# Mahalanobis Distances Critical Values (Chi-Squared?)

Say I work out the mahalanobis distance 'D' to measure the separation between two objects (which aren't normally distributed).

Say I now want to use 'D' against some critical values to decide if it's an outlier or not.

I've read that using Chi-Square Distribution is one way, using N-1 degree of freedom and converting the distance to Chi-square p values. However, it states that because isn't normally distributed some conversion is recommended.

In cases where the predictor variables are not normally distributed, the >conversion to Chi-square p-values serves to recode the Mahalanobis >distances to a 0-1 scale. Mahalanobis distances themselves have no upper >limit, so this rescaling may be convenient for some analyses.

In my case, where I have one distance 'D' and I can't re-scale it, is using the above still advisable?

If if it advisable, could one briefly explain the conversion where e.g., N=2 (used in degree of freedom N-1?) to get some critical value and what it represents?

If it isn't, what alternative method could I use to generate some critical values?

To my mind, you have a distance $D$ and a number of degrees of freedom $N$, and you just have to compute the value of the chi-squared distribution with these two parameters.
p = chi2pdf(D,N);