Designs balanced for residual effects

Abstract

The usual problem in long term experiments is that due to residual effects of treatments. The effect of a treatment that persists for a period after the application of the treatment is referred to as residual effect of that treatment. In the present study an attempt is made to construct designs which will balance for first order residual effects to suit the above mentioned situations. By definition a design is said to be balanced if every treatment follows every other treatment equally frequently. We have established three different methods of construction of such type of designs. The first method of construction is by using cyclic latin squares as in the line of Amble (1977) and we have shown that such an arrangement is balanced for first order residual effects. The second method of construction is based on the set of (v-1) orthogonal latin squares of order v in the case of v treatments. A third method of construction of designs balanced for first order residual effects is also given. This is based on the procedure given by Nair (1967) for the construction of designs balanced for pairs of residual effects. A general intuitive method of analysis is also given.