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.

Answer 1

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