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PeerJ. 2019 Jan 23;7:e6318. doi: 10.7717/peerj.6318. eCollection 2019.

P-curve accurately rejects evidence for homeopathic ultramolecular dilutions.

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SUNY Downstate College of Medicine, Brooklyn, NY, United States of America.



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.


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.


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.


Our results suggest that p-curve can accurately detect when sets of statistically significant results lack evidential value.


Evidential value; Homeopathy; Publication bias; Statistical significance; Statistics; Ultramolecular dilutions; p-curve; p-value

Conflict of interest statement

The authors declare there are no competing interests.

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