A Review of Three Simple Plant Models and Corresponding Statistical Tools for Basic Research in Homeopathy

Abstract

In this paper, we review three simple plant models (wheat seed germination, wheat seedling growth, and infected tobacco plants) that we set up during a series of experiments carried out from 1991 to 2009 in order to study the effects of homeopathic treatments. We will also describe the set of statistical tools applied in the different models. The homeopathic treatment used in our experiments was arsenic trioxide (As2O3) diluted in a decimal scale and dynamized. Since the most significant results were achieved with the 45th decimal potency, both for As2O3 (As 45x) and water (W 45x), we here report a brief summary of these results. The statistical analysis was performed by using parametric and nonparametric tests, and Poisson distribution had an essential role when dealing with germination experiments. Finally, we will describe some results related to the changes in variability, which seems to be one of the targets of homeopathic treatment effect.

Biological effects and physico-chemical properties of extremely diluted aqueous solutions as a function of aging-time

“…As done in previous experimentations (Betti et al 2010), we checked the goodness of fit of Poisson distribution by applying the Kolmogorov-Smirnov test (Stephens 1974), based on the comparison between the empirical cumulative distribution function and the theoretical one. After confirming the goodness of fit, we made an overall comparison between the experiments, in a sort of 'Poissonian ANOVA', using the test proposed by Sachs (1984).…”

“…• The choice of an undiluted/unsuccussed control was based on our previous findings (Betti et al , 2010Brizzi et al 2000;Elia et al 2004Elia et al , 2005 and is explained in considerable detail in the 'Discussion and conclusions' section.…”

“…At very high dilution levels (beyond the Avogadro limit) the probability of the presence of molecules of the original substance is near to zero (Marschollek et al 2010). This aspect represents one of the reasons why the biological effectiveness of EDS is still controversial, although there is emerging evidence for their in vitro activity (Brizzi et al , 2011Belon et al 2004;Witt et al 2007;Frenkel et al 2010;Endler et al 2011) as well as in vivo activity (Bellavite et al 2006;Welles et al 2007;Baumgartner et al 2008;Shah-Rossi et al 2009;Betti et al 2010;Jäger et al 2010;Magnani et al 2010;Wyss et al 2010). Based on physico-chemical measurements, it was hypothesized that the particular preparation technique of EDS could lead to a structural alteration of the aqueous solvent that appears to trigger the formation of molecular aggregates of water molecules (Samal and Geckeler 2001;Elia et al * Corresponding author.…”

“…In particular, the work of the Bologna University team (LB, GT, MZ and MB) centered on a series of experiments on an isopathic model, based on in vitro wheat germination and growth (Betti et al 2010). According to 'isopathy', the same substance causing the disease can be used in low doses or high dilutions to treat the disease itself (Bellavite et al 2007).…”

“…According to 'isopathy', the same substance causing the disease can be used in low doses or high dilutions to treat the disease itself (Bellavite et al 2007). In our model, a large number of wheat seeds were stressed with a sub-lethal dose of arsenic trioxide (As 2 O 3 ) and then treated with decimal dilutions/succussions of the same substance: the consistency of the different statistical analyses and the reproducibility of most of the experimental results are notable (Betti et al 2010). The Naples University research group (VE and EN) carried out systematic studies of the physico-chemical properties of EDS and have already shown that the process of iterated dilution and dynamization is able to permanently modify certain features of water.…”