Testing Hypotheses When You Have More Than a Few*

A common issue faced by spatial analysts is that of multiple testing. When hypotheses are tested at multiple points in time or space, care must often be taken to avoid results containing too many false positives. There are many ways to address this outcome, and these are reviewed in this article. We begin with a review of some of the basic, longstanding approaches to multiple testing. This is followed by a summary of the more recent objective of controlling the false discovery rate and the effects of spatial autocorrelation on it. The number of true null hypotheses is an important quantity, and some approaches to its estimation are reviewed. In the literature on spatial analysis, there have been several newer approaches to multiple testing, and these are also reviewed. These include some recent methods outside of the literature in geography, but they have potential applicability for many of the problems addressed by geographers, especially since they focus upon the discovery of clusters. The article includes an illustration and closes with some ideas for taking further steps in treating multiple hypotheses in the context of methods commonly used in geographical analysis.