Spatial Statistics

Spatial Data

As mentioned above, spatial statistics includes spatial data analysis. Spatial data may be defined as a database that contains information about certain variables and their distribution over space. In other words, a spatial data set consists of each record or observation accompanied by its spatial coordinates in the form of latitude and longitude or x andy coordinates as well as topology information. It can also be defined as data pertaining to location, shape, and geographical relationships. Thus, spatial statistics consists of the study of spatially referenced data that can be mapped digitally. Spatial data are represented typically in the form of points, lines, and polygons (including raster cells), with associated attribute information about each displayed spatial unit. Among the most important and commonly used measures in classical statistics are measures of central tendency, which include mean, median, and mode. However, these measures are not able to take into consideration the spatial locations in the final results. In spatial statistics, these essential statistical measures have been modified to include the individual location information in the final results. For instance, spatial mean can be used to determine the mean center or average center of a set of observations. Similarly, the concept of median has been extended to include the concept of the median center, which is mainly used for determining the spatial median of a set of observations.

Spatial Autocorrelation

In view of one of the main objectives of spatial statistics, which is the analysis of spatial patterns, there are different types of spatial patterns that may exist over space. These patterns include heterogeneous patterns (patterns that vary in a systematic manner from place to place), anisotropy (where there is directional bias in a particular spatial pattern), and clustering effects (where locations with similar attribute values are clustered close together). One of the main components of spatial statistics, as emphasized before, is the study of the underlying spatial relationships between different variables, collectively referred to as spatial autocorrelation. It is a function of similarities in both location and attribute values among the different data observations. Autocorrelation refers to the pairwise correlation of univariate observations; in more general terms, it can be referred to as self-correlation. Therefore, spatial autocorrelation refers to the spatial distribution of autocorrelation among different observations. This type of autocorrelation arises as a result of some form of ordering in the spatial distribution of variables. Spatial autocorrelation coefficients help in examining the clustering of a given set of observations based on attribute values. It is expressed in the form of positive and negative autocorrelations. Positive autocorrelation occurs when locations with similar attribute values that are clustered have more similar characteristics, while negative [Page 2665]autocorrelation occurs when attribute values of observations located close together are dissimilar. Two of the most effectively used measures of spatial autocorrelation are Geary's ratio and Moran's I. Both measures check for spatial autocorrelation by taking into consideration attribute value similarity and location proximity. Furthermore, the concept of spatial autocorrelation does not ignore randomness; rather, it takes into consideration both spatial pattern and error. Figure 1 shows hypothetical examples of different types of spatial autocorrelation.

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