For a two-factor ANOVA, if SSwithin treatments= 86, SSbetween treatments = 80, SSbetween subjects = 62, dfwithin treatments = 12, dfbetween treatments = 1, dfbetween subjects = 4, find the F-ratio.

a. F = 26.667 b. F = 2.389 c. F = 11.16 d. F = 72.833

Question

High School

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Answer :

AlbertFrancis AlbertFrancis · Answer 1 · 2025-05-27T20:53:08-04:00

The F-ratio for the given two-factor ANOVA is approximately F = 11.16.

To calculate the F-ratio for a two-factor ANOVA, we need to use the given information:

First, we calculate the mean square between treatments:

Mean Square Between Treatments = SSbetween treatments / dfbetween treatments

Mean Square Between Treatments = 80 / 1 = 80

Next, we calculate the mean square within treatments:

Mean Square Within Treatments = SSwithin treatments / dfwithin treatments

Mean Square Within Treatments = 86 / 12 = 7.167

Finally, we calculate the F-ratio:

F-ratio = Mean Square Between Treatments / Mean Square Within Treatments

F-ratio = 80 / 7.167 ≈ 11.16

Therefore, the correct answer is F = 11.16.

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