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Chapter 11: Multifactor Analysis of Variance48.a. The treatment conditions in the observed group are (in standard order) (1), ab, ac, bc, ad,bd, cd, and abcd. The alias pairs are {A, BCD}, {B, ACD}, {C, ABD}, {D, ABC}, {AB,CD}, {AC, BD}, and {AD, BC}.b.A B C D AB AC AD(1) = 19.09 - - - - + + +Ab = 20.11 + + - - + - -Ac = 21.66 + - + - - + -Bc = 20.44 - + + - - - +Ad = 13.72 + - - + - - +Bd = 11.26 - + - + - + -Cd = 11.72 - - + + + - -Abcd = 12.29 + + + + + + +Contrast 5.27 -2.09 1.93 -32.31 -3.87 -1.69 .79SS 3.47 .55 .47 130.49 1.87 .36 .08f 4.51 < 1 < 1 169.47 SSE=2.31 MSE=.770F. 05,1,3=10.13, so only the D main effect is judged significant.342

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