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Step‐down multiple tests for comparing treatments with a control in unbalanced one‐way layouts
Author(s) -
Dunnett Charles W.,
Tamhane Ajit C.
Publication year - 1991
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780100614
Subject(s) - bonferroni correction , multiple comparisons problem , computer science , sample size determination , type i and type ii errors , value (mathematics) , algorithm , control (management) , mathematics , statistics , artificial intelligence
We show how a well‐known multiple step‐down significance testing procedure for comparing treatments with a control in balanced one‐way layouts can be applied in unbalanced layouts (unequal sample sizes for the treatments). The method we describe has the advantage that it provides p ‐values, for each treatment versus control comparison, that take account of the multiple step‐down testing nature of the procedure. These joint p‐values can be used with any value of α, the fixed type I familywise error rate bound, that may be specified by the investigator. To determine the p ‐values, it is necessary to compute a multivariate Student t integral, for which a computer program is available. This procedure is more powerful than the step‐down Bonferroni procedure of Holm 1 and the single‐step procedure of Dunnett. 2 An example from the pharmaceutical literature is used to illustrate the procedure.