Suppose that three drugs used to reduce cholesterol are compared in a randomized

Question

Suppose that three drugs used to reduce cholesterol are compared in a randomized experiment in which three people use each drug for a month. The data for the reductions in cholesterol level for the N = 9 participants are as follows:

(a) Calculate the overall mean, x, and the group means, x1, x2 and x3.

(b) Calculate SS Groups, the sum of squares for groups.
SS Groups =  

(c) Calculate SS Total, the total sum of squares.
SS Total =  

(d) Determine SS Error, the sum of squared errors.
SS Error =  

(e) Calculate the F-statistic for comparing the mean cholesterol reductions for the three drugs. (Round the answer to the nearest hundredth.)
F =  

What are the degrees of freedom, df for this statistic?
df = (  ,  )

Drug 1 Drug 2 Drug 3 6 8 9 4 12 14 2 10 7

Explanation / Answer

grand total =G=72 , k=3=repititon of each drug

n=9=total number of observation

(a) x=8

x1= 4

x2= 10

x3= 10

(b) SS gorup=72

x12/k+x22/k+x32/k=42/3+102/3+102/3=72

(c) SS total=114

sum( x2)-G2/n=62+82+92+42+122+142+22+102+72-722/9=114

(d)SS error=42

SS Total - SS group=114-72=42

(e)F=5.14 , df=(2,6)

following information has been generated using ms-excel

Anova: Single Factor SUMMARY Groups Count Sum Average x1 3 12 4 x2 3 30 10 x3 3 30 10 x 9 72 8 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 72 2 36 5.142857 0.050007 5.143253 Within Groups 42 6 7 Total 114 8

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