 ## Cramming Sam's top tips from chapter 17

Click on the topic to read Sam's tips from the book

### MANOVA

• MANOVA is used to test the difference between groups across several outcome variables/outcomes simultaneously.
• Box’s test looks at the assumption of equal covariance matrices. This test can be ignored when sample sizes are equal because when they are, some MANOVA test statistics are robust to violations of this assumption. If group sizes differ this test should be inspected. If the value of Sig. is less than 0.001 then the results of the analysis should not be trusted (see Section 17.7.1).
• The table labelled Multivariate Tests gives us four test statistics (Pillai’s trace, Wilks’s lambda, Hotelling’s trace and Roy’s largest root). I recommend using Pillai’s trace. If the value of Sig. for this statistic is less than 0.05 then the groups differ significantly with respect to a linear combination of the outcome variables.
• Univariate F-statistics can be used to follow up the MANOVA (a different F-statistic for each outcome variable). The results of these are listed in the table entitled Tests of Between-Subjects Effects. These F-statistics can in turn be followed up using contrasts. Personally I recommend discriminant function analysis over this approach.

### Discriminant function analysis

• Discriminant function analysis can be used after MANOVA to see how the outcome variables discriminate the groups.
• Discriminant function analysis identifies variates (combinations of the outcome variables). To find out how many variates are significant look at the tables labelled Wilks’s Lambda: if the value of Sig. is less than 0.05 then the variate is significantly discriminating the groups.
• Once the significant variates have been identified, use the table labelled Canonical Discriminant Function Coefficients to find out how the outcome variables contribute to the variates. High scores indicate that an outcome variable is important for a variate, and variables with positive and negative coefficients are contributing to the variate in opposite ways.
• Finally, to find out which groups are discriminated by a variate look at the table labelled Functions at Group Centroids: for a given variate, groups with values opposite in sign are being discriminated by that variate.