| mad {stats} | R Documentation |
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.
mad(x, center = median(x), constant = 1.4826, na.rm = FALSE,
low = FALSE, high = FALSE)
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. |
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/ 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.
IQR which is simpler but less robust,
median, var.
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))