An alternative design with many similar patterns, but motivated by a strong desire to compare treatments 1
with 12, and 2 with 11, produced the following


Block 1(1,2,7,8,11,12)
Block 3 (1,4,6,7,10,12)
Block 5 (1,3,5,8,10,12)


Block 2 (3,4,5,6,9,10)
Block 4 (2 3 5 89 11)
Block 6 (2,4,6,7,9,11)


Pre-testing Precision:
It is possible to give confidence in a proposed design by calculating, before the use of the design, the
precision that will be achieved. The relative precision of different treatment comparisons within a design,
and of alternative designs, is a property of the designs. Of course the absolute precision achieved will
depend on the data and obviously that is not available before the experiment. However we can calculate the
relative precision in advance with various computer programs (details given in main paper on "Design of
on-farm experiments").

For the first design the range of standard errors for estimated treatment differences is

0.82 a to 0.91 a with a mean of 0.87 a

where a is the standard deviation of the random variation, estimated by the square root of the Error Mean
Square.

The smallest achievable standard error, with three observations per treatment would be

 ,(2a2/3) = 0.82 a

so that the precision of the design is really very good. Certainly we should intend to use only a single
standard error when presenting the treatment results from the analysis of the six block design.

For the second design with particular emphasis on comparing treatments 1 with 12 and 2 with 11 (this was
the design actually used at Chalco) the range of standard errors for estimated treatment differences is

0.82 a to 0.91 a with a mean of 0.87 a

exactly the same, to two figures as for the first design.

We consider four other designs to see how quickly the very high and consistent precision in both designs
thus far deteriorates as we take less thought over the design. We shall think of the treatments in terms of
their Varieties by Dates structure.


 V1 V2 V3 V4

D1 1 2 3 4
D2 5 6 7 8
D3 9 10 11 12