Hello,
I ran the two-way ANOVA, but the Box's Test of Equality of Covariance result is significant (p = 0.000257). I checked Levene's Test of Equality and none of the DVs shows a significant result (all p-values larger than .05, actually the minimum is p=.100). Could I proceed with this MANOVA? Also, how would I appropriately report it?
Thank you,
Levene's test separately each dependent variable.
Box’s M test the assumption of equality of covariance matrices. However, Box's M is sensitive to large data files; therefore, it can detect even small departures from homogeneity. Moreover, it can be sensitive to departures from the assumption of normality.
If Box’s M test is significant, Pillai’s trace criterion should be used because more robust to departures from assumptions.
Transformation of the variables could be an option. Others option in the link:
https://www.researchgate.net/post/How_do_I_continue_with_my_analysis_if_the_Boxs_M_and_Levenes_tests_are_significant_in_MANOVA
https://www.researchgate.net/post/Assumptions_of_a_MANOVA_failed_are_there_alternatives
Yes, Pillar's trace criterion can be applied. Pillai’s trace is argued to be the most robust statistic for general protection against departures from the multivariate normality and homogeneity of variance–covariance matrices (Tabachnick, Fidell, & Ullman, 2007)
I think the equality of sample size needs to be taken into consideration. If the sample size across the groups is the same, violating the assumption of the equality of covariance is not a major problem and thus you can use Pillai's trace.
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