If we mark out a square field into 16 plots we can envisage the Latin square as a
description of the field where the soil quality varies ‘vertically’ and ‘horizontally’.
The four fertilizers are then applied at random in the scheme labelled a, b, c
and d, so exactly one is applied in each row and column in an attempt to remove
the variation of soil quality. If we suspect another factor might influence crop
yield, we could deal with this too. Suppose we think that the time of day of
apllying treatment is a factor. Label four time zones during the day as A, B, C
and D and use orthogonal Latin squares as the design for a scheme to gather
data. This ensures each treatment and time zone is applied in one of the plots.
The design for the experiment would be:
Other factors can be screened out by going on to create even more elaborate
Latin square designs. Euler could not have dreamt of the solution to his officers’
problem being applied to agricultural experiments.