Moran's I Spatial Autocorrelation Test
Also known as: global Moran's I, spatial autocorrelation test, Moran's I Uzamsal Otokorelasyon Testi
Moran's I is a global statistic, introduced by Patrick Moran in 1950, that measures whether and how a continuous variable is spatially autocorrelated across mapped units. A positive value signals clustering of similar values, a negative value signals a dispersed (checkerboard) pattern, and it is most often used as a diagnostic before moving to spatial regression.
Key highlights
- Provides a single, interpretable global index of spatial autocorrelation, analogous to a correlation coefficient.
- Serves as a standard diagnostic step before choosing a spatial regression model.
- Sign and magnitude directly distinguish clustering (positive) from dispersion (negative).
Intuition
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How it works
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When to use it
Use Moran's I when you have a continuous variable attached to spatial units with known geography and want a single global verdict on spatial autocorrelation, typically with at least about 30 observations. It requires a defined spatial weights matrix W (for example k-nearest-neighbour, queen, or rook contiguity), and row-standardisation of W is the default practice. The variable should be continuous; for binary variables a Join-Count test is preferred. It is the natural first diagnostic before fitting a spatial lag or spatial error model.
Strengths & limitations
- Provides a single, interpretable global index of spatial autocorrelation, analogous to a correlation coefficient.
- Serves as a standard diagnostic step before choosing a spatial regression model.
- Sign and magnitude directly distinguish clustering (positive) from dispersion (negative).
- Requires coordinate or geographic data; without it spatial autocorrelation cannot be computed and ordinary correlation should be used instead.
- Results depend heavily on the chosen spatial weights matrix and its standardisation.
- Being global, it reports one number for the whole map and can mask local hot or cold spots.
Common pitfalls
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Applications
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Frequently asked
What does a positive versus negative Moran's I mean?
A positive value indicates spatial clustering — similar values tend to sit near one another. A negative value indicates dispersion, where high and low values alternate across space. A value near the expected -1/(n-1) suggests no spatial pattern.
What is the spatial weights matrix W?
W encodes which units are neighbours and how strongly they connect, built from rules such as k-nearest-neighbour, queen, or rook contiguity. Row-standardising W (so each row sums to one) is the default, and the choice of W materially affects the result.
How is significance assessed?
The observed I is compared with its null expectation through a z-score, with the reference distribution obtained analytically or, more commonly, by random permutation of the values across the map.
When should I use LISA instead?
Moran's I is a global statistic, so it gives one number for the entire map. When you need to locate specific clusters or spatial outliers, use Local Moran's I (LISA), which computes a separate statistic for each unit.
Sources
- 1.Moran, P.A.P. (1950). Notes on Continuous Stochastic Phenomena. Biometrika, 37(1/2), 17–23.
- 2.Cliff, A.D. & Ord, J.K. (1981). Spatial Processes: Models and Applications. Pion.ISBN 978-0850860818
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Cite this page
ScholarGate. (2026, June 1). Moran's I. ScholarGate. https://scholargate.app/spatial-analysis/morans-i-test