In a mixed design, I had two within-subjects factors (named Factor 1 and Factor 2) and one between-subjects factor (named Factor 3). Factor 1 had 15 levels, Factor 2 had 2 levels, an Factor 3 had 5 levels. Repeated measures ANOVA was used to check the main effects and interaction effects of three factors. Levene's test was used to check the equality of error variances among the 5 levels of Factor 3 under each combination of Factor 1 and Factor 2. The number of combinations of Factor 1 ad Factor 2 are 15 * 2, 30.
The question is that the 5 levels of Factor 3 in specific combinations of Factor 1 and Factor 2 did not pass Levene's test (p < 0.05).
What should I do?
I guess one solution is to remove those specific combinations of Factor 1 and Factor 2 in which the 5 levels of Factor did not have equal variance.
Can someone suggest some methods to address my problem or provide some resources/literature to deal with it?
Thanks a lot.
Peng.
Check for multiplicity in so many Levene test. And also check other assumptions (sphericity, normality and so on).
Your solution of removing a given combination does not seem a good idea to me, especially if you use traditional repeated measures ANOVA which very much likes balanced designs, and anyway because it does seem a very clean methodology to remove annoying data... Offering other solutions is difficult without more information.
At first glance, not: removing values for convenience does not seem very acceptable. Including variance heterogeneity in the model, or at least trying to understand why for these levels there is a different variance, seems a better approach. But once again, without more informations, it's difficult to say more.
Hi Dr. Curis, thanks
I have checked some resources (http://www.basic.northwestern.edu/statguidefiles/oneway_anova_ass_viol.html; http://www.ats.ucla.edu/stat/stata/library/homvar.htm), it may suggest to stay with all of the data, as you suggested. I have equal sample sizes between groups. The heterogeneity of some of my data set may not affect the F and p statistics. Do you think so?
No, I don't think so, it depends on the exact structure of the heterogeneity, the sample size... You'd better check that it indeed does not strongly affects your tests.
By the way, did you also checked normality? Sometime, hetereoskedasticity is just a consequence of non-normal values, and some transformations resolve both issues...
I have tried Square Root Transformation and other transformation methods. It showed that Square Root Transformation may be a better way. For the raw data, data of 6 levels of Factor 1 did not pass Levene's test. For the transformed data, data of 4 levels of Factor 1 did not pass Levene's test. So, it seemed that transformation did not work very well in my research.
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