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Posted by / 27-Apr-2019 14:01

Radiocarbon dating analysis

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.

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 D13C error can be estimated : 31 = [28^2 (D13C)^2]^0.5 D13C = [961 - 784]^0.5 = 13. The British Museum gave several versions, but no specific answer was given........ Leese explained also that the British Museum did not use the classical method, but a NEW method, developed by the Australian scientists Drs. Note : It seems a little strange, that in the W & W method, the LARGER the errors, the BETTER the CHI^2 test will become. [(646-672)^2/17^2] [(749-672)^2/31^2] (676-672)^2/24^2] = 8.43 The computer, with NO ROUNDING OFF of the values, will give X^2 = 8.76 5.99 states that there is a SIGNIFICANT DIFFERENCE between the results of the 3 laboratories.

Formula W & W : Consider a number of measurements - errors : A- a........ From the X^2 test result, one can determinate the % significance level : 2.718^-(8.43/2) = 1.3 %.

Analysis of variance : The multiplying factor for d=10 and 97.5% confidence = 2.23.

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 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.

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.

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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.

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