The 28 plots for the two replicates of the 14 treatments are in two rows of ten plots and two rows of four
plots. Differences between rows are likely to be large since the rows are at different contour levels.

Arrangement of plots:

 28 27 26 25
 21 22 23 24
 20 19 18 17 16 15 14 13 12 11
 1 2 3 4 5 6 7 8 9 10

 Each row of four plots should probably be treated as a block and the first replicate should be completed
 with the block of plots 15 to 20. The second replicate has one block of four plots (11 to 14) and the other
 ten plots should be split into two blocks of five plots. The block pattern is therefore

 1 1 1 1
 2 2 2 2
 3 3 3 3 3 3 4 4 4 4
 5 5 5 5 5 6 6 6 6 6

 We now have to divide the fourteen treatments into blocks of 4,4 and 6 in the first replicate, and into blocks
 of 4, 5 and 5 in the second replicate. The allocations should be such that treatments which occur together in
 a block in the first replicate do not again occur together in a block in the second replicate. We shall see that
 this requirement cannot be completely satisfied.

 The allocation for the first replicate must be

 (1,2,3,4), (5,6,7,8) and (9,10,11,12,13,14)

 where we can decide later which actual treatments correspond to the labels 1 to 14. In the second replicate
 the treatments in a block in the first replicate should be evenly spread between the three blocks of the
 second replicate. This leads quite directly to

 (1,5,9,10), (2,3,6,11,12) and (4,7,8,13,14).

Five pairs of treatments (2.3), (7,8), (9,10), (11,12) and (13,14) occur together twice and we should try to
ensure that these are treatment combinations which we would particularly like to be precisely compared.
Note, however, that the random variance with the blocks of 4, 5 and 6 should be much smaller than the
random variance within complete blocks of 14 plots ( 1 to 14, and 14 to 28) as originally planned so that
treatment comparisons should be more precise in the proposed design.

The range of standard errors for estimated treatment differences is

1.00 a to 1.26 a with a mean of 1.15 a.

Compared with the precision results for our previous designs the variation here is rather disappointing. The
minimum possible S.E. with blocks of 14 is 1.00 0(14) so we would be very confident that our more
sensible blocks will reduce a sufficiently that all S.E.'s will be smaller with the new design. The decision
on whether to use the average S.E. is marginal but the maximum would be only 10% higher than the
average so I would decide to use the average on the basis that if out S.E.'s are only 10% out from an
ordinary analysis of variance we're doing pretty well.