P-curve accurately rejects evidence for homeopathic ultramolecular dilutions

Background P -curve has been proposed as a statistical test of evidential value. The distributions of sets of statistically significant p -values are tested for skewness. P -curves of true effects are right-skewed, with greater density at lower p -values than higher p -values. Analyses of null effects result in a flat or left-skewed distribution. The accuracy of p -curve has not been tested using published research analyses of a null effect. We examined whether p -curve accurately rejects a set of significant p -values obtained for a nonexistent effect. Methods Homeopathic ultramolecular dilutions are medicinal preparations with active substances diluted beyond Avogadro’s number. Such dilute mixtures are unlikely to contain a single molecule of an active substance. We tested whether p -curve accurately rejects the evidential value of significant results obtained in placebo-controlled clinical trials of homeopathic ultramolecular dilutions. Results P -curve accurately rejected the evidential value of significant results obtained in placebo-controlled clinical trials of ultramolecular dilutions. Robustness testing using alternate p -values yielded similar results. Conclusion Our results suggest that p -curve can accurately detect when sets of statistically significant results lack evidential value.