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As we pointed out in these two articles, radiometric dates are based on known rates of radioactivity, a phenomenon that is rooted in fundamental laws of physics and follows simple mathematical formulas.
Dating schemes based on rates of radioactivity have been refined and scrutinized for several decades.
Several hundred laboratories around the world are active in radiometric dating.
The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
Other objections raised by creationists are addressed in [Dalrymple2006a].
The overall reliability of radiometric dating was addressed in some detail in a recent book by Brent Dalrymple, a premier expert in the field. 80-81]: These methods provide valid age data in most instances, although there is a small percentage of instances in which even these generally reliable methods yield incorrect results.
A recent survey of the rubidium-strontium method found only about 30 cases, out of tens of thousands of published results, where a date determined using the proper procedures was subsequently found to be in error.