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/