For example, in comparing means of a variable (commonly compositional) between different sampling areas, we often have (1) different numbers of data in each category (2) non-normal data, even after 'suitable' transformation, and (3) differences in variance between categories.
I understand that conventional ANOVA can handle this to some extent, but at what stage do I need to use something like a General Linear Model? Some good references would help!
It is not always easy to say how well robust ANOVA will perform on specific data sets but one way to check is to simulate some data which is similar to your application and see how the test performs. Another approach would be to use resampling or permutation methods which are not restricted by the standard ANOVA assumptions. If you use the R statistical programming language the coin package (http://cran.r-project.org/web/packages/coin/vignettes/coin_implementation.pdf) is useful. There are also nonparamteric methods such as the Kruskal Wallis and Friedman methods.
Thanks Mark - I am an R user, and will investigate the coin package. I also like your idea of a Monte-Carlo-like approach; if I can find enough time I will definitely play with that.
regards...
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