selected to answer is answered with minimum precision at each site because the answer involves the simple
comparison of two experimental treatments. A full factorial experiment with 3 bean varieties, 2 maize
varieties, 3(7) bean densities,2 fertilizer levels and + or the seed treatment would require 72 experimental
treatments and is plainly unthinkable.

The sequence of treatments 3 -4 -5 -6 -7 includes trying alternative varieties of beans and of maize
increasing bean density and increasing fertilizer level. Because these changes occur in a particular order
there is no opportunity to test different orders which would be appropriate if the relative sizes of the main
effects differ from site to site. Moreover, if we wish to demonstrate the benefit of
 (a) increased fertilizer,
 (b) bean variety 2,
 (c) maize variety B, and
 (d) increased bean density
a subset of factorial structure provides much better estimates of the four effects than a sequence. Some
possible changes to the treatment structure could involve:

(1) including all 8 combinations of bean(2or3) maize (A or b) and fertiliser(1 or 3) either at each site or in
 sets of 4 combinations per site;
(2) considering the seed treatment as an extra factor and treating half the combinations in each replicate;
(3) eliminating treatment 1 or 2;
(4) other variations on the lines of (1) incorporating the density change(treatment 4 to 5).

The detail of any experiment must always be determined through discussion and joint decision of the
experimenter and statistician. However, a possible design in two blocks of eight plots per block would be


 Variety Density Seed
Block Beans Maize Beans Maize Fertiliser Treatment


 1 1 A 8 16 100 NO
 1 2 A 12 16 100 YES
 1 3 B 12 16 100 NO
 1 3 A 16 16 100 YES
 1 2 B 16 16 100 NO
 1 2 A 16 16 300 YES
 1 3 A 12 16 300 NO
 1 3 B 16 16 300 YES

 2 1 A 8 16 100 YES
 2 2 A 12 16 100 NO
 2 3 A 12 16 100 YES
 2 2 A 16 16 100 NO
 2 2 B 16 16 300 YES
 2 2 A 12 16 300 NO
 2 3 B 12 16 300 YES
 2 3 B 16 16 100 NO


All but three of the factorial combinations of bean variety, maize variety, bean density and fertilizer level
are included, with two standard treatments repeated in each block, and the seed treatment imposed as an
extra across the sets of treatments in each block.