MANOVA Flashcards
MANOVA
Tests whether groups differ on a combination of multiple dependent variables. DVs must be conceptually related and there must be a theoretical reason for combining them.
Why do a MANOVA?
One-way ANOVA for each DV may result in no significant differences. In MANOVA, the DVs are combined to maximise group differences.
Assumptions of MANOVA
Normality (uni and multi variate), multicollinearity, independence, homogeneity of variance covariance matrices (Box’s), homogeneity of variance (Levene’s), linearity.
Variate
A linear combination of dependent variables. Also called discriminant functions, factors or latent variables.
Eigenvalue
A statistic that reflects the ratio of model variance to error variance. Used in MANOVA to assess group differences on a variate.
Interpreting MANOVA
Pillai’s Trace - use if assumptions are violated and sample size is equal
Wilks’s Lambda - use if assumptions are met
Hotelling’s T - similar to f-statistic
Roy’s Largest Root - only relies on first eigenvalue, thus most powerful
Discriminant Function Analysis
Follow up to MANOVA that uses the variate that best discriminates the groups to assess how well the combination predict the groups.
DFA Output
Eigenvalues - gives the % variance in group membership explained by each variate
Conical and Standardized conical… - coefficients for each DV (unstandardized and standardized)
Structure Matrices - indicates the relative contribution of each variable to the linear combination (variate)
Profile Analysis
Using a one-way MANOVA rather than a repeated measures ANOVA because the assumption of sphericity has been violated. Calculate a new variable for each pair of contrasts and use these as the DV in the MANOVA.
Following up MANOVA
Can use DFA or multiple one-way ANOVAs. The latter is debated because it may still increase the familywise error rate and the follow up ANOVAs may not be significant anyway (because it is the combination that is significant).
