Mahalanobis distances measure the distance of a sample unit from the mean of a distribution, taking into account the correlation between the units in the covariance matrix. If $x$ is an observation from a multivariate distribution with mean $\mu$ and covariance $\Sigma$, the Mahalanobis squared distance (MSD) of $x$ from $\mu$ is $D^{2}=(x − \mu)^{t} \Sigma^{-1} (x − \mu)$. When $x$ is from a $v$-dimensional multivariate normal with known mean and covariance, the population MSD is distributed as a chi-squared $\chi_{v}^{2}$ random variable with $\nu$ degrees of freedom (Mardia et al, 1979). Then, to test the deviation of an observation from the multivariate normal assumption we can compare its MSD with an appropriate quantile of the chi-squared distribution: the observation will be considered an outlier if the associated $D^{2}$ value is larger than the critical value of the chi-squared distribution. There are known limitations to the application of this cut-off, for example when the sample is high dimensional and its size is not sufficiently high. In this case the distribution of the sample MSD is a scaled Beta distribution (Gnanadesikan and Kettenring, 1972). For continuous Student-t samples, which account for heavy-tailed distributions, the appropriate cutoff value depends from a standard Beta distribution with shape parameters $v/2$ and $\nu/2$, as shown by Barabesi et al (2023).