Too good to be true: Underdispersion in geochronology

Abstract. Statistical hypothesis testing is widely used in geochronology to assess whether multiple analyses of a sample are consistent with a single age. Failure of such tests is evidence for excess scatter ('overdispersion'), suggesting geological complexity or faulty data. In contrast, this paper highlights the opposite and largely overlooked problem of 'underdispersion', in which datasets agree unrealistically well with the null hypothesis and appear "too good to be true". Underdispersion can arise from incorrect propagation of analytical uncertainties or from over-zealous outlier rejection that inflates p-values and suppresses genuine geological variability. This paper introduces a simple graphical diagnostic for identifying systematic underdispersion across collections of geochronological studies, based on the empirical cumulative distribution of p-values from chi-squared tests of data homogeneity. While overdispersion shifts p-value distributions above and to the left of the 1:1 line in cumulative probability space, there are no natural mechanisms that should produce an excess of very high p-values. The area below the 1:1 line in a cumulative probability plot defines a 'forbidden zone' and provides a meta-analytical signature of underdispersion.The proposed method is demonstrated using synthetic examples and applied to extensive compilations of published geochronological data, including fission-track analyses, mass-spectrometer-based chronometers reported in high-profile journals, datasets underlying the geologic time scale, and detrital zircon U–Pb age spectra. These case studies reveal widespread and sometimes extreme underdispersion, particularly in fission-track data and 40Ar/39Ar age plateaux, at levels that cannot be explained by chance alone. Underdispersion matters because it creates unwarranted confidence in apparently precise ages at the expense of accuracy and obscures meaningful geological information carried by excess scatter. The diagnostic plot introduced here provides a practical step towards recognising when data have been over-processed, and towards restoring a more balanced treatment of dispersion in geochronology.