Indicators of spatial association are

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

that evaluate the existence of

clusters may refer to: Science and technology Astronomy * Cluster (spacecraft), constellation of four European Space Agency spacecraft * Cluster II (spacecraft), a European Space Agency mission to study the magnetosphere * Asteroid cluster, a small ...

in the spatial arrangement of a given variable. For instance, if we are studying

cancer Cancer is a group of diseases involving Cell growth#Disorders, abnormal cell growth with the potential to Invasion (cancer), invade or Metastasis, spread to other parts of the body. These contrast with benign tumors, which do not spread. Po ...

rates among

census tract A census tract, census area, census district or meshblock is a geographic region defined for the purpose of taking a census. Sometimes these coincide with the limits of cities, towns or other administrative areas and several tracts commonly exis ...

s in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distribution in space.

Global indicators

Notable global indicators of spatial association include: * Global Moran's ''I'': The most commonly used measure of global

spatial autocorrelation Spatial analysis is any of the formal techniques which study entities using their topological, geometric, or geographic properties, primarily used in Urban Design. Spatial analysis includes a variety of techniques using different analytic appro ...

or the overall clustering of the spatial data developed by

Patrick Alfred Pierce Moran Patrick Alfred Pierce Moran FRS (14 July 1917 – 19 September 1988) was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics. Early years Patrick ...

. * Geary's ''C'' (Geary's Contiguity Ratio): A measure of global spatial autocorrelation developed by Roy C. Geary in 1954. It is inversely related to Moran's ''I'', but more sensitive to local autocorrelation than Moran's ''I''. * Getis–Ord ''G'' (Getis–Ord global G, Geleral G-Statistic): Introduced by

Arthur Getis Arthur Getis (July 6, 1934 – May 13, 2022) was an American geographer known for his significant contributions to spatial statistics and geographic information science (GIScience). With a career spanning over four decades, Getis authored more tha ...

and

J. Keith Ord J, or j, is the tenth letter of the English alphabet. J may also refer to: * Palatal approximant in the International Phonetic Alphabet * J, Cyrillic letter Je Astronomy * J, a provisional designation prefix for some objects discovered bet ...

in 1992 to supplement Moran's ''I''.

Local indicators

Notable local indicators of spatial association (LISA) include: * Local Moran's ''I'': Derived from Global Moran's ''I'', it was introduced by

Luc Anselin Luc E. Anselin (born December 1, 1953) is one of the developers of the field of spatial econometrics and the Stein-Freiler Distinguished Service Professor of Sociology and the College at the University of Chicago. Life and contributions Luc Ansel ...

in 1995 and can be computed using

GeoDa GeoDa is a free software package that conducts spatial analysis, spatial data analysis, geovisualization, spatial autocorrelation and spatial modeling. It runs on different versions of Microsoft Windows, Windows, Mac OS, and Linux. The package wa ...

. * Getis–Ord ''G_i'' (local ''G_i''): Developed by Getis and Ord based on their global ''G''. * INDICATE's I_N: Originally developed to assess the spatial distribution of stars, can be computed for any discrete 2+D dataset using python-based INDICATE tool available from GitHub.

Global indicators

Local indicators

See also

References

Further reading