Skip to main content
`Ctrl`+`K`
scipy.stats.

# zscore

scipy.stats.zscore(a, axis=0, ddof=0, nan_policy='propagate')

  Compute the z score.

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

  Parameters:
    a array_like

      An array like object containing the sample data.

    axis int or None, optional

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

    ddof int, 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:
    zscore array_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).

  `zscore` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  See Support for the array API standard for more information.

  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 ]])