According to Barnett and Lewis, a Mahalanobis distance value above 25 is a cause for concern in which situation?

• A. Small samples with two predictors.
• B. Large samples with ten predictors.
• C. Moderate samples with four predictors.
• D. Large samples (N=500) with five predictors.

Answer: (D)

Mahalanobis distance tells you how far an observation is from the center of a multivariate distribution, adjusting for how the predictors covary. A value above a practical cutoff suggests a potential multivariate outlier that doesn’t fit the overall pattern.

Barnett and Lewis give a rule of thumb: in a dataset with about five predictors and a reasonably large sample, a squared Mahalanobis distance above 25 is a cause for concern. In this setting the covariance structure is estimated reliably from many cases, so a large distance like 25 represents a truly unusual combination of values across the variables, not just random variation.

That particular scenario—large sample with five predictors—fits the guideline because the degrees of freedom (the number of predictors) is modest but the sample size ensures a stable covariance estimate, making D^2 > 25 a meaningful flag. With too few predictors, or with very large numbers of predictors, or with a small sample, the same cutoff wouldn’t be as reliable, since the reference distribution and variability change.