6.5 THREE FACTOR MODEL WITH REPEATED MEASURES ON TWO CROSS FACTORS Y = C|B|S'(A) Analysis of terms: C|B|A + C|B|S(A) - C*B*S(A) 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 Model 6.5(i) A, B and C are fixed factors, S is a random subject: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 44.34 0.006 44.34 0.006 2 S(A) 3 30.62 10.21 - - 0.63 0.673* 3 B 1 0.19 0.19 0.01 0.921 0.01 0.921 4 B*A 2 167.65 83.82 5.21 0.106 5.21 0.106 5 B*S(A) 3 48.27 16.09 - - 1.53 0.367 6 C 1 11.80 11.80 1.10 0.371 1.10 0.371 7 C*A 2 10.02 5.01 0.47 0.666 0.47 0.666 8 C*S(A) 3 32.12 10.71 - - 1.02 0.493 9 C*B 1 10.90 10.90 1.04 0.383 1.04 0.383 10 C*B*A 2 48.84 24.42 2.33 0.245 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.5(ii) A and C are fixed factors, B is a random factor, S is a random subject: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 5.81 0.177* 5.81 0.177* 2 S(A) 3 30.62 10.21 0.63 0.641 0.63 0.673* 3 B 1 0.19 0.19 0.01 0.921 0.00 0.966* 4 B*A 2 167.65 83.82 5.21 0.106 2.79 0.253* 5 B*S(A) 3 48.27 16.09 - - 1.53 0.367 6 C 1 11.80 11.80 1.06 0.556* 1.06 0.556* 7 C*A 2 10.02 5.01 0.20 0.834* 0.20 0.834* 8 C*S(A) 3 32.12 10.71 1.02 0.493 1.02 0.493 9 C*B 1 10.90 10.90 1.04 0.383 0.45 0.573 10 C*B*A 2 48.84 24.42 2.33 0.245 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.5(iii) A is a fixed factor, B and C are random factors, S is a random subject: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 7.76 0.286* 7.76 0.286* 2 S(A) 3 30.62 10.21 0.63 0.673* 0.00 0.966* 3 B 1 0.19 0.19 0.01 0.931* x x 4 B*A 2 167.65 83.82 2.79 0.253* 2.79 0.253* 5 B*S(A) 3 48.27 16.09 1.53 0.367 1.53 0.367 6 C 1 11.80 11.80 1.06 0.556* 1.06 0.556* 7 C*A 2 10.02 5.01 0.20 0.834* 0.20 0.834* 8 C*S(A) 3 32.12 10.71 1.02 0.493 1.02 0.493 9 C*B 1 10.90 10.90 1.04 0.383 0.45 0.573 10 C*B*A 2 48.84 24.42 2.33 0.245 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. Model6.5(iv) A is a random factor, B and C are fixed factors, S is a random subject: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 44.34 0.006 7.76 0.286* 2 S(A) 3 30.62 10.21 - - 0.63 0.673* 3 B 1 0.19 0.19 0.00 0.967 0.00 0.967 4 B*A 2 167.65 83.82 5.21 0.106 2.79 0.253* 5 B*S(A) 3 48.27 16.09 - - 1.53 0.367 6 C 1 11.80 11.80 2.36 0.265 2.36 0.265 7 C*A 2 10.02 5.01 0.47 0.666 0.20 0.834* 8 C*S(A) 3 32.12 10.71 - - 1.02 0.493 9 C*B 1 10.90 10.90 0.45 0.573 0.45 0.573 10 C*B*A 2 48.84 24.42 2.33 0.245 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.5(v) A and B are random factors, C is a fixed factor, S is a random subject: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 5.81 0.177* 7.76 0.286* 2 S(A) 3 30.62 10.21 0.63 0.641 0.63 0.673* 3 B 1 0.19 0.19 0.00 0.967 0.00 0.966* 4 B*A 2 167.65 83.82 5.21 0.106 2.79 0.253* 5 B*S(A) 3 48.27 16.09 - - 1.53 0.367 6 C 1 11.80 11.80 x x x x 7 C*A 2 10.02 5.01 0.20 0.834* 0.20 0.834* 8 C*S(A) 3 32.12 10.71 1.02 0.493 1.02 0.493 9 C*B 1 10.90 10.90 0.45 0.573 0.45 0.573 10 C*B*A 2 48.84 24.42 2.33 0.245 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. Model 6.5(vi) A, B and C are random factors, S is a random subject: Source DF SS MS F P 1 A 2 905.27 452.63 7.76 0.286* 2 S(A) 3 30.62 10.21 0.63 0.673* 3 B 1 0.19 0.19 0.00 0.966* 4 B*A 2 167.65 83.82 2.79 0.253* 5 B*S(A) 3 48.27 16.09 1.53 0.367 6 C 1 11.80 11.80 x x 7 C*A 2 10.02 5.01 0.20 0.834* 8 C*S(A) 3 32.12 10.71 1.02 0.493 9 C*B 1 10.90 10.90 0.45 0.573 10 C*B*A 2 48.84 24.42 2.33 0.245 11 C*B*S(A) 3 31.46 10.49 - - 12 P(C*B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. __________________________________________________________________ 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/