Not noted is, that a Chi^2 test value 5.99 DOES EXCLUDE the claimed 95 % confidence.In such cases, one should verify and reject possible "outliers." Possible "outliers" are the Arizona dates 591 and 606, and the Oxford date 795.
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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).
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.
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.
This can be illustrated by the Chi^2 and the significance level, given in table 2 ( COMMENT : The advice of Prof.
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.
Finally, it was decided to REPLACE the weighted mean 689- 16 by the UNWEIGHTED mean 691- 31 and to ENLARGE the multiplying factor 1.96 to 2.6, based on an analysis of variance on the 12 individual measurements.