In Anselin and Griffith (1988), it is shown in some detail how the results of data analyses may become invalid if spatial
dependence and/or spatial heterogeneity are ignored. Consequently, specialized techniques must be used instead of those that follow
the standard assumptions of independence and homogeneity. By now, a large body of such techniques has been developed, which
appears in the literature under the rubrics of spatial statistics, geostatistics, or spatial econometrics. The differences between these
"fields" are subtle and to some extent semantic. Spatial statistics is typically considered to be the most general of the three, with
geostatistics focused on applications in the physical (geological) sciences, and spatial econometrics finding application in economic
modeling.
A useful taxonomy for spatial data analysis was recently suggested by Cressie (1991). He distinguishes between three broad
classes of spatial data and identifies a set of specialized techniques for each. Crressie’s taxonomy consists of lattice data (discrete
variation over space, with observations associated with regular or irregular areal units), geostatistical data (observations associated
with a continuous variation over space, typically in function of distance), and point patterns (occurrences of events at locations in
space). In the remainder of this paper, I will focus exclusively on the first category (lattice data), due to space limitations, but also
because I have found it to be the most appropriate perspective for applications in the social sciences that utilize GIS. I chose not to
discuss geostatistics, since the requirement of continuous variation with distance in an isotropic space is typically not satisfied by
spatial samples in the social sciences. Such samples are mostly limited to data for areal units, which are often defined in a rather
arbitrary fashion, making an assumption of continuity tenuous at best. Recent reviews of geostatistical techniques can be found in
Davis (1986), Isaaks and Srivastava (1989), Webster and Oliver (1990), and Cressie (1991). In contrast to the geostatistical data
viewpoint, point patterns represent a very appropriate perspective for the study of many phenomena in the social sciences, such as the
analysis of the spatial arrangement of settlements, of store locations, occurences of crime, infectuous diseases, etc. I elected not to
discuss them in this paper because their study does not require much in terms of the functionality of a GIS, once the coordinates of the
locations have been determined. A very readable introduction to point pattern analysis is given in Boots and Getis (1988) and Upton
and Fingleton (1985). More advanced treatments can be found in Getis and Boots (1978), Ripley (1981) and Diggle (1983), as well as
in Cressie (1991).