scipy.stats.

spearmanrho#

scipy.stats.spearmanrho(x, y, /, *, alternative='two-sided', method=None, axis=0, nan_policy='propagate', keepdims=False)[source]#

Calculate a Spearman rho correlation coefficient with associated p-value.

The Spearman rank-order correlation coefficient is a nonparametric measure of the monotonicity of the relationship between two datasets. Like other correlation coefficients, it varies between -1 and +1 with 0 implying no correlation. Coefficients of -1 or +1 are associated with an exact monotonic relationship. Positive correlations indicate that as x increases, so does y; negative correlations indicate that as x increases, y decreases. The p-value is the probability of an uncorrelated system producing datasets with a Spearman correlation at least as extreme as the one computed from the observed dataset.

Parameters:
x, yarray-like

The samples: corresponding observations of the independent and dependent variable. The (N-d) arrays must be broadcastable.

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

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

  • ‘two-sided’: the correlation is nonzero

  • ‘less’: the correlation is negative (less than zero)

  • ‘greater’: the correlation is positive (greater than zero)

methodResamplingMethod, optional

Defines the method used to compute the p-value. If method is an instance of PermutationMethod/MonteCarloMethod, the p-value is computed using scipy.stats.permutation_test/scipy.stats.monte_carlo_test with the provided configuration options and other appropriate settings. Otherwise, the p-value is computed using an asymptotic approximation of the null distribution.

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.

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:

statisticfloating point array or NumPy scalar

Spearman correlation coefficient

pvaluefloating point array NumPy scalar

The p-value - the probabilitiy of realizing such an extreme statistic value under the null hypothesis that two samples have no ordinal correlation. See alternative above for alternative hypotheses.

Warns:
ConstantInputWarning

Raised if an input is a constant array. The correlation coefficient is not defined in this case, so np.nan is returned.

Notes

spearmanrho was created to make improvements to SciPy’s implementation of the Spearman correlation test without making backward-incompatible changes to spearmanr. Advantages of spearmanrho over spearmanr include:

  • spearmanrho follows standard array broadcasting rules.

  • spearmanrho is compatible with some non-NumPy arrays.

  • spearmanrho can compute exact p-values, even in the presence of ties, when an appropriate instance of PermutationMethod is provided via the method argument.

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

spearmanrho 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]

Zwillinger, D. and Kokoska, S. (2000). CRC Standard Probability and Statistics Tables and Formulae. Chapman & Hall: New York. 2000. Section 14.7

[2]

Kendall, M. G. and Stuart, A. (1973). The Advanced Theory of Statistics, Volume 2: Inference and Relationship. Griffin. 1973. Section 31.18

Examples

Univariate samples, approximate p-value.

>>> import numpy as np
>>> from scipy import stats
>>> x = [1, 2, 3, 4, 5]
>>> y = [5, 6, 7, 8, 7]
>>> res = stats.spearmanrho(x, y)
>>> res.statistic
np.float64(0.8207826816681233)
>>> res.pvalue
np.float64(0.08858700531354405)

Univariate samples, exact p-value.

>>> res = stats.spearmanrho(x, y, method=stats.PermutationMethod())
>>> res.statistic
np.float64(0.8207826816681233)
>>> res.pvalue
np.float64(0.13333333333333333)

Batch of univariate samples, one vectorized call.

>>> rng = np.random.default_rng()
>>> x2 = rng.standard_normal((2, 100))
>>> y2 = rng.standard_normal((2, 100))
>>> res = stats.spearmanrho(x2, y2, axis=-1)
>>> res.statistic
array([ 0.16585659, -0.12151215])
>>> res.pvalue
array([0.0991155 , 0.22846869])

Bivariate samples using standard broadcasting rules.

>>> res = stats.spearmanrho(x2[np.newaxis, :], x2[:, np.newaxis], axis=-1)
>>> res.statistic
array([[ 1.        , -0.14670267],
       [-0.14670267,  1.        ]])
>>> res.pvalue
array([[0.        , 0.14526128],
       [0.14526128, 0.        ]])
On this page