Statistical aspects of equivalent dose and error calculation and display in OSL dating: an overview and some recommendations
All Quaternary dating methods involve the measurement of one or more variables to estimate the age of a sample. Each measured quantity has an associated error and uncertainty, and may also be subject to natural variation. We review the statistical estimation of such uncertainties and variation for comparing and interpreting age estimates, with specific reference to the estimation of equivalent dose (De) values in the optically stimulated luminescence (OSL) dating of sediments. We discuss statistical aspects of OSL signal and background estimation, the determination of De values for multi-grain aliquots and individual mineral grains from the same and different samples, and the extent of variation commonly observed among such estimates. Examples are drawn from geological and archaeological contexts. We discuss the strengths and weaknesses of various graphical methods of displaying multiple, independent estimates of De, along with statistical tests and models to compare and appropriately combine them. Many of our recommendations are applicable also to the clear presentation of data obtained using other Quaternary dating methods. We encourage the use of models and methods that are based on well established statistical principles and, ideally, are validated by appropriate numerical simulations; and we discourage the adoption of ad hoc methods developed using a particular set of measurement conditions and tested on a limited number of samples, as these may not be applicable more generally. We emphasise that the choice of statistical models should not be made solely on statistical grounds (or arbitrary rules) but should take into account the broader scientific context of each sample and any additional pertinent information.