6.7 THREE FACTOR MODEL WITH REPEATED MEASURES ON ONE FACTOR Y = C|S'(B|A) Analysis of terms: C|B|A + S(B 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 6.7(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 34.42 0.001 34.42 0.001 2 B 1 0.19 0.19 0.01 0.909 0.01 0.909 3 B*A 2 167.65 83.82 6.37 0.033 6.37 0.033 4 S(B*A) 6 78.89 13.15 - - 1.24 0.400 5 C 1 11.80 11.80 1.11 0.332 1.11 0.332 6 C*A 2 10.02 5.01 0.47 0.645 0.47 0.645 7 C*B 1 10.90 10.90 1.03 0.350 1.03 0.350 8 C*B*A 2 48.84 24.42 2.30 0.181 2.30 0.181 9 C*S(B*A) 6 63.58 10.60 - - - - 10 P(C*S(B*A) 0 - - Total 23 1297.13 Model 6.7(ii) A and B are fixed factors, C 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 59.86 0.100* 59.86 0.100* 2 B 1 0.19 0.19 0.01 0.924* 0.01 0.924* 3 B*A 2 167.65 83.82 3.11 0.235* 3.11 0.235* 4 S(B*A) 6 78.89 13.15 1.24 0.400 1.24 0.400 5 C 1 11.80 11.80 1.11 0.332 x x 6 C*A 2 10.02 5.01 0.47 0.645 0.21 0.830 7 C*B 1 10.90 10.90 1.03 0.350 0.45 0.573 8 C*B*A 2 48.84 24.42 2.30 0.181 2.30 0.181 8 C*S(B*A) 6 63.58 10.60 - - - - 10 P(C*S(B*A) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. Model 6.7(iii) 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 5.40 0.156 5.40 0.156 2 B 1 0.19 0.19 0.01 0.909 0.00 0.966* 3 B*A 2 167.65 83.82 6.37 0.033 3.11 0.235* 4 S(B*A) 6 78.89 13.15 - - 1.24 0.400 5 C 1 11.80 11.80 1.08 0.487 1.08 0.487 6 C*A 2 10.02 5.01 0.21 0.830 0.21 0.830 7 C*B 1 10.90 10.90 1.03 0.350 0.45 0.573 8 C*B*A 2 48.84 24.42 2.30 0.181 2.30 0.181 9 C*S(B*A) 6 63.58 10.60 - - 10 P(C*S(B*A) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.7(iv) 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 7.03 0.239* 7.03 0.239* 2 B 1 0.19 0.19 0.01 0.924* 0.00 0.966* 3 B*A 2 167.65 83.82 3.11 0.235* 3.11 0.235* 4 S(B*A) 6 78.89 13.15 1.24 0.400 1.24 0.400 5 C 1 11.80 11.80 1.08 0.487 x x 6 C*A 2 10.02 5.01 0.21 0.830 0.21 0.830 7 C*B 1 10.90 10.90 1.03 0.350 0.45 0.573 8 C*B*A 2 48.84 24.42 2.30 0.181 2.30 0.181 9 C*S(B*A) 6 63.58 10.60 - - - - 10 P(C*S(B*A) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. Model 6.7(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 5.40 0.156 7.03 0.239* 2 B 1 0.19 0.19 0.00 0.967 0.00 0.966* 3 B*A 2 167.65 83.82 6.37 0.033 3.11 0.235* 4 S(B*A) 6 78.89 13.15 - - 1.24 0.400 5 C 1 11.80 11.80 x x x x 6 C*A 2 10.02 5.01 0.21 0.830 0.21 0.830 7 C*B 1 10.90 10.90 0.45 0.573 0.45 0.573 8 C*B*A 2 48.84 24.42 2.30 0.181 2.30 0.181 9 C*S(B*A) 6 63.58 10.60 - - - - 10 P(C*S(B*A) 0 - - Total 23 1297.13 * Quasi F-ratio. x Not an exact F-test; estimated denominator MS is <0. Model 6.7(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 7.03 0.239* 2 B 1 0.19 0.19 0.00 0.966* 3 B*A 2 167.65 83.82 3.11 0.235* 4 S(B*A) 6 78.89 13.15 1.24 0.400 5 C 1 11.80 11.80 x x 6 C*A 2 10.02 5.01 0.21 0.830 7 C*B 1 10.90 10.90 0.45 0.573 8 C*B*A 2 48.84 24.42 2.30 0.181 9 C*S(B*A) 6 63.58 10.60 - - 10 P(C*S(B*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/