Some Simple Ways to Use Multiple Uncertain Dates to Estimate Intervals

Summary

Sophisticated computer programs are available to make good use of multiple 14C dates, stratigraphic and other additional information, and produce estimates of true dates of intervals in calendar years. However, a rough idea of the likely duration of an interval (in 14C years) to which multiple 14C dates pertain can be obtained by using the equation Î = K[So2– σm2]1/2, where Î is the estimate of the true duration of the interval, So is the sample standard deviation of the set of reported dates, n is the number of reported dates, σm is the average of the reported standard errors of the dates, and K is a constant that depends on one's beliefs about the shape of the probability distribution of samples as a function of their date within the interval. If one thinks that dated objects were generated with roughly equal probability from the beginning to the end of the interval, then an appropriate probability distribution is "rectangular" and K is √12, or about 3.46. If one thinks that relatively few dated objects were generated near the beginning and end of the interval and most were generated near the middle, then an appropriate probability distribution is a truncated Gaussian (Normal) curve, and K will vary, depending upon where the normal curve is truncated. K ranges from about 3.71 for a distribution truncated beyond ±1 standard deviation to 4.55 for ± 2, and 6.08 for ±3. For other culturally plausible cases, K would likely be between 3.46 and 5.00.

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Contact(s): Keith Kintigh

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