Is the interaction between race/ethnicity and income significant?.
Now we can proceed with the ANCOVA analysis described in Exercise B1. Open the GLM Univariate dialog box again, which should already have the necessary variable information (unless you run Exercise B1 and B2 on different days).
Click the Model pushbutton, select Full factorial model, then click Continue to return to the main dialog box. Click the Options pushbutton and in the top panel (Estimated marginal means), select racethn and use the right arrow to move it into the box labeled “Display means for:” Now click “Compare main effects” to generate multiple pairwise comparisons, and below that select the Bonferroni adjustment from the pull-down menu. At the bottom (under Display), select Descriptive statistics and Estimates of effect size. Then click Continue and OK to run the analysis. Use the output to answer these questions: (a) Before any adjustments for the covariate, what is the range of group means? (b) In the full factorial model, was the covariate significantly related to physical health scores? (c) With income controlled, were racial/ethnic differences in physical health significant? (d) Compare the adjusted group means with the unadjusted group means. What happened as a result of the adjustment? Why do you think this happened? (e) What do the pairwise comparisons indicate? Was this analysis necessary?
You will be using the SPSS dataset Polit2SetC to do various analyses. For the first analysis (ANCOVA), you will be testing for racial/ethnic differences (racethn) in physical health scores (sf12phys), controlling for total household income (income). Begin by testing the assumption of homogeneity of regression across the three racial/ethnic groups (African American, Hispanic, and white/other). Select Analyze ➜ General Linear Model ➜ Univariate. In the opening dialog box, move the variable sf12phys into the slot for Dependent Variable; move racethn into the slot for Fixed Factors; and move income into the slot for Covariates. Click the Model pushbutton, which will have as the default the full factorial model. Click Custom and then on the left highlight both racethn and income in the Factors and Covariates box. Make sure that in the “Build Terms” section, the Type is set to Interaction, and then click the right arrow to move the interaction (income * racethn) into the Model box. Click Continue to return to the main dialog box and then click the Options pushbutton. Select Homogeneity tests as the option for Display. Then click Continue, and OK to run the analysis. Use the output to answer these questions: (a) What can you conclude from Levene’s test about the homogeneity of error variance of physical health scores across the three groups? (b) Is the interaction between race/ethnicity and income significant? What does this suggest about the homogeneity of regression assumption?