Women aged 6065 are randomly assigned to either a Calcium supplement or a Calcium plus Exercise group. The goal is to see whether the groups differ in their mean change in bone density (Change_BDens)....

Women aged 6065 are randomly assigned to either a Calcium supplement or a Calcium plus Exercise group. The goal is to see whether the groups differ in their mean change in bone density (Change_BDens). However, a potential covariate is a woman’s body mass index (BMI). The data are given in Table 11.18.

(a) Compare the mean change for the two groups using a simple independent samples t test and interpret the results.

(b) Conduct an ANCOVA with BMI as the covariate. Compute the expected change in each group using the overall BMI average to make the adjustment.

Do the groups differ significantly?

(c) Verify that an interaction between the group dummy variable and BMI does not improve the model.

(d) You should reach different conclusions in parts (a) and (b). What is the source of the difference? Is the ANCOVA analysis in part (b) valid?