P-curve accurately rejects evidence for homeopathic ultramolecular dilutions

Abstract

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.