Dissimilarity measures in detrital geochronology

The ability to quantify the (dis)similarity between detrital age distributions is an essential aspect of sedimentary provenance studies. This paper reviews three different ways to do this. A first class of dissimilarity measures is based on parametric hypothesis tests such as the t- or chi-square test. These are designed to objectively decide whether two samples were derived from a common population. Appealing though such tests may appear in theory, in practice they offer limited value to sedimentary geologists because their outcome depends on sample size. In contrast, the effect size of said tests is independent of sample size and can be used as an objective point of comparison between detrital age distributions. The main limitation of this approach is that it requires binning or averaging, which discards valuable information. A second class of dissimilarity measures is based on non parametric hypothesis tests such as the Kolmogorov-Smirnov test. These do not require pre-treatment of the data and are able to capture more subtle differences between age distributions. Unfortunately, non-parametric tests do not have well defined sample effect sizes and so it is not possible to use them as an absolute point of comparison that is independent of sample size. Nevertheless, non-parametric dissimilarity measures can be used to quantify the relative differences between samples. A third class of dissimilarity measures aims to account for the analytical uncertainties of the age determinations. The likeness and cross-correlation coefficients are ad-hoc dissimilarity measures that are based on Probability Density Plots (PDPs). These apply a narrow smoothing kernel to precise data, and a wide smoothing kernel to imprecise data. In contrast, the Sircombe-Hazelton L2 norm uses Kernel Functional Estimates (KFE5), which use exactly the opposite strategy as PDPs. They apply a wide smoothing kernel to precise data, and a narrow smoothing kernel to imprecise data. This paper shows that the KFE-based approach produces sensible results, whereas the likeness and cross-correlation methods do not. The added complexity of the KFE approach is only worth the effort in studies that combine data acquired on equipment with hugely variable analytical precision. In most cases, there is no need to account for the analytical uncertainty of detrital age distributions. The sample effect size, non-parametric statistics, or L2-norm can be used to graphically compare samples by Multidimensional Scaling (MDS). In contrast with previous claims, there is no need for these measures to be independent of sample size for this purpose.