Spatial Analysis

Moran's I: Do Your Values Cluster, or Are They Random?

Concept article · Updated · by Dr. Anant Kumar Pathak

Before you map hot spots or model spatial data, one question comes first: is there any spatial pattern at all? Moran's I gives a single, testable answer — whether similar values sit together, avoid each other, or fall where they may.

How it reads the surface

Moran's I correlates each value with the values of its neighbours, weighted by a spatial-weights matrix, and scales the result to roughly −1 to +1. Near +1 means strong clustering (highs by highs), near −1 means dispersion (a checkerboard), and around the expected value (≈ 0) means spatial randomness — judged against a z-score and p-value.

How it is calculated

Moran's I = I = (n / W) × ( ΣΣ wij(xi − x̄)(xj − x̄) ) / ( Σ(xi − x̄)² )

What the numbers mean

Typical range: ≈ −1 to +1

→ +1 clustered · ≈ 0 (technically −1/(n−1)) random · → −1 dispersed / checkerboard. Judge against a z-score / p-value.

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What it runs on

Operates onA point or polygon layer with a numeric attribute — not tied to specific spectral bands.

Where it is used

It is the standard first test for spatial autocorrelation in ecology, economics and epidemiology, and before any regression on spatial data, where ignoring autocorrelation invalidates ordinary statistics.

Limitations to know

A single global statistic that masks local variation, and it is sensitive to the spatial-weights matrix you choose.

Global Moran's I is a single summary — it can report "no pattern" while strong local clusters cancel out. Follow it with a local indicator (LISA / local Moran's I), and remember the spatial-weights choice drives the result.

Compute Moran's I on your own study area

Skip the code. Draw or upload a boundary and Spatial Research Suite runs Moran's I on live data — with cloud masking, exports and citations built in.

Run this analysis in GISforus →

Frequently asked

What does Moran's I actually measure?

Spatial autocorrelation — whether similar values cluster (near +1), disperse (near −1), or are randomly arranged (near 0), tested against a p-value.

Global or local Moran's I?

Use global Moran's I to test for any overall pattern; follow with local Moran's I (LISA) to locate the individual clusters and outliers.

Primary reference: Moran, P.A.P. (1950). Notes on continuous stochastic phenomena. Biometrika 37(1/2), 17–23.