6.3 TWO FACTOR MODEL WITH REPEATED MEASURES ON ONE CROSS FACTOR Y = B|S'(A) Analysis of terms: B|A + B|S(A) - B*S(A) Data: S A B Y 1 1 1 -3.8558 2 1 1 4.4076 3 1 1 -4.1752 4 1 1 1.4913 1 1 2 5.9699 2 1 2 5.2141 3 1 2 9.1467 4 1 2 5.8209 1 2 1 9.4082 2 2 1 6.0296 3 2 1 15.3014 4 2 1 12.1900 1 2 2 6.9754 2 2 2 14.3012 3 2 2 10.4266 4 2 2 2.3707 1 3 1 19.1834 2 3 1 18.3855 3 3 1 23.3385 4 3 1 21.9134 1 3 2 16.4482 2 3 2 11.6765 3 3 2 17.9727 4 3 2 15.1760 Model 6.3(i) A and B 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 48.17 <0.001 48.17 <0.001 2 S(A) 9 84.56 9.40 - - 0.61 0.766 3 B 1 0.19 0.19 0.01 0.915 0.01 0.915 4 B*A 2 167.65 83.82 5.41 0.029 5.41 0.029 5 B*S(A) 9 139.47 15.50 - - - - 6 P(B*S(A)) 0 - - Total 23 1297.13 Model 6.3(ii) A is a fixed factor, 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 5.82 0.173* 5.82 0.173* 2 S(A) 9 84.56 9.40 0.61 0.766 0.61 0.766 3 B 1 0.19 0.19 0.01 0.915 0.00 0.967 4 B*A 2 167.65 83.82 5.41 0.029 5.41 0.029 5 B*S(A) 9 139.47 15.50 - - - - 6 P(B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.3(iii) A is a random factor, B 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 48.17 0.000 5.82 0.173* 2 S(A) 9 84.56 9.40 - - 0.61 0.766 3 B 1 0.19 0.19 0.00 0.967 0.00 0.967 4 B*A 2 167.65 83.82 5.41 0.029 5.41 0.029 5 B*S(A) 9 139.47 15.50 - - - - 6 P(B*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.3(iv) A and B are random factors, S is a random subject: Source DF SS MS F P 1 A 2 905.27 452.63 5.82 0.173* 2 S(A) 9 84.56 9.40 0.61 0.766 3 B 1 0.19 0.19 0.00 0.967 4 B*A 2 167.65 83.82 5.41 0.029 5 B*S(A) 9 139.47 15.50 - - 6 P(B*S(A)) 0 - - Total 23 1297.13 * 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/