I am currently analysing data on whether there is a difference in the level of understanding between maths and science using a sample of year 1, year 2 and year 3 students. I am also looking at whether the level of understanding improves across the year groups. I am running a mixed ANOVA, however my homogeneity of variances for science were violated. Can I run it anyway?
You can use weights to account for heterogeneous variances. The weight are typically chosen proportional to the reciprocal of the variance (what will give lower weights to groups with higher variance).
Of these tests, the most common assessment for homogeneity of variance is Levene's test. The Levene's test uses an F-test to test the null hypothesis that the variance is equal across groups. A p value less than .05 indicates a violation of the assumption .
It is better to stop the process.
Jack Son,
you got trapped in abusing significance tests to justify the suitability of assumptions. The test is designed to identify a stochastic incompatibility of the data with a (null-)hypothesis. The test is essentially only an indicator of the sample size ("significant" -> sample is large enough, "non-significant" -> sample is not large enough). Noteably, even if the test is significant, the test is quiet on the (possible) relevance of the identified incompatibility. Thus, there are two possible outcomes/results the test may have, and both are not useful for the problem at hand: either it is "significant", then you know that the sample is large enough to see that the data does not resemble some idealized model, but you don't know if this is of any relevance for the purpose -- or it is "not significant", in which case you now that your sample is too small, but you don't know if you miss to see any relevant effect/difference. Conclusion: a significance test on an assumption (like tests for variance homogenetity and normal distribution) that another test is based upon, are not instructive. If an assumption makes sense or not is a subject-matter decision, based on arguments (and, well, on experience). It can't be substituted in any rational way by blind adherence to significance tests perfomred on the data at hand.
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