PROCEDURES FOR COMPARING AND COMBINING RADIOCARBON AGE DETERMINATIONS: A CRITIQUE

All but one set of 14C measurements on identical tree-rings were compatible with the assumption of representing the same 14C age within 95% probability limits, and were considered as weighted average values.

“All but one set of 14C measurements on identical tree-rings were compatible with the assumption of representing the same 14C age within 95% probability limits, and were considered as weighted average values [60].”

In all but one case (OxA-30897 & OxA-31521 from MBA relative rings 677-685), the 14C data on identical tree-rings are compatible to be combined as weighted averages to give the best available estimates of the appropriate 14C age.

“In all but one case, OxA-30897 & OxA-31521 from MBA relative rings (RY) 677–685, the data on the identical tree-rings are compatible to be combined as weighted averages to give the best available estimates of the appropriate 14C age [60].”

Raw 14C dates are estimates of the mean of a Normally distributed random variable.

“raw 14 C dates are estimates of the mean of a Normally distributed random variable.”

Multiple measurements on the same sample are naturally scattered over a range of values.

“multiple measurements on the same sample are naturally scattered over a range of values (see Ward and Wilson 1978; Buck 1991).”

The wiggle-match calendar placement of the Hd GOR time series uses the placement with satisfactory OxCal agreement indices after removing the 13 or 14 largest outliers; this places the last year of the chronology RY1,764, with bark (felling date) ~748BCE.

“The wiggle-match calendar placement of the Hd GOR time series22 uses the placement with satisfactory OxCal agreement indices after removing the 13 or 14 largest outliers (SSimple outlier model24 applied to individual dates, dates in weighted averages, and the weighted averages42). The minimum almost satisfactory case removes 13 individual outliers and achieves Amodel ~ 58 and Aoverall ~ 61, while”

The MBA time series initially comprised 76 14C dates, reduced to 40 elements after combining same mid-points; after removing three outliers and one suspect date, the remaining time series contains 72 dates and 39 elements.

“The MBA time series comprises 76 14C dates. After combining dates with the same mid-points the time series contains 40 elements.”

Three samples were pretreated and measured in duplicate and showed excellent agreement.

“Three samples were pretreated and measured in duplicate and showed excellent agreement (GrM-22708 and GrM-22709, χ2 = 0.01 versus 3.8, df = 1; GrM-24031 and GrM-24042, χ2 = 0.89 versus 3.8, df = 1; GrM-30071 and GrM-30094, χ2 = 0.18 versus 3.8, df = 1) [57].”

According to Ward and Wilson (W-W), one may combine data in Case I studies only when the homogeneity hypothesis is accepted.

“According to W-W, one may combine data in Case I studies (those in which a sample is divided and subjected to a series of independent measurements) only when the homogeneity hypothesis is accepted.”

Dates run on identical sample material were combined using the OxCal R_Combine function as long as they passed a Chi-square test indicating consistency.

“In cases where dates were run on the identical sample material, these were combined using the OxCal R_Combine function as long as they passed a Chi-square test indicating the measurements were consistent with this assumption [132].”

The 28-date set (set 2) of 14C measurements on short-lived sample matter from the Akrotiri volcanic destruction level passes a chi-squared test following Ward and Wilson (1978), with test statistic (7) = 31.5 < 39.9 at the 5% level for df 27.

“The 28-date set (set 2) of 1 4 C measurements on short-lived sample matter from the Akrotiri volcanic destruction level (VDL) employed in the Manning et al. (2006) study passes a chi-squared (χ2) test following the Ward and Wilson (1978) approach with a test statistic (7) = 31.5< 39.9 at 5% level for df27.”