Mahalanobis distance


Would you please explain when I should use Mahalanobis distance? Do I use it with a MANOVA? Also, is it used to describe effect size? And is there a very simple way to figure it?

Thanks a bunch.



TS Contributor
It's somewhat analogous to a z-score, but for a multivariate situation. Each data point will have a "distance" from some multi-dimensional central point, or centroid.

It's used in multivariate procedures (such as MANOVA, or multiple regression, etc.) to identify outliers.
easy to calculate

Tabachnick & Fidell's book goes over the process for identifying multivariate outliers really clearly in Chpt 4.

To calculate h2 distances in SPSS you just need to run a regression using the variables you plan to use in a set of analyses as the predictors and any variable (including ID number) as the outcome variable. Under the "save" button in the regression window, there is an option to save mahalanobis distances for each respondent. These are distributed on a chi-squared distribution with the degrees of freedom equaling the number of predictor variables used. Any participant with a significant mahalanobis distance would likely be an outlier.

To give a small piece of advice - when selecting scales to use for calculating these distances, I would avoid using extremely highly correlated scales (r of .75 or higher) as separate predictors as that seems to make the test exceedingly sensitive.