ANOVA for Metric Spaces, with Applications to Spatial Data

We give a review of some recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is derived from the classic Levene's test for detecting differences in dispersion. It uses only pairwise distances of data points and can be computed quickly and precisely in situations where the computation of barycenters ("generalized means") in the data space is slow, only by approximation or even infeasible. It also satisfies asymptotic normality. We discuss the relative merits of the various procedures based on simulation studies for spatial point patterns and image data in a 1-way ANOVA setting. As applications, we perform 1- and 2-way ANOVAs on a data set of bubbles in a mineral flotation process and a data set of local pest counts in Madrid.