Karl Pearson's meta-analysis revisited

Details Karl Pearson's meta-analysis revisited Karl Pearson's meta-analysis revisited

2009-11-18

arxiv.org/abs/0911.3531v1

Annals of Statistics 2009, Vol. 37, No. 6B, 3867-3892

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS697 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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