I would like to compare multiple means using a method such as an ANOVA. This would have to be followed up with either Scheffe's test or the Games-Howell post-hoc method (my data is non-normal - to different degrees and can't all be transformed to normality using the same transformation - heteroscedastic and has greatly differing sample sizes).
In their Opthalmic and Physiological Optics paper, Armstrong et al. (2000) state that these tests can only be performed after an ANOVA returns a significant result. My question is this - how can an ANOVA be appropriately applied to data such as mine, which require these post-hoc tests simply because they violate so many assumptions of the ANOVA? It seems odd to me that they should advocate the use of an ANOVA before post-hoc tests that are used in place of others because of the violations of the ANOVA assumptions.
Also - on a side note, does anyone have any advice as to whether to use the above approach or to use the multcomp package available in R?