Reassessment of Sites in Northwest Scotland: A New Statistical Approach

Ruggles C. L. N. (principal author), ‘Megalithic astronomy: A new archaeological and statistical study of 300 Western Scottish sites’ (Oxford, 1984).

Some areas are not quite as difficult as others in relation to architectural divisions, e.g. Cairn types in Ireland.

Neave Henry Selkirk Keith , ‘Nearest Neighbour analysis of the distribution of points on a circle’, University of Nottingham Research Report, 1983, 05–83.

Ibid. 05.

Fisher N. I. , Statistical analysis of circular data (Cambridge, 1993), 30–31.

Gerardi concluded that a choice for m ≤ 3 was most appropriate when dealing with the poor signal to noise ratio. In archaeoastronomical terms poor signal to noise ratio can be redefined as specific directions or clusters (signals) being embedded in what appears to be random orientations (noise). Gerardi G. Buccheri R. Sacco B. , Proceedings of COMPSTAT 82 (Vienna, 1982), 111, in Elton S. D. , ‘A search for celestial sources of very high gamma-ray emission using the Cerenkov technique’ (Ph.D. dissertation, University of Adelaide, 1989), 108. Nagel point out that when using m = 2 for your test it will be only marginally less powerful than when using m = 1 (the most powerful m for the detection of broad peaks), yet powerful enough to detect a narrow peak from a uniform background. Nagel D. E. Gaisser T. K. Protheroe R. J. , ‘Extensive air showers associated with discrete astrophysical sources’, Annual review of nuclear and particle science, xxxviii (1988), 609–57. Page 630 discusses the power of the tests in particular.

Elton , op. cit. 108.

Nagel , op. cit., 629–32.

Formula and description taken from Elton , op. cit., Formula 4.19, p. 108.

Statistical scores for the NNT range from 0 to 1. Where 0.5 represents the acceptance of the null hypothesis (that is, the distribution is random), zero (0) and smaller numbers represent clustering or the rejection of the null hypothesis and towards the other end of the spectrum (1) the database is considered to be uniformly distributed.

Ruggles , op. cit. (ref. 1), 59 for site source list; see Table 2.1 for full reference list, pp. 27–42.

Probability levels were not given by Ruggles for insignificant findings.

It has been duly noted by the authors that the number of orientations is different from Ruggles by 1, arising, it seems, from the different n for Mull. Why this was so we have not been able to discover.

Using χ² tables.

See Ruggles , op. cit. (ref. 1), 62–63 for the definitions of the six classes of indications.

Our trials have shown that the test correctly rejected the null hypothesis more often than did the NNT. We are currently in the process of preparing a paper containing a thorough investigation of the relative properties of the NNT and the test.

As the paired orientations indicate the same alignment in opposite directions (e.g. 195° and 15°), due to the absence of definite indicators of the preferred or intended direction, the graph has been designed with a mirroring effect to allow for this.

Elton, op. cit. (ref. 6), Formula 4.16, p. 107.

de Jaeger O. C. , ‘The analysis and interpretation of VHE gamma ray measurements’, Ph.D. dissertation, University of Potchefstroon for Christian Higher Education, 1987.