6.4 THREE FACTOR MODEL WITH REPEATED MEASURES ON NESTED CROSS FACTORS Y = C(B)|S'(A) Analysis of terms: B|A + B|S(A) + A|C(B) 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 6.4(i) A and B are fixed factors, C is a random factor, S is a random blocking factor: Restricted Unrestricted Source DF SS MS F P F P 1 A 2 905.27 452.63 31.59 0.034* 31.59 0.034* 2 S(A) 3 30.62 10.21 0.96 0.469 0.63 0.641 3 B 1 0.19 0.19 0.01 0.927* 0.01 0.927* 4 B*A 2 167.65 83.82 4.15 0.157* 4.15 0.157* 5 B*S(A) 3 48.27 16.09 1.52 0.303 1.52 0.303 6 C(B) 2 22.70 11.35 1.07 0.400 0.77 0.521 7 C(B)*A 4 58.86 14.72 1.39 0.342 1.39 0.342 8 C(B)*S(A) 6 63.58 10.60 - - - - 9 P(C(B)*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio. Model 6.4(ii) A is a fixed factor, B and C are random factors, S is a random blocking factor: 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 0.641 3 B 1 0.19 0.19 0.01 0.927* 0.00 0.966* 4 B*A 2 167.65 83.82 4.15 0.157* 4.15 0.157* 5 B*S(A) 3 48.27 16.09 1.52 0.303 1.52 0.303 6 C(B) 2 22.70 11.35 1.07 0.400 0.77 0.521 7 C(B)*A 4 58.86 14.72 1.39 0.342 1.39 0.342 8 C(B)*S(A) 6 63.58 10.60 - - 9 P(C(B)*S(A)) 0 - - Total 23 1297.13 * Quasi F-ratio Model 6.4(iii) A, B and C are all random factors, S is a random blocking factor: Source DF SS MS F P 1 A 2 905.27 452.63 5.81 0.177* 2 S(A) 3 30.62 10.21 0.63 0.641 3 B 1 0.19 0.19 0.00 0.966* 4 B*A 2 167.65 83.82 4.15 0.157* 5 B*S(A) 3 48.27 16.09 1.52 0.303 6 C(B) 2 22.70 11.35 0.77 0.521 7 C(B)*A 4 58.86 14.72 1.39 0.342 8 C(B)*S(A) 6 63.58 10.60 - - 9 P(C(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/