An article in the Journal of the American Medical Assocation described an experi

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 63 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 SS, MS, and F value answers).

Source of Variation df Sum of Squares Mean Square F Treatment Error 1.63 X Total 216.73 X X

Explanation / Answer

63 female subjects each was assigned at random to one the four treatments

Number of treatments = 4

Total sample size = 63

Degrees of freedom for Total = Total sample size -1 = 63-1 = 62

Degrees of freedom for Treatment = Number of treatments - 1 = 4-1=3

Degrees of freedom for error = Degrees of freedom for Total - Degrees of freedom for Treatment =62 - 3 =59

Given,

Mean sum of squares for error = 1.63

Mean sum of squares of error = Sum of squares of error / Degrees of freedom for error

Sum of Squares for Error = Mean sum of squares of error x Degrees of freedom for error = 1.63 x 59 = 96.17

Given

Sum of Squares for Total = 216.73

Sum of Squares for Treatment = Sum of Squares for Total - Sum of Squares for Error = 216.73 - 96.17=120.56

Mean sum of squares for treatment = Sum of squares of Tretment / Degrees of freedom for Treatment = 120.56/3 =40.19

Statisitc F = Mean sum of squares for treatment / Mean sum of squares for error = 40.19/1.63 = 24.65

Source of Variation df Sum of Squares Mean Square F Treatment 3 120.56 40.19 24.65 Error 59 96.17 1.63 X Total 62 216.73 X X

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