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Augmented Block Designs for Unreplicated Trials

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  • Linda M. Haines

    (University of Cape Town)

Abstract

This paper is concerned with augmented block designs for unreplicated trials for which the underlying model comprises fixed block and fixed treatment effects. Explicit expressions for the average scaled variances and the maximum variances of estimates of the pairwise differences between controls, between unreplicated test lines and between controls and unreplicated test lines are developed and demonstrate the crucial role of the control design in constructing the attendant A- and MV-optimal designs. The results extend quite naturally to p-rep block designs and a novel algorithm for generating such designs is introduced. Examples which illustrate the implications of the findings are also presented. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Linda M. Haines, 2021. "Augmented Block Designs for Unreplicated Trials," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 409-427, September.
    • Handle: RePEc:spr:jagbes:v:26:y:2021:i:3:d:10.1007_s13253-021-00445-3
    DOI: 10.1007/s13253-021-00445-3
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    References listed on IDEAS

    as
    1. Vo-Thanh, Nha & Piepho, Hans-Peter, 2020. "Augmented quasi-sudoku designs in field trials," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Brian R. Cullis & Alison B. Smith & Nicole A. Cocks & David G. Butler, 2020. "The Design of Early-Stage Plant Breeding Trials Using Genetic Relatedness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 553-578, December.
    3. Agnes Herzberg & Richard Jarrett, 2007. "A-Optimal Block Designs with Additional Singly Replicated Treatments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 61-70.
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