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

# sem

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

  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.

  Parameters:
    a array_like

      An array containing the values for which the standard error is returned. Must contain at least two observations.

    axis int 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.

    ddof int, 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.

    keepdims bool, 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.

  Returns:
    s ndarray or float

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

  Notes

  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`.

  Array API Standard Support

  `sem` 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

  `sem` also accepts MArrays backed by the backends indicated above; masked values will be treated as though they were not present.

  See Support for the array API standard for more information.

  Examples

  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)
      1.2893796958227628