MANOVA & ANCOVA

Question 1

When should you use a MANOVA

Answer 1

MANOVA:

1. SET of DV’s
2. you want to assess your set of related DVs at once
3. several between subjects ANOVAs as a single set.
4. One or more between-subjects predictors (IVs)
5. control the Type I error rate for the set of DVs

Only when you have a theoretical reason to consider all your DVs as a set

Without such a reason, just do separate ANOVAs

Question 2

Four assumptions and tests for MANOVA

Answer 2

1. Multivariate Normality QQ Plot
   (distribution, with means equal to zero)

2.Variance-covariance Box’s M test variance-covariance matrices of each group of residuals are equal

3. observations are independent *Look at data / by row, like with MR
4. Correlated DVs but not too much (below ±.90). Correlation matrix

Question 3

Which statistics should we look for in a MANOVA analysis

Answer 3

1. The Wilks’ Lambda most often reported
2. Pillai’s Trace is safer in most cases,

If they disagree pillai’s trace is right

Question 4

What should you do if there is a significant Wilk’s Lambda

Answer 4

1. Univariate ANOVA; one for each Dependent Variable jamovi, does not fully do it
2. significant univariate ANOVA = again follow-up with simple effects tests (planned comparisons) - (check two boxes)

Question 5

control Type 1 error rate with post hoc in MANOVA

Answer 5

1. Control our Type I error rate when we perform multiple tests,
2. jamovi will not adjust its Univariate ANOVA F s for us
3. There is no way to do all the post-hoc comparisons within MANOVA (we likely would not want to anyway)
4. To control Type I error, apply a simple Bonferroni correction to alpha

Divide your desired alpha (.05) by the number of DVs in the MANOVA

This becomes your new cut-off for all Univariate ANOVA p-values
E.g. alpha = 0.5/3 = .017

Question 6

What is a problem you may encounter with MANOVA post hoc significance

Answer 6

MANOVA can be significant despite none of the following univariate ANOVAs being significant.

Because those ANOVAs don’t control for the DV dependencies

*A Discriminant Analysis is the solution to this problem, and it’s probably what should actually be done for any MANOVA, but jamovi doesn’t provide this option (nor did SPSS for that matter)

Essentially, it identifies first whether related groups of variables differ and then how they differ from each other
As usual, it is possible to do using R code in jamovi
For our purposes, just knowing it exists is good enough!

Question 7

When should we use ANCOVA

Answer 7

1. categorical variable slices up our DV into comparison groups (an ANOVA predictor)
2. Non-categorical variable to help explain some extra variance in the DV

Question 8

What is the goal of running an ANCOVA

Answer 8

Add covariate to reduce just the error variance in the DV.

Increasing the probability that the IV can predict a significant amount of the remaining variance,

because there’s less variance left to predict

It does not matter whether the covariate is a significant predictor or not in this case

Question 9

Why should we run an ANCOVA (and why not)

Answer 9

Do: have a potential covariate measured &

want to have the best estimate of our IV’s effectiveness

DON’T: already ran an ANOVA, and it wasn’t significant

The covariate is meant to explain only the variance otherwise unexplained by the ANOVA model.

So, if your intended covariate is not independent of your categorical predictor, then you should not use it

Question 10

What assumption should you check for in ANCOVA

Answer 10

1. *Correlation IV + covariate
2. *Homogeneity (stat interaction not significant + scatterplot / lines of best fit = same

2 ways to check:

1. Plot a Covariate x DV regression line for each level of your predictor (the visual test method)
2. Temporarily add an IV/Covariate interaction term to your ANCOVA model (the statistical test method). If it’s significant, it fails.

*Important to take it out after

Question 11

How should you get the means of ANCOVA variables

Answer 11

Estimated marginal means only

Not a simple descriptive analysis to get the means.

The estimated marginal means have regressed the predictor on the outcome, while including the covariate

If you calculated the means any other way than the covariate’s effect would be dropped, and the means would be different

Question 12

How to get a proportion of variance explained from a MANOVA model fit statistic

Answer 12

1-Lambda = becomes proportion of variance explained

(like the R2 for regression)