The harmonic mean χ^2 test to substantiate scientific findings
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A new significance test is proposed to substantiate scientific findings from multiple primary studies investigating the same research hypothesis. The test statistic is based on the harmonic mean of the squared study-specific test statistics and can also include weights. Appropriate scaling ensures that, for any number of studies, the null distribution is a χ^2-distribution with one degree of freedom. The null distribution can be used to compute a one-sided p-value or to ensure Type-I error control at a pre-specified level. Further properties are discussed and a comparison with FDA's two-trials rule for drug approval is made, as well as with alternative research synthesis methods. An attractive feature of the new approach is that a claim of success requires each study to be convincing on its own to a certain degree depending on the significance level and the number of studies. As a by-product, the approach provides a calibration of the sceptical p-value recently proposed for the analysis of replication studies.
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