So a MANOVA is typically seen as an extension of an ANOVA
that has more than one continuous variable. The typical assumptions of an ANOVA
should be checked, such as normality, equality of variance, and univariate
outliers. However, there are additional assumptions that should be checked when
conducting a MANOVA.
The additional assumptions of the MANOVA include:
- Absence of multivariate outliers
- Linearity
- Absence of multicollinearity
- Equality of covariance matrices
Absence of multivariate outliers is checked 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 this is done, sort the
Mahalanobis Distances from greatest to least. To identify an outlier, the
critical chi square value must be known. This is derived from the critical chi
square value at p = .001 with the
degrees of freedom being the number of dependent variables. With 3 variables,
the critical value is 16.27, so any participants with a Mahalanobis Distance
value greater than 16.27 should be removed.
Linearity assumes that all of the dependent variables are
linearly related to each other. This can be checked by conducting a scatterplot
matrix between the dependent variables. Linearity should be met for each group
of the MANOVA separately.
Absence of multicollinearity is checked 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.
Equality of covariance matrices is an assumption checked 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.
