Lecture 8 - MANOVA Flashcards
What is MANOVA?
Multivariate Analysis of Variance. ANOVA with more than one DV.
How does MANOVA work?
It LINEARLY combines the DVs into one new DV, maximising group differences.
Thus, you want your DVs to be correlated
What are the advantages and disadvantage of MANOVA?
- improves chances of discovering what changes (increased power)
- may reveal diffs not shown in separate ANOVAs
- more complicated
What does MANOVA calculate and give you?
- sums of squares
- cross-products
What are cross-products? How are they calculated?
- correlations between the DVs!!!
- diff b/w observation and mean for one DV; for the other DV; then multiply
What is the HE-1 matrix?
Similar to the F ratio in ANOVA. SSCPhypothesised/SSCPerror
BUT instead of just one F ratio, we now have a whole matix of them
How do you summarise the HE-1 matrix?
- you form discriminant function variates (new DVs) that clearly discriminate b/w groups
- similar to principal components (extracts eigenvectors and eigenvalues)
What are the 4 multivariate significance tests?
Pillai-Bartlett trace
Hotellings T2
Wilks’ lambda
Roy’s largest root
When do you use each of the 4 multivariate significance tests?
- Roy: groups diffs concentrated on first variable
- PB: group diffs concentrated on more than one variable
- PB: most robust to violation of assumptions (if equal sample sizes)
- Wilks’: criterion of choice unless reason to use PB (i.e. robustness)
What are the 3 assumptions of MANOVA?
- correlations between DVs
- multivariate normality
- homogeneity of covariance matrices
How do you check for multivariate normality?
It is very difficult. If your DVs are normally distributed, then you should be fine
How do you check for homogeneity of covariance matrices?
- Box’s M test: v sensitive (want >.05)
- Levene’s test: only really for univariate (want >.05)
- Bartlett’s sphericity test: only for univariate repeated measures.
SO….
- use SYNTAX > want the log(determinant) values for each cell to be about the same
What is the difference between using MANOVA vs. many univariate ANOVAs?
- can sometimes get different results (significance wise)
- doing many univariates increasing chance of getting Type 1 error
- with many univariates, Bonferrroni adjustments might be made to F-tests
What are contrasts for? What do you look at?
- helpful to see where the differences lie
- simple contrasts: compare all categories to the last one (or first one)
- look at sig. and CI
How are MANOVA and ANOVA different/similar?
- BOTH: testing if mean groups diffs on one DV have occurred by chance
- MANOVA does this on a combination the DVs (want DVs correlated)
- ANOVA only uses sums of squares, MANOVA uses both SS and cross-products
