4.3 THREE FACTOR RANDOMISED BLOCK MODEL Y = S'|C|B|A Analysis of terms: S|C|B|A - S*C*B*A (Model 1) or S + C|B|A (Model 2) Data: S A B C Y 1 1 1 1 -3.8558 2 1 1 1 4.4076 1 1 1 2 -4.1752 2 1 1 2 1.4913 1 1 2 1 5.9699 2 1 2 1 5.2141 1 1 2 2 9.1467 2 1 2 2 5.8209 1 2 1 1 9.4082 2 2 1 1 6.0296 1 2 1 2 15.3014 2 2 1 2 12.1900 1 2 2 1 6.9754 2 2 2 1 14.3012 1 2 2 2 10.4266 2 2 2 2 2.3707 1 3 1 1 19.1834 2 3 1 1 18.3855 1 3 1 2 23.3385 2 3 1 2 21.9134 1 3 2 1 16.4482 2 3 2 1 11.6765 1 3 2 2 17.9727 2 3 2 2 15.1760 3 1 1 1 1.6092 4 1 1 1 -0.8717 3 1 1 2 -3.3315 4 1 1 2 -0.9298 3 1 2 1 7.1962 4 1 2 1 6.6215 3 1 2 2 4.8174 4 1 2 2 0.6114 3 2 1 1 8.4111 4 2 1 1 8.8944 3 2 1 2 13.9123 4 2 1 2 11.5584 3 2 2 1 13.8318 4 2 2 1 6.6577 3 2 2 2 12.4861 4 2 2 2 4.5600 3 3 1 1 16.9834 4 3 1 1 18.1502 3 3 1 2 22.8108 4 3 1 2 26.0103 3 3 2 1 19.3879 4 3 2 1 12.7458 3 3 2 2 16.5695 4 3 2 2 16.3987 Model 4.3(i) A, B and C are all fixed factors, S is a random blocking factor: Restricted Model_1 Model_2 Source DF SS MS F P F P 1 S 3 26.70 8.90 - - 1.13 0.350 2 A 2 2010.22 1005.11 120.24 <0.001 128.06 <0.001 3 B 1 0.25 0.25 0.02 0.909 0.03 0.860 4 C 1 10.72 10.72 1.69 0.284 1.37 0.251 5 B*A 2 277.09 138.55 19.12 0.002 17.65 <0.001 6 C*A 2 50.22 25.11 4.14 0.074 3.20 0.054 7 C*B 1 40.38 40.38 12.03 0.040 5.14 0.030 8 C*B*A 2 40.05 20.03 2.32 0.179 2.55 0.093 9 S*A 6 50.16 8.360 - - - - 10 S*B 3 48.22 16.08 - - - - 11 S*C 3 19.03 6.34 - - - - 12 S*B*A 6 43.48 7.25 - - - - 13 S*C*A 6 36.36 6.06 - - - - 14 S*C*B 3 10.07 3.36 - - - - 15 S*C*B*A 6 51.70 8.62 - - - - 16 P(S*C*B*A) 0 - - Total 47 2714.65 Model 4.3(ii) A and B are fixed factors, C 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 26.70 8.90 1.40 0.394 1.13 0.350 2 A 2 2010.22 1005.11 36.67 0.019* 40.03 0.024 3 B 1 0.25 0.25 0.00 0.953* 0.01 0.950 4 C 1 10.72 10.72 1.69 0.284 1.37 0.251 5 B*A 2 277.09 138.55 7.43 0.158* 6.92 0.126 6 C*A 2 50.22 25.11 4.14 0.074 3.20 0.054 7 C*B 1 40.38 40.38 12.03 0.040 5.14 0.030 8 C*B*A 2 40.05 20.03 2.32 0.179 2.55 0.093 9 S*A 6 50.16 8.36 1.38 0.353 - - 10 S*B 3 48.22 16.08 4.79 0.115 - - 11 S*C 3 19.03 6.34 - - - - 12 S*B*A 6 43.48 7.25 0.84 0.581 - - 13 S*C*A 6 36.36 6.06 - - - - 14 S*C*B 3 10.07 3.36 - - - - 15 S*C*B*A 6 51.70 8.62 - - - - 16 P(S*C*B*A) 0 - - Total 47 2714.65 * Quasi F-ratio. Model 4.3(iii) A is a fixed factor, B and C are random factors, S is a random blocking factor: Restricted Model_1 Model_2 Source DF SS MS F P F P 1 S 3 26.70 8.90 0.47 0.723* 1.13 0.350 2 A 2 2010.22 1005.11 6.82 0.118* 7.00 0.125* 3 B 1 0.25 0.25 0.00 0.953* 0.01 0.950 4 C 1 10.72 10.72 0.25 0.698* 0.27 0.697 5 B*A 2 277.09 138.55 7.43 0.158* 6.92 0.126 6 C*A 2 50.22 25.11 1.44 0.458* 1.25 0.444 7 C*B 1 40.38 40.38 12.03 0.040 5.14 0.030 8 C*B*A 2 40.05 20.03 2.32 0.179 2.55 0.093 9 S*A 6 50.16 8.36 1.78 0.554* - - 10 S*B 3 48.22 16.08 4.79 0.115 - - 11 S*C 3 19.03 6.34 1.89 0.307 - - 12 S*B*A 6 43.48 7.25 0.84 0.581 - - 13 S*C*A 6 36.36 6.06 0.70 0.660 - - 14 S*C*B 3 10.07 3.36 - - - - 15 S*C*B*A 6 51.70 8.62 - - - - 16 P(S*C*B*A) 0 - - Total 47 2714.65 * Quasi F-ratio. Model 4.3(iv) A, B and C are all random factors, S is a random blocking factor: Model 1 Model 2 Source DF SS MS F P F P 1 S 3 26.70 8.90 0.39 0.767* 1.13 0.350 2 A 2 2010.22 1005.11 6.82 0.118* 7.00 0.122* 3 B 1 0.25 0.25 0.00 0.973* 0.00 0.972* 4 C 1 10.72 10.72 0.21 0.716* 0.24 0.715* 5 B*A 2 277.09 138.55 7.43 0.158* 6.92 0.126 6 C*A 2 50.22 25.11 1.44 0.458* 1.25 0.444 7 C*B 1 40.38 40.38 2.73 0.345* 2.02 0.291 8 C*B*A 2 40.05 20.03 2.32 0.179 2.55 0.093 9 S*A 6 50.16 8.36 1.78 0.554* - - 10 S*B 3 48.22 16.08 8.09 0.702* - - 11 S*C 3 19.03 6.34 7.92 0.916* - - 12 S*B*A 6 43.48 7.25 0.84 0.581 - - 13 S*C*A 6 36.36 6.06 0.70 0.660 - - 14 S*C*B 3 10.07 3.36 0.39 0.765 - - 15 S*C*B*A 6 51.70 8.62 - - - - 16 P(S*C*B*A) 0 - - Total 47 2714.65 * 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/