## The Annals of Mathematical Statistics

### Equivalent Comparisons of Experiments

David Blackwell

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 28 April 2007

http://projecteuclid.org/euclid.aoms/1177729032

Digital Object Identifier
doi:10.1214/aoms/1177729032

Mathematical Reviews number (MathSciNet)
MR56251

Zentralblatt MATH identifier
0050.36004

JSTOR

#### Citation

Blackwell, David. Equivalent Comparisons of Experiments. Ann. Math. Statist. 24 (1953), no. 2, 265--272. doi:10.1214/aoms/1177729032. http://projecteuclid.org/euclid.aoms/1177729032.