Equivalent Comparisons of Experiments
1953/06/01 by David Blackwell · 1,461 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Applied mathematics #Artificial intelligence #Calculus (dental) #Class (philosophy) #Computer science #Dichotomy #Discrete mathematics #Mathematical economics #Mathematics #Optimal Experimental Design Methods #Statistics
paper · open access · doi:10.1214/aoms/1177729032
published in The Annals of Mathematical Statistics 24(2), 265-272 (Institute of Mathematical Statistics)
openalex publication_date 1953/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract
Sherman [8] and Stein [9] have shown that a method given by the author [1] for comparing two experiments is equivalent, for experiments with a finite number of outcomes, to the original method introduced by Bohnenblust, Shapley, and Sherman [4]. A new proof of this result is given, and the restriction to experiments with a finite number of outcomes is removed. A class of weaker comparisons--comparison in k-decision problems--is introduced, in three equivalent forms. For dichotomies, all methods are equivalent, and can be described in terms of errors of the first and second kinds.
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