Making the Most of Radiocarbon Dating: Some Statistical Considerations
Buck, C. E., Litton, C. D., Scott, E. M., Antiquity
The revised radiocarbon calibration curve, published last year, extends back into the Pleistocene the radiocarbon determinations that can be converted to real calendar years. For determinations of any age, the right judgements and statistical considerations must be followed if the real information held in the determinations is to be found. Here is advice with some worked examples.
Over the last decade the high-precision calibration curve for radiocarbon dating has been completed and revised (Pearson & Stuiver 1986; Stuiver & Pearson 1986; Pearson et al. 1986; Stuiver & Reimer 1993), yet aspirations to precise assessments about dates for many archaeological applications have not been realized. There are two major reasons. Firstly, the calibration curve has changes of slope and, more importantly, significant inversions (or wiggles) which result in a radiocarbon result (even if there were no measurement error) corresponding to more than one calendar date. In addition, the curve has a number of regions with a low gradient (i.e. it is almost flat) where even a high-precision radiocarbon result corresponds to a considerable length of time on the calendar scale. Secondly, radiocarbon results are imprecise; each result has an associated estimate of imprecision (its standard deviation). Typically, this standard deviation ranges from 10 years (for high-precision dating), through intermediate values of 40-50 years, and up to 100-150 years. It represents a best estimate of analytical uncertainty made by the laboratory; its value is a function of sample and laboratory parameters including sample size and counting time. Since concerns have been expressed regarding the meaning of the error and the interlaboratory reproducibility of 14C measurements, the 14C community has undertaken to employ measures to assure the quality of future results, and their comparability (Long & Kalin 1990; Scott et al. 1992).
In this paper we look at a number of issues that relate to maximizing the information gained from radiocarbon dating. First and foremost, we feel that archaeologists should always, whatever the purpose of their radiocarbon dating, bear two practical points in mind.
1 The interpretation of calibrated dates depends both on the accuracy and on the precision of the results supplied by the laboratories. Accuracy can be affected by three main sources of error:
a The quality of care of the archaeological sampling, ensuring that the organic samples do relate to the events we wish to date (Bowman 1990: chapter 5).
b The quality of care in taking and handling the samples on site in order to avoid contamination with older or younger material (Bowman 1990: 27-8).
c The quality of care in sample handling and preparation in the laboratory to ensure samples undergo appropriate pre-treatment and avoid contamination before analysis (Bowman 1990: 28-30).
Precision, as measured by the quoted standard deviation and determined by the laboratory, is based on the counting error (due to the random nature of radioactive disintegration detected in the counter for sample, background and modern standard); it includes further small contributions from chemical fractionation, quenching and environmental conditions within the laboratory. In addition, a laboratory will generally have undertaken replicate analyses of a secondary standard as experimental justification of the quoted standard deviation.
2 The making of archaeological inferences using radiocarbon results is commonly more complex than it appears and consequently it is advantageous to view it in three stages.
a Definition of the archaeological question in a quantitative manner, if necessary including development of mathematical models to relate events to one another.
b Design of the sampling framework, considering the archaeological questions posed, the size of the budget and the interplay with radiocarbon precision. …