Multivariate Analysis Of Variance

Question 1

What is MANOVA?

Answer 1

Multivariate analysis of variance is used to perform an ANOVA style analysis on several dependent variables simultaneously.

Question 2

MANOVA answers the question

Answer 2

• Does the combination of several DVs vary with respect to the IVs?
• For example, do surgeons and psychiatrists differ in terms of the following personality traits: Abasement, Achievement, Aggression, Dominance, Impulsivity, Nurturance?

Question 3

In MANOVA a new…

Answer 3

DV is created that attempts to maximise the differences between the treatment groups
•The new DV is a linear combination of the DVs

Question 4

In comparison to ANOVA, MANOVA has the following advantages…

Answer 4

• The researcher improves their chances of finding what changes as a result of the experimental treatment
• Since only ‘one’ DV is tested the researcher is protected against inflating the type 1 error due to multiple comparisons
• It can show differences that individual ANOVAs do not – it is sometimes more powerful

Question 5

Assumptions of MANOVA

Answer 5

Multivariate normality
Homogeneity of variance-covariance matrices
Linearity
Multicollinearity and singularity

Question 6

Multivariate Normality

Answer 6

The sampling distributions of the DVs and all linear combinations of them are normal.

Question 7

Homogeneity of Variance-Covariance Matrices

Answer 7

Box’s M tests this but it is advised that p<0.001 is used as criterion

Question 8

Linearity

Answer 8

It is assumed that linear relationships between all pairs of DVs exist

Question 9

Multicollinearity and Singularity

Answer 9

• Multicollinearity – the relationship between pairs of variables is high (r>.90)
• Singularity – a variable is redundant; a variable is a combination of two or more of the other variables.

Question 10

Example MANOVA

Answer 10

• A group of children with moderate learning difficulties were assessed on a number of measures
• IQ, Maths, Reading Accuracy, Reading Comprehension, Communication Skill.
• The children were divided into four groups on the basis of gender (male, female) and season of birth (summer, not summer)
• A MANOVA was performed using gender and season of birth as the IVs and IQ mathematics, reading accuracy, reading comprehension and communication skills as the dependent variables.

Based on Bibby et al (1996)

Question 11

MANOVA- testing assumptions

Answer 11

• Do not reject the assumption of homogeneity of variance-covariance matrices
• Do not reject the assumption of homogeneity of variance

Question 12

Wilks’ Lambda is the…

Answer 12

statistic of choice for most researchers

Question 13

MANOVAS use

Answer 13

Univariate tests

Question 14

The pattern of analysis of a MANOVA is similar to

Answer 14

ANOVA
•If there is a significant multivariate effect then examine the univariate effects (i.e. ANOVA for each DV separately)
•If there is a significant univariate effect then conduct post hoc tests as necessary

Question 15

The aim of discriminant functions analysis is to find a

Answer 15

set of variables that predict membership of groups.

Question 16

When is discriminant functions analysis used?

Answer 16

used when groups are already known and the researcher is trying to find out what the differences are between the groups.

Question 17

Discriminate function analysis shortened is

Answer 17

DFA

Question 18

A DFA is approximately a reversal of a

Answer 18

MANOVA

Question 19

The assumptions that underlie a DFA are

Answer 19

The same as MANOVA

Question 20

Predictors are usually chosen on the basis of

Answer 20

Theory

Question 21

The aim of discriminant functions analysis is to find a

Answer 21

set of variables that predict membership of groups.

Question 22

The basic principle used in DFA is that

Answer 22

groups of subjects can be divided on the basis of functions that are linear combinations of the classifying variables.

Question 23

In DFA analysis Different functions are calculated that maximise the ability to predict

Answer 23

Membership of groups

Question 24

The maximum number of functions calculated is either

Answer 24

• The number of levels of the grouping variable less one

* The number of degrees of freedom of the IV.

Question 25

DFA analysis

The questions that can be answered include

Answer 25

• Can group membership be predicted reliably from a set of predictors?
• What are the differences between the predictors that predict group membership?
• What is the degree of association between the predictors and the groups?
• What proportion of cases are successfully predicted?

Question 26

Example DFA

Answer 26

• Can IQ, mathematical ability, reading accuracy, reading comprehension and communication skills predict who is summer born and who is not?
• See earlier example description.
• Not summer born coded as 0 and summer born coded as 1