M9 - MANOVA

Question 1

In a _______, the ______ should be related to each other to ensure that a ________ can be found in the ________ along which the groups in the ________ are _______.

Choose from: factor solution, IV, MANOVA, different, data, DVs

Answer 1

In a MANOVA, the DVs should be related to each other to ensure that a factor solution can be found in the data along which the groups in the IV are different.

Question 2

What is MANOVA

Answer 2

MANOVA is an extension of ANOVA and Factor Analysis

Where ANOVA

• compares sample means
• Categorical IVs
• single interval or continuous DV

MANOVA
- tests similarity in the Variance-Covariance matrix between groups
- tries to maximally separate the groups
- One or more Categorical IVs
- Multiple continuous DVs
DVs should be related to maximise power
DVs should be normality distributed to be able to confidently compared means and know the proportion of scores at any point in the data

Question 3

What is a Matrix of Variance-Covariance?

Answer 3

• Basically unstandardised Correlations Matrix
• Gives us Box’s M to check the assumption that variance-covariance matrix is equal across groups

Box’s M test is like the multivariate homogeneity of variance - a test of variance covariance. If significant - we have a violation
Criteria for Box’s M is p = .001

Question 4

What is needed in order to run a MANOVA?

Answer 4

one or more categorical IVs
continuous Dvs
normally distributed DVs
DVs that are related
Homogeneity of DV variance over groups - Levine’s Test
Homogeneity of DV variance-covariance over groups - Box’s M test
Independent observations (except in repeated measures)

Question 5

Part A - Question: Drag the words into the correct boxes.

In _______we evaluate single DVs and one or more IVs, while in ________ we evaluate multiple DVs and one or more IVs.

choose from ANOVA and MANOVA

Answer 5

In ANOVA we evaluate single DVs and one or more IVs, while in MANOVA we evaluate multiple DVs and one or more IVs.

Question 6

Part B - Question 1: MANOVA uses Box’s M to:

Check that there is no violation of homogeneity of variance in the IV..
Check that there is no violation of homogeneity of variance in either the IV or DV..
Check that the matrix of variance-covariance is equal across groups..
Check that there is no violation of homogeneity of variance in the DV.

Answer 6

Check that the matrix of variance-covariance is equal across groups..

Question 7

Part B - Question 2: In the Variance-Covariance Matrix, where are the variances situated and where are the covariances situated?

Answer 7

Variances - along the primary diagonal

Covariances - off the primary diagonal

Question 8

Part C - Question 1: Do we need categorical variables?

For no variables, all should be continuously distributed.
For the DV.
For the IV.
For both the IV and the DV

Answer 8

For the IV.

Question 9

Part C - Question 2: Why do we need normally distributed DVs?

So we know what proportion of scores fall at any point in the data..
So we know what proportion of the IV falls at any point in the data..
So we know what proportion is likely to be a type II error..
So we know what proportion is likely to be a type I error.

Answer 9

So we know what proportion of scores fall at any point in the data..

Question 10

How many participants do you need for a MANOVA

Answer 10

Depends on how much power you have.

Power depends upon
Type I error (alpha) - false positive - rejection of null when null is true
Type II error (Beta) - false negative - (incorrect rejection) non rejection of null when null is false

Power is 1 - B - the ability of a test to correctly reject a false hypothesis

Work out using G*Power Statistical program
put in alpha (.05), Power of .8, samples size and number of DV groups to work out sample required

If your sample is smaller than what is required, look at the sensitivity to pickup effect size.
If the sensitivity is only enough to get an effect size smaller than what you have, suggests significant result might be a type 1 error.

Question 11

What do we conclude when we get scores from the tails of the distribution?

That we have made a type I error.
I don’t know, I always make errors.
That we have made a type II error.
That the score most likely came from the alternate distribution

Answer 11

That the score most likely came from the alternate distribution

Question 12

Part E - Question 1: When you undertake a statistical test, should you only consider the significance?

No, you should also consider the effect size..
No, you should also consider whether there was a sampling bias that led to the result..
No, you should consider whether a better experiment would get a better result..
No, you should also consider other possibilities, like the test being underpowered.

Answer 12

No, you should also consider the effect size..

Question 13

How do you interpret a MANOVA?

Answer 13

Look at Box’s M and whether assumptions have been met or violated

If all assumptions are met
Use Wilk’s Lambda

If Box’s M is sig, n is small and cells with smaller n have larger variance
Use Pillai’s Trace

If assumptions are violated
Use Hotelling’s Trace

If assumptions are badly violated
Use Roy’s Largest Root

Question 14

Part E - Question 2: Drag the words into the correct boxes.

We prefer to use 1)_______ when all assumptions are met, will prefer 2)_______when assumptions are nearly met and sample size is small, and will prefer to use 3)_______ when assumptions are not met, but we avoid it and 4)_________because these are both difficult to interpret.

Choose from:
Roy’s Largest Root, Hotelling’s Trace, Wilk’s Lambda and Pillai’s Trace

Answer 14

1) Wilk’s Lambda
2) Pillai’s Trace
3) Hotellings Trace
4) Roy’s Largest Root

Question 15

How do you evaluate the significance of MANOVA?

ie what stats?

Answer 15

F value, significance test and effect size (eta squared) of the most appropriate test out of:

Wilks’ Lambda
Pillai’s Trace
Hotelling’s Trace
Roys Largest Root

Question 16

What do you do when your MANOVA is significant?

Answer 16

Post Hoc Testing

Look at Univariate output table.
Look at Main effect IV on Dvs and Interaction

F test,
significance tests
Partial eta squared - transform to % (multiply*100)

If significant at the multivariate level
Means that out DVs as a group differ
- check which DV is most important
Do this by removing it as a DV and treating it as a covariate (MANCOVA)

Question 17

What is a MANCOVA?

Answer 17

Removing a DV of a significant MANOVA and treating it as a covariate to determine which DV has the strongest effect in terms of its effect on the difference between groups

If by taking it out and controlling for that variable the effect of the IV reduces it might be considered a strong determinant of the between group differences.
Can also look at the Partial eta squared for the DV testsed as covariate to see how much it explains (partial eta squared)

Question 18

Part F - Question 1: Can we just add up the univariate effect sizes to get the multivariate effect size?

No, because effects in univariate variables will overlap within the IVs..
Yes, because they measure variance across the IV, which is the same in all DVs..
Yes, because they measure essentially the same thing..
No, because they are different things.

Answer 18

No, because effects in univariate variables will overlap within the IVs..

Question 19

Part F - Question 2: Drag the words into the correct boxes.

We can assess which of the _______contributed most by successively _______and then ________ each in turn and using it as a ______with the _______.

choose from replacing, IV’s, DV’s, removing, covariate

Answer 19

DV's
Removing
Replacing
covariate
IVs