I'm using SPSS. I have a multi-level categorical IV and a few continuous DV's. My main analysis goals are to test the effect of the IV on the DV, and then to follow-up with pairwise comparisons of level 1 of the IV to each of the other levels. However, Levene's test for homogeneity of variance is significant for all of them, and the sample sizes are very unequal across levels of the IV. To deal with the heterogeneity of variance and unequal sample sizes, I conducted Welch tests in place of standard one-way ANOVA's, and followed up with independent sample t-tests, consulting the adjustment for unequal variances where appropriate (equivalent to a Welch t-test). However, I have now realised that my main IV is confounded with some of the measured demographic factors (age, sex, region) that also have an effect on the DV, so I'd like to control for that. To do this, it would make sense to run an ANCOVA, with pairwise comparisons using estimated marginal means, rather than raw means. However, ANCOVA (of course, as a variant of ANOVA) assumes equal sample sizes and homogeneity of variance. Is there a way I can simultaneously (i) correct for these assumption violations, while (ii) controlling for the possible effects of covariates? If not, which is the better route to take? I read that heterogeneity of variance is especially a problem if the variance ratio (largest variance/smallest variance) is greater than 2 and can perhaps be ignored if it's lower than that (though I don't know wh…

Full article content could not be extracted automatically. Read the original below.