.. 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_02_chi_square_tests.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_02_chi_square_tests.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_statistics_hypothesis_tests_plot_02_chi_square_tests.py:


Chi-square goodness-of-fit and independence tests
==========================================================

Pearson's chi-square statistic applied two ways: testing whether a
die's observed roll counts match a fair-die model (goodness-of-fit),
and testing whether two categorical variables in a contingency table
are independent.

.. GENERATED FROM PYTHON SOURCE LINES 12-16

.. code-block:: Python

    import numpy as np

    from mathematicskit.statistics import chi_square_goodness_of_fit, chi_square_independence








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Goodness-of-fit: is this die fair?
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-29

.. code-block:: Python


    rng = np.random.default_rng(0)
    rolls = rng.choice(6, size=600, p=[0.14, 0.16, 0.15, 0.15, 0.17, 0.23])
    observed = np.array([np.sum(rolls == face) for face in range(6)], dtype=float)
    expected = np.full(6, 100.0)

    gof_result = chi_square_goodness_of_fit(observed, expected)
    print(f"chi2={gof_result.statistic:.3f}, df={gof_result.df:.0f}, p={gof_result.p_value:.4f}")
    print("reject fair-die null at alpha=0.05:", gof_result.reject_null(alpha=0.05))





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

 .. code-block:: none

    chi2=41.040, df=5, p=0.0000
    reject fair-die null at alpha=0.05: True




.. GENERATED FROM PYTHON SOURCE LINES 30-32

Independence: does treatment outcome depend on treatment group?
-----------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 32-37

.. code-block:: Python


    contingency_table = np.array([[30.0, 10.0], [20.0, 40.0]])
    independence_result = chi_square_independence(contingency_table)
    print(f"chi2={independence_result.statistic:.3f}, df={independence_result.df:.0f}, p={independence_result.p_value:.6f}")
    print("expected counts under independence:\n", independence_result.extra["expected"])




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

 .. code-block:: none

    chi2=16.667, df=1, p=0.000045
    expected counts under independence:
     [[20. 20.]
     [30. 30.]]





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

   **Total running time of the script:** (0 minutes 0.001 seconds)


.. _sphx_glr_download_api_gallery_statistics_hypothesis_tests_plot_02_chi_square_tests.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_chi_square_tests.ipynb <plot_02_chi_square_tests.ipynb>`

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

      :download:`Download Python source code: plot_02_chi_square_tests.py <plot_02_chi_square_tests.py>`

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

      :download:`Download zipped: plot_02_chi_square_tests.zip <plot_02_chi_square_tests.zip>`


.. only:: html

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

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