Abstract
Where an experiment can be carried out by
applying different treatments in succession to the same unit of experimental
material, accurate comparisons can be made between the effects of different
treatments. To allow for the residual effect of previous treatments on the
result obtained for any given treatment, it is desirable to adjust the results
for such effects. Methods of constructing balanced designs for the estimation of
these residual effects are described in this paper, and are summarized as follows.
Designs balanced for effect of single
preceding treatment: When n, the number of treatments, is even, a
balanced design is possible with n replications ; when n is odd, 2n
replications are required.Designs balanced for the effects of any
number of preceding treatments, ignoring the interaction of residual effects:
When n is a prime or a power of a prime, a balanced design is possible
in n(n-1) replications, which may be set out as a set of n-1 mutually
orthogonal Latin squares, with the same first columns. Designs which are not
expressible as mutually orthogonal Latin squares are also possible. Designs balanced for the effect of the
two preceding treatments and their interactions : A design can be developed from a set of n-l mutually
orthogonal Latin squares obeying certain restrictions.
The method of analysis of designs of this
type is set out in detail, together with a numerical example. Direct effects of
treatments are shown to be only slightly confounded, the maximum confounding
being 4 per cent., when there are three treatments.
These designs have wide applicability
wherever successive treatments can be applied to the same unit of experimental
material.
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