A researcher is interested in studying the effect that the amount of fat in the
ID: 3131797 • Letter: A
Question
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.
Perform a two-way analysis of variance and explain the results.
Find the effect size for each factor and the interaction and explain the results.
Diet
Exercise
<30% fat
30% - 60% fat
>60% fat
<60 minutes
4
3
2
4
1
2
2
2
2
4
2
2
3
3
1
60 minutes
6
8
5
or more
5
8
7
4
7
5
4
8
5
5
6
6
Diet
Exercise
<30% fat
30% - 60% fat
>60% fat
<60 minutes
4
3
2
4
1
2
2
2
2
4
2
2
3
3
1
60 minutes
6
8
5
or more
5
8
7
4
7
5
4
8
5
5
6
6
Explanation / Answer
row factor here indicates amount of exercise of middle-aged women and column factor indicates effect of the amount of fat in the diet.
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
row factor 1 90.133 90.1333 135.20 0.000
column factor 2 6.200 3.1000 4.65 0.020
row factor*column factor 2 18.467 9.2333 13.85 0.000
Error 24 16.000 0.6667
Total 29 130.800
Effect size of interaction=18.467
For testing the significance of the interaction between row factor and column factor,we get p-value=0<0.05,so we reject H0 at 5% level of significance and we can conclude that there is significant effect of the interaction between amount of exercise of middle-aged women and the effect of the amount of fat in the diet.
Since the interaction effect is present in the model,we can't test for the row factor and column factor marginally.
If there is no interaction then we can test for row and column factor marginally.If we perform the marginal tests,
Effect size of row factor=90.133
For testing the significance of row factor,we get p-value=0<0.05,so we reject H0 at 5% level of significance and we can conclude that there is significant effect of the amount of exercise of middle-aged women.
Effect size of column factor= 6.2
For testing the significance of row factor,we get p-value=0.02<0.05,so we reject H0 at 5% level of significance and we can conclude that there is significant effect of the the amount of fat in the diet..
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