# Standard Distance (Spatial Statistics)

## Summary

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

## 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 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, and 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 Feature Class.

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

• If the underlying spatial pattern of the input features is concentrated in the center with fewer features toward the periphery (spatial normal distribution), a one standard deviation circle polygon will cover approximately 68 percent of the features; a two standard deviation circle will contain approximately 95 percent of the features; and three standard deviations will cover approximately 99 percent of the features in the cluster.

• Calculations based on either Euclidean or Manhattan distance require 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.

• Caution:

When using shapefiles, keep in mind that they cannot store null values. Tools or other procedures that create shapefiles from non-shapefile inputs may store or interpret null values as zero. This can lead to unexpected results. See also Geoprocessing considerations for shapefile output.

## Syntax

StandardDistance_stats (Input_Feature_Class, Output_Standard_Distance_Feature_Class, Circle_Size, {Weight_Field}, {Case_Field})
 Parameter Explanation Data 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 — 2_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 (stand-alone Python 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"
standardDistance = "auto_theft_SD.shp"
stardardEllipse = "auto_theft_SE.shp"
linearDirectMean = "auto_theft_LDM.shp"

try:
# 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...

except:
# If an error occurred while running a tool, print the messages
print arcpy.GetMessages()```

## Environments

Output Coordinate System

Feature geometry is projected to the Output Coordinate System prior to analysis. All mathematical computations are based on the Output Coordinate System spatial reference.

ArcView: Yes
ArcEditor: Yes
ArcInfo: Yes

3/7/2012