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/ 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
x <- c(1,2,3, 5,7,8)
sort(abs(x - median(x)))
c(mad(x, co=1), mad(x, co=1, lo = TRUE), mad(x, co=1, hi = TRUE))
```

[Package stats version 2.2.1 Index]