mad {base}R Documentation

Median Absolute Deviation

Description

Compute a scale estimate based on the median absolute deviation.

Usage

mad(x, center, constant = 1.4826, na.rm = FALSE)

Arguments

x a numeric vector.
center Optionally, the centre: defauls to the median.
constant scale factor.
na.rm if TRUE then NA values are stripped from x before computation takes place.

Details

The actual value calculated is constant * (median(abs(x - center))) with the default value of center being median(x).

The default constant = 1.4826 (approximately 1/ Phi^(-1)(3/4) = 1/qnorm(3/4)) ensures consistency, i.e.,

E[mad(X_1,...,X_n)] = σ

for X_i distributed as N(μ,σ^2) and large n.

If na.rm is TRUE then NA values are stripped from x before computation takes place. If this is not done then an NA value in x will cause mad to return NA.

See Also

IQR which is simpler but less robust, median, var.

Examples

mad(c(1:9))
print(mad(c(1:9),     constant=1)) ==
      mad(c(1:8,100), constant=1)       # = 2 ; TRUE
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