MANOVA

Question 1

What is MANOVA and what are its features

Answer 1

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

Question 2

Why are multiple ANOVAs not appropriate

Answer 2

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

Question 3

Situations when multiple ANOVAs are appropriate

Answer 3

1. when the DVs are conceptually independent
2. when research being conducted is exploratory in nature
3. when outcome variables have previously been studied in a univariate context

Question 4

what is the variable selection problem

Answer 4

if fewer outcome variables than total number initially chosen should form a basis for interpretation

Question 5

what is the variable ordering problem

Answer 5

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

Question 6

when is MANOVA most appropriate

Answer 6

when DVs are highly negatively correlated and when they are moderately correlated in either direction

Question 7

what are the advantages of MANOVA

Answer 7

1. controls Type 1 error rate compared to a series of multiple ANOVAs
2. looks at combined effects of all DVs
3. if there are low number of DVs, can be more powerful than a series of ANOVAs
4. inclusion of more DVs can result in a more robust model where sig effects are more likely to be found with reduced error variance

Question 8

what are the disadvantages of MANOVA

Answer 8

1. complex multivariate technique - issues with interpretation
2. questionability about whether it can actually control Type 1 error rate
3. selection of DVs require strong theoretical justification
4. redundancy with inclusion of highly correlated DVs

Question 9

What does Wilk’s Lambda measure

Answer 9

• 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

Question 10

what does Pillai’s Trace measure

Answer 10

• 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

Question 11

Roy’s Largest Root vs Hotellings T squared

Answer 11

• 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)

Question 12

What does the ‘on-diagonal’ measure in a matrix

Answer 12

sum of squared deviations of scores from the mean for that variable

Question 13

What does the ‘off-diagonal’ measure in a matrix

Answer 13

represents the combined effects of the DVs

Question 14

How is the final MANOVA statistic determined

Answer 14

Hypothesis SSCP matrix/error SSCP matrix

Question 15

What are MANOVA specific assumptions

Answer 15

1. Homogeneity of covariance matrices
2. Multivariate Normality
3. Multicollinearity and singularity

Question 16

What does the homogeneity of covariance matrices look at

Answer 16

• assumes that variance for each DV must be roughly equal AND the correlation between any two dependent DVs are similar in all groups

Question 17

when can you justifiably omit testing multivariate normality

Answer 17

when cell size is greater than 30 - MANOVA is considered robust to violations of normality

Question 18

What does multicollinearity expect

Answer 18

that the DVs should be moderately or negatively correlated with each other