# Directional Distribution (Standard Deviational Ellipse) (Spatial Statistics)

## Summary

Creates standard deviational ellipses to summarize the spatial characteristics of geographic features: central tendency, dispersion, and directional trends.

## Usage

• The Standard Deviational Ellipse tool creates a new Output Feature Class containing elliptical polygons, one for each Case (Case Field parameter). The attribute values for these ellipse polygons include X and Y coordinates for the mean center, two standard distances (long and short axes), and the orientation of the ellipse. The fieldnames are CenterX, CenterY, XStdDist, YStdDist, and Rotation. When a Case Field is provided, this field is added to the Output Feature Class, as well.

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

• When the underlying spatial pattern of features is concentrated in the center with fewer features toward the periphery (a spatial normal distribution), a one standard deviation ellipse polygon will cover approximately 68 percent of the features; 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.

• The value in the output Rotation field represents the rotation of the long axis measured clockwise from noon.

• 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 deviational ellipse is computed for each group. The case field can be of integer, date, or string type.

• The standard deviational ellipse calculation may be based on an optional Weight Field (to get the ellipses for traffic accidents weighted by severity, for example). The Weight Field should be numeric.

• 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

DirectionalDistribution_stats (Input_Feature_Class, Output_Ellipse_Feature_Class, Ellipse_Size, {Weight_Field}, {Case_Field})
 Parameter Explanation Data Type Input_Feature_Class A feature class containing a distribution of features for which the standard deviational ellipse will be calculated. Feature Layer Output_Ellipse_Feature_Class A polygon feature class that will contain the output ellipse feature. Feature Class Ellipse_Size The size of output ellipses in standard deviations. The default ellipse 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 directional distribution calculations. The case field can be of integer, date, or string type. Field

## Code Sample

DirectionalDistribution Example (Python Window)

The following Python Window script demonstrates how to use the DirectionalDistribution tool.

```import arcpy
arcpy.env.workspace = r"C:\data"
arcpy.DirectionalDistribution_stats("AutoTheft.shp", "auto_theft_SE.shp", "1_STANDARD_DEVIATION", "#", "#")```
DirectionalDistribution Example (stand-alone Python script)

The following stand-alone Python script demonstrates how to use the DirectionalDistribution 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