Note that we inevitably had to repeat some joint occurrences (6 with 7, 2 with 3,etc.). It is probably useful
at this stage to keep a note of which varieties have occurred with variety 1, with 2, and so on. Whether or
not this is done we move on to the third replicate.


Replicate 3
 Block 7
 (1,4,8,13,15)


 Block 8
(2,5,6,10,11)


 Block 9
(3,7,9,12,14)


In the fourth replicate we try both to include those pairs of treatments which have not previously occurred
together and to avoid any third repetitions of pairs


Replicate 4
 Block 10
 (1,4,9,11,14)


 Block 11
(2,6,8,12,15)


 Block 12
(3,5,7,10,13)


The ranges of standard errors are:

In blocks of 3 and 4

0.790 a to 0.828 a with a mean of 0.803 a.

In blocks of 5

0.730 a to 0.809 a with a mean of 0.774 o.

Again the precision of both designs is good compared with the minimum possible S.E. of 0.707 a (and
remembering that the a in smaller blocks should be a good deal smaller). The unequal blocks of the first
design and the loss of balance compared with the exact lattice have had only a marginal effect. The slightly
less friendly blocks of five have produced a larger range (10% compared with 5%) but the average S.E.
comes down (relative to a) quite a bit with the blocks of 5.

2 4 Six Treatments in Three Blocks of Eight Plots.

An experiment from Poza Rica, mentioned in part A, in the section on variation at the farm level. Six
varieties are to be compared and the natural blocking pattern for the 24 plots is three groups (rows) of eight
plots per group. Each treatment will be replicated four times and the design problem is how to allocate sets
of treatments to the three groups of eight plots.

The allocation must allow as many comparisons between different treatments in a block as possible.
Therefore each block must include each treatment at least once.


Block 1 treatments 1 2 3 4 5 6 ? 7

Block 2 treatments 1 2 3 4 5 6 ? ?

Block 3 Treatments 1 2 3 4 5 6 ? ?