A researcher is interested in studying the effect that the amount of fat in the
ID: 3022391 • 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.
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
Perform a two-way analysis of variance and explain the results. (Show all work to receive full credit)
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% 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
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
row factor 1 90.133 90.1333 67.99 0.000
column factor 2 6.200 3.1000 2.34 0.116
Error 26 34.467 1.3256
Lack-of-Fit 2 18.467 9.2333 13.85 0.000
Pure Error 24 16.000 0.6667
Total 29 130.800
where row factors are <60 minutes and 60 minutes or more and column factors are <30% fat,30-60%fat and >60% fat.
effect size of row factors=90.133
effect size of column factors=6.2
there is no interaction effect present.
From the anova table it can be seen that p-value for the row factor<0.05,so there is significant differnce between the row factors and p-value for the column factor> 0.05,so there is no significant differnce between the column factors.
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