## Statistical Analysis

The need for statistical analysis arises in archaeoastronomy because astronomical patterns we perceive in the archaeological record may have come about purely by chance, or to be more precise, as a result of factors quite unrelated to astronomy. Doubts about intentionality can apply to a whole range of types of evidence concerning ancient astronomy: monuments aligned upon the rising and setting positions of astronomical bodies; displays of sunlight and shadow only visible on rare occasions; groups of monuments placed so that their positions on the ground mimic the shape of a constellation; patterns of tally marks carved on rocks or portable artifacts that include could have functioned as calendars; and so on.

In the formative days of archaeoastronomy in the 1960s to 1980s, statistical analysis was most extensively applied in assessing monumental alignments. Indeed, this approach came to characterize the "green," or European, approach to archaeoastronomy, which focused on prehistoric monuments without the benefit of related historical or written evidence. Broadly speaking, the approach taken was that pioneered by the Scottish engineer Alexander Thom, which was to accumulate data from many alignments and determine the declination of the horizon point "indicated" by each alignment, and then to use statistical methods to determine whether observed declina tion "peaks"—repeated occurrences of particular declinations—were in fact significant. If so, then a consistent astronomical purpose was evident and the question could be asked, which astronomical body the given declination might have corresponded to.

Devising a suitable statistical test is by no means straightforward. Sometimes one can only resort to Monte-Carlo testing, a method by which one generates, for example, randomly oriented sets of monuments in the computer and sees in what proportion of cases they contain at least as many of a particular type of alignment as were found in the "real" data. If the answer is, say, only once in every thousand runs, then one can conclude that the chances of the real data having arisen fortuitously are only one in a thousand; as this probability is so small, it is fair to conclude that the alignments were deliberately intended. However, there are a number of dangers and pitfalls with this method. An obvious one is that the data must be fairly selected. Even leaving out one site simply because it seems to be pointing in a different direction from all the rest (and it is often easy enough to find retrospective reasons for doing this) can badly distort the results and so undermine any statistical conclusions.

A less obvious but more fundamental difficulty relates to the whole nature of hypothesis testing in this way. Many statistical procedures assume that the hypothesis preceded the data, whereas in an archaeological context, a particular interpretation is generally first suggested by the data (or most of it), since archaeologists do not have the opportunity for repeated experiments. The hypothesis that we choose to test may itself be selected from innumerable possibilities. To take an example, it is a well-known though astonishing fact that if twenty-three people are selected randomly, there is an even chance that two of them will have the same birthday. However, if we took such a group, observed that two of them had birthdays (say) on July 27, and on the basis of that chose to assess the chances (test the hypothesis) that two July 27 birthdays could have arisen among the group purely fortuitously, we would obtain the result "highly unlikely." The reason, of course, is that we chose to test the "July 27" hypothesis (rather than any one of 364 others) because the data contained that pattern in the first place. In short, statistical methods must be used with considerable care, especially where they purport to assign significance levels to particular results.

Nowadays there is a much greater reliance on simply displaying the data. If certain trends are strong enough, then their intentionality is obvious, as is the case for the orientations of numerous local groups of later prehistoric tombs and temples in western Europe. Where we need to assess sets of measured declinations, Alexander Thom's method of curvigrams—graphs showing accumulations of probability—seems as good a method of visualizing the likely significance of repeatedly occurring declinations as any. The fair selection of data remains a much more crucial issue.

In recent years archaeoastronomers have begun to recognize the potential of a rather different statistical approach: the Bayesian paradigm. This approach allows one to assess data repeatedly against different "prior" ideas and to take into account background information. It is especially useful where we are trying to integrate different types of evidence, such as historical records.

However, we must look beyond statistical analysis if we wish to do more than establish the intentionality of astronomical alignments or other astronomically related patterns evident in the archaeological record. No amount of statistical analysis can help with the interpretation of their significance and meaning to the people who built and used them.

Alignment Studies; Constellation Maps on the Ground; "Green" Archaeoas-tronomy; Methodology; Orientation; Thom, Alexander (1894-1985).

Prehistoric Tombs and Temples in Europe.

Declination.

Heggie, Douglas, ed. Archaeoastronomy in the Old World, 83-105. Cambridge: Cambridge University Press, 1982.

Iwaniszewski, Stanislaw, Arnold Lebeuf, Andrzej Wiercinski, and Mariusz Ziolkowski, eds. Time and Astronomy at the Meeting of Two Worlds, 497-515. Warsaw: Centrum Studiow Latynoamerykanskich, 1994.

Ruggles, Clive. Megalithic Astronomy: A New Archaeological and Statistical Study of 300 Western Scottish Sites. Oxford: British Archaeological Reports (British Series, 123), 1984.

-. "The General and the Specific," Archaeoastronomy: The Journal of

Astronomy in Culture 15 (2000), 151-177.

-. Astronomy in Prehistoric Britain and Ireland, 159-162. New

Haven: Yale University Press, 1999.

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