Combining independent p values: Extensions of the Stouffer and binomial methods.

The Stouffer z method, and other popular methods for combining p values from independent significance tests, suffer from three problems: vulnerability to criticisms of the individual studies being pooled, difficulty in handling the "file drawer problem," and vague conclusions. These problems can be reduced or eliminated by supplementing a test of combined probability with a variety of new analyses described here. Along with other advantages, these analyses provide a way to address the file drawer problem without making limiting assumptions about the nature of studies not included in the pooled analysis. These analyses can supplement a traditional meta-analysis, yielding conclusions not provided by widely used meta-analytic procedures.