Suppose I have five samples with unequal sample sizes (50, 9, 10, 30, 15). If the variances of the samples are similar (e.g. p>0.05 from Levene's test), is it OK to use 1-factor analysis of variance for testing if the means are equal?

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    $\begingroup$ A large p-value doesn't of itself imply the sample variances are similar, since if the sample sizes are small the variances may be pretty different and still not get a small p-value. $\endgroup$ – Glen_b Jan 6 '15 at 15:34
  • $\begingroup$ So maybe I should additionally refer to the 4:1 ratio of variances rule (min to max)? $\endgroup$ – limit Jan 6 '15 at 18:40
  • $\begingroup$ Well, certainly in comparing larger samples, the ratio of variances gives you a better idea of how different the population variances are (a measure of 'how wrong the assumption is' is more use than a p-value). In small samples you could get very different sample variances even when population variances are quite close. [While you might be alright with ANOVA, it may be better in small samples not to assume equality in the first place. What is your response measuring?] $\endgroup$ – Glen_b Jan 6 '15 at 23:21

The rule of thumb I learned back in grad school was that this should be OK.

But that was long ago. Nowadays, you can 1) Use a nonparametric test and compare results or 2) Do a permutation test.


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