scipy.stats.sem(a, axis=0, ddof=1, nan_policy='propagate', *, keepdims=False)[source]#

Compute standard error of the mean.

Calculate the standard error of the mean (or standard error of measurement) of the values in the input array.


An array containing the values for which the standard error is returned.

axisint or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

ddofint, optional

Delta degrees-of-freedom. How many degrees of freedom to adjust for bias in limited samples relative to the population estimate of variance. Defaults to 1.

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

Defines how to handle input NaNs.

  • propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.

  • omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.

  • raise: if a NaN is present, a ValueError will be raised.

keepdimsbool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

sndarray or float

The standard error of the mean in the sample(s), along the input axis.


The default value for ddof is different to the default (0) used by other ddof containing routines, such as np.std and np.nanstd.

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.


Find standard error along the first axis:

>>> import numpy as np
>>> from scipy import stats
>>> a = np.arange(20).reshape(5,4)
>>> stats.sem(a)
array([ 2.8284,  2.8284,  2.8284,  2.8284])

Find standard error across the whole array, using n degrees of freedom:

>>> stats.sem(a, axis=None, ddof=0)