Paper 163-30 A Macro for Computing Point Estimates and Confidence Intervals for Mahalanobis Distance

This paper discusses a SAS ® macro that provides three approaches to statistical inferences about Mahalanobis distance. Mahalanobis distance is useful as a multivariate effect size, being an extension of the standardized mean difference (i.e., Cohen’s d). This program calculates three point estimates of D2 (a sample estimate, a jackknife estimate, and an adjusted estimate advanced by Rao, 1973). Further, the program computes a series of confidence bands around each estimated value of D2. These confidence intervals are calculated employing two estimation procedures (an interval inversion approach and a common bootstrapping method). The paper presents a demonstration of the SAS/IML ® code employed in a macro entitled D2BAND, and provides a table with the resulting output