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Statistical analysis Inherent in GIS data is information on the attributes of features as well as their locations. This information is used to create maps that can be visually analyzed. Statistical analysis helps you extract additional information from your GIS data that might not be obvious simply by looking at a map—information such as how attribute values are distributed, whether there are spatial trends in the data, or whether the features form spatial patterns.
Unlike query functions—such as identify or selection, which provide information about individual features—statistical analysis reveals the characteristics of a set of features as a whole. Some of the statistical analysis techniques described in this document are most well-suited for interactive applications, such as ArcMap, that allow you to select and visualize data in an ad-hoc and fluid environment.
Some of the methods described here are found in ArcMap's menus and toolbars and don't have a geoprocessing tool counterpart. Other methods, such as the spatial statistics tools, are only implemented as geoprocessing tools.
Uses of statistical analysis Statistical analysis is often used to explore your data—for example, to examine the distribution of values for a particular attribute or to spot outliers extreme high or low values.
Having this information is useful when defining classes and ranges on a map, when reclassifying data, or when looking for data errors. In the example below, statistics have been calculated for the distribution of senior citizens by census tract in this region percentage age 65 and over in each tractincluding the mean and standard deviation, as well as a histogram showing the distribution of values.
Most tracts have a lower percentage of seniors than the mean, but a few tracts have a very high percentage. Another use of statistical analysis is to summarize data. Often this is done for categories, such as calculating the total area in each land use category.
You can also create spatial summaries, such as calculating the average elevation for each watershed. Summary data is useful for gaining a better understanding of conditions in a study area. In the example below, summary statistics have been calculated for each landuse class showing the number of parcels in that class, the size of the smallest and largest parcel, the average parcel size, and the total area in the class.
Statistical analysis is also used to identify and confirm spatial patterns, such as the center of a group of features, the directional trend, or whether features form clusters. While patterns may be apparent on a map, trying to draw conclusions from a map can be difficult-how you classify and symbolize the data can obscure or overemphasize patterns.
Statistical functions analyze the underlying data and give you a measure that can be used to confirm the existence and strength of the pattern.
Below is an example of analyses that show the mean center of a set of burglaries, and the standard deviation ellipse for a set of moose sightings showing the directional trend Below is an example of an analysis that shows statistically significant clusters of census tracts with many senior citizens orange or few blue.
Types of statistical analysis Statistical analysis functions in ArcGIS Desktop are either nonspatial tabular or spatial containing location.
Nonspatial statistics are used to analyze attribute values associated with features. The values are accessed directly from a layer's feature attribute table. Examples of nonspatial statistics include the mean and standard deviation. In this example, the Summary Statistics tool was used to calculate the number of vacant parcels for a set of census tracts, including the total, the mean, and the standard deviation.
Charts and graphs, such as a histogram or Q-Q plots, are another way of analyzing nonspatial data. In all cases, only the values are analyzed. The locations of the features with which the values are associated—and any spatial relationships between the features—are not considered.
In this example, the histogram shows the distribution of vacant parcels the number of vacant parcels along the x-axis and the number of tracts in each range along the y-axis.
A Normal Q-Q Plot is used to assess the similarity of the distribution of a set of values to that of a standard normal distribution the typical bell curve, when shown on a histogram. The line on the Normal Q-Q plot shows expected values for a normal distribution—the closer the values to the line, the closer the distribution is to normal.
In this example, the concentration of the elements Phosphorous for a set of soil samples is close to normally distributed. Spatial statistics, on the other hand, focus on the spatial relationships between features—how compact or dispersed the features are, whether they're oriented in a particular direction, and whether they form clusters.
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