  The median absolute deviation is a widely used robust measure of statistical
dispersion. Using a scale constant, we can use it as an asymptotically
consistent estimator for the standard deviation under normality. For finite
samples, the scale constant should be corrected in order to obtain an unbiased
estimator. The bias-correction factor depends on the sample size and the median
estimator. When we use the traditional sample median, the factor values are
well known, but this approach does not provide optimal statistical efficiency.
In this paper, we present the bias-correction factors for the median absolute
deviation based on the Harrell-Davis quantile estimator and its trimmed
modification which allow us to achieve better statistical efficiency of the
standard deviation estimations. The obtained estimators are especially useful
for samples with a small number of elements.
