## The Annals of Statistics

- Ann. Statist.
- Volume 19, Number 2 (1991), 1091-1097.

### Some Poset Statistics

#### Abstract

Statistics or functions are discussed that measure agreement between certain types of partially ordered data. These poset statistics are a generalization of two familiar classes of functions: the arrangement increasing functions and the decreasing reflection functions; those functions measure agreement between linearly ordered data. Specifically, the statistics in question are functions $h(\mathbf{X}_1, \mathbf{X}_2)$ of two matrix arguments, each having $N$ rows and they measure the agreement of the ordering of the $N$ rows of the two matrices. An example is used to illustrate and motivate the discussion. One statistic in this class is applied to the example; it generalizes Wilcoxon's rank sum statistic, Spearman's rank correlation and Page's statistic for ordered alternatives.

#### Article information

**Source**

Ann. Statist., Volume 19, Number 2 (1991), 1091-1097.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176348141

**Digital Object Identifier**

doi:10.1214/aos/1176348141

**Mathematical Reviews number (MathSciNet)**

MR1105865

**Zentralblatt MATH identifier**

0729.62045

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 06A10 20P05: Probabilistic methods in group theory [See also 60Bxx]

**Keywords**

Reflection group decreasing in transposition decreasing reflection function arrangement increasing function partial order rank tests

#### Citation

Rosenbaum, Paul R. Some Poset Statistics. Ann. Statist. 19 (1991), no. 2, 1091--1097. doi:10.1214/aos/1176348141. https://projecteuclid.org/euclid.aos/1176348141