Week 10: MANOVA

Question 1

What variables do you need for a MANOVA?

Answer 1

More than one DV

Question 2

MANOVA performs tests on which means?

Answer 2

The mean of the linear combination of DVs - looking for IV differences on the combination of DVs

Question 3

What is a linear combination?

Answer 3

A lump or sum of all different measures into a whole

Question 4

MANOVA allows the analysis of….

Answer 4

Several DVs that may be on different scales - a core MANOVA feature

Question 5

MANOVA promotes a lower…

Answer 5

Type 1 error rate than calculating several univariate ANOVAs for each DV

Question 6

What does the analysis of the DVs as a linear combination allow?

Answer 6

May be more powerful or sensitive to differences among groups as stacking them together instead of looking at them individually

Question 7

MANOVA is relatively sensitive to…

Answer 7

Violations of assumptions

Question 8

The DVs should be…

Answer 8

Conceptually related (good theoretical reason for combining)

Moderately correlated (if they are not, use separate ANOVA’s with bonferonni adjusted p values. If too high, redundancy of info and lose power)

Question 9

A correlation of above .85 means that the DVs are..

Answer 9

probably measuring the same thing

Question 10

How many DVs can we have in MANOVA?

Answer 10

The number of DVs should be less than the number of cases

Question 11

What are the MANOVA assumptions?

Answer 11

Independence of observations

Normal distribution

Homogeneity of variance

Question 12

Explain normal distribution in MANOVA?

Answer 12

Sampling distribution of all DVs in linear combination need to be normally distributed - very hard to meet!!

Should be robust if the sample size is substantial (>20)

Check through univariate normality and by checking outliers (+/-2SD)

Question 13

Homogeneity of variance in MANOVA?

Answer 13

Need for each group and correlation of between DVs needs to be the same in each group

However may be robust to violation here if there are equal numbers of participants per cell

Question 14

How do we check for homogeneity of variance?

Answer 14

Levene’s test

Box’s test

Question 15

You shouldn’t always pay attention to box’s test. When should you?

Answer 15

When there are unequal sample sizes

Question 16

When box’s test is significant, what does this mean? and what should you do?

Answer 16

Means the assumption has been violated

Can then go and check levene’s to see which one

Question 17

What multivariate tests of significance does MANOVA produce?

Answer 17

Wilks lambda
Pillai’s trace

Hotellings trace
Roy’s greatest characteristic root

Question 18

Which multivariate test of significance do you report?

Answer 18

It is Wilks Lambda that is recommended, UNLESS there are violations of assumptions in which case you should use Pillai’s trace (most powerful if the design is flawed e.g. small n, unequal numbers)

Report in F equation

Question 19

The effect sizes are provided by the multivariate tests. What do they tell us?

Answer 19

The amount of variance accounted for by the best linear combination of DVs use as a % (Pillai’s trace)

The amount of unexplained variance (Wilks Lambda) this means if you have e.g. 0365, 61% of the variance is accounted for by the BLC

Question 20

What do you do if a MANOVA is significant?

Answer 20

Look at one DV at a time with ANOVAs with bonferonni adjusted p values (with post hocs like tukey)

E.g. could say there is a univariate main effect of X, here we can see that this is because group 1(m, SD) is larger than group 2 (m, sd)

Question 21

What do you do if a MANOVA is not significant?

Answer 21

‘We did a MANOVA, there were no significant differences between the means, the effect size based on (multivarate stat) was really small so we are not going to do any further analysis’

If you want to look at the DVs individually, you need a good reason

Question 22

How do you set up a MANOVA in jamovi?

Answer 22

1x row per participant

1x column for each IV and DV

Question 23

How do you start a MANOVA in jamovi?

Answer 23

ANOVA -> MANCOVA module

Question 24

What do you tick when doing the MANOVA analysis?

Answer 24

All of the multivariate tests and all of the assumption checks

Question 25

What do you do once you’ve ran the analysis

Answer 25

Look at Box’s test or levenes, may also want to look at Q-Q plot (want a straight line, if not there are outliers)

Look at the multivariate stats and report

Look at univariate analysis: are the effects of IV on score DV1 and DV2

Question 26

How do you report the univariate tests?

Answer 26

‘this shows that there is a difference between the IV on the DV1 F(df,df)=F, p=p and a difference between the IV on DV2, F(df,df)=F, p=p’

Bonferonni adjustment

If more than 2 levels, would need tukey to see where the differences are (ANOVA)

Question 27

How do you run post hocs on univariate tests?

Answer 27

Use the ANOVA model

• put the DV you’re interested in, in the model
• ask for tukey and holm to see where differences are