Robust analogs to the coefficient of variation

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• The coefficient of variation (CV) is a standard metric for relative dispersion.
• CV is sensitive to outliers and can be unreliable for skewed distributions.
• Mean and standard deviation, used in CV, are problematic for non-normal data.

Purpose of the Study:

• To evaluate quantile-based measures as robust alternatives to the CV.
• To assess the suitability of interquartile range divided by median and median absolute deviation divided by median.
• To compare the performance of these robust estimators against the traditional CV.

Main Methods:

• Investigated two quantile-based measures: (Interquartile Range / Median) and (Median Absolute Deviation / Median).
• Analyzed influence functions, asymptotic biases, and variances of competing estimators.
• Conducted simulation studies to compare interval estimator coverage.

Main Results:

• Quantile-based measures demonstrate robustness against outliers.
• These alternative estimators provide reliable relative dispersion summaries for skewed data.
• Simulation results indicate favorable performance of robust estimators in interval estimation.

Conclusions:

• Quantile-based measures are superior alternatives to the coefficient of variation for relative dispersion.
• These robust estimators are recommended for skewed distributions and datasets with potential outliers.
• Further investigation into robust statistical measures is warranted for improved data analysis.