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A-Optimal Block Designs with Additional Singly Replicated Treatments

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  • Agnes Herzberg
  • Richard Jarrett

Abstract

Block designs to which have been added a number of singly-replicated treatments, known as secondary treatments, are particularly useful for experiments where only small amounts of material are available for some treatments, for example new plant varieties. The designs are of particular use in the microarray situation. Such designs are known as 'augmented designs'. This paper obtains the properties of these designs and shows that, with an equal number of secondary treatments in each block, the A-optimal design is obtained by using the A-optimal design for the original block design. It develops formulae for the variance of treatment comparisons, for both the primary and the secondary treatments. A number of examples are used to illustrate the results.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:1:p:61-70
    DOI: 10.1080/02664760600744512
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    References listed on IDEAS

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    1. anonymous, 1978. "Communication," Management Science, INFORMS, vol. 24(9), pages 919-919, May.
    2. M. Kathleen Kerr, 2003. "Design Considerations for Efficient and Effective Microarray Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 822-828, December.
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    Cited by:

    1. Hans-Peter Piepho & Emlyn R. Williams & Volker Michel, 2016. "Nonresolvable Row–Column Designs with an Even Distribution of Treatment Replications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(2), pages 227-242, June.
    2. 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.

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