5.7 THREE FACTOR SPLIT PLOT MODEL (III) Y = E|B|S'(A) with orthogonal contrasts on B Model-2 analysis of terms: A|E|B + S(A) for the main model Model-2 analysis of terms: A|E|C + A|E|D(C) + S(A) for the contrasts Data: S A B C D E Y 1 1 1 2 0 1 8.524 2 1 1 2 0 1 7.444 3 1 1 2 0 1 6.877 1 1 1 2 0 2 16.597 2 1 1 2 0 2 15.260 3 1 1 2 0 2 15.870 1 1 1 2 0 3 21.229 2 1 1 2 0 3 19.397 3 1 1 2 0 3 19.276 1 1 2 -1 1 1 9.068 2 1 2 -1 1 1 7.939 3 1 2 -1 1 1 6.370 1 1 2 -1 1 2 15.739 2 1 2 -1 1 2 12.980 3 1 2 -1 1 2 13.759 1 1 2 -1 1 3 21.121 2 1 2 -1 1 3 15.559 3 1 2 -1 1 3 19.113 1 1 3 -1 -1 1 8.671 2 1 3 -1 -1 1 7.726 3 1 3 -1 -1 1 8.270 1 1 3 -1 -1 2 13.037 2 1 3 -1 -1 2 11.683 3 1 3 -1 -1 2 11.786 1 1 3 -1 -1 3 14.705 2 1 3 -1 -1 3 15.109 3 1 3 -1 -1 3 15.267 1 2 1 2 0 1 9.206 2 2 1 2 0 1 8.915 3 2 1 2 0 1 8.876 1 2 1 2 0 2 18.118 2 2 1 2 0 2 15.513 3 2 1 2 0 2 20.010 1 2 1 2 0 3 19.519 2 2 1 2 0 3 21.530 3 2 1 2 0 3 21.710 1 2 2 -1 1 1 8.231 2 2 2 -1 1 1 9.062 3 2 2 -1 1 1 9.162 1 2 2 -1 1 2 14.448 2 2 2 -1 1 2 14.993 3 2 2 -1 1 2 15.362 1 2 2 -1 1 3 16.046 2 2 2 -1 1 3 17.364 3 2 2 -1 1 3 22.544 1 2 3 -1 -1 1 8.455 2 2 3 -1 -1 1 9.178 3 2 3 -1 -1 1 9.086 1 2 3 -1 -1 2 12.847 2 2 3 -1 -1 2 13.456 3 2 3 -1 -1 2 12.531 1 2 3 -1 -1 3 14.424 2 2 3 -1 -1 3 15.277 3 2 3 -1 -1 3 13.434 COMMENT: If B[1] is a control, and B[2], B[3] are treatment levels, contrasts C and D test for a control-versus-treatments effect, and a between-treatments effect. SS[C] + SS[D(C)] = SS[B]; likewise DF[C] + DF[D(C)] = DF[B]. Model 5.7(iv) A is a random factor, B and C are fixed factors, S is a random blocking factor: Restricted Source DF Seq SS Seq MS F P 1 A 1 8.105 8.105 1.45 0.295 2 S(A) 4 22.348 5.587 - - 3 B 2 97.196 48.598 30.17 0.032 C 1 65.240 65.240 40.46 0.024 = B[1] versus average{B[2],B[3]} D(C) 1 31.956 31.956 19.82 0.047 = B[2] versus B[3] 4 B*A 2 3.222 1.611 1.08 0.353 A*C 1 2.950 2.950 1.97 0.170 = A*(B[1] versus average{B[2],B[3]}) A*D(C) 1 0.272 0.272 0.18 0.674 = A*(B[2] versus B[3]) 5 E 2 844.912 422.456 286.57 0.003 6 E*A 2 2.948 1.474 0.98 0.385 7 E*B 4 62.946 15.737 123.93 <0.000 E*C 2 36.677 18.338 144.39 <0.001 = E*(B[1] versus average{B[2],B[3]}) E*D(C) 2 26.269 13.135 103.43 <0.001 = E*(B[2] versus B[3]) 8 E*A*B 4 0.508 0.127 0.08 0.987 E*A*C 2 0.322 0.161 0.11 0.896 = E*A*(B[1] versus average{B[2],B[3]}) E*A*D(C) 2 0.186 0.093 0.06 0.942 = E*A*(B[2] versus B[3]) 9 Error 32 47.899 1.497 Total 53 1090.084 Note: B and its contrasts are tested against the error MS[B*A] with only 2 error d.f.; since this term is far from significant it may be post-hoc pooled with the residual error term containing all of the interactions with S(A). Likewise for E and E*B, post-hoc pooling may also be applied to the error terms which have 2 and 4 d.f. respectively before post-hoc pooling. __________________________________________________________________ Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press. http://www.southampton.ac.uk/~cpd/anovas/datasets/