1.A researcher uses one-factor ANOVA to test the statistical significance of dif
ID: 3370947 • Letter: 1
Question
1.A researcher uses one-factor ANOVA to test the statistical significance of differences among five treatments, with a sample of n = 10 in each treatment group. The F-ratio for this analysis would have what df values?
A. df = 5, 100
B. df = 4, 95
C. df = 4, 45
D. None of the above.
2. For a one-factor ANOVA comparing four treatment groups, MSbetween = 32. What is the value of SSbetween?
A. 96
B. 80
C. 36
D. None of the above.
3. A one-factor ANOVA produces SSbetween = 75, SSwithin = 86, and an F-ratio with df = 5, 30. For this analysis, what is the F-ratio?
A. 0.50
B. 5.22
C. 3.68
D. Can't be answered without additional information.
Explanation / Answer
1) A researcher uses one-factor ANOVA to test the statistical significance of differences among five treatments, with a sample of n = 10 in each treatment group.
Here, treatment = k = 5
Total samples =N = nk = 10*5 = 50
For F-ratio we need treatment df and error df
Treatment df = k - 1= 5 -1 = 4
Error df = N - k = 50 - 5 = 45
Therefore df for F-ratio are,
df = 4, 45
Answer: C)
2) Treatment = k = 4
Treatment df = k - 1= 4 - 1= 3
MSbetween = 32
SSbetween = treatment df * MSbetween = 3 * 32 = 96
Answer: A) 96
3) A one-factor ANOVA produces SSbetween = 75, SSwithin = 86, and an F-ratio with df = 5, 30
MSbetween = SSbetween / between df = 75/5 = 15
MSwithin = SSwithin / within df = 86/30 = 2.87
Therefore,
F-ratio = MSbetween / MSwithin = 15/2.87 = 5.22
Answer: B) 5.22
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