Spatial Autocorrelation (Morans I) (Spatial Statistics)

Usage tips

• Given a set of features and an associated attribute, Global Moran's I evaluates whether the pattern expressed is clustered, dispersed, or random. When the Z score indicates statistical significance, a Moran's I value near +1.0 indicates clustering while a value near – 1.0 indicates dispersion.

• The Global Moran's I function also calculate a Z score value that indicates whether or not we can reject the null hypothsis. In this case, the null hypothesis states "there is no spatial clustering". In this tool, the Z Score is based on Randomization Null Hypothesis computation. For more information on Z scores, see What is a Z Score?.

• To determine if the Z score is statistically significant, compare it to the range of values for a particular confidence level. For example, at a significance level of 0.05, a z score would have to be less than – 1.96 or greater than 1.96 to be statistically significant.

• The Moran's I value and associated Z score are written to the Command window and passed as derived output.

• The input field you select should only contain positive numeric values. Negative weights will be converted to zero for the calculations.

• The values in the input field should have at least some variation. The statistic will not compute if the values have no variation (if they are all one value). If you have incident data, consider using the Collect Events tool before using this tool.

• The distance used for analysis should be based on your understanding of spatial interaction among the features being analyzed.

• The units of the "Distance Band or Threshold Distance" parameter are the units of the input feature class' coordinate system.

• Any value entered for the "Distance Band or Threshold Distance" parameter is not considered when "Inverse Distance", "Inverse Distance Squared", "Polygon Contiguity" or "Get Spatial Weights from File" are selected for the "Conceptualization of Spatial Relationships" parameter.

• When using the tool in scripting, use "false" for the Display Output Graphically parameter. If you do not select false, the popup graphic will appear and your script will not complete until you click "Close".

• When output is shown graphically, a separate graphics dialog box will be displayed. Therefore, the output should not be displayed graphically (set display_output_graphically to FALSE) in batch operations.

• For line and polygon features, feature centroids are used in the computations.

• 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 Moran's I operation.

• In ArcGIS version 9.2, the "Global" standardization option has been removed. Global standardization returns the same results as no standardization. Models built with previous versions of ArcGIS that use the Spatial Autocorrelation tool with the Global standardization option will need to be rebuilt.

• The "Display Output Graphically" parameter will only work on the windows operating system. When set to true it will display the results of the tool graphically.

• See the Modeling Spatial Relationships help page for further explanation of this tools parameters.

• Learn more about working with layers and table views

• The environment settings do not have an effect on this tool.

Command line syntax
An overview of the Command Line window
SpatialAutocorrelation_stats <Input_Feature_Class> <Input_Field> <Display_Output_Graphically> <Inverse Distance | Inverse Distance Squared | Fixed Distance Band | Zone of Indifference | Polygon Contiguity (First Order) | Get Spatial Weights From File> <Euclidean Distance | Manhattan Distance> <None | Row > <Distance_Band_or_Threshold_Distance> {Weights_Matrix_File}

Command line example

workspace e:\project93\data
SpatialAutocorrelation cancernm.shp RATE true 'Inverse Distance' 'Euclidean Distance' None # #

Scripting syntax
About getting started with writing geoprocessing scripts
SpatialAutocorrelation_stats (Input_Feature_Class, Input_Field, Display_Output_Graphically, Conceptualization_of_Spatial_Relationships, Distance_Method, Standardization, Distance_Band_or_Threshold_Distance, Weights_Matrix_File)

Script example

# Analyze crime data to determine if spatial patterns are statistically significant

# Import system modules
import arcgisscripting

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

# Local variables...
workspace = "C:/project93/data"
crime_data = "burglaries.shp"

try:
    # Set the current workspace (to avoid having to specify the full path to the feature classes each time)
    gp.workspace = workspace

    # Obtain Nearest Neighbor Ratio and Z Score
    # Process: Average Nearest Neighbor...
    nn_output = gp.AverageNearestNeighbor_stats(crime_data, "Euclidean Distance", "false", "#")
    nn_values = nn_output.split(";")
    print "The nearest neighbor index is: " + nn_values[0]
    print "The z score of the nearest neighbor index is: " + nn_values[1]

    # Obtain General G  and Z Score
    # Process: High/Low Clustering (Getis-Ord General G)...
    hlc_output = gp.HighLowClustering_stats(crime_data, "Count", "false", "Inverse Distance", "Euclidean Distance", "None", "#", "#")
    hlc_values = hlc_output.split(";")
    print "The General G value is: " + hlc_values[0]
    print "the z score of the General G value is: " + hlc_values[1]

    # Obtain Moran's Index and Z Score
    # Process: Spatial Autocorrelation (Morans I)...       
    sa_output = gp.SpatialAutocorrelation_stats(crime_data, "Count", "false", "Inverse Distance", "Euclidean Distance", "None", "#", "#")
    sa_values = sa_output.split(";")
    print "The Moran's I value is: " + sa_values[0]
    print "The z score of the Moran's I value is: " + sa_values[1]

except:
    # If an error occurred when running the tool, print out the error message.
    print gp.GetMessages()