Week 10: MANOVA Flashcards
What variables do you need for a MANOVA?
More than one DV
MANOVA performs tests on which means?
The mean of the linear combination of DVs - looking for IV differences on the combination of DVs
What is a linear combination?
A lump or sum of all different measures into a whole
MANOVA allows the analysis of….
Several DVs that may be on different scales - a core MANOVA feature
MANOVA promotes a lower…
Type 1 error rate than calculating several univariate ANOVAs for each DV
What does the analysis of the DVs as a linear combination allow?
May be more powerful or sensitive to differences among groups as stacking them together instead of looking at them individually
MANOVA is relatively sensitive to…
Violations of assumptions
The DVs should be…
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)
A correlation of above .85 means that the DVs are..
probably measuring the same thing
How many DVs can we have in MANOVA?
The number of DVs should be less than the number of cases
What are the MANOVA assumptions?
Independence of observations
Normal distribution
Homogeneity of variance
Explain normal distribution in MANOVA?
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)
Homogeneity of variance in MANOVA?
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
How do we check for homogeneity of variance?
Levene’s test
Box’s test
You shouldn’t always pay attention to box’s test. When should you?
When there are unequal sample sizes
When box’s test is significant, what does this mean? and what should you do?
Means the assumption has been violated
Can then go and check levene’s to see which one
What multivariate tests of significance does MANOVA produce?
Wilks lambda
Pillai’s trace
Hotellings trace
Roy’s greatest characteristic root
Which multivariate test of significance do you report?
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
The effect sizes are provided by the multivariate tests. What do they tell us?
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
What do you do if a MANOVA is significant?
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)
What do you do if a MANOVA is not significant?
‘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
How do you set up a MANOVA in jamovi?
1x row per participant
1x column for each IV and DV
How do you start a MANOVA in jamovi?
ANOVA -> MANCOVA module
What do you tick when doing the MANOVA analysis?
All of the multivariate tests and all of the assumption checks
What do you do once you’ve ran the analysis
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
How do you report the univariate tests?
‘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)
How do you run post hocs on univariate tests?
Use the ANOVA model
- put the DV you’re interested in, in the model
- ask for tukey and holm to see where differences are
