3.1 TWO FACTOR FULLY CROSS-FACTORED MODEL Y = B|A + e Analysis of response Y to terms: X|A Data for Figure 8: X A Y 5.27 1 57.55 5.47 1 55.36 6.70 1 48.49 9.19 1 43.48 10.23 1 38.84 11.25 1 38.04 17.29 1 12.86 14.97 1 15.61 14.58 1 22.10 13.98 1 26.50 11.83 1 24.99 9.65 1 33.47 9.51 2 40.70 9.29 2 35.59 7.93 2 35.90 5.19 2 37.99 7.62 2 37.31 4.79 2 30.99 12.64 2 32.98 11.03 2 34.60 12.81 2 33.21 16.40 2 29.94 15.62 2 32.40 17.17 2 29.15 Model 3.1(iv) A is a fixed factor, X is a covariate of the response: Source DF Seq SS Seq MS F P 1 X 1 1400.59 1400.59 124.50 <0.001 2 A 1 2.25 2.25 0.20 0.660 3 X*A 1 912.99 912.99 81.16 <0.001 4 Residual 20 224.99 11.25 Total 23 2540.35 COMMENT: This example is balanced and therefore orthogonal, so uses Type I (sequential) SS. Use of Type II adjusted SS would give the same result, but eroneous use of Type III adusted SS would give a different result for main effects. __________________________________________________________________ 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/