.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statistics/nonparametric/plot_02_wilcoxon_mann_whitney.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_statistics_nonparametric_plot_02_wilcoxon_mann_whitney.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_statistics_nonparametric_plot_02_wilcoxon_mann_whitney.py:


Wilcoxon and Mann-Whitney rank tests
=========================================

Rank tests throw away the raw values and keep only their order, so a
few extreme observations cannot dominate. With heavy-tailed data they
detect a shift that the t-test misses.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.statistics import mann_whitney_u_test, two_sample_t_test, wilcoxon_signed_rank_test








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Two independent samples with heavy tails
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-28

.. code-block:: Python


    rng = np.random.default_rng(1)
    a = rng.standard_cauchy(size=60)
    b = rng.standard_cauchy(size=60) + 1.0
    mw = mann_whitney_u_test(a, b)
    tt = two_sample_t_test(a, b, equal_var=False)
    print(f"Mann-Whitney: U = {mw.statistic:.0f} of {a.size * b.size}, p = {mw.p_value:.4f}")
    print(f"Welch t-test: t = {tt.statistic:.3f}, p = {tt.p_value:.4f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Mann-Whitney: U = 1416 of 3600, p = 0.0441
    Welch t-test: t = -0.584, p = 0.5605




.. GENERATED FROM PYTHON SOURCE LINES 29-31

Paired measurements
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 31-42

.. code-block:: Python


    before = rng.normal(loc=120.0, scale=10.0, size=15)
    after = before - 4.0 + rng.standard_t(df=2, size=15) * 3.0
    paired = wilcoxon_signed_rank_test(before, after)
    print(f"Wilcoxon signed-rank on before - after: p = {paired.p_value:.4f}")

    fig, ax = plt.subplots()
    ax.boxplot([a, b])
    ax.set_xticks([1, 2], ["sample a", "sample b (shifted by 1)"])
    ax.set_ylim(-10, 10)
    ax.set_title("Cauchy samples, clipped to [-10, 10]")



.. image-sg:: /api/gallery/statistics/nonparametric/images/sphx_glr_plot_02_wilcoxon_mann_whitney_001.png
   :alt: Cauchy samples, clipped to [-10, 10]
   :srcset: /api/gallery/statistics/nonparametric/images/sphx_glr_plot_02_wilcoxon_mann_whitney_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Wilcoxon signed-rank on before - after: p = 0.0125

    Text(0.5, 1.0, 'Cauchy samples, clipped to [-10, 10]')




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.024 seconds)


.. _sphx_glr_download_api_gallery_statistics_nonparametric_plot_02_wilcoxon_mann_whitney.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_wilcoxon_mann_whitney.ipynb <plot_02_wilcoxon_mann_whitney.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_wilcoxon_mann_whitney.py <plot_02_wilcoxon_mann_whitney.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_wilcoxon_mann_whitney.zip <plot_02_wilcoxon_mann_whitney.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_