5. A researcher is interested in studying the effect that the amount of fat in t

Question

5. A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

1

a. Perform a two-way analysis of variance and explain the results. (Show all work to receive full credit)

b. Find the effect size for each factor and the interaction and explain the results. (Show all work to receive full credit)

Diet Exercise <30% fat 30%-60% fate >60% fat <60 minutes 4 3 2 4

1

2 2 2 2 4 2 2 3 3 1 60 minutes or more 6 8 5 5 8 7 4 7 5 4 8 5 5 6 6

Explanation / Answer

a)

Using Excel

if p-value is less than level of significance

the variable is significant

here all three factors are significant . (Exercise ,Diet and interaction} at level of significance 0.05

b)

h2 = SSeffect / SStotal

for exercise -

h2 = SSeffect / SStotal = 90.13333/130.8 = 0.689

for diet

h2 = SSeffect / SStotal = 6.2 /130.8 = 0.04740

for interaction

h2 = SSeffect / SStotal = 18.46666/130.8 = 0.141182

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Anova: Two-Factor With Replication SUMMARY <30% fat 30%-60% fate >60% fat Total <60 minutes Count 5 5 5 15 Sum 17 11 9 37 Average 3.4 2.2 1.8 2.466666667 Variance 0.8 0.7 0.2 0.980952381 60 minutes or more Count 5 5 5 15 Sum 24 37 28 89 Average 4.8 7.4 5.6 5.933333333 Variance 0.7 0.8 0.8 1.923809524 Total Count 10 10 10 Sum 41 48 37 Average 4.1 4.8 3.7 Variance 1.211111111 8.177777778 4.455555556 ANOVA Source of Variation SS df MS F P-value F crit Sample 90.13333333 1 90.13333333 135.2 2.39383E-11 4.259677273 Columns 6.2 2 3.1 4.65 0.019642832 3.402826105 Interaction 18.46666667 2 9.233333333 13.85 0.000100149 3.402826105 Within 16 24 0.666666667 Total 130.8 29

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