# Radiocarbon dating analysis

*22-May-2019 10:46*

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).

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.

The number of degrees of freedom (d), lying between (3-1) inter- and (12-3) intra- laboratory degrees of freedom was ESTIMATED at 5.

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.

When applying statistical tests, caution should be observed with data suspected of appreciably differing from a normal distribution. In practice : Any Chi^2 test value LARGER than 5.99, excludes the claimed 95 % confidence.

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.

The best results were obtained by averaging the paired errors. Normal statistical and systematic errors are 0.25 %.

[41 45]/2=43 [51 49]/2=50 [57 59]/2=58 [47 47]/2=47 Error on the mean : [1/(1/43^2 1/50^2 1/58^2 1/47^2)]^0.5 = 24. At first, I believed that the error was due to the fact, that Arizona included the error in delta 13C at a later stage. The total error will be : [0.25^2 0.25^2]^0.5 = 0.356 %. 1/n^2) Error x = [1/(1/a^2 ...1/n^2)]^0.5 Chi^2 = (A-X)^2/a^2 ....(N-x)^2/n^2 Calculations : Arizona : Error = [1/0.0062747]^0.5 = 159.37^0.5 = 12.62 = 13 X^2 test: Maximum 5.99 for 95% confidence and (3-1) degrees of freedom.

A (federally-funded) handling and analysis surcharge applies to small samples (2-9 µmol).