R: Median Absolute Deviation

mad {stats}

R Documentation

Median Absolute Deviation

Description

Compute the median absolute deviation, i.e., the (lo-/hi-) median of the absolute deviations from the median, and (by default) adjust by a factor for asymptotically normal consistency.

Usage

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

Arguments

`x`	a numeric vector.
`center`	Optionally, the centre: defaults to the median.
`constant`	scale factor.
`na.rm`	if `TRUE` then `NA` values are stripped from `x` before computation takes place.
`low`	if `TRUE`, compute the ‘lo-median’, i.e., for even sample size, do not average the two middle values, but take the smaller one.
`high`	if `TRUE`, compute the ‘hi-median’, i.e., take the larger of the two middle values for even sample size.

Details

The actual value calculated is constant * cMedian(abs(x - center)) with the default value of center being median(x), and cMedian being the usual, the ‘low’ or ‘high’ median, see the arguments description for low and high above.

The default constant = 1.4826 (approximately 1/ Φ^(-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.

Examples

mad(c(1:9))
print(mad(c(1:9),     constant = 1)) ==
      mad(c(1:8, 100), constant = 1)       # = 2 ; TRUE
x <- c(1,2,3,5,7,8)
sort(abs(x - median(x)))
c(mad(x, constant = 1),
  mad(x, constant = 1, low = TRUE),
  mad(x, constant = 1, high = TRUE))