Error variance bias in neighbour balance and evenness of distribution designs

Abstract

Neighbour balance and evenness of distribution designs help to address user concerns in the two-dimensional layout of agricultural field trials. This is done by minimising the occurrence of pairwise treatment plot neighbours and ensuring that the replications of treatments are spread out across rows and columns of a trial. Such considerations result in a restriction on the normal randomisation process for a row-column design which can lead to error variance bias. In this paper, uniformity trial data is used to assess the degree of this bias for both resolvable and non-resolvable designs. Comparisons are made with a similar investigation using Linear Variance spatial designs.

Popularity leads to bad habits: Alternatives to “the statistics” routine of significance, “alphabet soup” and dynamite plots

“…Frequently, only the number of replicates and treatments used are provided (Haddaway & Verhoeven, 2015), perhaps because it is assumed that the design is always a randomised complete block design. There is a huge range of potential designs, old (Fisher, 1926) to recent (Williams & Piepho, 2019), and sound experimental design underpins effective and efficient studies (Finney, 1988; Kilkenny et al, 2009; Smith & Cullis, 2019). Appropriate analysis methods can vary substantially between different design types.…”

Generating row–column field experimental designs with good neighbour balance and even distribution of treatment replications

“…From a researcher's point of view, the average efficiency factor, which we use for design optimization, needs to be balanced against other properties of the design, and ED and NB may be given preference. This would normally mean that some loss in average efficiency factor can be tolerated if NB&ED properties can such as the knights move Latin squares that Tedin (1931) studied, as this could result in increased error variance bias (Williams & Piepho, 2019). Thus, we mainly aim to provide a reasonable guard against clumping, without wanting to impose a very specific pattern.…”

“…The strategy taken here is to impose restrictions in the design search that directly target both NB and ED properties and within those constraints to optimize the average efficiency factor. Our objective is to not achieve extreme examples of ED, such as the knights move Latin squares that Tedin (1931) studied, as this could result in increased error variance bias (Williams & Piepho, 2019). Thus, we mainly aim to provide a reasonable guard against clumping, without wanting to impose a very specific pattern.…”

“…The spatial restrictions imposed on neighbourhood configurations imposed under the model‐free approach imply restrictions on randomization. We have investigated the error variance bias due to the randomization restriction and found this to be acceptably small based on analysis of uniformity trials (Williams & Piepho, 2019).…”

Fully and Partially Replicated Experimental Designs for Evaluating Intravarietal Variability in Grapevine

“…Tere are many variants of these designs, but the most relevant for working with many treatments are alpha designs [12], which constitute a particular class of generalized lattice designs; row-column designs [13] impose blocks in both row and column directions; these designs correspond to groups of more complex Latin square designs [14] and resolvable spatial row-column designs [15]. Generating efcient row-column designs is a very important topic in experimental design research [15][16][17][18][19]. Te overall objective is optimizing neighbour balance, ensuring that the number of pairwise adjacencies is as equal as possible across pairs of treatments over the feld layout.…”