4.2 TWO FACTOR RANDOMISED BLOCK MODEL Y = S'|B|A Analysis of terms: S|B|A - S*B*A (Model 1) or S + B|A (Model 2) Data: S A B Y 1 1 1 4.5924 2 1 1 -0.5488 3 1 1 6.1605 4 1 1 2.3374 1 1 2 5.1873 2 1 2 3.3579 3 1 2 6.3092 4 1 2 3.2831 1 2 1 7.3809 2 2 1 9.2085 3 2 1 13.1147 4 2 1 15.2654 1 2 2 12.4188 2 2 2 14.3951 3 2 2 8.5986 4 2 2 3.4945 1 3 1 21.3220 2 3 1 25.0426 3 3 1 22.6600 4 3 1 24.1283 1 3 2 16.5927 2 3 2 10.2129 3 3 2 9.8934 4 3 2 10.0203 Model 4.2(i) A and B are fixed factors, S is a random blocking factor: Restricted Model_1 Model_2 Source DF SS MS F P F P 1 S 3 9.07 3.02 - - 0.27 0.850 2 A 2 745.36 372.68 67.58 <0.001 32.67 <0.001 3 B 1 91.65 91.65 4.13 0.135 8.03 0.013 4 B*A 2 186.37 93.18 7.82 0.021 8.17 0.004 5 S*A 6 33.09 5.51 - - - - 6 S*B 3 66.51 22.17 - - - - 7 S*B*A 6 71.51 11.92 - - - - 8 P(S*B*A) 0 - - Total 23 1203.56 Model 4.2(ii) A is a fixed factor, B is a random factor, S is a random blocking factor: Restricted Model_1 Model_2 Source DF SS MS F P F P 1 S 3 9.07 3.02 0.14 0.932 0.27 0.850 2 A 2 745.36 372.68 4.29 0.214* 4.00 0.200 3 B 1 91.65 91.65 4.13 0.135 8.03 0.013 4 B*A 2 186.37 93.18 7.82 0.021 8.17 0.004 5 S*A 6 33.09 5.51 0.46 0.815 - - 6 S*B 3 66.51 22.17 - - - - 7 S*B*A 6 71.51 11.92 - - - - 8 P(S*B*A) 0 - - Total 23 1203.56 * Quasi F-ratio. Model 4.2(iii) A and B are random factors, S is a random blocking factor: Model_1 Model_2 Source DF SS MS F P F P 1 S 3 9.07 3.02 0.19 0.893* 0.27 0.850 2 A 2 745.36 372.68 4.29 0.214* 4.00 0.200 3 B 1 91.65 91.65 0.89 0.433* 0.98 0.426 4 B*A 2 186.37 93.18 7.82 0.021 8.17 0.004 5 S*A 6 33.09 5.51 0.46 0.815 - - 6 S*B 3 66.51 22.17 1.86 0.237 - - 7 S*B*A 6 71.51 11.92 - - - - 8 P(S*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/