papyri
{ } Raw JSON

bundles / scipy 1.17.1 / scipy / stats / _morestats / ansari

function

scipy.stats._morestats:ansari

source: /scipy/stats/_morestats.py :2885

Signature

def   ansari ( x ,  y ,  alternative = two-sided ,  * ,  axis = 0 ,  nan_policy = propagate ,  keepdims = False )

Summary

Perform the Ansari-Bradley test for equal scale parameters.

Extended Summary

The Ansari-Bradley test ([1], [2]) is a non-parametric test for the equality of the scale parameter of the distributions from which two samples were drawn. The null hypothesis states that the ratio of the scale of the distribution underlying x to the scale of the distribution underlying y is 1.

Parameters

x, y : array_like

Arrays of sample data.

alternative : {'two-sided', 'less', 'greater'}, optional

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

  • 'two-sided': the ratio of scales is not equal to 1.

  • 'less': the ratio of scales is less than 1.

  • 'greater': the ratio of scales is greater than 1.

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.

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

statistic : float

The Ansari-Bradley test statistic.

pvalue : float

The p-value of the hypothesis test.

Notes

The p-value given is exact when the sample sizes are both less than 55 and there are no ties, otherwise a normal approximation for the p-value is used.

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

ansari 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                   ⚠️ no JIT             ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import numpy as np
from scipy.stats import ansari
rng = np.random.default_rng()
✓
For these examples, we'll create three random data sets. The first two, with sizes 35 and 25, are drawn from a normal distribution with mean 0 and standard deviation 2. The third data set has size 25 and is drawn from a normal distribution with standard deviation 1.25. 
x1 = rng.normal(loc=0, scale=2, size=35)
x2 = rng.normal(loc=0, scale=2, size=25)
x3 = rng.normal(loc=0, scale=1.25, size=25)
✓
First we apply `ansari` to `x1` and `x2`. These samples are drawn from the same distribution, so we expect the Ansari-Bradley test should not lead us to conclude that the scales of the distributions are different. 
ansari(x1, x2)
✗
With a p-value close to 1, we cannot conclude that there is a significant difference in the scales (as expected). Now apply the test to `x1` and `x3`: 
ansari(x1, x3)
✗
The probability of observing such an extreme value of the statistic under the null hypothesis of equal scales is only 0.03087%. We take this as evidence against the null hypothesis in favor of the alternative: the scales of the distributions from which the samples were drawn are not equal. We can use the `alternative` parameter to perform a one-tailed test. In the above example, the scale of `x1` is greater than `x3` and so the ratio of scales of `x1` and `x3` is greater than 1. This means that the p-value when ``alternative='greater'`` should be near 0 and hence we should be able to reject the null hypothesis: 
ansari(x1, x3, alternative='greater')
✗
As we can see, the p-value is indeed quite low. Use of ``alternative='less'`` should thus yield a large p-value: 
ansari(x1, x3, alternative='less')
✗

See also

fligner

A non-parametric test for the equality of k variances

mood

A non-parametric test for the equality of two scale parameters

Aliases

  • scipy.stats.ansari

Referenced by

This package