Researchers tend to report only studies that are positive, while leaving negative trials unpublished. This publication bias can mislead us when looking at the totality of the published data. One solution to this problem is the p-curve. A significant p-value indicates that obtaining the result within the null distribution is improbable. The p-curve is the distribution of statistically significant p-values for a set of studies (ps < .05). Because only true effects are expected to generate right-skewed p-curves – containing more low (.01s) than high (.04s) significant p-values – only right-skewed p-curves are diagnostic of evidential value. By telling us whether we can rule out selective reporting as the sole explanation for a set of findings, p-curve offers a solution to the age-old inferential problems caused by file-drawers of failed studies and analyses.

The authors of this article tested the distributions of sets of statistically significant p-values from placebo-controlled studies of homeopathic ultramolecular dilutions. Such dilute mixtures are unlikely to contain a single molecule of an active substance. The researchers tested whether p-curve accurately rejects the evidential value of significant results obtained in placebo-controlled clinical trials of homeopathic ultramolecular dilutions.

Their inclusion criteria were as follows:

  1. Study is accessible to the authors.
  2. Study is a clinical trial comparing ultramolecular dilutions to placebo.
  3. Study is randomized, with randomization method specified.
  4. Study is double-blinded.
  5. Study design and methodology result in interpretable findings (e.g., an appropriate statistical test is used).
  6. Study reports a test statistic for the hypothesis of interest.
  7. Study reports a discrete p-value or a test statistic from which a p-value can be derived.
  8. Study reports a p-value independent of other p-values in p-curve.

The first 20 studies, in the order of search output, that met the inclusion criteria were used for analysis.

The researchers found that p-curve analysis accurately rejects the evidential value of statistically significant results from placebo-controlled, homeopathic ultramolecular dilution trials (1st graph below). This result indicates that replications of the trials are not expected to replicate a statistically significant result. A subsequent p-curve analysis was performed using the second significant p-value listed in the studies, if a second p-value was reported, to examine the robustness of initial results. P-curve rejects evidential value with greater statistical significance (2nd graph below). In essence, this seems to indicate that those studies of highly diluted homeopathics that reported positive findings, i. e. homeopathy is better than placebo, are false-positive results due to error, bias or fraud.

The authors’ conclusion: Our results suggest that p-curve can accurately detect when sets of statistically significant results lack evidential value.

True effects with significant non-central distributions would have a greater density of low p-values than high p-values resulting in a right-skewed p-curve (like the dotted green lines in the above graphs). The fact that such a shape is not observed for studies of homeopathy confirms the many analyses previously demonstrating that ULTRAMOLECULAR HOMEOPATHIC REMEDIES ARE PLACEBOS.

30 Responses to A p-curve analysis confirms: ultramolecular homeopathic remedies are placebos

  • Articles like this make me wonder how difficult it must be for future generations to understand why scientists today had to spend a lot of time on public discussions, clinical trials and sophisticated statistical analyses to defend the conclusion that “remedies” devoid of any effective molecules do not have supernatural health-promoting effects.

  • Something must be wrong if P curve fails to detect its effectiveness…..but P curve has its challenges too it seems…

    You are dedicating your energies as to why homeopathy shouldn’t work…whereas, I with mine, as to why it works. ..


    • good luck!
      (btw, I dedicate my energies to informing people by providing critical analyses)

    • Dear Mr. Barrett,
      “Homeopathy works” is too general of a statement to be tested, therefore this is an unfalsifiable claim and I would never even think about putting my “energies as to why homeopathy shouldn’t work”.

      However, as has been discussed in this forum very often:
      As soon as falsifiable, specific claims regarding homeopathic remedies are tested via well-designed and unbiased clinical trials, specific effects beyond placebo are pretty much NEVER detected.

      Please keep in mind: The burden of proof lies on the person MAKING the claim, so if you promote homeopathy or sell homeopathic remedies, it is YOUR obligation to present evidence that it works. It is NOT the obligation of scientists to try to disprove your claim (which is impossible anyways for unfalsifiable claims, as illustrated e.g. by Russell’s teapot analogy

      Like it or not, by far the most reproducible way to generate evidence for a claim is via the scientific method. “Beliefs”, “Feelings”, “Hope”, etc. are not reliable ways to come to truth.

      As a sceptic, I (at least try to) form my opinions on the availabe EVIDENCE for it, which -as a human- can be difficult at times. But in case of homeopathy it is not. Both, lack of evidence for efficacy and lack of any proven or even plausible mode of action leads me to conclude that homeopathy is complete rubbish.
      However, if you seriously want to spend more energy on showing that homeopathy works (and even get great financial rewards for your efforts), might I suggest that you accept the GWUP challenge?
      I have suggested this to several proponents of homeopathy, but for some unknown reason nobody want to do it… Maybe you can explain to me why that might be?


  • But you are making a claim, albeit indefinite, when you say “ultra-molecular” solutions are “placebos”. Placebo? You hefined placebo.
    You’re making a claim when you say there’s no detectable trace of the solute in 6x10E23 dilutions, you’re making a claim when you say homeopathy doesn’t work, or when you say it’s a fraud, or it’s criminal. So far you haven’t proven anything and you never will, homeopathy abides.

    • Dear Mr. Benneth,
      Quote:“ So far you haven’t proven anything and you never will, homeopathy abides.”

      This is an obvious attempt to shift the burden of proof.
      My stance towards any “new” claim is skeptical but neutral, i.e. I am not convinced that the claim is TRUE, but I am also not convinced that it is NOT TRUE. My position is: I don´t know if it is true or not, so I withhold judgement, unless the claim is investigated.

      If the claim is supported by evidence during the investigations, my level of confidence rises in accordance with the amount and quality of the evidence. The better the evidence, the higher my level of confidence that the claim is true, i.e. in agreement with reality. If, however, the investigations repeatedly fail to provide evidence, I will progressively become convinced that the claim is not true.

      S. Hahnemann invented homeopathy. He made the claim that homeopathic remedies have specific effects and can improve heath. His successors adopted this claim. However, this claim needs to be supported by reliable evidence.
      For medical treatments, this means that efficacy has to be shown in double-blinded, randomized controlled clinical trials (RCTs).
      Since the overwhelming majority of well-conducted RCTs show no evidence to support the claim that homeopathy “works” (beyond placebo) to improve ANY health condition, my confidence in this claim is very close to zero.

      I hope that you begin to understand why it is YOU who has to provide evidence FOR your claim, it is NOT our job to provide evidence AGAINST it.

    • Now, now, that’s not how it works. Inviting Burden of Proof along without its BFF Null Hypothesis is Laurel without Hardy; Rogers without Astaire; Dullman without laughtrack. Without evidence of efficacy above and beyond placebo, what you have is not medicine, it is Religion. Which is perfectly fine if that’s what floats your fantabulist boat, but do be honest about this when dealing with others as that’s the pint at which it becomes their funeral, not yours.

    • Rightly said Sir. To define placebo as ultra molecular solutions itself nullifies the objectivity of the article. Homoeopathy is not a faith science but desperate attempts are made to prove it one. This shows its popularity and its effect. To understand homoeopathic system of medicine the whole dynamic model of understanding health and disease has to change and that would be a paradigm change which I feel is in process with pandemics around.

      • oh dear!

      • @ Arpita Chatterjee

        To define placebo as ultramolecular solutions itself nullifies the objectivity of the article.

        You got it the wrong way round: All ‘ultramolecular'(*) solutions are placebos, but not all placebos are ‘ultramolecular’ solutions.
        Just like all homeopaths are deluded people, but not all deluded people are homeopaths.

        Homoeopathy is not a faith science …

        Homeopathy is not even science period.

        This shows its popularity and its effect

        Popularity does not prove anything, least of all efficacy.

        To understand homoeopathic system of medicine the whole dynamic model of understanding health and disease has to change …

        … as well as our current scientific models of chemistry and physics.

        So you’re basically telling us that we should abandon most of modern science in order to accommodate your outmoded and long-discredited belief system.

        I am quite sorry happy to tell you that this is not going to happen any day soon.

        *: Also note that ‘ultramolecular’ is a meaningless term that is used exclusively by SCAMmers.

  • You know, what’s laughable about the homeopathic terror of pathological scientists, is that in classical Hahnemannian homeopathy when we speak of proving a remedy it neans something quite different than it does in Knoxville. The opponent of the homeopath is what is nomered as “a proving.” To prove a remedy is to manifest the rubric, to aggravate the symptoms rather than pacify them, and this is done by giving the patient the wrong remedy, or too much of the right one, and you, the skeptomaniacs, are chasing a red herring, you’re doing what every inept, soulless homeopath secretly wants you to do, tell everybody it’s magic, tell everybody it’s a placebo, there’s nothing in it, it’s made with nothing but just plain water,YOU’VE got the science, YOU’VE got the math, YOU’VE got the chops to prove it with, because you’re “a scientist” and you can “do the math.”
    In doing this, you relieve the homeopath of his greatest terror, his responsibility to his patient not to harm him, and the manufacturer thanks you as well for mitigating his liabilities too. This is because there are secret tests and assays and explanations for the results by math in classical chemistry and what’s left in nuclear and infinitesimal physics which threaten to hold the incompetent practitioner to account, The fact is, you can kill a man or graft symptoms on him for life, as my blog at will affirm.
    I will teach, you will learn. Let us begin with replacing Avogadro’s Constant with Kolrausch’s Law for Infinite Dilution:

    • “The fact is, you can kill a man or graft symptoms on him for life, as my blog at will affirm.”

      • Read Kent, Professor, he made the claim, not me. Kent says you may kill a few of your patients by improper administration of a high potency dilute before you become aware of what you have done. Placebo’s a nice dodge for the guilty, and all murdering homeopaths will quietly thank you for all the hard work you’ve done in convincing the authorities it’s not verum.

        You having presumably administered homeopathic medicines, doctor, did anyone die while under your care? To deal with the guilt of knowing you actually killed someone by misuse of these materials would, I presume, drive one mad with anxiety and guilt, and make refuge in skepticism a lively comfort, a place to exercise your hubris . . and would explain the belittlement that often accompanies your responses to those of us who regard homeopathics as verum.

        I have an article coming to be posted on my blog. I will teach, you will learn.

    • Seems like the web has caught up with your bogus activities, John. Your link produces the following result:

      ” Connection not protected
      The security of your connection is reduced. Criminals can attempt to steal your data from the website. You are advised to leave this website.
      Invalid name of certificate. Either the name is not on the allowed list, or was explicitly excluded. View certificate
      I understand the risks and wish to continue”

    • @John Benneth

      It never ceases to amaze me, the total ignorance you (and your pal Dullman) are willing to display to the public.

      “Let us begin with replacing Avogadro’s Constant with Kolrausch’s Law for Infinite Dilution”. Sorry, no. You can’t replace Avogadro’s constant; both are valid. Kolrausch’s Law is valid only for low electrolyte concentrations. Avogadro’s constant defines the number of molecules in a one molar solution. It therefore predicts for a given starting concentration of a substance, the dilution at which there are no molecules of solute left — the point at which Kolrausch’s Law becomes pointless.

      For homeopathic dilutions, the point at which there are no molecules left is any dilution >12C.

      In any case, what the heck does molar conductivity have to do with treating disease? Put a drop of a 30C preparation on a sugar pill and you immediately invalidate Kolrausch’s requirements anyway.

      • Nice try. Avogadro doesn’t take into account molecular dissociation.

      • Frank,
        Actually you’re wrong about 12c being the molecular limit in step dilutions . . it happens much earlier than that.
        As hydrolysis dissociates the molecules in dilution, conductivity of the solution increases, revealing a phase shift from molecule to electron, particle to wave. This happens when the molecular solute hits 1ppm, at approx. the sixth decimal dilution. As mass is reduced, energy increases. There are a number of tests that reveal. The dilution of chlorine in tap water is about 5X, btw, 10ppm I reckon. It dissipates quickly, due to dissociation. The ions expand and contract above the asymptote in each dilution.
        So you can dump Avogadro, it’s irrelevant to the chemistry of homeopathy. Dielectric tests, Tritium measures, beta scintiilation, low EM signal detection show conclusively supramolecular homeopathics are radiometric.


        • John Benneth, you’re priceless!!

          Congratulations for not including anything about quantum theory, gamma spectroscopy, nanocrystals, neutrinos or leptoquarks in your fascinating explanation.

    • “The fact is, you can kill a man or graft symptoms on him for life, as my blog at will affirm.”

      Oh aye, John?

      The delusions you embrace are quite breathtaking. Care to let we the uninitiated know which remedies are so spine-chillingly dangerous? We promise not to point and laugh too much.

      • Do knee surgons not embrace thier own delusions ?

        In this 2-year follow-up of patients without knee osteoarthritis but with symptoms of a degenerative medial meniscus tear, the outcomes after APM were no better than those after placebo surgery. No evidence could be found to support the prevailing ideas that patients with presence of mechanical symptoms or certain meniscus tear characteristics or those who have failed initial conservative treatment are more likely to benefit from APM.”

        • even if you are right, you are basically implying that, because your neighbour beats up his wife, you might as well do the same.
          it’s called a logical fallacy – you should read up about them [even though you are good at using them].

      • Read Kent, lectures on the MM, Hepar and Thuja. Now off you go . .

  • Oh man, this John Benneth is fantastic! Here I thought Chiroquackers had the most compelling gobbledygook and arcane reasoning…they have met their match. I suspect Mr. Benneth may have been part of the development of the Turboencabulator. Though his homeopathetic explanations even make that seem comprehensible.
    I think he may have choked on a sugar pill and been damaged by hypoxia?

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Subscribe via email

Enter your email address to receive notifications of new blog posts by email.

Recent Comments

Note that comments can be edited for up to five minutes after they are first submitted but you must tick the box: “Save my name, email, and website in this browser for the next time I comment.”

The most recent comments from all posts can be seen here.