How Likely Is Simpson's Paradox?

被引：31

作者：

Pavlides, Marios G. ^{[1
]}

Perlman, Michael D. ^{[2
]}

机构：

[1] Frederick Univ Cyprus, CY-1303 Nicosia, Cyprus

[2] Univ Washington, Dept Stat, Seattle, WA 98195 USA

来源：

AMERICAN STATISTICIAN | 2009年 / 63卷 / 03期

关键词：

Bayes factor; Bayes test; Dirichlet distribution; Multinomial distribution; Simpson's Paradox; Simpson reversal; SUBDIVISIONS; PROPORTION;

D O I：

10.1198/tast.2009.09007

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

What proportion of all 2 x 2 x 2 contingency tables exhibit Simpson's Paradox? An exact answer is obtained for large sample sizes and extended to 2 x 2 x l tables by Monte Carlo approximation. Conditional probabilities of the occurrence of Simpson's Paradox are also derived. If the observed cell proportions satisfy a Simpson reversal, the posterior probability that the population parameters satisfy the same reversal is obtained. This Bayesian analysis is applied to the well-known Simpson reversal of the 1995-1997 batting averages of Derek Jeter and David Justice.

引用

页码：226 / 233

页数：8

共 20 条

[1]

[Anonymous], PHILOS T ROYAL SOC A

[2] SEX BIAS IN GRADUATE ADMISSIONS - DATA FROM BERKELEY [J].