RM ANOVA / RM MANOVA

Question 1

When is profile analysis (PA) used?

Answer 1

RM mixed model ANOVA + more than 1 DV

Question 2

What are the deisgn features of PA?

Answer 2

– can be ‘between-within’ design
– can be same DV repeatedly measured (e.g. one DV at time point t1, t2, t3 - An achievement test is given at various points during term to test the effects of alternative educational programs (e.g., traditional classroom vs. computer- assisted) – could use a standard RM mixed-model ANOVA
– can be several DVs measured (on same scale) (perhaps all different qu’s on Likert scale e.g. Patients with major depression or anxiety complete different scales (anxiety, anger, paranoia, etc.), all measured on the same scale)
– As alternative to RM ANOVA

Question 3

What is Doubly multivariate design?

Answer 3

Doubly multivariate design is like RM MANOVA but the DVs don’t have to be measured on the same scale

Question 4

Advantages of PA?

Answer 4

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

Question 5

Concerns of PA?

Answer 5

Ð Order effects
Ð 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.
Ð Sensitisation - sensitised to treatment for instance

Question 6

what to do if DVs are not commensurate?

Answer 6

One way to produce commensurability is to use standardized scores, such as z-scores, instead of raw scores for the DVs. In this case, each DV is standardized using the pooled within-groups standard deviation (the square root of the error mean square for the DV) provided by univariate one-way between-subjects ANOVA for the DV

Question 7

what is main reason one might choose between profile analysis and RM ANOVA?

Answer 7

In the choice between univariate repeated-measures ANOVA and profile analysis, sample size per group is often the deciding factor.

Question 8

how does PA roughly work?

Answer 8

Profile Analysis Looks at whether groups have different profiles on a set of measures – all scores must have same meaning/value – profile analysis looks at the difference between these scores.

The differences are called SEGMENTS

Question 9

What do these SEGMENTS represent in PA?

Answer 9

The DV

Question 10

What are the three null hypotheses being tested in PA?

Answer 10

1) Parallelism hypothesis – Do different groups have a parallel profile across the within groups measures? (Rejecting the null hypothesis corresponds to a between groups x within groups interaction)
2) Levels hypothesis – Does one group score higher than the other. Standard between-groups main effect.
3) Flatness hypothesis – Are the profiles flat across the different levels. Do all the DVs elicit the same average response. Within groups main effect.

Question 11

Details of Parallelism?

Answer 11

IS THERE AN INTERACTION?

If groups are parallel, then it implies one group scored uniformly the same or better across all profiles, or within factors. No interaction.

If not parallel, then there is a GROUP X VARIABLE interaction + you would need to clarify the source of this interaction.

Question 12

Details of Levels?

Answer 12

ARE THE PROFILES LEVEL WITH ONE ANOTHER?

Just interested in the standard between-groups effect. Main effect of group.

Question 13

Details of Flatness?

Answer 13

ARE THE PROFILE FLAT?

Do all DVs show same average score? Take mean of all groups and look at within varaiation. Is the result flat?

Ð Mostly only relevant when parallel, as if not parallel, then not necessarily flat.
Ð Can ask about flatness separately
Ð Profile may be non-parallel but none may deviate significantly from flatness
Ð SAME QU as within-groups main effect

Question 14

What needs to be done post PA?

Answer 14

FOLLOW UP WITH CONTRAST ANALYSES for more than two groups to find out exactly where effect is.

Question 15

A limitation of PA?

Answer 15

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

Question 16

What are the main assumptions of PA?

Answer 16

Sample Size 
Normality 
Outliers 
Linearity 
Multicollinearity 
Homogeneity of variance-covariance

Question 17

Expand on sample size…

Answer 17

More N in smallest group than DV. This is because of power. If it is small, use RM ANOVA

However, RM MANOVA has greater power when sphericity is violated in RM ANOVA

Unequal sample sizes is not really a problem here.

Question 18

Expand on Normality…

Answer 18

Multivariate normality should be normally distributed – however Robust against violations of normality when in greater N sizes – (e.g. >20 in smallest group) – not so much problem if N is equal across groups and smallest N is greater than total DVs.

Question 19

Expand on Linearity…

Answer 19

For parallelism & flatness tests, linear among DVs is assumed. Loss of power if not. Curvilinear or non-linear will cause issues. +N to get around this.

Question 20

Expand on Multicollinearity …

Answer 20

AVOID – omit redundant variable – Tolerance

Question 21

Expand on Homogeneity of variance-covariance …

Answer 21

Variance should be similar across groups

Ð For equal sample sizes between groups = no test necessary

Covariance Matrices = Covariance among variables should be similar across groups
Ð Correlation is covariance of standardised variables
Ð If not same, interferes with the estimate of error variance (critical for F statistic)

Question 22

how do we test for Homogeneity of variance-covariance?

Answer 22

Box’s Test for unequal sample sizes

Ð Sensitive to violations (rather than alpha .05 use .001.
Ð Use p

Question 23

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

Answer 23

Ð The univariate is more powerful, but makes more assumptions

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 24

IN RM ANOVA….which critical assumption did you leave out?

Answer 24

Sphericity

Question 25

details of RM ANOVA sphericity?

Answer 25

Critical assumption of RM ANOVA = Variance of the differences between all pairs of dependent variables (levels) in a within-groups variable should be uniform.
But the other type is that sphrecity can also be between ALL-PAIRs of levels of the within-groups variables have equivalent correlations
(time and longitudinal time points are most sensitive to this)

Question 26

what happens in sphericity is not met?

Answer 26

Ð If the sphericity assumption is not met, then the F value is positively biased (we are rejecting falsely too often) (Box, 1954)
Ð

Question 27

how is sphericity measured ?

Answer 27

The extent to which a covariance matrix deviates from sphericity is reflected in a parameter called epsilon

Ð For sphericity to be perfectly met, epsilon= 1

Question 28

What to do when RM ANOVA sphericity is not met?

Answer 28

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

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

Question 29

RM ANOVA or MANOVA?

Answer 29

Ð Clean counterbalanced designs “fit” better within the univariate model
Ð “Contaminated” designs may require multivariate model which is statistically more robust but more difficult to interpret

Question 30

where does TREND ANALYSIS fit into all this?

Answer 30

Can replace or supplement RM-ANOVA or profile analysis.

Question 31

details of TREND ANALYSIS?

Answer 31

Ð Free from assumptions of sphrericity and multivariate assumptions
Ð Suitable for longitudinal / time related studies
Ð Can analyze linear / quadratic / cubic distributions
Ð SPSS gives stats for all of this

Question 32

Choose trend analysis if…..

Answer 32

levels of the IV differ along a single dimension (time, dose)

Question 33

Choose univariate RM if…

Answer 33

a “clean” (well controlled / counter balanced / no violations) experiment

Question 34

Choose profile analysis if…

Answer 34

“contaminated” designs with spericity violations

Question 35

if you have more than X groups you need to do contrasts

Answer 35

2

Question 36

Univariate repeated-measures ANOVA with more than 1 df for the repeated-measure IV requires ……..

Answer 36

sphericity

Question 37

Sphericity is related to…..

Answer 37

homogeneity of covariance

Question 38

Both homogeneity of covariance and Sphericity mean…

Answer 38

All pairs of levels of the within-subjects variable need to have equivalent correlations

For example, consider a longitudinal study in which children are measured yearly from ages 5 to 10. If there is homogeneity of covariance, the correlation between scores on the DV for ages 5 and 6 should be about the same as the correlation between scores between ages 5 and 7, or 5 and 8, or 6 and 10, and so on (like between 5 & 8 or between 7 &10). In applications like these, however, the assumption is almost surely violated.

Things measured closer in time tend to be more highly correlated than things measured far- ther away in time;

Question 39

If there is violation of sphericity, we must….

Answer 39

use corrected version … e.g. Greenhouse–Geisser or Huynh–Feldt

Question 40

we wan’t to be wh0le - we want …

Answer 40

Sphericity

Question 41

the multi variate approach to RM ANOVA is…. and is a way around …….

Answer 41

Profile analysis, called the multivariate approach to repeated measures, is a statistically acceptable alternative to repeated- measures ANOVA. Other requirements such as homogeneity of variance–covariance matrices and absence of multicollinearity and singularity must be met, but they are less likely to be violated.

Question 42

however, profile analysis requires …

Answer 42

Profile analysis requires more cases than univariate repeated-measures ANOVA—more cases than DVs in the smallest group. If the sample is too small, the choice between multivariate and uni- variate approaches is automatically resolved in favor of the univariate approach, with adjustment for failure of sphericity, as necessary.

Question 43

post hoc tests?

Answer 43

With a single control group, Dunnett’s procedure often makes most sense. Or if all pairwise comparisons are desired, the Tukey test is most appropriate.

Question 44

RM ANOVA / PA contrasts … some details

Answer 44

Contrasts in repeated-measures ANOVA with both grouping variables and repeated measures is not the easiest of topics, as you probably recall.

First, when parallelism (interaction) is significant, there is the choice between a simple-effects analysis and an interaction-contrasts analysis.

Second, there is a need in some cases to develop separate error terms for some of the contrasts.

Third, there is a need to apply an adjustment such as Scheffé to the F test to avoid too liberal a rejection of the null hypothesis.

Question 45

how do you get a z score?

Answer 45

z = (x – μ) / σ

Question 46

ANOVA tests whether mean differences xxxx on a xx DV are likely to have occurred by chance. MANOVA tests whether mean differences among groups on a xxxx of xxx are likely to have occurred by chance.

Answer 46

ANOVA tests whether mean differences among groups on a single DV are likely to have occurred by chance. MANOVA tests whether mean differences among groups on a combination of DVs are likely to have occurred by chance.

Question 47

what does MANOVA use to test significance?

Answer 47

MANOVA emphasizes the mean differences and statistical significance of differences among groups