Example data for Figure 7(a) on Irrigation treatment A with levels randomly allocated to plots in blocks (S), and cross factored with sowing density treatment B with levels randomly allocated to sub-plots in plots, in a split plot design: S A B Y 1 Control Low 2.046 2 Control Low 1.780 3 Control Low 4.020 4 Control Low 8.150 1 Control High 16.778 2 Control High 21.105 3 Control High 23.142 4 Control High 22.871 1 Water Low 13.651 2 Water Low 19.100 3 Water Low 12.300 4 Water Low 14.991 1 Water High 11.953 2 Water High 14.240 3 Water High 7.900 4 Water High 14.043 5.1 TWO FACTOR SPLIT PLOT MODEL (I) Y = B|P'(S'|A) Analysis of terms: B|A + S|A Model 5.1(i) A in plots and B in sub-plots are fixed factors, S is a random blocking factor: Restricted Unrestricted Source DF SS MS F P F P 1 S 3 40.39 13.46 - - 0.85 0.552 2 A 1 4.29 4.29 0.27 0.6391 0.27 0.639 3 S*A 3 47.63 15.88 - - - - 4 B 1 195.96 195.96 74.49 <0.001 74.49 <0.001 5 B*A 1 398.06 398.06 151.32 <0.001 151.32 <0.001 6 Residual 6 15.78 2.63 - - - - Total 15 702.12 COMMENT: With this model, the coding of Block S describes 4 blocks each containing all four combinations of levels of irrigation and sowing density. Example data for Figure 7(b) on Irrigation treatment A with levels randomly allocated to blocks (S), cross factored with sowing density treatment B with levels randomly allocated to plots in blocks, in a split plot design: S A B Y 1 Control Low 2.046 2 Control Low 1.780 3 Control Low 4.020 4 Control Low 8.150 1 Control High 16.778 2 Control High 21.105 3 Control High 23.142 4 Control High 22.871 1 Water Low 13.651 2 Water Low 19.100 3 Water Low 12.300 4 Water Low 14.991 1 Water High 11.953 2 Water High 14.240 3 Water High 7.900 4 Water High 14.043 5.6 TWO FACTOR SPLIT PLOT MODEL (II) Y = B|S'(A) Analysis of terms: B|A + B|S(A) - B*S(A) Model 5.6(i) A in plots and B in blocks are fixed factors, S is the random blocking factor: Restricted Unrestricted Source DF SS MS F P F P 1 A 1 4.29 4.29 0.29 0.608 0.29 0.608 2 S(A) 6 88.03 14.67 - - 5.58 0.028 3 B 1 195.96 195.96 74.49 <0.001 74.49 <0.001 4 B*A 1 398.06 398.06 151.32 <0.001 151.32 <0.001 5 B*S(A) 6 15.78 2.63 - - - - Total 15 702.12 COMMENT: With this model, the coding of Block S describes 4 blocks nested in the Control treatment and four (different) blocks nested in the Water treatment, and each block measured once at high and once at low sowing density. This design has more power to test the effect of treatment A than the design for model 5.1 (Figure 7a). __________________________________________________________________ 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/