The Rational Distribution Hypothesis: Descriptive Statistics
Contrary to the claims or the opinions of archaeologists, the existence of the Megalithic Yard has not been proven to be false by statistical analysis. The two academic papers that sealed its fate, Kendall (1974) and Freeman (1976), are not as emphatic on the matter as some critics choose to assert. Thom presented two sets of data, for England and Wales and for Scotland, which he claimed from analysis introduced by Broadbent (1955, 1956) suggested the presence of a common unit of 5.44 feet (two Megalithic Yards). Kendall and Freeman used more advanced and Bayesian analysis to determine whether such is truly indicated and found insufficient support in Thom’s data for England and Wales. However, this was not the case with the Scottish data. Kendall’s summation is that, “my inclination is to suspect that evidence for the quantum resides in the Scottish data only”, (Kendall, 1974: 255) the emphasis being in the original, and Freeman came to much the same conclusion. However, thereafter, Kendall’s inclination and suspicion were converted into fact. Critics chose to interpret this to mean that there is no evidence of a uniform and common (ubiquitous) unit. This would be a logical conclusion, though based on a potentially false premise. In essence, Kendall had issued a cautionary note that might have led to the matter being left open. However, leading archaeologists of the time chose to close the book on the subject, for example, see Angell (1979) and the pace hypothesis of Porteous (1973, 1977). A Common Unit hypothesis did not fit with the archeological model of the age, and if one or the other had to go then it would be the Megalithic Yard. Baxter (2003) quotes Fieller (1993: 283), “It is a sad fact that the megalithic yard hypothesis is of negligible interest to archaeologists ... From what is known ... the hypothesis is not worth entertaining. It belongs to the semi-mystical fringe of archaeology concerned with ley lines, Atlantis and the like.” Thus was the Megalithic Yard relegated to the realms of pseudoarchaeology. | |||||||||||||||||||||||||||||||||||||||||||
Implications of a Rational Distribution Hypothesis
A key consideration in this work is that the measurement and rational distribution of perimeters has had the effect of introducing the Megalithic Yard into diameters, and the discussion of each ring illustrates how this comes about. Thus, there should be little doubt that, in this form, the Megalithic Yard is present in the data, and subject to error or variance, whether or not it was a unit employed by the builders. It would follow that performing statistical procedures on this data similar to those applied to Thom’s should highlight the impact of the errors on the determination of a quantum, and a model data set created with no errors or variance should illustrate the efficacy of the procedures employed. The overriding question would then be are the perimeters truly rationally divided? Although it appears that there may have been a Bi-Metric system of measurement, both a perimetric and an associated diametric unit co-existing (witness the coppiced pole found at Seahenge), this is not presented as being necessarily the case. The diametric unit will inevitably appear on diameters as a consequence of the perimetric unit whether it was introduced or not. The Megalithic Yard features in the analysis not only because it has previously been mooted by Thom but also being the quantum specified in the null hypothesis here: that a measure of 829mm is supported statistically from the diameters of stone circles in the UK and Republic of Ireland based on the distribution of orthostats on the perimeters. From the analysis to date, derived from surveys of some 300 stone circles in Great Britain and Ireland analysed according to the Rational Distribution Hypothesis, the perimetric unit, assumed to lie at the heart of the system, ranges from 157mm to 168mm with a mean, median and mode of 163mm and a standard deviation of 2mm. As a consequence, were it to have existed as a physical unit, the site Megalithic Yard would tend towards 829.6mm as a median, the data being technically bi-modal at 828mm and 830mm with a mean of 829.1mm overall. As might be appreciated from the histogram at Figure 16, the data is negatively skewed. | |||||||||||||||||||||||||||||||||||||||||||
Figure 16: Histogram for the Length of the Megalithic Yard. |
|||||||||||||||||||||||||||||||||||||||||||
The overall rounded mode spans 828mm (21 cases), 829mm (19) and 830mm (20) being 60 cases from a total of 230. The breakdown by geographical area is as in the following table. | |||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||
The data for Ireland includes only one site located in Northern Ireland where the perimeters of stone circles tend to be composed of contiguous stones. Tables of sites included together with the computed Megalithic Yard are provided at this link. From the analysis, it is envisaged that any sample of stone circle diameters across Britain and Ireland extracted from these tables would produce a mean of about 83cm from the comuted Megalithic Yard.
Therefore, it is difficult to understand why analysis suggested that the Megalithic Yard might be present in the Scottish data but not that for England and Wales where the range here is tighter and the standard deviation lower. However, Thom analysed diameters, pure and simple, whereas this procedure analyses the distribution of orthostats on the perimeters and derives a Megalithic Yard as a consequence. While this form of analysis might demonstrate why the Megalithic Yard appears in stone circle diameters it also suggests that there would be far greater variation in Thom’s unit of measure than he suggests. Davis concludes that a significant proportion of circles were set out to better than 5% accuracy (Davis, 1983; 11). Such variance might explain why so many diameters are not a whole number of Thom’s Megalithic Yard - the unit on the circumference is mathematically linked by π to a smaller unit on the diameter and this can be seen to vary by as much as 3% either side of the mean. In general, diameters might best be expressed in quarters of a Megalithic Yard. This would doubtless improve the apparent fit of Thom’s data. The derived Megalithic Yard ranges from 800mm to 854mm with a standard deviation of some 10mm. Concern over cases at the extremes of the range led to thoughts that the data set might be appreciated in the three statistical divisions. Beyond two standard deviations the unit would be particularly degraded and it may even be possible that there is another unit in use. The Statistical Controversy Burl states that the paper by Freeman, added to that of Kendall, “conclusively disproves the existence of a national yardstick that was used in the design of megalithic rings,” and with such spatial and temporal diversity, “it seems unlikely that an identical quantum should have been known and accepted in all parts of these islands.” However, could archaeologists have made a serious mistake as a result of being too limiting in their investigations, preferring to negate in order to avoid a Type I error rather than putting the matter on hold? |
< Back | ToC | Next> |