15.4 A preliminary experiment is conducted to study the effects of four factors and their interactions on the output of a certain machining operation. Two runs are made at each of the treatment combinations in order to supply a measure of pure experimental error. Two levels of each factor are used, resulting in the data shown next page. Make tests on all main effects and interactions at the 0.05 level of significance. Draw conclusions.

Source of Sum of Degrees of Mean Computed Variation Effects Squares Freedom Square f P-Value Main effect :
A B C D Two-factor interaction :
AB AC AD BC BD CD Three-factor interaction :
ABC ABD ACD BCD Four-factor interaction :
ABCD Error −1.2000 −1.2250 −2.2250 1.4875 0.9875 0.6125 −1.3250 1.1875 0.6250 0.7000 −0.5500 1.7375 1.4875 −0.8625 0.7000 11.52 12.01 39.61 17.70 7.80 3.00 14.05 11.28 3.13 3.92 2.42 24.15 17.70 5.95 3.92 39.36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 11.52 12.01 39.61 17.70 7.80 3.00 14.05 11.28 3.13 3.92 2.42 24.15 17.70 5.95 3.92 2.46 4.68 4.88 16.10 7.20 3.17 1.22 5.71 4.59 1.27 1.59 0.98 9.82 7.20 2.42 1.59 0.0459 0.0421 0.0010 0.0163 0.0939 0.2857 0.0295 0.0480 0.2763 0.2249 0.3360 0.0064 0.0163 0.1394 0.2249 Total 217.51 31 Treatment Combination Replicate 1 Replicate 2 (1)
a b c d ab ac ad bc bd cd abc abd acd bcd abcd 7.9 9.1 8.6 10.4 7.1 11.1 16.4 7.1 12.6 4.7 7.4 21.9 9.8 13.8 10.2 12.8 9.6 10.2 5.8 12.0 8.3 12.3 15.5 8.7 15.2 5.8 10.9 21.9 7.8 11.2 11.1 14.3