MANOVA Flashcards
What is MANOVA and what are its features
MANOVA is a multivariate technique that looks at group differences across multiple DVs
It is useful for when a DV is can’t be captured by a single variable
considers combined effects of the DVs and how they work together to separate groups
Why are multiple ANOVAs not appropriate
understanding of resulting MANOVA effects may not be gained by studying the significance of multiple ANOVAs
A significant MANOVA difference need not imply that any significant ANOVA effect/s exist
Situations when multiple ANOVAs are appropriate
- when the DVs are conceptually independent
- when research being conducted is exploratory in nature
- when outcome variables have previously been studied in a univariate context
what is the variable selection problem
if fewer outcome variables than total number initially chosen should form a basis for interpretation
what is the variable ordering problem
to make an assessment of the relative contribution of the outcome variables to the resultant group differences or to the resultant effects of the treatment variable
when is MANOVA most appropriate
when DVs are highly negatively correlated and when they are moderately correlated in either direction
what are the advantages of MANOVA
- controls Type 1 error rate compared to a series of multiple ANOVAs
- looks at combined effects of all DVs
- if there are low number of DVs, can be more powerful than a series of ANOVAs
- inclusion of more DVs can result in a more robust model where sig effects are more likely to be found with reduced error variance
what are the disadvantages of MANOVA
- complex multivariate technique - issues with interpretation
- questionability about whether it can actually control Type 1 error rate
- selection of DVs require strong theoretical justification
- redundancy with inclusion of highly correlated DVs
What does Wilk’s Lambda measure
- The amount of variance in the variate not accounted for by the IV
- If multiple DVs, then the final value will be the product of the unexplained variance from each variate
- most commonly used and appropriate when assumptions are met
what does Pillai’s Trace measure
- The amount of variance in the variate accounted for by the IV
- If multiple DVs, the final value is the sum of explained variance in the variate
- robust to assumption violations and when sample sizes are equal
Roy’s Largest Root vs Hotellings T squared
- Both look at eigenvalues
- Hotellings looks at explained variance/unexplained variance for EACH variate
- Roy’s only looks at it for first variate (very powerful if only one variate in analysis and assumptions are met)
What does the ‘on-diagonal’ measure in a matrix
sum of squared deviations of scores from the mean for that variable
What does the ‘off-diagonal’ measure in a matrix
represents the combined effects of the DVs
How is the final MANOVA statistic determined
Hypothesis SSCP matrix/error SSCP matrix
What are MANOVA specific assumptions
- Homogeneity of covariance matrices
- Multivariate Normality
- Multicollinearity and singularity