Megalithic art ideas of J. Dronfield

From the first table it looks that the distinction between the distribution of type of shapes is able to indicate the type of art.

Evaluation

Remarks 1

My remarks on Dronfield's methodology [1996]:

• There is a certain amount of circularity in his argument; the distinction between diagnostic and undiagnostic (type of shapes) is determined by the same set of types of art. Don't know how serious the consequences are.
• The endogenous diagnostic shapes were caused/defined by sensory (electrical stimulation, deep pressure and flickering lights) and intraneural (hallucinogenic substances, pathological syndromes) stimulation. A large scope of causes!
  
• Chi-Square method is used to determine the significance. He used the percentages of occurrences in the Chi-Square method, which is not correct (as he say himself). The significance is also not very high (~88%). But it still might be ok-ish.
  
• One can use Chi-square for many types of distributions, so perhaps also ok for the distribution of type of shapes?
• Because of the large scope of the above definition of endogenous diagnostic shapes, it is not possible to proof that endogenous diagnostic shapes are due to hallucinogenic substances only.
  

Remarks 2

My remarks on Dronfield [1995]:

• Looking at the Irish Megalithic art (see the Type of art table) there looks to a similarity with the S1 and S2 type of art.
• In this study Dronfield [1995], uses results  from:
• Sensory stimulation (electrical stimulation; no deep pressure or light flickering were included)
• Intraneural stimulation (hallucinogenic substances; no pathological syndromes were included )
  
• Remember, I don't relate endogenous diagnostic shapes strongly to only intraneural stimulation (hallucinogenic substances and pathological syndromes), because of its larger scope.
  
• Dronfield uses the statistical analysis Correlation analysis (although I have my doubt about its validity, see below), and from this it is quite clear (due to high coefficient of determination, like in Table 6) that some Irish Megalithic art could be due to sensory manipulation (electrical).  Intraneural stimulation (huichol) only scores a few times with r² higher then 0.4.
• He does not do a significance analysis on his Correlation analysis (Kreyszig, chapter 18.4, [1970])
• IMHO Correlation analysis can be used only for a two dimensional population that has a normal distribution and not for two different populations with an undetermined distribution. So I think Correlation analysis might be the wrong analysis method.
  
• The Chi-Square method can be used, but only on the absolute number of sample and not percentages. In case one uses this method, no significance is found. 
• A non-parametric method could also be used: like Equality of distributions (Kreyszig, chapter 20.4, [1970]). When using this non-parametric method no significance what so ever is found.
• A lot of text (3 columns) is attributed to hallucinogenic substances, which has the lowest significance. While the one with the highest significance (electrical stimulation) only gets 1 column of text.
  
• A very small typo: the r² (coefficient of determination) can not be negative. The correlation coefficient r can be negative.

At this moment I am not really convinced about the conclusions of Dronfield, mainly due to idea I have that the statistical methods used might not be the best ones.
I though have a feeling that Megalithic art is more then an abstract expressions due to intraneural simulation (like hallucinogenic substances). Looking at the way the stones are decorated, the time involved in these processes and the repetition of certain combinations makes that the Megalithic art must be representing something, IMHO. I know that this feeling could be misleading, but at least I recognize my tendency;-).

Even if the Megalithic art resembles the shapes that are also seen with sensory/intraneural stimulation; it does not have to say there is any (causual) relation between intraneural stimulation and Megalithic art.

Any feedback on this would be helpful. I am also in search of Jeremy Dronfield; I tried several persons (and the place where he was working), no results. If you have more info, let me know

Acknowledgments

I would like to thank the following people for their help and constructive feedback: John Miller and all unmentioned other people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.