Tied-Double-Change-Over Designs

Abstract

Abstract : The construction and analysis for a class of experimental designs denoted as tied-double change-over designs are presented. These designs are useful for situations wherein the treatments are applied in sequence to an experimental unit and where the effect of a treatment persists for one period after the period in which the treatment was applied; they allow estimation of direct and residual treatment effects. Tied-double change-over designs are constructed utilizing one, two, ..., t - 1 orthogonal latin squares for t treatments. Although the analysis is for r rows and for c columns in general, particular attention is given to the case where r tq 1 rows and c ts columns for sq k(t - 1), for k a positive integer; explicit solutions are obtained for the situations where the first period results are omitted from the analysis and where the first period results are included. A numerical example is used to illustrate the application of the results to experimental data.