scipy.stats.mood#

scipy.stats.mood(x, y, axis=0, alternative='two-sided', *, nan_policy='propagate', keepdims=False)[source]#

Perform Mood’s test for equal scale parameters.

Mood’s two-sample test for scale parameters is a non-parametric test for the null hypothesis that two samples are drawn from the same distribution with the same scale parameter.

Parameters:

x, yarray_like

Arrays of sample data.

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.

alternative{‘two-sided’, ‘less’, ‘greater’}, optional

Defines the alternative hypothesis. Default is ‘two-sided’. The following options are available:

‘two-sided’: the scales of the distributions underlying x and y are different.
‘less’: the scale of the distribution underlying x is less than the scale of the distribution underlying y.
‘greater’: the scale of the distribution underlying x is greater than the scale of the distribution underlying y.

Added in version 1.7.0.

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.

Returns:

resSignificanceResult

An object containing attributes:

statisticscalar or ndarray: The z-score for the hypothesis test. For 1-D inputs a scalar is returned.
pvaluescalar ndarray: The p-value for the hypothesis test.

See also

fligner: A non-parametric test for the equality of k variances
ansari: A non-parametric test for the equality of 2 variances
bartlett: A parametric test for equality of k variances in normal samples
levene: A parametric test for equality of k variances

Notes

The data are assumed to be drawn from probability distributions f(x) and f(x/s) / s respectively, for some probability density function f. The null hypothesis is that s == 1.

For multi-dimensional arrays, if the inputs are of shapes (n0, n1, n2, n3) and (n0, m1, n2, n3), then if axis=1, the resulting z and p values will have shape (n0, n2, n3). Note that n1 and m1 don’t have to be equal, but the other dimensions do.

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.

References

[1] Mielke, Paul W. “Note on Some Squared Rank Tests with Existing Ties.”: Technometrics, vol. 9, no. 2, 1967, pp. 312-14. JSTOR, https://doi.org/10.2307/1266427. Accessed 18 May 2022.

Examples

>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()
>>> x2 = rng.standard_normal((2, 45, 6, 7))
>>> x1 = rng.standard_normal((2, 30, 6, 7))
>>> res = stats.mood(x1, x2, axis=1)
>>> res.pvalue.shape
(2, 6, 7)

Find the number of points where the difference in scale is not significant:

>>> (res.pvalue > 0.1).sum()
78

Perform the test with different scales:

>>> x1 = rng.standard_normal((2, 30))
>>> x2 = rng.standard_normal((2, 35)) * 10.0
>>> stats.mood(x1, x2, axis=1)
SignificanceResult(statistic=array([-5.76174136, -6.12650783]),
                   pvalue=array([8.32505043e-09, 8.98287869e-10]))