Suppose that in Problem 6-1 we had confounded ABC in replicate I, AB in replicate II, and

Question:

Suppose that in Problem 6-1 we had confounded ABC in replicate I, AB in replicate II, and BC in replicate III. Calculate the factor effect estimates. Construct the analysis of variance table.

Problem 6-1.

An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results follow:

Replicate Treatment A B C Combination I II III (1) 22 31 25 a 32 43 29 35 34 50 + ab 55 47 46 44 45 38 ac 40 37 36 bc 60 50 54 + abc 39 41 47 UIII I + + + + ||| + +