One may wonder why, the British Museum, did not use the X^2 test for each laboratory.
X^2 test for Arizona (For 4-1 degrees of freedom X^2 = The X^2 test indicates INCONSISTENCY for Arizona and the Mean.
AMS date for 1 run are the mean of about 10 measurements and assuming that the quoted error is equal to the standard error, given in This test indicates that the Arizona date 591- 30 is probably an OUTLIER.The reason for a statistical analysis of radiocarbon dates, is the FACT that, theoretically, no experimental result is absolute, and to some extent, subject to chance error. The British Museum, selected the Chi^2 to be the criterion for the assessment of the radiocarbon dating results for the Shroud.Even an EXACT measurement is still due, to some extent, to chance. The MAXIMUM Chi^2 test value for 95% confidence and (3-1) degrees of freedom is 5.99.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.
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.