MANOVA

Question 1

Summarise what cole et al (1994) say about power in MANOVA

Answer 1

• Cole et al (1994) found that power of MANOVA depends on a combination of the correlation between dependant variables and the effect size to be detected- i.e. the group difference expected to be exhibited by the DV.
• These effects are related to the way that the linear composites for the groups are separated in space (recall that LC’s are constructed in a way that aims to maximally separate the groups to increase power).
• ***This is only for 2 group designs, i.e. 1 IV with 2 levels. Power issues in more complex designs are more complicated.

Question 2

How should DV’s be correlated to increase power when a large effect of group is expected on all DV’s?

Answer 2

MANOVA will have greater power if the measures of DV’s are somewhat different or even negatively correlated and if the group differences are in the same direction for each measure.

Question 3

How should DV’s be correlated to maximise power when groups are expected to have large effects on some DV’s and small effects on other DV’s?

Answer 3

If you have 2 DV’s, one that exhibits small or no group difference and one that exhibits a large group difference, then power will be increased if the 2 DV’s are highly correlated (either positively or negatively)

Question 4

How should DV’d be correlated to maximise power when groups are expected the have small effects oon DV’s?

Answer 4

Same as large effect, as correlation between DV’s with small effects becomes more negative, power increases (this is assuming that there are still some strong DV’s in the design).

Question 5

Advantages and disadvantages of MANOVA

Answer 5

• The main advantage- less type 2 error rate, due to not having to correct for multiple comparisons
• Under rare circumstances can be more powerful than ANOVA (see ellipses diagram and explanation)
• Usually lacks power in comparison to ANOVA. (This lack of power is related to the correlations between DV’s, ideally it should be strong and negative- again see ellipses diagram)
• Can’t look at differential effects of DV’s- ambiguous where the effect lies

Question 6

Advantages and disadvantages of ANOVA

Answer 6

• Usually has more power
• Can look at differential effects on separate DV’s
• Only requires homogeneity of variance and not variance-covariance like MANOVA
• More type 2 error- multiple testing
• Sometimes less powerful than MANOVA

Question 7

What is step-down analysis?

Answer 7

finding out effects on individual DV’s.
• Another procedure is the Roy-Bargman step-down procedure which uses ANCOVA on each individual DV, with higher priority DVs as covariates.

Step 1: Dependent variables are ordered prior to the experiment of their importance to difference between groups.

Step 2: ANOVA carried out with the most important dependent variable.

Step 3: ANCOVA carried out with the second most important variable as a response and the most important one as a covariate.

Step 4: ANCOVA carried out with the third most important variable as a response and the most and second most important ones as a covariates. This is the done sequentially for all the variables

This procedure allows us to see whether the groups have an effect on each dependent variable, that it not accounted for by the other conceptually related dependent variables.