Extended semi-Latin squares for use in field and glasshouse trials

TL;DR

This paper introduces extended semi-Latin squares, a specialized design for field and glasshouse trials, optimizing experimental efficiency through the average efficiency factor.

Contribution

It defines extended semi-Latin squares as a new class of latinized row-column designs and analyzes their optimality for experimental trials.

Findings

Extended semi-Latin squares improve experimental efficiency.

Optimality is assessed using the average efficiency factor.

Designs are suitable for contiguous replicates in trials.

Abstract

Semi-Latin squares have been extensively studied. They can be interpreted as a special case of latinized block designs where the number of columns is equal to the number of replicates in the design. Latinized row-column designs are frequently used in field and glasshouse trials when replicates are contiguous. These designs allow for the efficient adjustment of row and column effects within replicates. Here we define extended semi-Latin squares as a special case of latinized row-column designs and investigate optimality using the average efficiency factor.