Statistics of large detrital geochronology datasets

Abstract:

Implementation of quantitative metrics for inter-sample comparison of detrital geochronological data sets has lagged the increase in data set size, and ability to identify sub-populations and quantify their relative proportions. Visual comparison or application of some statistical approaches, particularly the Kolmogorov-Smirnov (KS) test, that initially appeared to provide a simple way of comparing detrital data sets, may be inadequate to quantify their similarity. We evaluate several proposed metrics by applying them to four large synthetic datasets drawn randomly from a parent dataset, as well as a recently published large empirical dataset consisting of four separate (n = ~1000 each) analyses of the same rock sample. Visual inspection of the cumulative probability density functions (CDF) and relative probability density functions (PDF) confirms an increasingly close correlation between data sets as the number of analyses increases. However, as data set size increases the KS test yields lower mean p-values implying greater confidence that the samples were not drawn from the same parent population and high standard deviations despite minor decreases in the mean difference between sample CDFs. We attribute this to the increasing sensitivity of the KS test when applied to larger data sets, which in turn limits its use for quantitative inter-sample comparison in detrital geochronology.

Proposed alternative metrics, including Similarity, Likeness (complement to Mismatch), and the coefficient of determination (R²) of a cross-plot of PDF quantiles, point to an increasingly close correlation between data sets with increasing size, although they are the most sensitive at different ranges of data set sizes. The Similarity test is most sensitive to variation in data sets with n < 100 and is relatively insensitive to further convergence between larger data sets. The Likeness test reaches 90% of its asymptotic maximum at data set sizes of n = 200. The PDF cross-plot R² value is sensitive across the maximum range of data set sizes, reaching 90% of its maximum at n = 400. These alternatives are easily implemented, provide quantitative comparisons regardless of the relative sample sizes, and, particularly in the case of the PDF cross-plot approach, are sensitive over a large range of data set sizes.