Counter-Intuitive Effect of Null Hypothesis on Moran’s I Tests Under Heterogenous Populations (Short Paper)

Authors Hayato Nishi , Ikuho Yamada

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Hayato Nishi
  • Graduate School of Social Data Science, Hitotsubashi University, Tokyo, Japan
Ikuho Yamada
  • Center for Spatial Information Science, The University of Tokyo, Japan

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Hayato Nishi and Ikuho Yamada. Counter-Intuitive Effect of Null Hypothesis on Moran’s I Tests Under Heterogenous Populations (Short Paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 56:1-56:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We examine the effect of null hypothesis on spatial autocorrelation tests using Moran’s I statistic. There are two possible variable states that do not exhibit spatial autocorrelation. One is that they have the same average values in all small regions, and the other is that they are not the same, but their variations are spatially random. The second state is less restrictive than the first. Thus, it intuitively appears suitable for the null hypothesis of Moran’s I test. However, we found that it can make false discoveries more frequently than the nominal rate of the test when the first state is the true data generation process.

Subject Classification

ACM Subject Classification
  • Information systems → Geographic information systems
  • Moran’s I statistic
  • spatial autocorrelation
  • spatial heterogeneity
  • false discovery
  • null hypothesis


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  1. Renato M. Assunção and Edna A Reis. A new proposal to adjust Moran’s I for population density. Statistics in Medicine, 18(16):2147-2162, 1999. Google Scholar
  2. Abhranil Das and Wilson S. Geisler. A method to integrate and classify normal distributions. Journal of Vision, 21(10):1, September 2021. Google Scholar
  3. P. A. P. Moran. Notes on Continuous Stochastic Phenomena. Biometrika, 37(1/2):17, June 1950. Google Scholar
  4. Neal Oden. Adjusting Moran’s I for population density. Statistics in Medicine, 14(1):17-26, January 1995. Google Scholar
  5. Michael Tiefelsdorf. Some practical applications of Moran’s I’s exact conditional distribution. Papers in Regional Science, 77(2):101-129, 1998. Google Scholar
  6. Michael Tiefelsdorf. The saddlepoint approximation of Moran’s I’s and local Moran’s Ii’s reference distributions and their numerical evaluation. Geographical Analysis, 34(3):187-206, 2002. Google Scholar
  7. Thomas Waldhör. The spatial autocorrelation coefficient Moran’s I under heteroscedasticity. In Statistics in Medicine, volume 15, pages 887-892, 1996. Google Scholar