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The Size‐adjusted Critical Region of Moran's I Test Statistics for Spatial Autocorrelation and Its Application to Geographical Areas
Author(s) -
Terui Nobuhiko,
Kikuchi Masayoshi
Publication year - 1994
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1994.tb00321.x
Subject(s) - autocorrelation , spatial analysis , statistic , statistics , sample size determination , test statistic , mathematics , statistical hypothesis testing , spatial dependence , sample (material) , statistical physics , econometrics , physics , thermodynamics
In this article, we explore the expression of the asymptotic approximation of the distribution function of Moran's I test statistic for the check of spatial autocorrelation, and we derive a more accurate critical value, which gives the rejection region similar to significant level α to the order of N −1 (N = sample size). We show that in some cases our procedure effectively finds the significance of positive spatial autocorrelation in the problem testing for the lack of the spatial autocorrelation. Compared with our method, the testing procedure of Cliff and Ord (1971) is clearly ad hoc and should not be applied blindly, as they pointed out. Our procedure is derived from the theory of asymptotic expansion. We numerically analyze four types of county systems with rectangular lattices and three regional areas with irregular lattices.