Mahalanobis' distance

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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).

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