From this test, one may conclude, that the probability of obtaining, by chance alone, a scatter as high as that observed for the Shroud, is only 13 in 1000.Because we assume all *radiocarbon* dates to be correct, we must conclude, that the SMALL samples, taken at the same place, do not have the same radioactivity and are not REPRESENTATIVE for the Shroud.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.Here one "forgets" that quoted **errors** in AMS are deviated from NBS standards and blanks, measured during the SAME run with a series of targets, from the Shroud.Note that for samples 2, 3 and 4, the limits were obtained in the usual way.First I reworked the data given in Tables 1 & 2, using the classical statistical analyzing method, based on the "Central Limit Theorem." I used the method given in "Perry's Chemical Engineer's Handbook", my technical bible for many years.

Hoel (University of California) is : "In the case of a X^2 test value close to the limit, it is better not to use such dates in further calculations, but to ask for more and better dates." Despite the use of the NBS standard (Oxalic Acid Standard SRM 4990) the results for the **radiocarbon** **dating** of the Shroud show a SYSTEMATIC BIAS and UNEXPLAINED VARIABILITY.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.report : The spread of measurements for sample 1 (Shroud) is somewhat greater than would be expected from the *errors* quoted.The X^2 test shows that it is UNLIKELY, that the quoted **errors** FULLY reflect the overall scatter.

Hoel (University of California) is : "In the case of a X^2 test value close to the limit, it is better not to use such dates in further calculations, but to ask for more and better dates." Despite the use of the NBS standard (Oxalic Acid Standard SRM 4990) the results for the **radiocarbon** **dating** of the Shroud show a SYSTEMATIC BIAS and UNEXPLAINED VARIABILITY.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.report : The spread of measurements for sample 1 (Shroud) is somewhat greater than would be expected from the *errors* quoted.The X^2 test shows that it is UNLIKELY, that the quoted **errors** FULLY reflect the overall scatter.For 95% confidence, and (3-1) - (12-3) degrees of freedom the maximum F-test, value is 4.26. , a certain amount of unexplained variation of the individual runs within and between laboratories is indicated. The t test compares the sub mean - error to the final mean.