NEW EXAM RM MANOVA (PROFILE ANALYSIS)

Question 1

What is a design with multiple DVs measured at multiple time points, but the multiple DVs do not have to be measured on the same scale?

Answer 1

Doubly Multivariate

Question 2

Outline the 4 similarities between repeated measures analysis of variance (ANOVA) and repeated measures MANOVA

Answer 2

1) address the same questions
2) test the same effects in the design (main effects and interactions)
3) applied to the same (repeated-measures) designs.
4) They are identical when the repeated-measures factors have only 2 levels.

Question 3

Highlight the 2 differences between repeated measures analysis of variance (ANOVA) and repeated measures MANOVA

Answer 3

Differences occur for any repeated-measures factor with >2 levels and they relate to:

1) assumptions: in particular RM ANOVA requires compound symmetry of the variance-covariance matrix often tested via sphericity (homogeneity of covariance) whereas RM MANOVA does not
2) test statistics: there are 4 for RM MANOVA (Wilks lamda etc) whereas only 1 (F-ratio) for RM ANOVA

Question 4

Profile analysis is a special application of multivariate analysis of variance (MANOVA) to a situation where

Answer 4

there are several dependent variables (DVs), all measured on the same scale.

Question 5

The set of DVs can either come from 2 routes

Answer 5

1)

one DV measured several different times -

(so between groups factor measured on DV1 time 1 - DV2 time 2 - DV3 time 3)

2)

or several different DVs all measured at one time (baseline - treat - post - baseline - treat - post = all on one composite DV)

Question 6

The choice between profile analysis and univariate repeated-measures ANOVA depends on 3 main things….

Answer 6

1)

sample size

2) power

3)

whether statistical assumptions of repeated-measures ANOVA are met.

Question 7

what 3 hypotheses are tested?

Answer 7

flatness
levels
parallelism

Question 8

Main limitation to profile analysis

Answer 8

1)

Choice of DVs is more limited in profile analysis than in usual applications of multivariate statistics, because DVs must be commensurate except in the doubly multivariate application. That is, they must all have been subjected to the same scaling techniques.

Way round is Z score DVs - but…

There is some danger in generalizing results with this approach, however, because sample standard deviations are used to form z-scores.

Question 9

In the choice between univariate repeated-measures ANOVA and profile analysis, xxxxxx xxxxxx is often the deciding factor.

Answer 9

sample size per group is often the deciding factor.

The sample size in each group is an important issue in profile analysis, as in MANOVA, because there should be more research units in the smallest group than there are DVs. This is recommended both because of considerations of power and for evaluation of the assumption of homogeneity of variance–covariance matrices

Question 10

what is not an issue with profile analysis ?

Answer 10

Unequal sample sizes typically provide no special difficulty in profile analysis because each hypothesis is tested as if in a one-way design and, as discussed in Section 6.5.4.2, unequal n creates difficulties in interpretation only in designs with more than one between-subjects IV

Question 11

what is the rule of thumb from terbachnick about sample sizes?

Answer 11

there should be more research units in the smallest group than there are DVs.

If it is small, use RM ANOVA

Question 12

If sample sizes are equal, what is not necessary?

Answer 12

If sample sizes are equal, evaluation of homogeneity of variance–covariance matrices is not necessary.

Question 13

what are the two main advantages of RM ANOVA?

Answer 13

1)

Reduced error (within-group) variance (P’s function as own control group – e.g. perhaps placebo condition were just better on that task)

2)

Statistical power increased – fewer P’s needed.

Question 14

what are the three main limitations or concerns of RM ANOVA?

Answer 14

1)

Order effects

2)

Carry over effects - A carryover effect is an effect that “carries over” from one experimental condition to another. Whenever subjects perform in more than one condition (as they do in within-subject designs) there is a possibility of carryover effects.

3)

Sensitisation - sensitised to treatment for instance

Question 15

one main limitation of profile analysis given by Devin?

Answer 15

Scaling – Limited as DV has to be on same scale (can use Z scores, but harder to interpret)

Question 16

RM MANOVA has greater power when what is violated in RM ANOVA?

Answer 16

Sphericity

Question 17

What is the one very serious assumption for RM MANOVA?

Answer 17

Multicollinearity – AVOID – omit redundant variable – Tolerance

Question 18

what is covariance?

Answer 18

Correlation is covariance of standardised variables

Question 19

what happens if Covariance among variables is not similar across groups?

Answer 19

If not same, interferes with the estimate of error variance (critical for F statistic)

Homogeneity of variance-covariance – Variance should be similar across groups

Question 20

what is the test for Homogeneity of variance-covariance ?

Answer 20

Box’s M

Question 21

What value for Boxs M?

Answer 21

less than .001 (more strict than .05)

Question 22

when do we not need to do Box’s M?

Answer 22

when sample sizes are equal across groups

Question 23

Why would you choose a profile analysis over a standard mixed model ANOVA?

Answer 23

The univariate is more powerful, but makes more assumptions

Question 24

what assumptions are different then?

Answer 24

1) Independence of observations (RM ANOVA sensitive to this, but PA is less so)
2) Multivariate normality
3) Sphericity needs to be assumed (univariate with 3 or more levels)

Question 25

what is RM ANOVA Sphericity then?

Answer 25

Critical assumption of RM ANOVA = It refers to the condition where the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal.

The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the conditions are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that would be inflated

Question 26

But the other type is that sphrecity can also be between

Answer 26

between ALL-PAIRs of levels of the within-groups variables have equivalent correlations
(time and longitudinal time points are most sensitive to this)

Question 27

what is the correction if sphericity is violated?

Answer 27

When violating assumption, consider using correction - Greenhous Geisser correction is most common as not too conservative or too liberal – moderate!

Question 28

or….

Answer 28

USE MULTIVARIATE STATISTICS (PROFILE ANALYSIS) AS DOESN’T DEPEND ON SPHERICITY

Question 29

what is a simple contrast? and the two possible ways to make one?

Answer 29

1) Simple contrast between two measures (of however many RM were taken) from one group IV
2) Simple contrast between two measures of the between groups values (from on RM)

Multiple simple contrasts could be made between any combination

Question 30

what is a simple effect?

Answer 30

a comparison between say all groups on one DV measure

or

a comparison between all RMs from one group

Question 31

where to look for a parallel effect in output?

Answer 31

the interaction term

remember to state the output and interpret what it would mean in relation to the given study

Question 32

where to look to see if profiles are flat in output?

Answer 32

main effect of RM

remember to state the output and interpret what it would mean in relation to the given study

Question 33

where to look for a levels effect in output?

Answer 33

the ANOVA main between groups effect

remember to state the output and interpret what it would mean in relation to the given study

Question 34

from exam paper:

What is the assumption of sphericity ?

Answer 34

Sphericity is a mathematical assumption about the structure of the covariance matrix in a repeated measures design [3 mark] –

an extension of the homogeneity of variance assumption in independent measures design [1 mark]

and a less restrictive form of compound symmetry [1 mark]. (Maximum 5 marks)

Question 35

How is sphericity commonly tested in RM ANOVA design?

Answer 35

If there is k repeated measures, then transform to (k-1) new variables (T1-T2, T2-T3 etc).

The sphericity assumption requires that the variances of all transformed variables are equal. [3 marks].

Commonly Mauchley’s test is used [subtract 2 mark]. **dont mention Mauchley lol **

Estimate epsilon and if it is 1 then the sphericity condition is strictly met, worse violated if it is 1/(k-1) [2 marks]. (Maximum 5 marks

Question 36

What are the options available if sphericity is violated? (4)

Answer 36

1) lower-bound
2) Greenhouse-Geisser
3) Huynh-Feldt Correction
4) Or use multivariate statistics since they are not dependent upon the assumption of sphericity

Question 37

Describe why the sphericity assumption is likely to be especially important when a within-subjects factor involves repeated measurements over time.

Answer 37

Sphericity requires that all pairs of levels of the within subjects need to have equal correlations.

For RM design, this assumption is likely to violated since things measured closer in time tend to be highly correlated than things measured farther away in time: for example, the correlation between verbal recall performance measured at ages 5 and 6 yrs is likely to be higher than the correlation between performance scores measured at age 5 and 10 yrs.