Efficient Designs in Small Blocks for Comparing Consecutive Pairs of Treatments

TL;DR

This paper develops an efficient method for designing small-block experiments to compare consecutive treatments, providing optimal, nested, and practical designs with illustrative examples and tables.

Contribution

It introduces a new approximate theory and multiplicative algorithm for optimal small-block designs focusing on consecutive treatment comparisons, enabling nested and resource-efficient experiments.

Findings

Highly efficient exact designs for small blocks

Nested designs suitable for multi-stage experiments

Provision of tables of optimal design measures

Abstract

Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative algorithm for obtaining optimal design measures. This, in turn, yields highly efficient exact designs even when the number of blocks is rather small. Moreover, our approach is seen to allow nesting of such efficient exact designs which is an advantage when the resources for the experiment are available possibly in several stages. Illustrative examples are given. Tables of optimal design measures are also provided.