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.The best results were obtained by averaging the paired errors. Normal statistical and systematic errors are 0.25 %.
Note that I only verify the assessment of the radiocarbon dating results, NOT the conversion into calendar ages.
All calculations are made on a Sharp PC 4700, using an Ability (Lotus) Spreadsheet. Due to rounding up numbers, small differences may occur.
For non-mathematical minds, all calculations are worked out completely.
The use of complicated formulas is limited to the minimum.
It is unusual for a bivalve colony this size to mostly be dead, raising questions as to what caused their death.
In this study we document the radiocarbon 14C age of these bivalve shells to attempt analysing the possible methane seep bahaviour in the past.
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.
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.
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.
report : The spread of measurements for sample 1 (Shroud) is somewhat greater than would be expected from the errors quoted.
[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.