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bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / stats / _morestats / median_test

function

scipy.stats._morestats:median_test

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_morestats.py:4164

Signature

def median_test(*samples, ties = below, correction = True, lambda_ = 1, nan_policy = propagate)

Summary

Perform a Mood's median test.

Extended Summary

Test that two or more samples come from populations with the same median.

Let n = len(samples) be the number of samples. The "grand median" of all the data is computed, and a contingency table is formed by classifying the values in each sample as being above or below the grand median. The contingency table, along with correction and lambda_, are passed to scipy.stats.chi2_contingency to compute the test statistic and p-value.

Parameters

*samples : array_like

The set of samples. There must be at least two samples. The samples are not required to have the same length. Arrays may be multidimensional, in which case each slice along the last axis is treated independently.

ties : str, optional

Determines how values equal to the grand median are classified in the contingency table. The string must be one of 

"below":
    Values equal to the grand median are counted as "below".
"above":
    Values equal to the grand median are counted as "above".
"ignore":
    Values equal to the grand median are not counted.

The default is "below".

correction : bool, optional

If True, and there are just two samples, apply Yates' correction for continuity when computing the test statistic associated with the contingency table. Default is True.

lambda_ : float or str, optional

By default, the statistic computed in this test is Pearson's chi-squared statistic. lambda_ allows a statistic from the Cressie-Read power divergence family to be used instead. See power_divergence for details. Default is 1 (Pearson's chi-squared statistic).

nan_policy : {'propagate', 'raise', 'omit'}, optional

Defines how to handle when input contains nan. 'propagate' returns nan, 'raise' throws an error, 'omit' performs the calculations ignoring nan values. Default is 'propagate'.

Returns

res : MedianTestResult

An object containing attributes:

statistic

The test statistic. The statistic that is returned is determined by lambda_. The default is Pearson's chi-squared statistic.

pvalue

The p-value of the test.

median

The grand median.

table

The contingency table. The shape of the table is (2, n), where n is the number of samples. The first row holds the counts of the values above the grand median, and the second row holds the counts of the values below the grand median. The table allows further analysis with, for example, scipy.stats.chi2_contingency, or with scipy.stats.fisher_exact if there are two samples, without having to recompute the table. If nan_policy is "propagate" and there are nans in the input, the return value for table is None.

Notes

Examples

A biologist runs an experiment in which there are three groups of plants. Group 1 has 16 plants, group 2 has 15 plants, and group 3 has 17 plants. Each plant produces a number of seeds. The seed counts for each group are:: Group 1: 10 14 14 18 20 22 24 25 31 31 32 39 43 43 48 49 Group 2: 28 30 31 33 34 35 36 40 44 55 57 61 91 92 99 Group 3: 0 3 9 22 23 25 25 33 34 34 40 45 46 48 62 67 84 The following code applies Mood's median test to these samples. 
g1 = [10, 14, 14, 18, 20, 22, 24, 25, 31, 31, 32, 39, 43, 43, 48, 49]
g2 = [28, 30, 31, 33, 34, 35, 36, 40, 44, 55, 57, 61, 91, 92, 99]
g3 = [0, 3, 9, 22, 23, 25, 25, 33, 34, 34, 40, 45, 46, 48, 62, 67, 84]
from scipy.stats import median_test
res = median_test(g1, g2, g3)
✓
The median is 
res.median
✗
np.float64(34.0)
and the contingency table is 
res.table
✓
array([[ 5, 10,  7],
       [11,  5, 10]])
`p` is too large to conclude that the medians are not the same: 
res.pvalue
✗
np.float64(0.12609082774093244)
The "G-test" can be performed by passing ``lambda_="log-likelihood"`` to `median_test`. 
res = median_test(g1, g2, g3, lambda_="log-likelihood")
✓
res.pvalue
✗
np.float64(0.12224779737117829)
The median occurs several times in the data, so we'll get a different result if, for example, ``ties="above"`` is used: 
res = median_test(g1, g2, g3, ties="above")
✓
res.pvalue
✗
np.float64(0.06387327606955327)

res.table
✓
array([[ 5, 11,  9],
       [11,  4,  8]])
This example demonstrates that if the data set is not large and there are values equal to the median, the p-value can be sensitive to the choice of `ties`.

See also

kruskal

Compute the Kruskal-Wallis H-test for independent samples.

mannwhitneyu

Computes the Mann-Whitney rank test on samples x and y.

Aliases

  • scipy.stats.median_test

Referenced by

This package