I know that one of the key conditions of performing an ANOVA test is that the variances of the groups has to be broadly similar. I have some data sets that I need to compare and the variance of some of them is very different to the rest. Surely this in itself proves (indicates?) that the samples are taken from different populations so I don't need to go any further?
Could I perform some type of test on the difference in variances and get a p value for likelihood that the variances are actually different? If p is significant then wouldn't this show that the groups are actually different anyway, regardless of whether or not their means are similar?