KARL PEARSON'S META-ANALYSIS REVISITED

• 成果类型: Article
• 署名作者: Owen, Art B.
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS697
• 发表日期: 2009
• 页码: 3867-3892
• 关键词: GOODNESS-OF-FIT; independent tests; probability; hypotheses

摘要

This paper revisits a meta-analysis method proposed by Pearson [Biometrika 26 (1934) 425-442] and first used by David [Biometrika 26 (1934) 1-11]. It was thought to be inadmissible for over fifty years, dating back to a paper of Birnbaum [J. Amer Statist. Assoc. 49 (1954) 559-574]. It turns out that the method Birnbaum analyzed is not the one that Pearson proposed. We show that Pearson's proposal is admissible. Because it is admissible, it has better power than the standard test of Fisher [Statistical Methods for Research Workers (1932) Oliver and Boyd] at some alternatives, and worse power at others. Pearson's method has the advantage when all or most of the nonzero parameters share the same sign. Pearson's test has proved useful in a genomic setting, screening for age-related genes. This paper also presents an FFT-based method for getting hard upper and lower bounds on the CDF of a sum of nonnegative random variables.