Robustness of balanced incomplete block designs to randomly missing observations
Robustness of balanced incomplete block designs to randomly missing observations
Practical experimenters must always be aware of the possibility that some of their observations could become unavailable for analysis. In an experiment involving treatments and blocks, it could be desirable to select a design that is resistant to the loss of a complete block or treatment, or a small number of observations distributed at random throughout the initial design. In this paper, we examine the robustness of binary, variance-balanced, incomplete block designs using the eigenvalues of the associated information matrix when specific observations are missing. Results are presented for up to three missing observations and the procedure is illustrated using an example involving eight treatments arranged in 14 blocks of four treatments per block. On the basis of these considerations, it is recommended that, to guard against a substantial loss of efficiency due to a small number of randomly missing observations, it is preferable to use designs with as few treatments common to pairs of blocks as possible.
balanced incomplete block design, missing observations, information matrix, eigenvalues, variance of treatment differences
283-296
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Mansson, Ralph
9788f5c4-af4d-4cc5-94bc-a4922d637a5a
January 2001
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Mansson, Ralph
9788f5c4-af4d-4cc5-94bc-a4922d637a5a
Prescott, Philip and Mansson, Ralph
(2001)
Robustness of balanced incomplete block designs to randomly missing observations.
Journal of Statistical Planning and Inference, 92 (1-2), .
(doi:10.1016/S0378-3758(00)00147-6).
Abstract
Practical experimenters must always be aware of the possibility that some of their observations could become unavailable for analysis. In an experiment involving treatments and blocks, it could be desirable to select a design that is resistant to the loss of a complete block or treatment, or a small number of observations distributed at random throughout the initial design. In this paper, we examine the robustness of binary, variance-balanced, incomplete block designs using the eigenvalues of the associated information matrix when specific observations are missing. Results are presented for up to three missing observations and the procedure is illustrated using an example involving eight treatments arranged in 14 blocks of four treatments per block. On the basis of these considerations, it is recommended that, to guard against a substantial loss of efficiency due to a small number of randomly missing observations, it is preferable to use designs with as few treatments common to pairs of blocks as possible.
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Published date: January 2001
Keywords:
balanced incomplete block design, missing observations, information matrix, eigenvalues, variance of treatment differences
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Statistics
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Local EPrints ID: 29986
URI: http://eprints.soton.ac.uk/id/eprint/29986
ISSN: 0378-3758
PURE UUID: fc4be822-4739-46c4-b0cf-7f7d965766f4
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Date deposited: 11 May 2006
Last modified: 15 Mar 2024 07:36
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Author:
Ralph Mansson
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