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Statistical Matrices


Generating Statistical Matrices:

This function provides a quick way to generate tables containing the mean vector, covariance matrix, inverse covariance matrix, Pearson’s r correlation matrix, and Spearman’s rho rank correlation matrix from multiple fields in the current table. The mean vector and covariance matrix tables can be used with the Mahalanobis functions described elsewhere in this manual.  Options to generate a Pearson’s r and/or Spearman’s rho correlation matrix are included because the author of the extension needed them for something and decided to leave them available for others to use.

Pearson’s r correlations measure how much one variable changes as a second variable changes, and in which direction. Values range between -1 and 1, with negative values implying a negative relationship (i.e. as one variable increases, the other decreases). Values close to 1 or -1 have high correlation while values close to 0 have low correlation.  Spearman’s rho correlations are identical to Pearson’s r except that they are calculated from the relative rank of each value rather than the value itself (see Conover 1980:252).  Spearman's rho correlations are generally considered more appropriate when the variables are not normally distributed or when the researcher wants to reduce the importance of outliers.

Open your table and click the “Create Statistical Matrices” button to start the process. You will be prompted to identify the fields to include in the analysis:

The list labeled “Available Fields” contains all the numeric fields available in your open table and the list labeled “Selected Fields” contains all the fields currently selected for analysis. Select the fields you would like to analyze and click the “Add” button to add them to the Selected list. If you need to change the order of the selected fields for any reason, click on one of the fields and use the arrow buttons on the left to shuffle it up or down. If any of your records are selected, you have the option to analyze either the full set of records or only the selected set.

Next, choose which matrices you would like to generate:

Click ‘OK’ and the tables will be generated and opened, along with a Report dialog describing the analysis. See the description of the Report window for more details on the report components.

Statistical Matrix Methods:


Variance/Covariance Matrix:

bulletInverse Covariance Matrix: Matrix inversion is computationally complex, and the author refers interested readers to the Lower/Upper (LU) Decomposition method in chapter 2 of Press et al (2002).
bulletPearson Correlation Matrix:

bulletSpearman Correlation Matrix: Computationally identical to the Pearson Correlation Matrix except that ranks are used in place of original values. For example, the list of values {12, 3, 56, 23, 1} would be replaced with {3, 2, 5, 4, 1}, and the replacement list would then be used to generate the correlation matrix.


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

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