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A Bayes Rule for the Symmetric Multiple Comparisons Problem
Abstract
A simple LSD (least significant difference) rule is presented for simultaneously testing the differences between n treatments considered in all possible pairs. This rule is a simpler, fully completed, version of the Bayes rule presented for special cases in Duncan [4]. It is based on the same multiple decision theory model except for a modified and extended use of a conjugate chi-square density in the prior. The new rule has the same intuitively appealing dependence on the between-treatment F ratio, varying from a sensitive comparisonwise-α-like rule when F is large or moderate, to a conservative experimentwise-α-like rule when F is small. Tables of t for computing the LSD are presented for three choices of a type-1 to type-2 error-seriousness ratio, k = 50, 100 and 500 (analogous to the usual choices of α = .10, .05 and .01 in testing a single difference), and for full ranges of F and its degree of freedom q and f.
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Citations
Cites
Fisher, R. A. (1936) · BMJ · doi:10.1136/bmj.1.3923.554-a · Cited by 4,980
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An exploration of aspects of Bayesian multiple testing
Scott, J. G., & Berger, J. O. (2006) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2005.08.031 · Cited by 330
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Metadata
- Authors
- Waller, R. A., & Duncan, D. B.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1969-12
- Volume
- 64
- Issue
- 328
- Pages
- 1484-1503
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2075509996
- Cited by
- 723
- References
- 1
- FWCI
- 3.43
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
