MANOVA

Question 1

In MANOVA, we replace single DVs with ____________________

Answer 1

the list of observed values

Question 2

With a vector, the variability is ___________________________

Answer 2

a combination of variance and covariance

Question 3

MANOVA removes the __________ between the DVs

Answer 3

covariance

Question 4

For MANOVA, we take _______________(SSCP)

We then make these SSCP into _____________ matrices by ____________________________

Answer 4

sums of squares and the ‘cross products’

we then make these SSCP into co-variance matrices by dividing the entries by the degrees of freedom

Question 5

H0 of MANOVA

Answer 5

no systematic differene between the means
BetweenCovariance= ErrorCovariance
BetweenSSCP * Error^(-1)SSCP = I

Question 6

what happens after discriminating 2 groups using MANOVA

Answer 6

transformed DV1 discriminates between groups better than the raw DV1
Transformed DV2 not as good as raw DV2, but loss compensated by new DV1
Get two new uncorrelated variables
Each variable tries to maximise some discrimination
‘New DV1’ pulled group A away from B
Nothing left for ‘new DV2’ to do
Get maximum discrimination
The ‘new DV1’ gives the best possible discrimination between the two groups

Question 7

what happens after discriminating 3 groups using MANOVA

Answer 7

Get two new uncorrelated variables
Each variable tries to maximise some discrimination
‘New DV1’ pulled group C away from A&B
‘New DV2’ pulled group A from B
Combined, get maximum discrimination
Using ‘new DV1’ can tell if its C.
If it is not C, use the ‘new DV2’ to tell if it’s A or B

Question 8

What is MANOVA doing in general

Answer 8

1. Creates a set of uncorrelated variables
   A ‘new DVs’ for each DV entered
   Can’t predict one ‘new DV’ from others
2. Each variable tries to maximise some aspect of discriminating between groups
   Need to think of all of the ‘new DVs’ together
3. Combined, get maximum discrimination
   Bear in mind each ‘new DV’ is linear

Question 9

what are the assumptions of MANOVA

Answer 9

1. Multivariate normality
   all distributions and their combinations are normally distributed
2. Homogeneity of variance/ covariance
   Leven’s test for homogeneity of (error) variance
   Important criteria assessed by Box’s M. Adjust alpha level if Box’s M indicates violation of assumption
3. Sensitive to outliers
   Outliers will influence many correlations/ covariance estimates
4. Linearity of relationships between variables
   Do not use MANOVA if theoretically expect non-linear relationships
   Remember that floor/ ceiling effects with, for example, accuracy also introduce non-linearities.
5. Don’t run MANOVA if DV not correlated (no point of running) or too correlated (no variability for DV2 to be orthogonal)

Question 10

what does significance in MANOVA indicate

Answer 10

there are the number of combinations - but now the differences could be the combinations of the DVs as well as combinations of individual means

Question 11

What statistics can be used to estimate the significance of MANOVA

Answer 11

Generally go with Wilks lambda
Use Pillai’s trace if heterogeneous covariances
Don’t use Roy’s Largest Trace