Statistical tests for the local spatial variance

The concept of local variance is used in the literature on image processing, and, to a lesser extent, in spatial analyses of local heterogeneity. Ord and Getis' local statistic of heterogeneity (LOSH) is used to test the null hypothesis that the local variance is no different from the variance for the entire study area. LOSH is a ratio of two variances, and it is shown here to also be closely related to the Geary statistic, which measures spatial autocorrelation. In this article, the Brown-Forsythe statistic is proposed as a way to test a similar null hypothesis—namely, that the local spatial variance is no different from that observed elsewhere in the study area. Rejection of the null in favor of significant homogeneity can be interpreted as an indicator of local positive spatial autocorrelation. The merits of the proposed test are illustrated via simulations of both null and alternative hypotheses, and the statistic is used to find local areas of homogeneous values in the classic spatial dataset on wheat yields in Rothamsted, England.