.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statistics/hypothesis_tests/plot_03_fisher_exact_lady_tea.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_hypothesis_tests_plot_03_fisher_exact_lady_tea.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_statistics_hypothesis_tests_plot_03_fisher_exact_lady_tea.py:


Fisher's exact test and the lady tasting tea
=================================================

Fisher's thought experiment: a lady claims she can tell whether milk or
tea was poured first. She is given 8 cups, 4 of each, and told so. If
she is only guessing, the number of milk-first cups she identifies
correctly follows a hypergeometric distribution, and getting all 4 right
happens with probability exactly 1/70.

.. GENERATED FROM PYTHON SOURCE LINES 13-19

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats

    from mathematicskit.statistics import fisher_exact_test








.. GENERATED FROM PYTHON SOURCE LINES 20-22

The null distribution of correct identifications
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 22-34

.. code-block:: Python


    k = np.arange(5)
    pmf = stats.hypergeom.pmf(k, 8, 4, 4)
    for correct in range(5):
        table = [[correct, 4 - correct], [4 - correct, correct]]
        p = fisher_exact_test(table, alternative="greater").p_value
        print(f"{correct} of 4 correct: P(exactly) = {pmf[correct] * 70:.0f}/70, one-sided p = {p:.4f}")

    fig, ax = plt.subplots()
    ax.bar(k, pmf * 70)
    ax.set_xlabel("milk-first cups correctly identified")
    ax.set_ylabel("ways out of 70")



.. image-sg:: /api/gallery/statistics/hypothesis_tests/images/sphx_glr_plot_03_fisher_exact_lady_tea_001.png
   :alt: plot 03 fisher exact lady tea
   :srcset: /api/gallery/statistics/hypothesis_tests/images/sphx_glr_plot_03_fisher_exact_lady_tea_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    0 of 4 correct: P(exactly) = 1/70, one-sided p = 1.0000
    1 of 4 correct: P(exactly) = 16/70, one-sided p = 0.9857
    2 of 4 correct: P(exactly) = 36/70, one-sided p = 0.7571
    3 of 4 correct: P(exactly) = 16/70, one-sided p = 0.2429
    4 of 4 correct: P(exactly) = 1/70, one-sided p = 0.0143

    Text(46.722222222222214, 0.5, 'ways out of 70')




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

   **Total running time of the script:** (0 minutes 0.019 seconds)


.. _sphx_glr_download_api_gallery_statistics_hypothesis_tests_plot_03_fisher_exact_lady_tea.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_fisher_exact_lady_tea.ipynb <plot_03_fisher_exact_lady_tea.ipynb>`

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

      :download:`Download Python source code: plot_03_fisher_exact_lady_tea.py <plot_03_fisher_exact_lady_tea.py>`

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

      :download:`Download zipped: plot_03_fisher_exact_lady_tea.zip <plot_03_fisher_exact_lady_tea.zip>`


.. only:: html

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

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