The Annals of Mathematical Statistics

Equivalent Comparisons of Experiments

David Blackwell

Full-text: Open access


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.

Article information

Ann. Math. Statist. Volume 24, Number 2 (1953), 265-272.

First available in Project Euclid: 28 April 2007

Permanent link to this document


Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Blackwell, David. Equivalent Comparisons of Experiments. The Annals of Mathematical Statistics 24 (1953), no. 2, 265--272. doi:10.1214/aoms/1177729032.

Export citation