The Annals of Statistics

Karl Pearson’s meta-analysis revisited

Art B. Owen

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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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Ann. Statist., Volume 37, Number 6B (2009), 3867-3892.

First available in Project Euclid: 23 October 2009

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Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62C15: Admissibility 65T99: None of the above, but in this section 52A01: Axiomatic and generalized convexity

Admissibility fast Fourier transform hypothesis testing microarrays


Owen, Art B. Karl Pearson’s meta-analysis revisited. Ann. Statist. 37 (2009), no. 6B, 3867--3892. doi:10.1214/09-AOS697.

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