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?

  • 1
    $\begingroup$ 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.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.