The use of complicated formulas is limited to the minimum.
Because the errors based on the scatter are NOT quoted errors, I did not use the X^2 test, but the more powerful F-test, based on the combination of the 3 means and 12 independent measurements.
An analysis of variance based on 3 laboratories and 16 measurements will only differ for Arizona : 36587/8 = 4573..4^2/9 = 2323973.1 These small differences may seem of little importance, but it is one more indication of a "biased" assessment, with the only purpose of a systematic enlargement of the error range.
The same goes for the estimation of the error for the Shroud from the scatter.
The X^2 test shows that it is UNLIKELY, that the quoted errors FULLY reflect the overall scatter.The EIGHT "dependent" dates were combined in FOUR "independent dates, given in Table 1 ( Yet mathematically correct, this "re-calculation" should have been notified by the authors of the report. It took more than TWO years before Arizona confirmed the combination made at the request of the British Museum. The method is based on the QUOTED error for each measurement.The arbitrary "enlarging" of the error from 17 to 31 was never solved. Quoted errors do incorporate the statistical (counting) error, the error of the scatter of results for standard and blanks, and the (small) uncertainty in the delta 13C determination.Analysis of variance : The multiplying factor for d=10 and 97.5% confidence = 2.23.(This is for a two tail test and 1 -(2x0,25) = 95 % confidence).