STATISTICAL ANALYSIS OR DUST IN THE EYES?


These tables present the results of all the supposedly "individual" measurements performed in each of the laboratories. The vertical axis: radiocarbon age, in number of years before 1950 (BP: before present); the horizontal axis: the years corresponding to the calendar or "calendar age", in number of years after Jesus Christ. The conversion of radiocarbon age into calendar age, or "calibration", is provided by the intersection of each of the measurements with a calibration curve established by dendrochronology.

A simple glance at each of these tables (figures 22, 23, 24) indicates why Oxford (figure 24) creates a "separate band" on figure 8, as a straggler of flight no 1:

Oxford provides an average radiocarbon age of 750 years ± 30 years, which corresponds to the 1260-1274 age range with a 68% degree of probability, enlarged to 1229-1280 with a 95 % degree of probability. Figure 25 shows the gap between these results and those of Arizona. The whole question is to know whether this gap is normal, statistically, that is to say, whether it corresponds to the Laplace-Gauss law, the classical law of errors performed on large samples, provided the observations are made independently.

To answer this question, not by guess work but scientifically, there exists a test known as x2. Applied to the results of the three laboratories for sample 1, it shows that these results come from measurements which are not the effects of one and the same normal law. Therefore, the three samples Al, 01 and Z1 do not form a homogeneous group from a statistical point of view. That is simple mathematics. Especially as when applied to the other samples 2, 3 and 4, the answer given by the x2 is positive, with no possible hesitation: samples A2, 02 and Z2 are taken from the same cloth. Likewise for samples 3 and 4. That can be seen with the naked eye on our figure 8.

Calibration made by Zurich

Figure 22: Calibration of individual averages of sample 1 supplied by Zurich (cf. table 1 in Nature).

Calibrations made by Arizona and Oxford

Figure 23: Calibration of individual averages of sample 1 supplied by Arizona. (cf. table 1 in Nature).

Figure 24: Calibration of individual averages of sample 1 supplied by Oxford (cf. table 1 in Nature).

 

Combined calibrations of the three laboratories
Figure 25: Extract from the Stuiver and Pearson curve (cf. reference 5 and figure 2 of Nature) for the period covering the 13th-14th and 15th centuries, and calibration of the sixteen radiocarbon dates supplied by the three laboratories. There is a slight uncertainty associated with the calibration curve itself, in certain places estimated at a deviation of up to ± 20 years, illustrated by the two curves surrounding the mean curve. A noticeable peak appears in the 14th century, corresponding to carbon ages 576-639 BP (or 1330-1370 AD), revealing that the isotopic radioactive 14C content of the atmosphere’s carbonic gas suffered a perceptible decrease as a result of some natural phenomenon affecting the cosmic radiation at this period. This disturbance complicates the interpretation of radiocarbon ages as calendar dates, shown by the fact that Arizona’s results hesitate between two ranges: 13th-14th and 14th-15th centuries. Notice how Oxford’s results come down in favour of the 13th century avoiding all intersection with this peak and thereby breaking with the calendar ranges defined by Arizona.