A two-factor experiment designed to compare two diets and to analyze whether results depend on gender randomly assigns 20 men and 20 women to the two diets, 10 of each to each diet. After three months the sample mean weight losses are as shown in the table.

a. Identify the two factors (explanatory variables) and the response variable.
b. What would the study have concluded if it did only a one-factor analysis on diet, looking at the overall results and not having the information about gender?
c. What could the study learn from the two-factor study that it would have missed by doing a one factor study on diet alone or a one-factor study on gender alone?

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Sample Mean Weight Loss by Diet Type and Gender Gender Diet Low-carb Low-fat Overall Female Male Overall 12 12