Optimally weighted Z-test is a powerful method for combining probabilities in meta-analysis
Open Access
- 23 May 2011
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of Evolutionary Biology
- Vol. 24 (8), 1836-1841
- https://doi.org/10.1111/j.1420-9101.2011.02297.x
Abstract
The inverse normal and Fisher's methods are two common approaches for combining P‐values. Whitlock demonstrated that a weighted version of the inverse normal method, or ‘weighted Z‐test’, is superior to Fisher's method for combining P‐values for one‐sided T‐tests. The problem with Fisher's method is that it does not take advantage of weighting and loses power to the weighted Z‐test when studies are differently sized. This issue was recently revisited by Chen, who observed that Lancaster's variation of Fisher's method had higher power than the weighted Z‐test. Nevertheless, the weighted Z‐test has comparable power to Lancaster's method when its weights are set to square roots of sample sizes. Power can be further improved when additional information is available. Although there is no single approach that is the best in every situation, the weighted Z‐test enjoys certain properties that make it an appealing choice as a combination method for meta‐analysis.Keywords
This publication has 9 references indexed in Scilit:
- Is the weighted z-test the best method for combining probabilities from independent tests?Journal of Evolutionary Biology, 2011
- Computing the distribution of quadratic forms: Further comparisons between the Liu–Tang–Zhang approximation and exact methodsComputational Statistics & Data Analysis, 2010
- Choosing an optimal method to combine P‐valuesStatistics in Medicine, 2009
- Combining probability from independent tests: the weighted Z‐method is superior to Fisher's approachJournal of Evolutionary Biology, 2005
- Truncated product method for combining P‐valuesGenetic Epidemiology, 2002
- Algorithm AS 204: The Distribution of a Positive Linear Combination of χ 2 Random VariablesJournal of the Royal Statistical Society Series C: Applied Statistics, 1984
- A Multiple Comparison Procedure for Comparing Several Treatments with a ControlJournal of the American Statistical Association, 1955
- Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way ClassificationThe Annals of Mathematical Statistics, 1954
- A statistical consideration in psychological research.Psychological Bulletin, 1951