Mixed ANOVA & MANOVA

Question 1

What is a mixed ANOVA?

Answer 1

Where there is 1+ within-subjects variable and 1+ between-group variable.

Question 2

What can G*Power be used for?

Answer 2

It can be used before conducting a study to know the sample size needed for that study.

Question 3

In G*Power what values are alpha and power usually?

Answer 3

Alpha = 0.05. 
Power = 0.8.

Question 4

What are the effect sizes for power?

Answer 4

Small = 0.10. 
Medium = 0.25. 
Large = 0.40.

Question 5

What are the two options when you have non-normally distributed data in a mixed design?

Answer 5

1. Transform data - log, square root… If assumptions are then met - can perform a mixed ANOVA.
2. Multiple non-parametric tests. Mann-Whitney + Wilcoxon + correction for number of tests.

Question 6

Is a Bonferroni adjustment conservative or not?

Answer 6

It is very conservative.

Question 7

What is the equation for a Bonferroni adjustment?

Answer 7

Alpha = alpha / number of comparisons.

Question 8

Name a less conservative adjustment (as opposed to Bonferroni).

Answer 8

Holm’s sequential Bonferroni.

Question 9

What is a MANOVA?

Answer 9

It is an ANOVA when we have multiple DVs.

Question 10

What is a strength of using a MANOVA as opposed to multiple ANOVAs?

Answer 10

Avoids family-wise error.

Also takes into account correlations between DVs.

Question 11

What type of test is a MANOVA?

Answer 11

Omnibus test.

Question 12

State the MANOVA assumptions.

Answer 12

Independence of measures. 
Interval/ratio data. 
Multivariate normality. 
Homogeneity of covariance matrices. 
DVs should correlate.
Equal group sizes - makes MANOVA more robust.

Question 13

How do we test for multivariate normality?

Answer 13

We can’t in SPSS.

Can only test for normal distribution in each DV individually.

Question 14

What are the 4 MANOVA statistics?

Answer 14

Pillai’s trace - V.
Hotelling’s T-squared.
Wilks’ lambda.
Roy’s largest root.

Question 15

How robust are the MANOVA statistics when the sample sizes are equal?

Answer 15

All 4 are pretty robust.

Roy’s root not robust under some circumstances. Pillai’s trace more robust.

Question 16

What tests are used to test for homogeneity of covariance matrices and what must they be?

Answer 16

Levene’s test - across groups of each DV. Must be non-significant.
Box’s test - variance-covariance matrices compared between groups. Must be non-significant.
Test is very sensitive so only an issue if p is less than 0.001.

Question 17

What is the main issue with Box’s test?

Answer 17

More easily significant when sample size is large.

Question 18

What should you do if Box’s test is significant?

Answer 18

Field suggests ignoring it if sample sizes are equal because it is an unstable test and Pillai’s trace is still robust anyway.
If samples uneven… Pillai’s trace is still robust (as long as assumptions are met) BUT MANOVA tests are not robust.

Question 19

What should DV correlations be between?

Answer 19

0.3-0.7.

Question 20

What should we do if correlations between DVs are too low/too high?

Answer 20

Too low: Shouldn’t use MANOVA.

Too high: Could be multicollinearity - might have to remove a DV.

Question 21

What MANOVA statistic should we generally use if we have more than two groups and why?

Answer 21

Pillai’s trace.

It is the most powerful test. Robust to assumptions being violated.

Question 22

What should be reported in a MANOVA?

Answer 22

• Descriptives.
• Assumption checks.
• Box’s test. Should be non-significant (F, df, p).
• Levene’s test. Should be non-significant. Must report for both DVs.
• Multivariate statistics (IV effect) - Pillai’s trace (V, F, df, p, np-squared).
• Univariate statistics (IV source) - follow up ANOVAs for each DV (F, df, p, np-squared). HOWEVER; Field recommends using discriminant analysis instead.
• Bonferroni correction - only count the follow-up ANOVAs not the MANOVA.
• Post-hoc tests - Bonferroni if HoV is met, Games-Howell if not.
• Estimated marginal means for both DVs.
• Conclusion on what results show.