You are interested in seeing if weight lose depends on the interaction between 3

Question

You are interested in seeing if weight lose depends on the interaction between 3 diet plans and 2 exercise plans. Here are the cell means for weight lose in pounds:

       Diet Plan 1 Diet Plan 2 Diet Plan 3

Exercise 1   10   20         30

Exercise 2 20   30        40

Assuming the study has high power and any difference is significant, what F-statistics would be significant? Drawing an interaction plot and calculating marginal means, may be helpful.

Main effect of exercise is the only significant f-statistic.

Main effect of diet is the only significant f-statistic.

Main effects of both diet and exercise are significant. The interaction is not significant.

Main effects of both diet and exercise, and the interaction is significant.

Only the interaction is significant.

The main effect of diet and the interaction is significant. The main effect of exercise is not significant.

The main effect of exercise and the interaction is significant. The main effect of diet is not significant.

Main effect of diet is the only significant f-statistic.

Main effects of both diet and exercise are significant. The interaction is not significant.

Main effects of both diet and exercise, and the interaction is significant.

Only the interaction is significant.

The main effect of diet and the interaction is significant. The main effect of exercise is not significant.

The main effect of exercise and the interaction is significant. The main effect of diet is not significant.

Explanation / Answer

The main effect of both diet and exercise are significant. However, the interaction effect will not be significant as we can see that the results increase linearly in both the diet and exercise cases

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