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False Positive Risk for Spatial Analysis

Authors: Jamison Conley*, West Virginia University
Topics: Quantitative Methods, Spatial Analysis & Modeling
Keywords: False Positive Risk, Spatial Statistics, Spatial Autocorrelation, p-value
Session Type: Paper
Presentation File: No File Uploaded

The discipline of statistics is currently rocked by concerns about the validity of null hypothesis significance testing using p-values. Highlighting this discussion, a recent special issue of The American Statistician devoted to “Moving to a world beyond ‘p < 0.05’” contained suggestions of how to improve the practice of statistics to avoid the misuse and abuse of p-values which prompted these concerns. Several proposals were made, one of which is to report the False Positive Risk (FPR) in addition to the p-value. (Colquhoun 2019) The FPR represents a quantity often misattributed to the p-value: the probability that the observed results were due to random chance.

This discussion of the flaws of using p-values, however, has yet to substantially influence the practice of spatial analysis. To influence this practice, this presentation applies the FPR to spatial autocorrelation statistics, both global (Moran’s I) and local (LISA). Examples are given with both simulated data and U.S. election results, to illustrate the impact of sample size and the strength of spatial autocorrelation on FPR, and to provide examples with real data. The primary obstacle to the implementation of a spatial FPR is that a prior probability of the effect being studied, in this case, whether the data are spatially autocorrelated, must be given, although this is rarely known. Following the recommendation of Colquhoun, a prior probability of 0.5 is presented for these results, although the impacts of this prior probability are as substantial as the effects of sample size.

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