12.54 Massage therapy for osteoarthritis of the knee. Various studies have shown the benefits of massage to manage pain. In one study, 125 adults suffering from osteoarthritis of the knees were randomly assigned to one of five eight-week regimens.¹⁴ The primary outcome was the change in the Western Ontario and McMaster Universities Arthritis Index (WOMAC-Global). This index is used extensively to assess pain and functioning in those suffering from arthritis. Negative values indicate improvement. The following table summarizes the results of those completing the study.

Regimen	n		s
30 min massage 1 × /wk	22	−17.4	17.9
30 min massage 2 × /wk	24	−18.4	20.7
60 min massage 1 × /wk	24	−24.0	18.4
60 min massage 2 × /wk	25	−24.0	19.8
Usual care, no massage	24	−6.3	14.6

(a) What proportion of adults dropped out of the study before completion?
(b) Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer.
(c) Find the pooled standard deviation.
(d) The SS(Regimen) = 5060.346. Test the null hypothesis that the mean change in WOMAC-Global score is the same for all regimens.
(e) There are 10 pairs of means to compare. For the Bonferroni multiple-comparisons method, the critical t -value is 2.863. Which pairs of means are found to be significantly different? Write a short summary of your analysis.