Rectangular augmented row-column designs generated from contractions

TL;DR

This paper introduces a novel method for generating efficient augmented row-column experimental designs using contractions, enabling faster computational search and improved control of error sources in agricultural experiments.

Contribution

It proposes a new approach that leverages contractions to generate augmented designs efficiently, enhancing design construction in experimental research.

Findings

Efficient contractions can be identified via computer search.

The method produces augmented designs with good error control.

Two real-world examples demonstrate the approach's effectiveness.

Abstract

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of experimental units are a prominent example. In plant breeding, the amount of seed available for the treatments to be tested may be so limited that only one experimental unit per treatment can be accommodated. In such settings, augmented designs become an interesting option, where a small set of treatments, for which sufficient seed is available, are replicated across the rectangular layout so that row and column effects, as well as the error variance can be estimated. Here, we consider the use of an auxiliary design, also known as a contraction, to generate an augmented row-column design. We make use of the fact that the efficiency factors of the contraction and the associated augmented design are closely interlinked. A major advantage of this approach is that an efficient contraction can be found by computer search at much higher computational speed than is required for direct search for an efficient augmented design. Two examples are used to illustrate the proposed method.