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DISTRIBUTION FREE MULTIPLE COMPARISONS FOR MONOTONICALLY ORDERED TREATMENT EFFECTS
Author(s) -
Hayter Anthony J.,
Stone Glenn
Publication year - 1991
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1991.tb00439.x
Subject(s) - monotonic function , confidence interval , a priori and a posteriori , pairwise comparison , simple (philosophy) , mathematics , distribution (mathematics) , statistics , sample size determination , confidence distribution , mathematical analysis , philosophy , epistemology
Summary A method of calculating simultaneous one‐sided confidence intervals for all ordered pairwise differences of the treatment effects j – i , 1 i < j k, in a one‐way model without any distributional assumptions is discussed. When it is known a priori that the treatment effects satisfy the simple ordering 1 k , these simultaneous confidence intervals offer the experimenter a simple way of determining which treatment effects may be declared to be unequal, and is more powerful than the usual two‐sided Steel‐Dwass procedure. Some exact critical points required by the confidence intervals are presented for k = 3 and small sample sizes, and other methods of critical point determination such as asymptotic approximation and simulation are discussed.