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.
147] has highlighted the fact that measurements of specimens from a 1801 lava flow near a volcano in Hualalai, Hawaii gave apparent ages (using the Potassium-Argon method) ranging from 160 million to 2.96 billion years, citing a 1968 study [Funkhouser1968].
In the particular case that Morris highlighted, the lava flow was unusual because it included numerous xenoliths (typically consisting of olivine, an iron-magnesium silicate material) that are foreign to the lava, having been carried from deep within the earth but not completely melted in the lava.
The latest high-tech equipment permits reliable results to be obtained even with microscopic samples.
We scientists who measure isotope ages do not rely entirely on the error estimates and the self-checking features of age diagnostic diagrams to evaluate the accuracy of radiometric ages.
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.
The isochron techniques are partly based on this principle.
The use of different dating methods on the same rock is an excellent way to check the accuracy of age results.