English: For each method the ellipses show contours of probability that indicate if a location in environmental space has a Mahalanobis distance that is greater than would be expected by chance. The sensitivity of the sample mean and variance-covariance matrix method to outlying data can be seen, which contrasts with both the minimum covariance determinant and minimum volume ellipsoid methods, which both focus on where data is concentrated.
This image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.
It is recommended to name the SVG file “Mahalanobis-distance-location-and-scatter-methods.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
to share – to copy, distribute and transmit the work
to remix – to adapt the work
Under the following conditions:
attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Hypothetical two-dimensional example of Mahalanobis distance with three different methods of defining the multivariate location and scatter of the data.