3.4 NESTED CROSS-FACTORED MODEL Y = C(B|A) + e Analysis of terms: B|A + C(B A) Data: A B C Y 1 1 1 -3.8558 1 1 1 4.4076 1 1 2 -4.1752 1 1 2 1.4913 1 2 1 5.9699 1 2 1 5.2141 1 2 2 9.1467 1 2 2 5.8209 2 1 1 9.4082 2 1 1 6.0296 2 1 2 15.3014 2 1 2 12.1900 2 2 1 6.9754 2 2 1 14.3012 2 2 2 10.4266 2 2 2 2.3707 3 1 1 19.1834 3 1 1 18.3855 3 1 2 23.3385 3 1 2 21.9134 3 2 1 16.4482 3 2 1 11.6765 3 2 2 17.9727 3 2 2 15.1760 COMMENT: This example is balanced and therefore orthogonal, so use Type I (sequential) SS. In the event of non-orthogonality, use Type III (adjusted) SS. Model 3.4(i) A and B are both fixed, C is a random factor: Source DF SS MS F P 1 A 2 905.27 452.63 33.30 0.001 2 B 1 0.19 0.19 0.01 0.910 3 B*A 2 167.65 83.82 6.17 0.035 4 C(B*A) 6 81.56 13.59 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 Total 23 1297.13 Model 3.4(ii) A is fixed, B and C are random factors: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 5.40 0.156 5.40 0.156 2 B 1 0.19 0.19 0.01 0.910 0.00 0.967 3 B*A 2 167.65 83.82 6.17 0.035 6.17 0.035 4 C(B*A) 6 81.56 13.59 1.14 0.395 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 Total 23 1297.13 Model 3.4(iii) A, B and C are all random factors: Source DF SS MS F P 1 A 2 905.27 452.63 5.40 0.156 2 B 1 0.19 0.19 0.00 0.967 3 B*A 2 167.65 83.82 6.17 0.035 4 C(B*A) 6 81.56 13.59 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 Total 23 1297.13 Model 3.4(iv) A is a fixed factor, B is a covariate of the response, C is a random factor: Source DF Seq SS MS F P 1 A 2 905.27 452.63 33.31 0.001 2 B 1 0.19 0.19 0.01 0.910 3 B*A 2 167.65 83.82 6.17 0.035 4 C(B*A) 6 81.56 13.59 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 Total 23 1297.13 Model 3.4(v) A and C are random factors, B is a covariate of the response Source DF Seq SS MS F P 1 A 2 905.27 452.63 33.31 0.001 2 B 1 0.19 0.19 0.00 0.967 3 B*A 2 167.65 83.82 6.17 0.035 4 C(B*A) 6 81.56 13.59 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 Total 23 1297.13 Model 3.4(vi) A and B are covariates of the response, C is a random factor Source DF Seq SS MS F P 1 A 1 901.12 901.12 73.44 0.001 2 B 1 0.19 0.19 0.02 0.905 3 B*A 1 155.20 155.20 12.65 0.007 4 C(B*A) 8 98.16 12.27 1.14 0.395 5 S(C(B*A)) 12 142.47 11.87 1.03 0.463 Total 23 1297.13 __________________________________________________________________ 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/