Quantifying change in distributions: a new departure index that detects, measures and describes change in distributions from population structures, size-classes and other ordered data

Abstract

Many statistics are available to compare distributions. Some are limited to nominal data while others, such as skew, Kullback-Leibler, Kolmogorov-Smirnov and the Gini coefficient, are useful for providing information about ordered distributions. While many of these tests are useful for determining properties of data in histograms, there has not been a test until now that allows for the detection of differences between distributions, describes the difference and is sensitive to the location of the departures. Such a test could be critical for comparing pre-and post-event distributions, such as a change in the distribution of biomass due to fire, for example, or for comparing data from different locations, such as soil size distributions, and even for evaluating economic disparity or examining differences in age demographics. We present a new statistic, a departure index, which allows a test distribution to be compared with any reference distribution. The resulting index contains information about the location, magnitude and direction of departure from the reference distribution to the test distribution. The departure index in turn provides a standardized response range that allows for a comparison of results from different analyses. A case study of actual fire data demonstrates the sensitivity and range of the test.