Mahalanobis' distance

Mahalanobis' distance (MD) is a statistical measure of the extent to which cases are multivariate outliers, based on a chi-square distribution, assessed using p < .001.

The critical chi-square values for 2 to 10 degrees of freedom at a critical alpha of .001 are shown below.

A maximum MD larger than the critical chi-square value for df = k (the number of predictor variables in the model) at a critical alpha value of .001 indicates the presence of one or more multivariate outliers.

df	Critical value
2	13.82
3	16.27
4	18.47
5	20.52
6	22.46
7	24.32
8	26.13
9	27.88
10	29.59

For df > 10, refer to a chi-square table (Google search).

See also

• Multiple linear regression

External links

• Detecting outliers - Multivariate (PsychWiki)