The Annals of Statistics

Some Poset Statistics

Paul R. Rosenbaum

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G10: Hypothesis testing
Secondary: 06A10 20P05: Probabilistic methods in group theory [See also 60Bxx]

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


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

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