12.71 Contrasts for the massage study. Refer to Exercise 12.54 (page 690). There are several comparisons of interest in this study. They are (1) usual care versus the average of the massage groups; (2) the average of the two 30-minute massage groups versus the average of the two 60-minute massage groups; and (3) the difference between a 30-minute massage once a week and twice a week versus the difference between a 60-minute massage once a week and twice a week.

  1. (a) Express each contrast in terms of the means (μ’s) of the treatments.

  2. (b) Give estimates with standard errors for each of the contrasts.

  3. (c) Perform the significance tests for the contrasts. Summarize the results of your tests and your conclusions.