


Generating Pvalue grid from Mahalanobis Distance Grid: When the predictor variables used to generate the mean vector and covariance matrix are normally distributed, then Mahalanobis distances are distributed approximately according to a Chisquare distribution with n1 degrees of freedom. In such cases it may be useful to convert the Mahalanobis distance grid into a grid of pvalues. If the predictor variables are not normally distributed, it may still be useful to make this conversion because it rescales the unbounded Mahalanobis values such that they are all between 0 and 1. For more details on the uses of converting to pvalues, see the discussion on ChiSquare values or refer to Clark et al. 1993. The button provides an easy way to convert Mahalanobis grids into pvalue grids. Click the button and you will be prompted to identify your Mahalanobis grid and the appropriate degrees of freedom:
The degrees of freedom should be equal to n1, where n = # predictor variables used to generate the original mean vector and covariance matrix. The Mahalanobis grid in this example was generated from 2 predictor variables (Slope and Elevation), so there would only be 1 degree of freedom. Click the OK button to generate the pvalue grid:
Due to a limitation in Spatial Analyst, this function does not generate exact pvalues for each cell but rather classifies the grid into 26 pvalue ranges. The pvalue for each cell reflects the probability of seeing a Mahalanobis value as large or larger than the actual Mahalanobis value for that cell, assuming the vector of predictor values that produced that Mahalanobis value was sampled from a population with an ideal mean (i.e. equal to the vector of mean predictor variable values used to generate the original Mahalanobis grid). Pvalues close to 0 reflect high Mahalanobis distance values and are therefore very dissimilar to the ideal combination of predictor variables. Pvalues close to 1 reflect low Mahalanobis distances and are therefore very similar to the ideal combination of predictor variables. Calculating Pvalues for individual Mahalanobis Distance Grid cells: The tool allows you to calculate exact pvalues for individual Mahalanobis surface grid cells, assuming a Chisquare distribution with n1 degrees of freedom where n = # predictor variables used to generate the mean vector and covariance matrix. See the discussion of ChiSquare values for an explanation of this concept. When you initially click the tool, you will be asked to identify the degrees of freedom to use in the calculations:
After you enter a number, you can start clicking on the screen to calculate pvalues. Your cursor should be represented with a symbol. As you click on different places on the grid, you will generate a running list of pvalues:
Mahalanobis Intro  Mahalanobis Description  Generating Mahalanobis Grids  Mahalanobis Distances for Feature Themes  Mahalanobis Distances for Tables  Additional Mahalanobis Matrices  Mahalanobis References Download Extension  Download Manual Jenness Enterprises  ArcView Extensions  GIS Consultation  Unit Converter
