ANOVA preconditions I've got m samples coming from n different groups.
What tests do I have to do before applying ANOVA to ensure that the preconditions are satisfied?
Thanks in advance.
 A: *

*The ANOVA assumptions will usually only matter much if you're doing inference that relies on assumptions (e.g. hypothesis testing, confidence intervals)

*Generally speaking it's easier to examine assumptions after the fact rather than before (in particular, for the usual normal theory ANOVA they relate to the conditional distribution of the response vector - equivalently the error term) and are best considered in terms of residuals from the fitted model.

*I would not recommend formal tests of any assumptions; that answers the wrong question (the question is not "are the assumptions true" -- it would be rare that any of them are exactly true, but that often doesn't matter). What matters is the effect on your inference -- such as significance level and power in a hypothesis test -- of the manner in which the assumptions fail, and the extent to which those failures occur. Because it's a question of "how much" -- a kind of effect size -- statistical significance is not really relevant (at large samples you can reject trivial differences from assumptions, while at small sample sizes you may fail to reject even very serious failures)

*If you can't reasonably reliably say that the assumptions will be quite close to true you simply shouldn't make those assumptions. In many cases, inference can be performed quite well (often just as well) with much weaker assumptions.

So let's imagine you mean to do normal theory hypothesis testing in a one-way ANOVA, where it appears you have equal sample sizes.
What assumptions do we need to consider:


*

*equality of variance
With equal sample sizes, the procedure is insensitive to differences in variance, so this isn't going to impact the properties very much
I would assess it with diagnostic displays (e.g. dotplots / stripcharts or similar displays that indicate spread against group)

*normality
ANOVA is reasonably robust to mild deviations from normality -- or rather it has pretty good level-robustness especially at large sample sizes. The power, however, is affected by non-normality and I'd be particularly concerned if there were heavy tails or strong skewness. If I didn't have a good idea - before collecting the data - that the data would be close to normal, I would consider alternative analyses, (depending on circumstances I might consider a GLM, a permutation test, a robust version of ANOVA, a Kruskal-Wallis test, etc)
I'd assess this by looking at a Q-Q plot of residuals (assuming the spreads weren't very different)

*independence 
This is an important assumption but one that's hard to check because there's so many ways in which it might be violated. Suitable checks will depend on what kinds of non-independence you might see as most likely. 
