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/