arXiv subjects

E. R. Williams

Publications and source records attributed to E. R. Williams.

5 recordsLinked to original sources

arXiv2025

The construction of augmented designs in square arrays

Augmented designs are typically used in early-stage breeding programs to compare single replicates of test entries by combining them with replicated check varieties. One or two dimensional incomplete blocking can be incorporated in the design to accommodate possible site variation. An augmented design in a square array can be derived from a smaller row-column design (the contraction). In a recent paper Bailey and Haines (2025) investigated the link between an augmented design in a square array and its contraction. Here we formally establish this connection by expressing the average efficiency factor of the augmented design in terms of that of its contraction. A consequence of this is that an optimal contraction can be used to construct an optimal augmented design. The table of cyclic contractions presented by Bailey and Haines (2025) is updated in terms of optimality. Specifically, in cases where a cyclic contraction is not optimal, an augmented design with optimal or near-optimal efficiency can be obtained via computer search.

stat.ME↗

arXiv2025

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

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.

stat.ME↗

arXiv2024

Projection matrices and the sweep operator

These notes have been adapted from an undergraduate course given by Professor Alan James at the University of Adelaide from around 1965 and onwards. This adaption has put a focus on the definition of projection matrices and the sweep operator. These devices were at the heart of the development of the statistical package Genstat which initially focussed on the analysis of variance using the sweep operator. The notes provide an algebraic background to the sweep operator which has since been used to effect in a number of experimental design settings.

stat.ME↗

arXiv2019

Substitutes for the non-existent square lattice designs for 36 varieties

Square lattice designs are often used in trials of new varieties of various agricultural crops. However, there are no square lattice designs for 36 varieties in blocks of size six for four or more replicates. Here we use three different approaches to construct designs for up to eight replicates. All the designs perform well in terms of giving a low average variance of variety contrasts. Supplementary materials are available online.

stat.ME↗

arXiv2015

A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST

Researchers at the National Institute of Standards and Technology have been using a watt balance, NIST-3, to measure the Planck constant $h$ for over ten years. Two recently published values disagree by more than one standard uncertainty. The motivation for the present manuscript is twofold. First, we correct the latest published number to take into account a recently discovered systematic error in mass dissemination at the Bureau International des Poids et Mesures (BIPM). Second, we provide guidance on how to combine the two numbers into one final result. In order to adequately reflect the discrepancy, we added an additional systematic uncertainty to the published uncertainty budgets. The final value of $h$ measured with NIST-3 is $h = 6.626\,069\,36(37)\times 10^{-34}\,\mbox{J\,s}$. This result is $77(57) \times 10^{-9}$ fractionally higher than $h_{\mathrm{90}}$. Each number in parentheses gives the value of the standard uncertainty in the last two digits of the respective value and $h_{\mathrm{90}}$ is the conventional value of the Planck constant given by $h_{\mathrm{90}}\equiv 4 /( K_{\mathrm{J-90}}^2 R_{\mathrm{K-90}})$, where $K_{\mathrm{J-90}}$ and $R_{\mathrm{K-90}}$ denote the conventional values of the Josephson and von Klitzing constants, respectively.

physics.ins-det↗