In a study of the psychosocial changes in individuals who participated in a community-based intervention program, individuals who were clinically identified as hypertensives were randomly assigned to one of two treatment groups (with n individuals in each group). Group 1 was given the usual care that existing community facilities provide for hypertensives; group 2 was given the special care that the intervention study team provided. Among the variables measured on each individual were SP1, an index of the individual's self-perception of health immediately after being identified as hypertensive but before being assigned to one of the two groups; SP2, an index of the individual's self-perception of health one year after assignment to one of the two groups; AGE; and SEX. One main research question of interest was whether the change in self-perception of health after one year would be greater for individuals in group 2 than for those in group 1. Several different analytical approaches to answering this question are possible, depending on the dependent variable chosen and on the treatment of the variables SP1, AGE, and SEX in the analysis. Among these approaches are the following six:
• Matching pairwise on AGE and SEX (which we assume is possible) and then performing a paired-difference t test to determine whether the mean of group 1 change scores significantly differs from the mean of group 2 change scores.
• Matching pairwise on AGE and SEX and then performing a regression analysis, with the change score Y = (SP2 - SP1) as the dependent variable and with SP1 as one of the independent variables.
• Matching pairwise on AGE and SEX and then performing a regression analysis, with SP2 as the dependent variable and with SP1 as one of the independent variables.
• Controlling for AGE and SEX (without any prior matching) via analysis of covariance, with the change score Y = (SP2 - SP1) as the dependent variable.
• Controlling for AGE and SEX via analysis of covariance, with the change score Y = (SP2 - SP1) as the dependent variable and with SP1 as one of the independent variables.
• Controlling for AGE and SEX via analysis of covariance, with SP2 as the dependent variable and with SP1 as one of the independent variables.
a. What regression model is associated with each of the preceding six approaches? Make sure to define your variables carefully.
b. For each of the preceding regression models, state the appropriate null hypothesis (in terms of regression coefficients) for testing for group differences with respect to self-perception scores. For each regression model, indicate how to set up the appropriate ANOVA table to carry out the desired test.
c. Assuming that you have decided to match pairwise on AGE and SEX, which of the preceding regression models would you prefer to use, and why?