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 59 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
Error			1.4	X
Total		226.37	X	X

Answer 1

Given:

Total sample size = 59, Number of Treatments = 4

Mean square error: 1.4

Calculation:

df_Treatment = 4-1 = 3

df_Total = n-1 = 59-1 = 58

df_error = df_Total - df_Treatment = 58 - 3 = 55

Mean square error = Sum of Squares of error / df_error

1.4 = Sum of Squares of error / 55

Sum of Squares of error = 1.4 * 55 = 77

Sum of Squares of Treatment = Sum of Squares of Total - Sum of Squares of error

Sum of Squares of Treatment = 226.37 - 77 = 149.37

Mean square Treatment = Sum of squares Treatment / df_Treatment

Mean square Treatment = 149.37/3 = 49.79

F = Mean Square Treatment / Mean Square error

F = 49.79 / 1.4 = 35.56

ANOVA TABLE:

Source of Variation	df	Sum of Squares	Mean Square	F
Treatment	3	149.37	49.79	35.56
Error	55	77	1.4
Total	58	226.37

Critical value:

F_tabulate = F,(t-1,n-t) = F_0.05,(3,55) = 2.7725

CONCLUSION:

Test statistic (F) > Critical value, i.e. 35.56 > 2.7725,   We conclude that data provide us enough evidence against the null hypothesis Ho, and hence Reject Ho at 5% level of significance.

Therefore, There is a significant difference in those Treatment mean.