For this exercise, you will use MANOVA to test the hypothesis that there are racial/ethnic differences in scores on the SF-12, using scores from both the physical health component (sf12phys) and mental health component (sf12ment) as the dependent variables and racethn as the independent variable. Open the main dialog box through Analyze ➜ General Linear Model ➜ Multivariate. Move the two SF-12 variables into the box for Dependent Variables and racethn into the box for Fixed Factor. Click the Post Hoc pushbutton and make sure that racethn is in the box “Post hoc tests for:” Select Bonferroni, then click Continue. On the main dialog box click the Options pushbutton. From the list of Display options, select Descriptives, Estimates of effect size, Parameter estimates, and Homogeneity tests. Then click Continue and OK to run the analysis. Answer the following questions based on the output: (a) Is the assumption of homogeneous variance–covariance matrices violated? (b) Is the overall multivariate test for differences in racial/ethnic group means statistically significant? (c) Can we accept the assumption of homogeneous variances for this analysis? (d) In the panels for univariate results, were group differences statistically significant? (e) If overall group differences were significant, which groups were significantly different from other groups, and what was the nature of the differences?
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