3.1 TWO FACTOR FULLY CROSS-FACTORED MODEL Y = B|A + e Analysis of terms: B|A Example datasets for Figure 10: A B Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 1 1 5.7337 0.1764 2.1024 1.1314 3.3183 1.4721 0.2474 1.2411 1 1 5.3192 1.1106 2.5362 1.3115 2.5451 0.3957 1.7203 1.3419 1 2 5.9372 1.4972 7.5387 5.0930 8.3304 6.1040 8.8462 8.7013 1 2 5.4137 0.7646 6.5774 5.7946 9.5124 5.7264 8.9788 8.6669 2 1 5.7085 5.3218 2.6092 2.3283 2.4552 5.7716 4.3090 4.2463 2 1 5.4576 5.1872 2.8321 2.8571 2.6713 4.8364 2.0933 5.0720 2 2 5.7340 5.2312 6.5402 6.2666 4.4558 5.4723 6.4203 4.1774 2 2 5.4731 5.2725 6.5428 5.8069 5.4356 5.5179 7.3639 5.0964 3 1 4.7645 9.4146 2.5460 4.3336 1.7907 9.0624 6.2963 9.4765 3 1 5.6968 9.4135 2.2342 4.5636 1.0416 8.8608 6.2108 9.9858 3 2 5.5372 9.2539 7.1767 8.2476 3.1919 4.0543 2.9512 1.1049 3 2 6.0335 9.1106 7.6754 8.7781 2.5121 3.4816 2.6017 0.2041 Model 3.1(i) A and B are both fixed factors (a) Response Y1: Source DF SS MS F P 1 A 2 0.0213 0.0106 0.08 0.928 2 B 1 0.1748 0.1748 1.24 0.308 3 B*A 2 0.1555 0.0777 0.55 0.603 4 S(B*A) 6 0.8462 0.1410 Total 11 1.1978 (b) Response Y2: Source DF SS MS F P 1 A 2 141.557 70.778 585.84 <0.001 2 B 1 0.021 0.021 0.18 0.689 3 B*A 2 0.270 0.135 1.12 0.387 4 S(B*A) 6 0.725 0.121 Total 11 142.573 (c) Response Y3: Source DF SS MS F P 1 A 2 0.171 0.085 0.68 0.542 2 B 1 61.613 61.613 490.32 <0.001 3 B*A 2 0.802 0.401 3.19 0.114 4 S(B*A) 6 0.754 0.126 Total 11 63.340 (d) Response Y4: Source DF SS MS F P 1 A 2 20.755 10.378 92.25 <0.001 2 B 1 45.869 45.869 407.74 <0.001 3 B*A 2 0.338 0.169 1.50 0.295 4 S(B*A) 6 0.675 0.112 Total 11 67.638 (e) Response Y5: Source DF SS MS F P 1 A 2 28.969 14.484 43.18 <0.001 2 B 1 32.066 32.066 95.60 <0.001 3 B*A 2 11.549 5.774 17.22 0.003 4 S(B*A) 6 2.012 0.335 Total 11 74.595 (f) Response Y6: Source DF SS MS F P 1 A 2 17.970 8.985 42.34 <0.001 2 B 1 0.000 0.000 0.00 0.980 3 B*A 2 51.824 25.912 122.10 <0.001 4 S(B*A) 6 1.273 0.212 Total 11 71.067 (g) Response Y7: Source DF SS MS F P 1 A 2 0.640 0.320 0.47 0.644 2 B 1 22.100 22.100 32.68 0.001 3 B*A 2 66.477 33.238 49.14 <0.001 4 S(B*A) 6 4.058 0.676 Total 11 93.275 (h) Response Y8: Source DF SS MS F P 1 A 2 0.606 0.303 1.39 0.318 2 B 1 0.970 0.970 4.46 0.079 3 B*A 2 136.066 68.033 312.97 <0.001 4 S(B*A) 6 1.304 0.217 Total 11 138.947 __________________________________________________________________ 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/