Evaluating Outlier Identification Tests: Mahalanobis D Squared and Comrey Dk.

TLDR: A Monte Carlo simulation used to compare Dk and D squared in terms of their hit and false alarm rates, their extent of overlap, and their effect on correlation coefficients resulting from outlier removal indicated that D squared had a higher hit rate than Dk with approximately the same false alarm rate.

Abstract: Comrey (1985) presented a statistic, Dk, to detect outliers. Its purported advantage over the more well-known Mahalanobis D squared is that it might be more sensitive to outliers that distort the correlation coefficient. The present study used a Monte Carlo simulation to compare Dk and D squared in terms of their hit and false alarm rates, their extent of overlap, and their effect on correlation coefficients resulting from outlier removal. The results indicated that D squared had a higher hit rate than Dk with approximately the same false alarm rate. The statistics identified the same cases as outliers 19 to 55 percent of the time. Surprising, the average correlations that resulted from outlier removal by D squared were closer to the population correlations than were those resulting from outlier removal by Dk. Under the conditions investigated, D squared was preferable to Dk as an outlier removal statistic.