Abstract:
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Combining p-values from hypothesis tests, also known as second-level significance testing, could be argued to be of increasing importance in the advent of ubiquitous "Big Data" problems where signals from highly multivariate data sources must be combined. This presentation provides a review of different methods in the statistics literature for combining p-values, highlighting theoretical results where available. Particular emphasis will be placed on heterogeneous meta analyses, where under the global alternative hypothesis, only some of the individual null hypotheses may be false. Theoretical results are more limited in this scenario, although Donoho an Jin (2004) provided valuable insight into the asymptotic behaviour of a method they developed and refer to as "higher criticism", which extended an idea originating from Tukey. Based on empirical results, some new p-value combiners are tentatively proposed for this context.
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