For tests that may be dependent. Native implementation of the asymptotically exact harmonic mean p-value (Wilson 2019): the statistic \(mean(1/p)\) is referred to its Landau asymptotic distribution. Cross-validated against harmonicmeanp.
Examples
# Combined p-value robust to dependence between tests.
harmonic_mean_p(c(0.001, 0.05, 0.5))
#> [1] 0.004710834
# Dominated by the smallest p-values (a few strong signals carry it).
harmonic_mean_p(c(0.0001, 0.9, 0.9, 0.9))
#> [1] 0.0005962707
# All-null inputs stay large.
harmonic_mean_p(c(0.4, 0.5, 0.6))
#> [1] 0.7037525
# Unlike Fisher/Stouffer, valid even under arbitrary dependence.
set.seed(1)
harmonic_mean_p(c(runif(5, 0, 0.01), runif(5)))
#> [1] 0.01157731