds true even if I refit my ANOVA with gls using a varIdent variance structure to address the heteroscedasticity? In other words: Can I use Tukey contrasts after managing heteroscedasticity with gls and a variance structure, or do I still need to look for alternative Post-hoc tests?

Thanks in advance

Answer 1

I don't agree with your premise: If you wanted to do all pairwise comparisons, why would you change that objective just because some underlying assumption is violated?

Instead, you can compute the t statistics for each pairwise comparison using the estimated standard errors for each difference, and adjust the P values using a Bonferroni correction (conservative); or, for an approximate critical value for comparing the ith and jth means, use $\sqrt{1/2}q_\alpha(k,d_{ij})$ from the Studentized Range tables, where $k$ is the number of means and $d_{ij}$ is the df for that comparison.

The lsmeans package in R implements this procedure but you need to wait for the next update or contact its developer because there was a bug in the support for the varIdent structure.