Archive:MANOVA

File:Wikademia.logo.png Resource type: this resource contains a tutorial or tutorial notes. Template:0%done The purpose of this tutorial is to teach use of multivariate analysis of variance (MANOVA), with practical exercises based on using SPSS.

What is MANOVA?

• A multivariate extension of univariate ANOVA
• If you have two or more dependent variables (ANOVA analyses only a single DV at a time)

Example

Effects of chemotherapy and memory enhancement training on cognitive functioning in Alzheimer's patients

IVs (factors)

1. Chemotherapy (drug vs no-drug)
2. Memory training (training vs no-training)

DVs

Several measures of cognitive functioning:

1. Test of reading comprehension and retention
2. Memory for names and faces
3. Ratings provided by family members

Usage

• Alternatively, could use a series of univariate ANOVAs - one for each dependent variable - MANOVA does all these univariate tests simultaneously.
• Most commonly used in laboratory research (where we experimentally manipulate factors), but can be used in any design where we want to answer questions about whether different levels of the IVs affect a combination of DVs.
• "Because of the increase in complexity and ambiguity of results with MANOVA, one of the best overall recommendations is: Avoid it if you can." Tabachnick and Fidell (1983, p.230)
• In other words - be sure it is really the best approach to use (e.g., sometimes a mixed ANOVA could be a better approach).

Assumptions

1. Sample size - sample size rule of thumb:the sample in each cell must be greater that the number of dependent variables
2. Univariate and multivariate normality - (when cell size > 30 this is less important)
3. Linearity - linear relationships among all pairs of dependent variables
4. Homogeneity of regression - covariates must have a homogeneity of regression effect (must have equal effects on the dependent variable across the groups)
5. Homogeneity of variance-covariance matrix (Box's M) – the F test from Box’s M statistics should be interpreted cautiously in that a significant result may be due to violation of the multivariate normality assumption and a nonsignificant result may be due to small sample size and lack of power– fairly robust if equal sample sizes
6. Multicollinearity and singularity - when there is strong multicollinearity, you have redundant dependent measures and this decreases statistical efficiency
7. Outliers - MANOVA is very sensitive to the effect of outliers because they impact on the Type I error (use Mahalanobis distance to check for multivariate outliers)

References

• Hair et al. (1998) Chapter 6
• Tabachnick & Fidell (1996) Chapter 9 (more recent editions are available)

See also

• MANOVA

External links

• MANOVA (ucspace)
  • MANOVA Notes (Handout)