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Table Distances

bullet Generating Mahalanobis Distances for Tables
bulletAdditional Options


Generating Mahalanobis Distances for Tables:

This function generates individual Mahalanobis distances for each record in a table based on independent variable fields contained in the table. The function adds a field to the table labeled “Mahalanobis” containing the Mahalanobis distances.

If you cannot or do not wish to modify your table by adding a field with Mahalanobis distances, use the “Generate Mahalanobis Distances for Feature Themes” function to create a separate Results table. This separate table can then be joined with the current table for further analysis. The tools for generating Mahalanobis distances for feature themes and for tables are essentially identical, except that the Table function adds a field to the table while the Theme function creates a separate Results table. If you have no theme associated with this table, you can create a temporary one using the “Add Event Theme” menu item in the View menu (see ArcView Help files).

Begin by clicking the “Calculate Mahalanobis Distances” button in the Table button bar. You will be prompted to identify the fields in the open table containing the independent variable values for each record, and specify whether you would like to generate the mean vector and covariance matrix directly from the data or use existing mean vector and covariance matrix tables:

The “Available Fields” list on the left contains all the numeric fields available in the current table, and the “Selected Fields” list on the right contains all the fields to be used in the analysis. Select one or more fields from the “Available” list and click the “Add” button to add them to the “Selected” list. If you need to reorder the selected fields (if, for example, you need to generate a mean vector or covariance matrix in a particular order, or if you need to reorder your fields to match an existing mean vector or covariance matrix), click on any of the selected fields and use the arrow buttons on the left to shuffle it up or down.

You have the option to generate your mean vector and covariance matrix directly from the data, in which case the Mahalanobis distances will reflect the distance of each individual feature from the internal mean vector of the group. Such values may be useful for determining within-group variability. Alternatively you can generate distances of each record from a separate mean vector, possibly generated from a control group or based on earlier research, by clicking the “Use existing mean vector and covariance matrix tables” option. See Knick and Dyer (1997) for an example of substituting a weighted mean and covariance matrix when certain input variables are better measured than others. If you choose this second option, you will next be asked to identify the tables containing your Mean vector and Covariance matrix:

Additional Options:

If any of your records are currently selected, you will have the option to use either all records in the analysis or only the selected records.

You also have the option to generate p-values for each Mahalanobis value, based on a Chi-square distribution with n-1 degrees of freedom. See the discussion of Chi-square p-values for a description of the relationship between Chi-square p-values and Mahalanobis values. The button opens up a help window briefly discussing Chi-square p-values.

Click the ‘OK’ button to start the analysis. As soon as computations are done, the tool will add a new field to your table named “Mahalanobis” containing the Mahalanobis distance values and open a report window containing information about the analysis:

See the description of the Report window for more details on the report components.

Mahalanobis Intro  |  Mahalanobis Description  |  Generating Mahalanobis Grids  |  Mahalanobis Chi-Square Tools  |  Mahalanobis Distances for Feature Themes  |  Additional Mahalanobis Matrices  |  Mahalanobis References

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