15.9 The experiment described in Example 15.4 also gave data on change in body fat mass for men (“Growth Hormone and Sex Steroid Administration in Healthy Aged Women and Men,” Journal of the American Medical Association [2002]: 2282–2292). Each of 74 male subjects who were over age 65 was assigned at random to one of the following four treatments:

1. placebo “growth hormone” and placebo “steroid”

(denoted by P 1 P);

2. placebo “growth hormone” and the steroid testosterone

(denoted by P 1 S);

3. growth hormone and placebo “steroid” (denoted by G 1 P); and 4. growth hormone and the steroid testosterone (denoted by G 1 S).

The accompanying table lists data on change in body fat mass over the 26-week period following the treatment that are consistent with summary quantities given in the article.
Change in Body Fat Mass (kg)
Treatment P 1 P P 1 S G 1 P G 1 S 0.3 23.7 23.8 25.0 0.4 21.0 23.2 25.0 21.7 0.2 24.9 23.0 20.5 22.3 25.2 22.6 22.1 1.5 22.2 26.2 1.3 21.4 23.5 27.0 0.8 1.2 24.4 24.5 1.5 22.5 20.8 24.2 21.2 23.3 21.8 25.2 20.2 0.2 24.0 26.2 1.7 0.6 21.9 24.0 1.2 20.7 23.0 23.9 0.6 20.1 21.8 23.3 0.4 23.1 22.9 25.7 21.3 0.3 22.9 24.5 20.2 20.5 22.9 24.3 0.7 20.8 23.7 24.0 20.7 24.2 20.9 24.7 22.0 20.6 n 0.117 0.121 0.117 0.119 x 0.100 20.933 23.112 24.605 s 1.139 1.443 1.178 1.122 s2 1.297 2.082 1.388 1.259 Also, N 5 74, grand total 5 2158.3, and x 5 2158.3 74 5 22.139.
Carry out an F test to determine if mean change in body fat mass differs for the four treatments.