Robust measures of scale

In statistics, robust measures of scale are methods which quantify the statistical dispersion in a sample of numerical data while resisting outliers. These are contrasted with conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers.

The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). Alternatives robust estimators have also been developed, such as those based on pairwise differences and biweight midvariance.

These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics.

Note that, in domains such as finance, the assumption of normality may lead to excessive risk exposure, and that further parameterization may be needed to mitigate risks presented by abnormal kurtosis.