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Biometrika 1954 41(1-2):170-176; doi:10.1093/biomet/41.1-2.170
© 1954 by Biometrika Trust
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A TOW-SAMPLE MULTIPLE DECISION PROCEDURE FOR RANKING MEANS OF NORMAL POPULATIONS WITH A COMMON UNKNOWN VARIANCE{dagger}

ROBERT E. BECHHOFER, CHARLES W. DUNNETT {ddagger} and MILTON SOBEL

Cornell University

A multiple decision approach to the problem of ranking populations according to their population means hes been formulated by Bechhofer (1954). A single-sample solution to this problem waa presented by him for the case of normal populations with known variances. In the present paper the case of normal populations with unknown equal variances is considered. A two-sample procedure is proposed as a solution to the latter problem; this procedure is of the type used by Stein (1945) for obtaining a test of Student's hypothesis with power independent of the variance. Tables are available which enable the experimenter to apply this procedure with little computational effort to the ranking of two or three populations with unknown but equal variances. The same tables can be used when the variance ratios are arbitrary and known. Graphic comperisons of the expected sample size are made for the single-sample and two-sample procedures.


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