2.2 THREE FACTOR NESTED MODEL Y = C(B(A)) + e Analysis of terms: A + B(A) + C(B A) Data: A B C Y 1 1 1 4.5924 1 1 1 -0.5488 1 1 2 6.1605 1 1 2 2.3374 1 2 1 5.1873 1 2 1 3.3579 1 2 2 6.3092 1 2 2 3.2831 2 1 1 7.3809 2 1 1 9.2085 2 1 2 13.1147 2 1 2 15.2654 2 2 1 12.4188 2 2 1 14.3951 2 2 2 8.5986 2 2 2 3.4945 3 1 1 21.3220 3 1 1 25.0426 3 1 2 22.6600 3 1 2 24.1283 3 2 1 16.5927 3 2 1 10.2129 3 2 2 9.8934 3 2 2 10.0203 Model 2.2(i) A is a fixed or random factor, B and C are random factors: Source DF SS MS F P 1 A 2 745.36 372.68 4.02 0.142 2 B(A) 3 278.02 92.67 5.24 0.041 3 C(B(A)) 6 106.08 17.68 2.86 0.057 4 S(C(B(A))) 12 74.10 6.18 Total 23 1203.56 Model 2.2(ii) A is a covariate of the response, B and C are random factors: Source DF SS MS F P 1 A 1 745.20 745.20 10.72 0.030 2 B(A) 4 278.18 69.55 3.93 0.067 3 C(B(A)) 6 106.08 17.68 2.86 0.057 4 S(C(B(A))) 12 74.10 6.18 Total 23 1203.56 __________________________________________________________________ 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/