ArcMap

Standard Distance

Summary

Measures the degree to which features are concentrated or dispersed around the geometric mean center.

Learn more about how Standard Distance works

Illustration

Standard Distance illustration

Usage

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

  • The Standard Distance tool creates a new feature class containing a circle polygon centered on the mean for each case. Each circle polygon is drawn with a radius equal to the standard distance. The attribute value for each circle polygon is its standard distance value.

  • The Case Field parameter is used to group features prior to analysis. When a Case Field is specified, the input features are first grouped according to case field values. Then a standard distance circle is computed for each group. The case field can be of integer, date, or string type and will appear as an attribute in the Output Standard Distance Feature Class. Records with NULL values for the Case Field will be excluded from analysis.

  • The standard distance calculation can be based on the optional Weight Field parameter (to get the standard distance of businesses weighted by employees for example). The Weight Field should be numeric.

  • When the underlying spatial pattern of features is concentrated toward the center with fewer features toward the periphery (following a Rayleigh distribution), a one standard deviation Circle Size will cover approximately 63 percent of the features; a two standard deviations Circle Size will contain approximately 98 percent of the features; and a three standard deviations Circle Size will cover approximately 99 percent of the features in two dimensions.

  • This tool requires projected data to accurately measure distances.

  • For line and polygon features, feature centroids are used in distance computations. For multipoints, polylines, or polygons with multiple parts, the centroid is computed using the weighted mean center of all feature parts. The weighting for point features is 1, for line features is length, and for polygon features is area.

  • Map layers can be used to define the Input Feature Class. When using a layer with a selection, only the selected features are included in the analysis.

Syntax

StandardDistance(Input_Feature_Class, Output_Standard_Distance_Feature_Class, Circle_Size, {Weight_Field}, {Case_Field})
ParameterExplanationData Type
Input_Feature_Class

A feature class containing a distribution of features for which the standard distance will be calculated.

Feature Layer
Output_Standard_Distance_Feature_Class

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

The size of output circles in standard deviations. The default circle size is 1; valid choices are 1, 2, or 3 standard deviations.

  • 1_STANDARD_DEVIATION —1 standard deviation
  • 2_STANDARD_DEVIATIONS —2 standard deviations
  • 3_STANDARD_DEVIATIONS —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 integer, date, or string type.

Field

Code sample

StandardDistance example (Python window)

The following Python window script demonstrates how to use the StandardDistance tool.

import arcpy
arcpy.env.workspace = r"C:\data"
arcpy.StandardDistance_stats("AutoTheft.shp", "auto_theft_SD.shp", "1_STANDARD_DEVIATION")
StandardDistance example 2 (stand-alone script)

The following stand-alone Python script demonstrates how to use the StandardDistance tool.

# Measure the geographic distribution of auto thefts
 
# Import system modules
import arcpy
 
# Local variables...
workspace = "C:/data"
locations = "AutoTheft.shp"
links = "AutoTheft_links.shp"
standardDistance = "auto_theft_SD.shp"
stardardEllipse = "auto_theft_SE.shp"
linearDirectMean = "auto_theft_LDM.shp"
 
# Set the workspace (to avoid having to type in the full path to the data every time)
arcpy.env.workspace = workspace
 
# Process: Standard Distance of auto theft locations...
arcpy.StandardDistance_stats(locations, standardDistance, "1_STANDARD_DEVIATION")
 
# Process: Directional Distribution (Standard Deviational Ellipse) of auto theft locations...
arcpy.DirectionalDistribution_stats(locations, standardEllipse, "1_STANDARD_DEVIATION")
 
# Process: Linear Directional Mean of auto thefts...
arcpy.DirectionalMean_stats(links, linearDirectMean, "DIRECTION")

Environments

Licensing information

  • Basic: Yes
  • Standard: Yes
  • Advanced: Yes

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