The descriptive statistics presented above are effectively based upon the assumption that the Megalithic Yard exists as a consequence of a unit present on the circumferences of stone circles. It might reasonably be argued, therefore, that it emerges here because it is assumed to be present.
The procedure does not determine a quantum, but may provide an explanation as to why the Megalithic Yard appears in analyses of stone circle diameters, and nor does it demonstrate that the unit actually exists. It is perhaps more accurate to suggest that should the Megalithic Yard be present in the data as a consequence of rationally distributed perimeters, as described, then it would have a mean of 829.1mm based on the surveys given. It would follow that any sub-sample of the appended data set of computed Megalithic Yards with H0: μ = 829mm should result in very few rejections, though not making it right.
The existence of the perimetric unit that generates the assumed diametric unit (a component of the Megalithic Yard) has not been demonstrated statistically here or elsewhere. The preceding presentation is descriptive rather than analytical. In particular, there is the prevailing view of archaeologists that the placing of orthostats on perimeters is effectively unmeasured. This being so, the Megalithic Yard as derived here, and as illustrated, must be a consequence of chance if not data manipulation.
Professor Douglas Heggie presents a summary of the debate concerning claims of statistical support for the unit (Heggie, 1981: 32-59). He concludes that there is insufficient support for a unit as precise as claimed by Thom. Also touched upon is the problem of small unit analysis and an observation on clustering suggesting that stone circle diameters may be the result of a mix of random values and approximations to another value.
The main debate concerns statistical confidence levels, a topic not addressed above. It is therefore difficult to see how the observations made here concerning perimeters might affect the assessment, because the suggested presence of a different unit and the rational distribution of orthostats combined with pattern and balance are entirely new considerations. It could be that a Bayesian approach to the additional requirement might have some impact on confidence levels.
It is hoped that the problem of the small unit might be reduced given the incidence of diameters made up of multiples of the proposed unit mostly involving lengths in excess of 2.5 metres. For example, at Barbrook NE, for the hypothesis to hold true, the diameter would have to be a multiple of a considerable 8.7 metres - which it is. In this context, diametric analysis never involves small lengths.
There is also the possibility that statistical analysis might be able to check the distribution of stones as a match to the suggested rational perimetric divisions, but most importantly to check for the regularity of key points on balanced Axial Frames.
The greatest criticisms of this work are sure to be claims of coincidence, selectivity and approximation. However, one advantage of such objections would be that because the Megalithic Yard is demonstrably present in the data, even if introduced or appearing by coincidence, then the statistical procedures of Kendall and Freeman should clearly and convincingly demonstrate the fact using the data presented here. Otherwise, there might be a weakness in the procedures perhaps influenced by the range of values and the observed variance about the mean.
Assuming that the unit did exist, the variance in the perceived length may have resulted from its size having been described in terms of body measure such as eight hands or thirty-two thumbs, such being applied when immediate access to the unit as implemented at a major site was not possible.
It might be assumed that a pure data set resulting from dividing the given diametric measures by 16 and multiplying by 829mm must demonstrate that the Megalithic Yard is present, not least because of the likely criticism that it has been introduced. If it has been introduced then it is obviously present.
As the process described demonstrates how the Megalithic Yard might be drawn out of the data, and that the imputed unit has a mean equal to that suggested by Thom, this may well be why the Megalithic Yard emerged as a quantum. Thus, the presence of the Megalithic Yard might be inferred from the data whether it existed or not. However, the significance and impact on analysis of the perceived variance, or tolerance, would need to be evaluated.
It might be anticipated that the entire work would need to be reassessed using professional surveys as a base. Some of these may need to be updated as a consequence of recent restorations and many might profit from the addition of stone locations as determined from excavation reports.
A consistent method of stating diameters would be advantageous, perhaps measuring through the centres of the stones, as might also confirmation of the correct orientation and alignment to true north. It is possible that the diameters from some older surveys may have been rounded to whole numbers of feet.
It would be undesirable to permit the current model of the megalithic age to dictate the answer to the research question. Some may feel that, despite the spread of stone axes, Grooved Ware, Beaker ware and funerary practices, a common unit could not have been disseminated across such a vast and disparate area.
In this case, the earliest use of the measure in this work being Stonehenge Phase 1 (and potentially sites at Brú na Bóinne), consideration might be given to the possibility that the unit may have been carried by early colonists and settlers.
R.J. Atkinson (1986)
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