Resolution power of radiocarbon dating method
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Adam Walanus

The wiggled shape of the radiocarbon calibration curve, do influence the resolving power of radiocarbon concentration measurements. Two samples of given true (expected, unknown) age, for example, 1865AD and 1900AD, can give statistically different radiocarbon ages only in case of very precise measurements. The pair 1380AD 1445AD, however, will be resolved in any case. The decisive here is the value of difference between the radiocarbon ages for the two calendar ages considered.

**The figure below gives these age differences in form of five shades**, and white color for almost no difference.

The five boundaries are as follow: **25, 50, 100, 200, and 400 radiocarbon years**.

Therefore, in case of the firs shade the radiocarbon age difference for two samples is in between 25 and 50yr. Assuming the value of 35yr, in the middle of that area, the measurement error σ need to be about 12yr, to give the significant difference between two measurements, at the standard significance level α=0.05 (2σ). In fact, the errors of both measurements should be even smaller since the error of the calibration curve has not been taken into account in the given below map construction.

The general rule for calculation of radiocarbon ages difference is connected with the errors summing formula (square root of sum of squares), and 2σ distance necessary to achieve p-value at least equal to 0.05. As a result, **the difference between the radiocarbon ages need to be at lest 2.8σ** (or simply 3σ), where σ is the measurement error (assumed to be the same for both samples).

IntCal09 was used for generation of the map below. The time step is as in the calibration data.