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Median Absolute Deviation (robust dispersion)

Source: R/ops-timefreq.R
medianAbsDev.Rd

Computes the median absolute deviation (MAD) of a one-dimensional signal – \(\mathrm{MAD} = c \cdot \mathrm{median}(|x - \mathrm{median}(x)|)\) – a robust measure of dispersion that, unlike the standard deviation, is not inflated by a small number of extreme values (spikes, movement artifacts). With the default constant = 1 it returns the raw MAD; set constant = 1 / stats::qnorm(0.75) (approximately 1.4826) to obtain the normal-consistent robust estimate of the standard deviation (the scale MAD and SD share for Gaussian data).

Usage

medianAbsDev(x, constant = 1)

Arguments

x

A numeric vector (the time series).

constant

Scale factor (default 1, the raw MAD). Use 1 / stats::qnorm(0.75) for the normal-consistent robust SD estimate.

Value

A single numeric value, the (scaled) median absolute deviation.

Details

The robust dispersion companion of signalMoments (whose SD is the classical, non-robust dispersion). Comparing the normal-consistent MAD with the SD is a quick artifact check: they agree for clean, near-Gaussian data and diverge (MAD-scale below SD) when heavy-tailed artifacts inflate the SD.

See also

signalMoments for the classical moments (mean, SD, skewness, kurtosis).

Examples

medianAbsDev(c(1, 2, 3, 4, 100))                         # robust to the outlier
#> [1] 1
set.seed(1); medianAbsDev(rnorm(1000), 1 / stats::qnorm(0.75))  # ~1 (robust SD)
#> [1] 1.031688