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.
Note that I only verify the assessment of the radiocarbon dating results, NOT the conversion into calendar ages.
Statistical analysis enables the analyst, to determine, with a pre-determined degree of confidence, (here claimed to be at least 95% ) the degree of variations which are due to chance and to known and unknown influences. Theoretically, if the calculated Chi^2 test value could have occurred only by chance, with a probability LESS than that selected, then the set of data would be considered as being DIFFERENT.The laboratory has over 30 years of experience in the application of radiocarbon dating and associated research and is happy to help with all aspects of the radiocarbon dating process from project design to calibration and statistical analysis.This enables the best use to be made of the radiocarbon technique.In all cases we encourage a collaborative approach to dating projects where we work together with users of the facility to answer the relevant research questions.In particular ORAU routinely undertakes: ORAU is happy to perform dating analyses for archaeologists; environmental scientists, biologists or anyone else interested in determining the radiocarbon content of material.