pingouin.mad#

pingouin.mad(a, normalize=True, axis=0)[source]#

Median Absolute Deviation (MAD) along given axis of an array.

Parameters:

aarray-like: Input array.
normalizeboolean.: If True, scale by a normalization constant $c \approx 0.67$ to ensure consistency with the standard deviation for normally distributed data.
axisint or None, optional: Axis along which the MAD is computed. Default is 0. Can also be None to compute the MAD over the entire array.

Returns:

madfloat: mad = median(abs(a - median(a))) / c

See also

madmedianrule, numpy.std

Notes

The median absolute deviation (MAD) computes the median over the absolute deviations from the median. It is a measure of dispersion similar to the standard deviation, but is more robust to outliers.

SciPy 1.3 and higher includes a similar function: scipy.stats.median_abs_deviation().

Please note that missing values are automatically removed.

Examples

>>> from pingouin import mad
>>> a = [1.2, 5.4, 3.2, 7.8, 2.5]
>>> mad(a)
2.965204437011204

>>> mad(a, normalize=False)
2.0

2D arrays with missing values (axis handling example)

>>> import numpy as np
>>> np.random.seed(123)
>>> w = np.random.normal(size=(5, 10))
>>> w[3, 2] = np.nan
>>> mad(w)  # Axis = 0 (default) = iterate over the columns
array([0.60304023, 2.35057834, 0.90350696, 1.28599837, 1.16024152,
       0.38653752, 1.92564066, 1.2480913 , 0.42580373, 1.69814622])

>>> mad(w, axis=1)  # Axis = 1 = iterate over the rows
array([1.32639022, 1.19295036, 1.41198672, 0.78020689, 1.01531254])

>>> mad(w, axis=None)  # Axis = None = over the entire array
1.1607762457644006

Compare with Scipy >= 1.3

>>> from scipy.stats import median_abs_deviation
>>> median_abs_deviation(w, scale='normal', axis=None, nan_policy='omit')
1.1607762457644006