Happy new year. not least to the folks at the homeopathy4health site . They are jubilant about a “proof” that homeopathic dilutions could produce effects. albeit only on wheat seedlings. But guess what? After some questioning it was found that they hadn’t actually read the paper. Well I have read it, and this is the result.

The paper is “A Biostatistical Insight into the As_{2}O_{3} High Dilution Effects on the Rate and Variability of Wheat Seedling Growth”. Brizzi,

Lazzarato, Nani, Borghini, Peruzzi and Betti, *Forsch Komplementärmed Klass Naturheilkd* 2005;12:277–283

The authors compared these treatments (30 seedlings each).

- C1, C2, C3 (untreated water p.a. Merck, control);
- WP (potentized water p.A. Merck) 5x, 15x, 25x, 35x, 45x;
- AD (diluted arsenic trioxide) 10–5, 10–15, 10–25, 10–35, 10–45;
- AP (potentized arsenic trioxide) 5x, 15x, 25x, 35x, 45x.

The allocation of seedlings to treatments was stated to be blind and randomised. So far, so good.

But just look at the results in Figure 1. They are all over the place, with no obvious trend as ‘potency’ (i.e. dilution) is increased. The

results with homeopathic arsenic at 45 days (the only effect that is claimed to be real) is very little different from the that of shaken water (water that has been though the same process but with no arsenic present initially).

For some (unstated) reason the points have no standard errors on them. Using the values given in Table 3 I reckon that the observation for AP45 is 1.33 ± 0.62 and for the plain water (WP45). it is 1.05 ± 0.69. The authors claim (Table 3) that the former is ‘significant’ (with a profoundly unimpressive P = 0.04) and the latter isn’t. I can’t say that I’m convinced, and in any case, even if the effect were real, it would be tiny.

Later the authors do two things that are a very dubious from the statistical point of view. First they plot cumulative distributions which are notoriously misleading about precision (because the data in adjacent bins are almost the same). They then do some quite improper data snooping by testing only the half of the results that came out lowest. If this were legitimate (it isn’t) the results would be even worse for homeopaths, because the difference between the controls and plain water (WP45) now, they claim, comes out “significant”.

Homeopaths claim that the smaller the dose, the bigger the effect (so better water down your beer as much as possible, making sure to bang the glass on the bar to potentise it). I have yet to see any dose-response curve that has the claimed negative slope. Figure 1 most certainly doesn’t show it.

Of course there is no surprise at all for non-homeopaths in the discovery that arsenic 45x is indistinguishable from water 45x.

That is what we have been saying all along.

I haven’t read the paper (I’m not paying $25 for the privilege) but the graph you show raises a question. The variation between different treatment groups for a particular dilution appears narrower than between different dilutions. As all the treament groups are the same ie water, I would expect a similar variation across all points. It appears that the methodology may be suspect.

The next paper in the same issue of the journal is on a similar topic. It’s an attempt at reproducing the results of a 1997 trial of the effects of 45x arsenic on wheat seedling growth. I haven’t seen the full paper, only the abstract, but the conclusion there looks, er, interesting:

“CONCLUSION: The result of this replication trial is a reversal of the original study, since Arsenicum album 45x inhibited wheat shoot growth instead of enhancing it. Nevertheless, high homeopathic potencies may induce statistically significant effects in biological systems. However, the magnitude and direction of these effects seem to depend on yet unknown parameters.”

Binder M, Baumgartner S, Thurneysen A.

The effects of a 45x potency of arsenicum album on wheat seedling growth — a reproduction trial.

Forsch Komplementärmed Klass Naturheilkd 2005;12:284-291

http://www.ncbi.nlm.nih.gov/pubmed/16230858

I haven’t managed to track down any reference for the 1997 trial.

WTF is potentised water? Any parallel with an empty vacuum?

Just bang the water when you dilute it (with water). You couldn’t make it up uh?

Another thing you can say about the figure is that it appears to be an experiment without a positive control. Surely it wouldn’t have been that difficult to add groups with some real growth enhancing (or inhibiting) compound just to show what a real (as opposed to p less than 0.05) effect looks like

Oh dear, homeopathy4health has got in a huff again –

Quote (as on the blog at the moment)

I have no further comment to make. Further comments will be deleted. If you want to discuss it further please take the issue to your own blogs.Comment by homeopathy4health — January 3, 2008 @ 6:38 pmuhuh, pity, Just when we were getting a good dialogue going, homeopathy4health seems tp have decided against it.

I haven’t read the paper, but it seems like a simple case of multiple comparisons. They seem to have made 15 comparisons against control. Assuming none of the treatments work, and that all the comparisons are independent, the chance that all the P values will be larger than 0.05 equals 0.95^15, or 46%. So the chance of happening to get one (or more) P value less than 0.05 is 54%. In other words, what they saw (one smallish P value) is exactly what you’d expect to see if homeopathy did NOT work.

I’ve got hold of a copy of the second paper. The 1997 study it was attempting to repeat was Betti L, Brizzi M, Nani D, Peruzzi M, Effect of high dilutions of Arsenicum album on wheat seedlings from seeds poisoned with the same substance, Br Hom J 1997;86:86-89.

Just so I can follow whats being said here, would someone clarify two points from the paper and DC’s analysis.

When the paper says that the AP result is significant, but the WP result is not, what are they comparing to? Does it mean significant in relation to zero on the graph?

Second, why is a P of 0.04 unsatisfactory? Doesn’t that mean a 1 in 25 chance of coming out randomly? Maybe this is what is being addressed by hmotulsky in comment 8, but I am not positive.

Thanks!