COMMUNICATING THE MEANING OF GEOCHRONOLOGIC AGE UNCERTAINTIES TO NON-SPECIALISTS

A hypothetical granite sample is dated at 544 ± 5 Ma and a nearby rhyolite at 540 ± 3 Ma. Are the two rocks the same age or are their ages different? The two ages overlap within their uncertainties. If they are the same age then are they Precambrian or Paleozoic? On the other hand, their most probable ages are separated by four million years – a long time by just about any standard. Is it uniformly likely that the true age of the granite might be anywhere within the range 539-549 Ma? The answers to these questions lie in understanding the meaning of the number following the ± sign.

The ± 5 and ± 3 represent either 95% (2-sigma) or 68% (1-sigma) of the area under a probability curve (which here we will assume to be a Gaussian or normal distribution curve). Ages with large uncertainties have short, flat probability curves and ages with small uncertainties have tall, narrow probability curves. This curve is sometimes misunderstood as the probability that any given age is the true age. It is not. It represents the probability that any given result would be obtained if the experiment were repeated a large number of times.

Precision is the fractional uncertainty of all the quantifiable sources of error propagated through all of the age calculation mathematics; for the granite 5/544x100 = 0.92% precision. Accuracy is the percentage difference between the measured age and the true age. Because we do not know the true age, accuracy is difficult to evaluate. Precise ages (small uncertainties) may sometimes be inaccurate (wrong). Age uncertainties, therefore, can be thought of more as a measure of the reproducibility of the analytical method than as the limits on the true age. Reliable analytical methods have a long track record of precise, reproducible, and geologically sensible results and are commonly deemed most likely to yield accurate ages.

So are 544 ± 5 Ma and 540 ± 3 Ma the same age or different? The answer is neither – it can only be said that if the dating experiments were to be repeated a large number of times, then a certain percentage of the results would fall within any arbitrarily defined age range. While this may not seem a very satisfying answer it resolves the types of dilemmas posed above and leads to a better understanding of the meaning of uncertainties in geochronology.