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# Standard Distance (Spatial Statistics)

Release 9.2

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Measures the degree to which features are concentrated or dispersed around the points (or feature centroids) in an input feature class.

Illustration

Usage tips

• Standard Distance measures the degree to which features are concentrated or dispersed around the points (or feature centroids) in an input feature class.

• The standard distance calculation may be based on an optional weight (to get the standard distance of businesses weighted by employees, for example).

• The standard distance is a useful statistic, as it provides a single summary measure of feature distribution around any given point (similar to the way a standard deviation measures the distribution of data values around the statistical mean).

• Standard Distance creates a new feature class containing a circle polygon centered on each of the central features (mean centers). Each circle polygon is drawn with a radius equal to the standard distance. The attribute value for each circle polygon is its standard distance.

• If the underlying pattern in the data is truly random, the one standard deviation polygon will cover approximately 68percent of the features in the cluster. Two standard deviations will contain approximately 95 percent of the features, and three standard deviations will cover approximately 99 percent of the features in the cluster.

• A mean center calculation is used to determine the geographic centers of the input feature class.

• If a case field is specified, the input features are grouped according to case field values, and a mean center is calculated from the average x and average y values for the centroids in each group.

• For line and polygon features, geometric centroids are calculated before the central feature is identified. The geometric centroid of a feature may be located outside a feature's boundary. If centroids must be within feature boundaries, use the Features to Points (Inside option) to create centroids before performing the Standard Distance operation.

• Calculations are based on either Euclidean or Manhattan distance and require projected data to accurately measure distances.

• Current map layers may be used to define the input feature class. When using layers, only the currently selected features are used in the Standard Distance operation.

• The following environment settings affect this tool: Cluster Tolerance, Extent, M Domain, Configuration Keyword, Coordinate System, Output has M Values, Output Spatial Grid, Output has Z Values, Default Z Value, Output XY Domain, and Output Z Domain.

Command line syntax
An overview of the Command Line window
StandardDistance_stats <Input_Feature_Class> <Output_Standard_Distance_Feature_Class> <1 Standard Deviation | 2 Standard Deviations | 3 Standard Deviations> {Weight_Field} {Case_Field}

 Parameter Explanation Data Type A feature class containing a distribution of features for which the standard distance will be calculated. Feature Layer A polygon feature class that will contain a circle polygon for each input center. These circle polygons graphically portray the standard distance at each center point. Feature Class <1 Standard Deviation | 2 Standard Deviations | 3 Standard Deviations> The size of output circles in standard deviations. The default circle size is 1; valid choices are 1, 2, or 3 standard deviations. String {Weight_Field} The numeric field used to weight locations according to their relative importance. Field {Case_Field} Field used to group features for separate standard distance calculations. The case field can be of numeric, date, or string type. Field
Data types for geoprocessing tool parameters

### Command line example

```workspace e:\project93\data
StandardDistance robberies.shp robbery_SD.shp '2 Standard Deviation' LOSS_VAL TYPE```

Scripting syntax
About getting started with writing geoprocessing scripts
StandardDistance_stats (Input_Feature_Class, Output_Standard_Distance_Feature_Class, Circle_Size, Weight_Field, Case_Field)

 Parameter Explanation Data Type Input_Feature_Class (Required) A feature class containing a distribution of features for which the standard distance will be calculated. Feature Layer Output_Standard_Distance_Feature_Class (Required) A polygon feature class that will contain a circle polygon for each input center. These circle polygons graphically portray the standard distance at each center point. Feature Class Circle_Size (Required) The size of output circles in standard deviations. The default circle size is 1; valid choices are 1, 2, or 3 standard deviations. String Weight_Field (Optional) The numeric field used to weight locations according to their relative importance. Field Case_Field (Optional) Field used to group features for separate standard distance calculations. The case field can be of numeric, date, or string type. Field

Data types for geoprocessing tool parameters

### Script example

```# Measure the geographic distribution of auto thefts
# Import system modules
import arcgisscripting

# Create the Geoprocessor object
gp = arcgisscripting.create()

# Local variables...
workspace = "C:/data"
auto_theft_locations = "AutoTheft.shp"
auto_theft_sd = "auto_theft_SD.shp"
auto_theft_se = "auto_theft_SE.shp"
auto_theft_ldm = "auto_theft_LDM.shp"

try:
# Set the workspace (to avoid having to type in the full path to the data every time)
gp.Workspace = workspace

# Process: Standard Distance of auto theft locations...
gp.StandardDistance_stats(auto_theft_locations, auto_theft_sd, "1 Standard Deviation", "#", "#")

# Process: Directional Distribution (Standard Deviational Ellipse) of auto theft locations...
gp.DirectionalDistribution_stats(auto_theft_locations, auto_theft_se, "1 Standard Deviation", "#", "#")

# Process: Linear Directional Mean of auto thefts...