New statistical methods for the comparison and characterisation of particle shape

This paper presents novel methods for robust statistical testing of particle shape data. Shape (the relative lengths of three orthogonal axes) is a key property of sedimentary particles, providing information on provenance, transport history and depositional environment. However, the usefulness of shape data, including the ability to make robust comparisons between samples, has been constrained by the absence of a satisfactory definition of the mean shape for a sample of particles. Such a definition is proposed and used to develop confidence regions for the population mean shape using both parametric (theoretical) and computational (bootstrap) methods. These techniques are based on a transform that permits multivariate statistical methods for the analysis of compositional data to be extended to shape. These techniques are validated with reference to a dataset of 169 clast samples and found to perform well. A statistical test on the mean – using the multivariate extension of Student's t‐test, Hotelling's T2 – is presented. The benefits of the methods presented are demonstrated with reference to a case study