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bundles / scipy latest / scipy / stats / _morestats / median_test

function

scipy.stats._morestats:median_test

source: /scipy/stats/_morestats.py :3961

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

sample1, sample2, ... : array_like

The set of samples. There must be at least two samples. Each sample must be a one-dimensional sequence containing at least one value. The samples are not required to have the same length.

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

statistic

pvalue

pvalue

median

median

table

table

Notes

Array API Standard Support

median_test 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 dev-arrayapi for more information.

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
✗
and the contingency table is 
res.table
✓
`p` is too large to conclude that the medians are not the same: 
res.pvalue
✗
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
✗
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
✗
res.table
✓
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