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

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

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

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

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

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?

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

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

Example from the Literature

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

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

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

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

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

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

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

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?

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