Abstract
PROBABILITIES from independent significance tests, in which usually none of the separate probabilities is significant, are usually pooled by Fisher's method1, which is based on the product of the individual probabilities. Although Fisher states that a χ2 transformation provides an exact test of significance in this situation, Wallis2 pointed out some time ago that this is only true if the separate probabilities are derived from continuous distributions. When the original distributions comprise a limited number of finite probabilities, Fisher's transformation often results in a considerable over-evaluation of the true probability of the product.
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References
Fisher, R. A., Statistical Methods for Research Workers, thirteenth ed. revised (Oliver and Boyd, Edinburgh, 1958).
Wallis, W. A., Econometrica, 10, 229 (1942).
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MCLAUGHLIN, R. Combination of Probabilities from Significance Tests. Nature 220, 1250–1251 (1968). https://doi.org/10.1038/2201250a0
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DOI: https://doi.org/10.1038/2201250a0
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