7.2 THREE FACTOR CROSS FACTORED UNREPLICATED MODEL Y = C|B|A Analysis of terms: C|B|A - C*B*A Data: A B C Y 1 1 1 4.5924 1 1 2 -0.5488 1 1 3 6.1605 1 1 4 2.3374 1 2 1 5.1873 1 2 2 3.3579 1 2 3 6.3092 1 2 4 3.2831 2 1 1 7.3809 2 1 2 9.2085 2 1 3 13.1147 2 1 4 15.2654 2 2 1 12.4188 2 2 2 14.3951 2 2 3 8.5986 2 2 4 3.4945 3 1 1 21.3220 3 1 2 25.0426 3 1 3 22.6600 3 1 4 24.1283 3 2 1 16.5927 3 2 2 10.2129 3 2 3 9.8934 3 2 4 10.0203 Model 7.2(i) A, B and C are all fixed factors: Source DF SS MS F P 1 A 2 745.36 372.68 - - 2 B 1 91.65 91.65 - - 3 B*A 2 186.37 93.18 - - 4 C 3 9.07 3.02 - - 5 C*A 6 33.09 5.51 - - 6 C*B 3 66.51 22.17 - - 7 C*B*A 6 71.51 11.92 - - 8 S(C*B*A) 0 - - Total 23 1203.56 Model 7.2(ii) A and C are fixed factors, B is a random factor: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 745.36 372.68 4.00 0.200 4.00 0.200 2 B 1 91.65 91.65 - - 0.89 0.433* 3 B*A 2 186.37 93.18 - - 7.82 0.021 4 C 3 9.07 3.02 0.14 0.932 0.14 0.932 5 C*A 6 33.09 5.51 0.46 0.815 0.46 0.815 6 C*B 3 66.51 22.17 - - 1.86 0.237 7 C*B*A 6 71.51 11.92 - - - - 8 S(C*B*A) 0 - - Total 23 1203.56 * Quasi F-ratio. Model 7.2(iii) A is a fixed factor, B and C are random factors: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 745.36 372.68 4.29 0.214* 4.29 0.214* 2 B 1 91.65 91.65 4.13 0.135 0.89 0.433* 3 B*A 2 186.37 93.18 7.82 0.021 7.82 0.021 4 C 3 9.07 3.02 0.14 0.932 0.19 0.893* 5 C*A 6 33.09 5.51 0.46 0.815 0.46 0.815 6 C*B 3 66.51 22.17 - - 1.86 0.237 7 C*B*A 6 71.51 11.92 - - - - 8 S(C*B*A) 0 - - Total 23 1203.56 * Quasi F-ratio. Model 7.2(iv) A, B and C are all random factors: Source DF SS MS F P 1 A 2 745.36 372.68 4.29 0.214* 2 B 1 91.65 91.65 0.89 0.433* 3 B*A 2 186.37 93.18 7.82 0.021 4 C 3 9.07 3.02 0.19 0.893* 5 C*A 6 33.09 5.51 0.46 0.815 6 C*B 3 66.51 22.17 1.86 0.237 7 C*B*A 6 71.51 11.92 - - 8 S(C*B*A) 0 - - Total 23 1203.56 * Quasi F-ratio. __________________________________________________________________ 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/