What do I do if I have unequal group covariance matrices when doing a MANOVA?
Tabachnick and Fidell (2007) suggest that Wilks Lambda should be used to compare 2 or more mean vectors between groups when doing a multivariate analysis of variance (MANOVA). If, however, Box's M test signifies that the group covariance matrices differ they suggest using Pillai's criterion as it has been found to have a more robust multivariate significance when the homogeneity of variance assumption is violated (Olson, 1979). Both these multivariate generalizations of the F test are outputted by the SPSS GLM and MANOVA procedures.
References
Olson CL (1979) Practical considerations in choosing a MANOVA test statistic: A rejoinder to Stevens. Psychological Bulletin, 86, 1350-1352.
(A PDF copy of the above paper is available for CBSU users via ScienceDirect).
Tabachnick BG and Fidell LS (2007) Using Multivariate Statistics. Pearson Education:Boston.