Week 9 (MANOVA)

Question 1

What is a multivariate ANOVA

Answer 1

-Used when we have multiple DVs that may be correlated

Question 2

MANOVA Assumptions

Answer 2

-Independence
-Random sampling
-Multivariate normality
-Homogeneity of covariance matrices

Question 3

Assumption of homogeneity of covariance matrices

Answer 3

-In ANOVA, we assume that variances in each group are roughly equal (homogeneity of variance)
-In MANOVA, we assume that this is true for each outcome variable too
-Also assume correlation between any two DVs is approx the same in all groups

Question 4

How to test whether the covariances between the DVs are equal across groups? (Homogeneity)

Answer 4

Box’s Test of Equality of Covariance Matrices

Question 5

Box’s Test of Equality of Covariance Matrices

Answer 5

-Should be non-significant if covariance matches are similar

Important to note
-Box’s test very sensitive to multivariate normality
-In large samples Box’s test could be significant even when covariance matrices are relatively similar
-Some researchers suggest using sig level of .0005 as criterion
-If group sizes are equal people tend to disregard Box’s test

Question 6

When to use MANOVA

Answer 6

-2 or more continuous DVs
-1 or more categorical IVs

-In MANOVA, we create the composite DV to test whether groups differ along a combination of the DVS

Question 7

What does a non-significant MANOVA imply

Answer 7

There is no significant difference in the composite DV across levels of the IV

Question 8

Two Commonly Used MANOVA Outputs

Answer 8

-Pillai’s Trace: often denoted V, similar to R squared
-Wilk’s Lambda

Question 9

Example of a Pillai’s Trace report

Answer 9

-V = 0.32, F (4,54) = 2.56, p = 0.49

Question 10

Why would we combine the DVs in this MANOVA format instead of just running another ANOVA

Answer 10

-Avoids inflated Type 1 error due to multiple testing, and accounts for the relationship between DVs