Another example is given below showing how the inter- and intra-block estimates are combined for an experiment with a balanced lattice design.
Pig diets
An experiment was conducted to study the effects of nine feeding treatments on the growth rate of pigs. For a given breed, previous experience indicated that much of the variation in growth rate between pigs is caused by differences between litters, so litters of three pigs were used as the basis of blocks in the experiment. In each experimental block, two groups of three litter-mates were used and the experimental units were pairs of pigs, one from each litter. The response was the total weight gain (pounds per day) of the two pigs in an experimental unit. The experiment was laid out as a balanced lattice design and the results are shown below. (The treatments are shown in brackets.)
Block 1 | 2.20 (1) | 1.84 (2) | 2.18 (3) | Block 4 | 1.19 (1) | 1.20 (4) | 1.15 (7) | |
---|---|---|---|---|---|---|---|---|
Block 2 | 2.05 (4) | 0.85 (5) | 1.86 (6) | Block 5 | 2.26 (2) | 1.07 (5) | 1.46 (8) | |
Block 3 | 0.73 (7) | 1.60 (8) | 1.76 (9) | Block 6 | 2.12 (3) | 2.03 (6) | 1.63 (9) | |
Block 7 | 1.81 (1) | 1.16 (5) | 1.11 (9) | Block 10 | 1.77 (1) | 1.57 (6) | 1.43 (8) | |
Block 8 | 1.76 (2) | 2.16 (6) | 1.80 (7) | Block 11 | 1.50 (2) | 1.60 (4) | 1.42 (9) | |
Block 9 | 1.71 (3) | 1.57 (4) | 1.13 (8) | Block 12 | 2.04 (3) | 0.93 (5) | 1.78 (7) |
The inter-block and intra-block estimates of the effects of the nine feeding treatments are shown below:
Observe that the intra-block estimates are again more accurate than the inter-block estimates. Click Combine estimates to form the best linear combination of estimates, noting that they are closer to the intra-block estimates than the inter-block estimates.
The combined estimates have similar standard errors to the intra-block estimates, so again little has been gained from the inter-block information.