Statistical comparisons of sediment particle size distributions

Particle size distributions of marine sediments are key factors affecting biodiversity. It is, therefore, often important to make statistical comparisons between groups of distributions to assess whether natural or anthropogenic impacts have changed sediment composition over time or spatial area. We derive two new metrics to measure particle size distributions. One, Difference in Means, is a general index that can be used to compare groups of reference and test samples. The second, the Unusual Index, was specifically developed to compare a single test distribution with a set of reference distributions, although its use can be extended for when there are multiple test distributions. These two indices, along with more established measures, are embedded in a randomisation procedure to assess statistical significance of differences between test and reference distributions. A statistical power study to assess the ability of the new and established metrics to detect change shows that simple summary statistics such as the mean, standard deviation and 10th percentile can have high power under some change scenarios but can fail badly in others. The Difference in Means approach, along with the established ANOSIM method, has consistently high power under all scenarios. The Unusual Index does not have such high power as these two approaches. However, the index is shown to provide a clear way to communicate differences between a site and surrounding reference sediment distributions, as illustrated in a case study of Norfolk, U.K., sediments. Overall, our findings and R software provide a methodological framework, and extend the 'statistical toolkit' for comparing particle size distributions.