Investigating classical χ² test methods for high-precision calibration of radiocarbon measurements

Sudden annual rises in radiocarbon concentration have proven to be valuable assets for achieving exact-year calibration of radiocarbon measurements. These extremely precise calibrations have usually been obtained through the use of classical χ² tests in conjunction with a local calibration curve of single-year resolution encompassing a rapid change in radiocarbon levels. As the latest Northern Hemisphere calibration curve, IntCal20, exhibits single-year resolution over the last 5000 years, in this study we investigate the possibility of performing calibration of radiocarbon dates using the classical χ² test and achieving high-precision dating more extensively, examining scenarios without the aid of such abrupt changes in radiocarbon concentration. In order to perform a broad analysis, we simulated 171 sets of radiocarbon measurements over the last two millennia, with different set lengths and sample spacings, and tested the effectiveness of the χ² test compared to the most commonly used Bayesian wiggle-matching technique for temporally ordered sequences of samples such as tree-rings sequences, the OxCal D_Sequence. The D_Sequence always produces a date range, albeit in certain cases very narrow; the χ² test proves to be a viable alternative to Bayesian wiggle-matching, as it achieves calibrations of comparable precision, providing also a highest-likelihood estimate within the uncertainty range.