Estimating the error in equivalent dose values obtained from SAR

Abstract

Central to all aspects of application of SAR (SingleAliquot-Regenerative-dose) procedures to dating is the accurate estimation of errors in equivalent dose values (De). Some approximation approaches have been outlined by others. Here a more rigorous approach is outlined that incorporates the contributions to the total error in De from not only error in L0/T0 (undosed and unbleached ratio) and the contribution from the scatter of data about the best-fit curve, but also contributions from errors in the bestfit regression parameters and from their covariances. Unequal weighting of data points is included. Algorithms and procedures are detailed for two [saturating exponential (E), and saturating exponential-plus-linear (E+L)] of the 4 most common dose-response models [which include linear (L) and quadratic (Q)]. Computed De values and errors are compared for 6 new and three previously published data sets, using the approach of this paper and two of the approaches of Duller (2007). Differences in De and its error estimate from these comparisons are often, but not always, small and insignificant, thus indicating that errors in best-fit parameters and their covariances make a small contribution to total error in De in most situations. One example data set evaluates the effects of dose-point spacing on the estimated De error.