The stone circle diameter data provided (Thom [1967], table 5.1, pages 37-39) has been evaluated with the proposed statistical method of Broadbent (1955, 1956). The category within that method used, was named

- No a priori knowledge of some periodicy in the diameter
- The offset (b) may be different from zero

This picture tells us when a possible periodicy (quantum) provides
statistical
confidence (when C_{quantum}>=C(1%)~1). So using the table
of measured
diameters from the Thom book, this happens at 5.44 [feet]. Thom calls
this
length the Megalithic Fathom (1967, page
41).

Analyzing this deductions, I come to the following issues:

- Thom makes the b (the y-axis offset)
equal
to
zero, but using category
**Case IIb**, one sees a b of some 0.3 [feet], this is not zero compared to the so called Megalithic Fathom (which is 5.44 [feet])! - Did Thom measure the radius or the diameter of the circles? It is very important to know, because depending on the method, the variation will be different. It is expected that he measured the diameter (see also text with table 5.1 of him).
- Thom deducts (page 41) from the fact that: radius = diameter / 2
- One is perhaps allowed to divided by two, if it is for sure that neolithic man made a stone circle by using a string and a pin in the ground at the center. If the length of the string (the radius) was set out with the help of the megalithic yard, then the diameter would be set out by a Megalithic Fathom.
- I think Thom should not have divided the Megalithic Fathom by two (there is no valid reason for that!). The Megalithic Fathom should have been good enough. Other people (like Kendall, Freeman and Barnatt and Moir) have found a measure that is coparable to the MF.
- Hawinks G. (Beyond Stonehenge [1973], page 241) assumes that people linking hands wirst to wirst will average double the meglalithic yard of Thom. This is comparable to my ideas.
- A good natural standard is available for determining the Megalithic Fathom, see my explanation.

that

megalithic yard = Megalithic Fathom / 2

The question is, is one allowed to do this on statistical grounds!? I would say

Remember that determining the radius is not easy! One has to know where the center of the circle is and this introduces another error.

- Some calculations have been done using the data set of Thom (table 5.1). This data set has been used as the base to calculate the standard deviation (using Monte Carlo analysis) . The following is analyzed:
- The raw data set of Thom is used.
The
standard
deviation has been calculated for every group of circles that were
build
with an equal number of quantum's (blue). (C
_{5.44}~ 1.3). Also a Monte Carlo analyses (the average is taken over 23 runs) is determined assuming an s of 0.33 foot (table 5.1) in the circle diameter (red). (C_{5.44}~ 1.3) - The same distribution of number of quanta in the circle
diameter as above.
The quantum is now the human height (5.40, s=0.095
ft) and it includes an overall variation (b=0,
s=1.15 ft). The behavior of the average standard deviation using
Monte Carlo analysis (dark green) and the average standard deviation of
the raw data (red) are almost same (the averages are taken over 23
runs).
(C
_{5.40}~ 1.1) - If using
a
*standard rod*(5.440, s=0.003 ft) with an overall variation (b=0, s=1.3 ft). The following standard deviation is gotten (light green): (C_{5.44}~ 1.5) - Is the Broadbent method still the best way to deal with periodicy (quantum's) in measurements? Or are there already better methods available?

By using the same data and the Broadbent method (1955, 1956), in the below picture one can see the value C, that determines the likeness of a possible quantum.

There is no real likeness of a quantum at 0.817, but another strange thing is that Thom now does not use the factor two that has been discussed in the above section!

A paper that discusses the megalithic inch (by Alan Davis, paper in
Records
in stone), finds beside 1 MI also quantum's of close to 3 MI and
close
to 5 MI (1% probability level).

He also provides an other idea, supported by me, why 3 MI, 5 MI, 1
MI, 1 MY, etc. could be common:

*Alternatively, one might justifiable argue that the 5 MI quantum
is very close to the mean width of a human hand, and interpret 1 MI as
a mean finger width. It would be extremely difficult, if not
impossible,
to distinguish between these two hypothesis on the basis of present
data.*

I fully agree with this statement!

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