DISTRIBUTION FREE MULTIPLE COMPARISONS FOR MONOTONICALLY ORDERED TREATMENT EFFECTS |
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| Authors: | Anthony J. Hayter Glenn Stone |
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| Affiliation: | Georgia Institute of Technology and University of Bath;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA.;School of Mathematical Sciences, University of Bath, Bath, BA2 7AY, U.K. |
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| Abstract: | A method of calculating simultaneous one-sided confidence intervals for all ordered pairwise differences of the treatment effectsj–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 ordering1k, 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. |
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| Keywords: | Nonparametric statistics one-way model order restricted inference simultaneous confidence intervals critical point calculation unbalanced models |
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