The accuracy of megalithic units of measurement

Much of the controversy surrounding the megalithic yard arose because Alexander Thom claimed a very high degree of precision in its use in prehistoric times. There is a passage in Megalithic Sites in Britain (p.43) which suggests how this conviction first arose. Thom presents the results of his statistical analysis of stone circle diameters in England, and compares it with the result he obtains from stone circles in Scotland. He deduces the value of the megalithic yard to have been 2.719 feet in both cases, and concludes:

'It is evident ... that it is not possible to detect by statistical examination any difference between the values determined from the English and Scottish circles. There must have been a headquarters from which standard rods were sent out ... . The length of the rods in Scotland cannot have differed from that in England by more than 0.03 in or the difference would have shown up ... . If each small community had obtained the length by copying the rod of its neighbour to the south the accumulated error would have been much greater than this.'

It's clear from this that Thom misunderstood the results of the statistical tests he was using. The values he quotes represent the mean values of the unit in England and Scotland, and while these mean values can be established to great accuracy by statistical analysis, we can't deduce from this that they were used with great precision in prehistoric times. For example, suppose we measure the heights of several hundred men in Yorkshire, chosen at random; and then repeat the exercise in Lancashire. If we analyse the result we will find that the mean height of Lancastrians is almost identical to the mean height of Yorkshiremen, even though the heights of individuals will vary considerably.

So it's important to understand that while the mean value of the 'megalithic inch' (if it is real) can be determined very accurately (normally quoted at 2.0725 cm) by statistical analysis, this tells us nothing about the precision with which it was used in prehistory. That must be determined (if it can be determined) by other means. Most of the results of my own work on cup and ring marks are readily explicable in terms of rough measures such as hand- and finger-widths.