Evaluating Outlier Identification Tests: Mahalanobis D Squared and Comrey Dk

Area of Science:

• Statistics
• Data Analysis
• Outlier Detection

Background:

• Outlier detection is crucial in statistical analysis to ensure data integrity.
• Comrey's Dk statistic was proposed as a sensitive alternative to Mahalanobis D squared for identifying outliers.
• The potential advantage of Dk lies in its sensitivity to outliers affecting correlation coefficients.

Purpose of the Study:

• To compare the performance of Comrey's Dk and Mahalanobis D squared outlier detection statistics.
• To evaluate hit rates, false alarm rates, overlap, and the impact on correlation coefficients after outlier removal.

Main Methods:

• A Monte Carlo simulation was employed for a robust comparison.
• Key performance metrics included hit rates, false alarm rates, and outlier identification overlap.
• The effect of outlier removal on resulting correlation coefficients was analyzed.

Main Results:

• Mahalanobis D squared exhibited a higher hit rate than Dk, with comparable false alarm rates.
• The two statistics identified the same outliers in 19% to 55% of cases.
• Outlier removal using Mahalanobis D squared resulted in correlations closer to population values than Dk.

Conclusions:

• Mahalanobis D squared is preferable to Dk for outlier detection under the simulated conditions.
• The study provides empirical evidence supporting the efficacy of Mahalanobis D squared over Dk.