week 9

Question 1

Univariate ANOVA

Answer 1

assesses the effect of a factor on one DV
What to do if we have multiple DVs that maybe correlated- Multivariate ANOVA

Question 2

Multivariate ANOVA (manova)

Answer 2

factors in the relationship between the DVs. It has the power to detect whether groups differ along a combination of DVs

Question 3

Choosing outcome variables

Answer 3

You need to have good theoretical or empirical basis to combine the outcome variables together in MANOVA
In other words, the outcome variables should be conceptually related and mean something in combination

Question 4

MANOVA assumptions

Answer 4

Same as ANOVA, there are a number of assumptions to be met before you run a MANOVA.
Independence: Residuals should be statistically independent.
Random sampling: Data should be randomly sampled from the population of interest.
Multivariate normality: Residuals have multivariate normality.
Homogeneity of covariance matrices

Question 5

Homogeneity

Answer 5

In univariate models, it is assumed that the variances in each group are roughly equal (homogeneity of variance).
In MANOVA, we assume that this is true for each outcome variable too.
In MANOVA, we also assumes that the correlation between any two DVs is approximately the same in all groups.
Whether the covariances between the DVs are equal across groups is tested using Box’s Test of Equality of Covariance Matrices.

Question 6

Box’s test of equality of covariance matrices

Answer 6

Box’s Test of Equality of Covariance Matrices should be non-significant if covariance matrices are similar. However,
Box’s test is very sensitive to multivariate normality.
In large samples Box’s test could be significant even when covariance matrices are relatively similar.
Practical advice:
Some researchers suggest using the significance level of .005 as criterion (p < .005)
If group sizes are equal then people tend to disregard Box’s test.

Question 7

MANOVA when to use

Answer 7

When to use MANOVA -
2 or more continuous DVs
1 or more categorical IVs
You can extend a MANOVA the same way you can do with an ANOVA, e.g. 2x3 ANOVA
In MANOVA, we create the composite DV to test whether groups differ along a combination of the DVs.