Testing for Regional Differences in Means: Distinguishing Inherent from Spurious Spatial Autocorrelation by Restricted Randomization

Abstract

Tests for differences among regional means are typically carried out by analysis of variance (ANOVA). When such data are spatially autocorrelated (SA), the assumptions of ANOVA are not met, giving rise to excessive type I error rates. Two spatially adjusted ANOVA methods, Griffith's and COCOPAN, have been proposed to overcome this problem. In this study we show, by means of extensive simulations, the magnitude of the error rates introduced by SA induced in isolation‐by‐distance models typical of those used in population genetics. For data suspected of exhibiting such SA, we propose a strategy for distinguishing between inherent SA, generated within the data by a contagious process, and spurious SA, introduced by regional differences in means. The approach adopted is that of restricted randomization of distance matrices. We also furnish error rates and power estimates for both Griffith's method and COCOPAN. In addition to the simulated data, the methods are applied to an actual example from plant population biology.