Question

An article in the Journal of the American Medical Assocation described an experiment to investigate the effect of four treatments on various body characteristics. In this double-blind experiment, each of 61 female subjects age 65 or older was assigned at random to one of the following four treatments:

1) P + P: placebo "growth hormone" and placebo "steroid"
2) P + S: placebo "growth hormone" and the steroid estradiol
3) G + P: growth hormone and placebo "steroid"
4) G + S: growth hormone and the steroid estradiol

The change in body fat mass was measured over the 26-week period following the treatments. Using the information provided above and in the partial table below, complete the ANOVA table (use 2 decimals for your answers).

Source of Variation	df	Sum of Squares	Mean Square	F
Treatment	(No Response)	(No Response)	(No Response)	(No Response)
Error	(No Response)	(No Response)	1.26	X
Total	(No Response)	223.68	X	X

Answer 1

First we have to find the degrees of freedom

there are four treatments hence dof for treatments = 4 - 1 = 3

total degrees of freedom = total number of subjects -1 = 61 - 1 = 60

dof for error = total dof - dof of treatments = 60 - 3 = 57

MSE is give = 1.26

SSE = MSE*dof of error = 1.26*57 = 71.82

SStotal = SST + SSE => SST = 223.68 - 71.82 = 151.86

MStreatment = SST/dof of SST = 151.86/3 = 50.62

F statistic = MStreatment / MSE = 50.62/1.26 = 40.17

Source of Variation	df	Sum of Squares	Mean Square	F
Treatment	3	151.86	50.62	40.17
Error	57	71.82	1.26	X
Total	60	223.68	X	X