Confidence intervals for median absolute deviations

Abstract

The median absolute deviation (MAD) is a robust measure of scale that is simple to implement, easy to interpret and often reported as a measure of dispersion when data is skewed. However, confidence intervals either for a single MAD or for the comparison of two MADs are lacking, meaning that interpretations may be subjective. We introduce interval estimators of the MAD to make reliable inferences for dispersion based on MADs. Our simulation results show that the coverages of the intervals are very close to the nominal for a variety of distributions, including those heavily skewed. We also present examples that clearly highlight the advantages of using these intervals instead of the heavily criticized intervals derived from sample variances for skewed data.