Open Access
December 2009 Karl Pearson’s meta-analysis revisited
Art B. Owen
Ann. Statist. 37(6B): 3867-3892 (December 2009). DOI: 10.1214/09-AOS697


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.


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Art B. Owen. "Karl Pearson’s meta-analysis revisited." Ann. Statist. 37 (6B) 3867 - 3892, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62023
MathSciNet: MR2572446
Digital Object Identifier: 10.1214/09-AOS697

Primary: 52A01 , 62C15 , 62F03 , 65T99

Keywords: Admissibility , fast Fourier transform , Hypothesis testing , microarrays

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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