A sequential procedure for deciding among three hypotheses. (English) Zbl 0816.62065

Summary: Abraham Wald developed the Sequential Probability Ratio Test in the 1940’s to perform simple vs. simple hypothesis tests that would control both Type I and Type II error rates. Some applications require a test of three hypotheses. In addition, to perform a simple vs. composite two- sided test, a three-hypotheses test with all hypotheses simple has been suggested. Methods have been proposed that will test three hypotheses sequentially. They range widely in simplicity and accuracy.
In this paper, approximate probabilities of error for Armitage’s test are derived. A method of adjusting the error rates used to establish the decision boundaries in order to attain the nominal error rates is developed. The procedure is compared to existing ones by Monte-Carlo simulation.


62L10 Sequential statistical analysis


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[1] Anderson S.L., Textile Inst 45 pp 472– (1954)
[2] DOI: 10.2307/2984117
[3] Armitage P., J.of the Roy.Statist.Soc.Ser 12 pp 137– (1950)
[4] DOI: 10.2307/2286937 · Zbl 0346.62057
[5] Billard L., J.of the Roy.Statist.Soc.Ser. 31 pp 285– (1969)
[6] Fowler G.W., Forum:Environmental Entomology 16 pp 345– (1987)
[7] Ghosh B.K., Sequential tests of statistical hypotheses (1970) · Zbl 0223.62097
[8] DOI: 10.1214/aos/1176346081 · Zbl 0521.62065
[9] DOI: 10.1090/S0002-9947-1936-1501854-3 · JFM 62.0611.03
[10] Lye B., Ento.Soc.of Amer. 18 pp 139– (1989)
[11] Rivett B.H.P., Statistical Method in Industrial Production, pp 86– (1951)
[12] SAS Institutes IncSAS User’s Guide (Ver. 6 ed.), Cary, NC. : Author.1990
[13] DOI: 10.1214/aoms/1177698692 · Zbl 0161.38601
[14] DOI: 10.1214/aoms/1177729944 · Zbl 0034.23001
[15] Waters W.E., Forest Science 1 pp 68– (1955)
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