FURTHER STATISTICAL METHODS FOR THE CALIBRATION OF FLOATING TREE-RING CHRONOLOGIES

This paper describes the application of some further statistical methods for the calibration of floating treering chronologies to data pertaining to the Neolithic settlement at Auvernier. The more general statistical approach utilizes the information contained in the successive time-derivatives as well as the absolute values of the bristlecone pine calibration curve, by fitting polynomial or piecewise polynomial curves, thereby producing better estimates, in general, of the absolute dates of the floating chronologies. Presentation of results in terms of joint confidence regions enables the relevant stratigraphic evidence to be included in the analysis by simple graphical means. In addition, the paper offers a new approach, using only floating tree-ring chronologies, to the testing of Libby's principle of simultaneity.     

RADIOCARBON MEASUREMENTS ON A FLOATING TREE-RING CHRONOLOGY FROM NORTH-EAST SCOTLAND

Radiocarbon measurements have been performed on a 250 year ‘floating’ tree-ring section recovered from an archaeological site in north-east Scotland. Short term fluctuations in atmospheric concentration appear to be superimposed on a general trend of decreasing ambient ¹⁴Cparallel with tree growth. The most significant finding is the range of dates obtained from the sequence, namely 400 years, since it implies that the error on a single radiocarbon date is considerably greater than at present accepted on the basis of analytical precision alone.     

PROBLEMS OF THE RADIOCARBON CALENDAR AND ITS CALIBRATION

Both the growing body of literature on the tree-ring calibration of radiocarbon dates, and the variety of statistical approaches used, make it appropriate to review the basic principles involved in the construction of a calibration curve. While its ultimate validity is in part a geophysical problem, the appropriate form for the calibration function, given a specific body of data, is a statistical question centering upon the analysis of the measurement errors involved. The relationship between the calibration function and the inverse calibration function is examined, and the shortcomings of the available published calibration curves considered in the light of this examination. It is concluded that there is no reason to doubt the general principles on which the calibration is based, but a need exists for a more critical handling of the measurement data with a statistical treatment of the errors involved. The quality of the data could itself be improved by the use of replicate samples for inter-laboratory projects specifically designed to investigate the magnitude of measurement error.     

DISPERSION DIAGRAMS: A NEW APPROACH TO THE DISPLAY OF CARBON-14 DATES

A statistical approach to the display of sets of ¹⁴C dates is suggested. All available dates of any particular culture are used to calculate the two quartiles and the median dates for it. The ‘dispersion’of the dates is then displayed as a bar showing the extreme dates, the quartiles and the median; thus neither individual dates nor their standard deviations are shown. This ‘dispersion diagram’saves much space when the dates of several cultures are to be displayed. The argument is developed that the inter-quartile range, which does not change very much when new dates become available and are added to the set, is a good index of the time span during which a culture flourished, and this range should normally be quoted rather than the mean, median or extreme dates of the culture. With samples of nine or more it can be shown by the Hypergeometric Distribution that there is a 97% chance of two cultures being different if their inter-quartile ranges just fail to overlap, so that this method of display is useful in assessing the overlap of cultures. The fact that the dispersion diagram contains within it a measure of the statistical uncertainties of the individual estimates and therefore can replace the standard deviation of each individual ¹⁴C date is discussed.     

RADIOCARBON DATES FOR BEESWAX FIGURES IN THE PREHISTORIC ROCK ART OF NORTHERN AUSTRALIA

Accelerator mass spectrometry radiocarbon ages have been taken for a test suite of small samples of material removed from some of the ‘beeswax’art figures found in rock shelters in northern Australia. The results indicate that we can reliably date this unique form of rock art with no noticeable damage. We had not expected to find figures of any great antiquity, and so we were surprised to find that the ages obtained spanned the time period from the recent past to about 4000 BP.