Checking the Additional Assumptions of a MANOVA
Researchers typically view a MANOVA as an extension of an ANOVA with more than one continuous variable. You should check the typical assumptions of an ANOVA, such as normality, equality of variance, and univariate outliers. Additionally, you must check other assumptions when conducting a MANOVA.
The additional assumptions of the MANOVA include:
Equality of covariance matrices
Absence of multivariate outliers
Linearity
Absence of multicollinearity
You check the absence of multivariate outliers by assessing Mahalanobis distances among the participants. To do this in SPSS, run a multiple linear regression with all of the dependent variables of the MANOVA as the independent variables of the multiple linear regression. The dependent variable would be simply an ID variable. There is an option in SPSS to save the Mahalanobis Distances when running the regression. Once you sort the Mahalanobis distances from greatest to least, identify outliers by comparing the values to the critical chi-square value. This value is derived at p = .001, with degrees of freedom equal to the number of dependent variables. For 3 variables, the critical value is 16.27, so remove any participants with a Mahalanobis distance greater than 16.27.
Linearity assumes that all of the dependent variables are linearly related to each other. You can check this by conducting a scatterplot matrix between the dependent variables. Ensure that you meet linearity for each group of the MANOVA separately.
You check the absence of multicollinearity by conducting correlations among the dependent variables. The dependent variables should all be moderately related, but any correlation over .80 presents a concern for multicollinearity.
You check the equality of covariance matrices by running a Box’s M test. Unlike most tests, the Box’s M test tends to be very strict, and thus the level of significance is typically .001. So as long as the p value for the test is above .001, the assumption is met.