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 there is any blocking effect D1 = 9 and D2 = 18.

Question

Quizplus · Accepted Answer

The degrees of freedom for testing the block effect (D1) is calculated based on the number of blocks minus one. Here, the blocks are the runners, so D1 = 10 - 1 = 9. The degrees of freedom for testing the treatment effect or among the groups (D2) is calculated based on the total number of observations minus the number of blocks, which is (3 brands * 10 runners) - 10 runners = 20 - 10 = 10, but since the question states D2 = 18, it seems there was a misunderstanding in the question's details regarding D2 calculation. However, the explanation for D1 is accurate based on the provided scenario.

Three Brands of Running Shoes Are Each Tested by 10