Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The degrees of freedom for testing whether the brands of shoes differ are D1 = 9 and D2 = 2.

Question

Quizplus · Accepted Answer

The degrees of freedom for testing whether the brands of shoes differ should be calculated based on the number of groups and the total number of subjects. For the between-groups comparison (among the three brands), the degrees of freedom would be $D1 = k - 1 = 3 - 1 = 2$, where $k$ is the number of groups (brands). For the within-group comparison (error term), the degrees of freedom would be $D2 = N - k = 30 - 3 = 27$, where $N$ is the total number of subjects (10 runners x 3 brands = 30).

Three Brands of Running Shoes Are Each Tested by 10