Module 5

Question 1

How much do we want our DVs to be correlated?

Answer 1

Preferably .2-.4 would be a nice correlation. Anything above .6 is problematic

Question 2

What is more important than deciding on DVs that are statistically related?

Answer 2

It is more important that DVs work together to explain a greater concept, rather than be correlated statistically.

Question 3

What does MANOVA protect against?

Answer 3

MANOVA protects against inflated Type I error (only when DVs are correlated)

Question 4

In what case is MANOVA more useful than just running multiple ANOVAs?

Answer 4

MANOVA is more useful when provides greater insight and explanation about the variables, beyond doing multiple ANOVAs

Question 5

How many IVs and DVs do we require for MANOVA. What types of variables should they be?

Answer 5

We need at least 1 IV (continuous or categorical)

We need at least 2 continuous DVs

Question 6

What is another name for the rows and columns in a matrix?

Answer 6

Vectors

Question 7

What are two other names for the individual values in a matrix?

Answer 7

Components or elements

Question 8

How many rows and columns are in a 3x6 matrix?

Answer 8

3 rows, 6 columns

Question 9

What is a square matrix?

Answer 9

A matrix with an equal number of rows and columns

Question 10

What is an identity matrix?

Answer 10

A matrix where the diagonal values are all 1, and the off-diagonal values are all 0

Question 11

What are the 3 additional data cleaning requirements for MANOVA?

Answer 11

Homogeneity of matrices
Multivariate normality
Multicollinearity and singularity

Question 12

What are the two assumptions underlying the assumption of homogeneity of covariance matrices?

Answer 12

1) The variances for each DV are equal
2) The correlation between 2 DVs is the same for all groups
It is testing the assumption that each cell of the matrix is from the same population

Question 13

What statistic tells us about homogeneity of covariance matrices?

Answer 13

Box’s M. We want a non-significant result. This test can be ignored when sample sizes are equal because some MANOVA test statistics are robust to violations of this assumption

Question 14

How does Field (2013) suggest we check for the assumption of multivariate outliers?

Answer 14

Check the assumption of univariate normality of residuals for each DV in turn. But this does not guarantee multivariate normality.

Question 15

To avoid multicollinearity, how should we select our DVs? What correlation indicates multicollinearity?

Answer 15

We should select DVs that are moderately or negatively correlated. Anything above .9 or below -.9 correlation represents multicollinearity.

Question 16

What are the 4 MANOVA test statistics?

Answer 16

1) Pillai’s trace (preferred when sample sizes are equal)
2) Wilk’s Lambda
3) Hotelling’s trace
4) Roy’s Largest Root

Question 17

What does the ‘Multivariate Tests’ table tell us?

Answer 17

The results of the MANOVA

Question 18

What does the ‘Tests of Between Subjects Effects’ tell us?

Answer 18

The results of the individual ANOVAs performed after the MANOVA

Question 19

What is Discriminant Function Analysis?

Answer 19

DFA is an assessment on how a set of groups can be best discriminated using the linear variates (functions) of several predictors. i.e. how the DVs can separate the groups

Question 20

How does Roy Bargman’s method work? What conditions do we require to use it?

Answer 20

Roy Bargman’s is a step-down method which sequentially covaries out DVs. To use it, we need to have a significant MANOVA, but non-significant individual ANOVAs. This method will show where the true differences are when ANOVAs cannot.

Question 21

What is a variate? What does a significance < .05 mean for a variate?

Answer 21

A variate is a combination of DVs and if significant it means this variate is significantly discriminating the groups

Question 22

After you’ve identified your variates, what will the ‘Standardised Canonical Discriminant Function Coefficients’ table tell you?

Answer 22

This table will tell us how a DV contributes to a variate. A high score means it contributes a lot, and a both positive and negative score means it contributes to the variate in opposite ways

Question 23

What does the ‘Functions at Group Centroids’ table tell us?

Answer 23

It tells us which group are being discriminated by a variate. For a given variate, a group with positive and negative signs is being discriminated by that variate.

Question 24

When testing for assumptions, when do we need to have the data split by groups?

Answer 24

When checking for univariate outliers/normality, and when checking linearity

Question 25

Which assumption is checked in the main analysis?

Answer 25

Homogeneity of covariance matrices

Question 26

Imagine we get a significant MANOVA, but non-significant univariate ANOVA. What does Field recommend we do? What does Hills recommend?

Answer 26

Field says MANOVA has more power to detect group differences, so we should trust it and follow-up with DFA.
Hills says we should follow up with Roy Bargman’s method. Remember, it’s all about how you justify using the test you choose.

Question 27

In the literature, what is the most used statistic? What is the most robust?

Answer 27

Wilk’s Lambda is most used in literature. However, Pillai’s trace is considered most robust, especially when we have assumption violations or our sample sizes are equal