1. Differences Among Group Means: Multifactorial Analysis of Variance
Chapter 7
Differences Among Group Means: Multifactorial Analysis of Variance

2. ANOVA Type of Data Required Nominal-level independent variable/s
Continuous dependent variable

3. ANOVA Assumptions Mutually exclusive groups
Normally distributed dependent variable
Homogeneity of variance

4. ANALYSIS OF VARIANCE Interactions - plot cell means
Ordinal - lines do not intersect
Disordinal - lines do intersect

5. ANOVA Degrees of Freedom Total = n - 1 Between = k-1 Within = n - k
(k = # of groups)

6. Research Questions
1. Do men and women report significantly different joy in their hearts?
2. Do married people report significantly different joy in their hearts than non-married people?
3. Is there an interaction between gender and marital status in relation to joy in the heart?

7. New Marital Status Variable
Recode marital status into a new variable where:
never married = 0
married = 1

8. SPSS - ANOVA ANALYZE General Linear Model
Univariate (only 1 dependent variable)
Options
Display means
Homogeneity of variance

9. Example from the Literature

10. MANOVA Advantages over univariate model to keep alpha at a known level
to increase power
for ease in computation and interpretation

11. MANOVA Assumptions Random sample Independent observations
Dependent variables - multivariate normal distribution within each group
Common within-group covariance matrix
Homogeneity of variance, each dependent variable
Correlation between any two variables must be same in all groups

12. Multivariate Test Statistics
Wilk's Lambda
Pillai-Bartlett Trace
Roy's Greatest Characteristic Root
Hotelling-Lawley Trace

13. Wilks' Lambda U
Product of the unexplained variances on each of the discriminant variates
Small value indicates significance

14. Pillai Bartlett Trace V
Sum of the explained variances of the discriminant variates

15. Roy's Greatest Characteristic Root
GCR
Based only on first discriminant variate

16. Hotelling-Lawley Trace
The sum of the between/within sum of squares ratios for each of the discriminant variates.

17. Research Questions
Do the three work groups differ significantly on confidence and life satisfaction?
Do the three smoking groups differ significantly on confidence and life satisfaction?
Is there an interaction between work status and smoke status in relation to confidence and life satisfaction?

18. SPSS - MANOVA ANALYZE General Linear Model Multivariate Plots
Interactions
Post hoc
3 or more groups
Options
Display cell means
Effect size
Power
Homogeneity of variance