scipy.stats.

zscore#

scipy.stats.zscore(a, axis=0, ddof=0, nan_policy='propagate')[source]#

Compute the z score.

Compute the z score of each value in the sample, relative to the sample mean and standard deviation.

Parameters:
aarray_like

An array like object containing the sample data.

axisint or None, optional

Axis along which to operate. Default is 0. If None, compute over the whole array a.

ddofint, optional

Degrees of freedom correction in the calculation of the standard deviation. Default is 0.

nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’. Note that when the value is ‘omit’, nans in the input also propagate to the output, but they do not affect the z-scores computed for the non-nan values.

Returns:
zscorearray_like

The z-scores, standardized by mean and standard deviation of input array a.

See also

numpy.mean

Arithmetic average

numpy.std

Arithmetic standard deviation

scipy.stats.gzscore

Geometric standard score

Notes

This function preserves ndarray subclasses, and works also with matrices and masked arrays (it uses asanyarray instead of asarray for parameters).

References

[1]

“Standard score”, Wikipedia, https://en.wikipedia.org/wiki/Standard_score.

[2]

Huck, S. W., Cross, T. L., Clark, S. B, “Overcoming misconceptions about Z-scores”, Teaching Statistics, vol. 8, pp. 38-40, 1986

Examples

>>> import numpy as np
>>> a = np.array([ 0.7972,  0.0767,  0.4383,  0.7866,  0.8091,
...                0.1954,  0.6307,  0.6599,  0.1065,  0.0508])
>>> from scipy import stats
>>> stats.zscore(a)
array([ 1.1273, -1.247 , -0.0552,  1.0923,  1.1664, -0.8559,  0.5786,
        0.6748, -1.1488, -1.3324])

Computing along a specified axis, using n-1 degrees of freedom (ddof=1) to calculate the standard deviation:

>>> b = np.array([[ 0.3148,  0.0478,  0.6243,  0.4608],
...               [ 0.7149,  0.0775,  0.6072,  0.9656],
...               [ 0.6341,  0.1403,  0.9759,  0.4064],
...               [ 0.5918,  0.6948,  0.904 ,  0.3721],
...               [ 0.0921,  0.2481,  0.1188,  0.1366]])
>>> stats.zscore(b, axis=1, ddof=1)
array([[-0.19264823, -1.28415119,  1.07259584,  0.40420358],
       [ 0.33048416, -1.37380874,  0.04251374,  1.00081084],
       [ 0.26796377, -1.12598418,  1.23283094, -0.37481053],
       [-0.22095197,  0.24468594,  1.19042819, -1.21416216],
       [-0.82780366,  1.4457416 , -0.43867764, -0.1792603 ]])

An example with nan_policy='omit':

>>> x = np.array([[25.11, 30.10, np.nan, 32.02, 43.15],
...               [14.95, 16.06, 121.25, 94.35, 29.81]])
>>> stats.zscore(x, axis=1, nan_policy='omit')
array([[-1.13490897, -0.37830299,         nan, -0.08718406,  1.60039602],
       [-0.91611681, -0.89090508,  1.4983032 ,  0.88731639, -0.5785977 ]])
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