.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/qtest/plot_02_grubbs_outlier_test.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_analytical_qtest_plot_02_grubbs_outlier_test.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_qtest_plot_02_grubbs_outlier_test.py:


Grubbs' outlier test: the extreme value in standard deviations
=================================================================

:func:`~chemistrykit.analytical.grubbs_test` computes
:math:`G=\max_i|x_i-\bar x|/s` and compares it with the critical value
:func:`~chemistrykit.analytical.grubbs_critical_value`, derived from
Student's `t` distribution so that it exists for any sample size. A Monte
Carlo run on outlier-free normal data confirms that the test falsely
rejects a point at the nominal rate :math:`\alpha`.

.. GENERATED FROM PYTHON SOURCE LINES 14-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import grubbs_critical_value, grubbs_test

    replicates = [24.51, 24.55, 24.48, 24.53, 24.50, 24.54, 24.79]  # mL, one suspicious endpoint
    result = grubbs_test(replicates, alpha=0.05)
    print(f"suspect = {result.suspect_value}, G = {result.G_statistic:.3f}, G_crit(n=7, 5%) = {result.G_critical:.3f} -> {'REJECT' if result.reject else 'retain'}")





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

 .. code-block:: none

    suspect = 24.79, G = 2.208, G_crit(n=7, 5%) = 2.020 -> REJECT




.. GENERATED FROM PYTHON SOURCE LINES 24-25

False-rejection rate on clean normal data, for several sample sizes:

.. GENERATED FROM PYTHON SOURCE LINES 25-33

.. code-block:: Python

    rng = np.random.default_rng(2024)
    sizes = [4, 6, 10, 20, 40]
    rates = []
    for n in sizes:
        rejections = sum(grubbs_test(rng.normal(size=n), alpha=0.05).reject for _ in range(4000))
        rates.append(rejections / 4000)
        print(f"n = {n:2d}: G_crit = {grubbs_critical_value(n):.3f}, false-rejection rate = {rates[-1]:.3f} (nominal 0.05)")





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

 .. code-block:: none

    n =  4: G_crit = 1.481, false-rejection rate = 0.051 (nominal 0.05)
    n =  6: G_crit = 1.887, false-rejection rate = 0.050 (nominal 0.05)
    n = 10: G_crit = 2.290, false-rejection rate = 0.048 (nominal 0.05)
    n = 20: G_crit = 2.708, false-rejection rate = 0.054 (nominal 0.05)
    n = 40: G_crit = 3.036, false-rejection rate = 0.053 (nominal 0.05)




.. GENERATED FROM PYTHON SOURCE LINES 34-54

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    x = np.asarray(replicates)
    z = (x - x.mean()) / x.std(ddof=1)
    axes[0].stem(np.arange(1, len(x) + 1), z)
    axes[0].axhline(result.G_critical, color="crimson", linestyle="--", label=f"$\\pm G_{{crit}}$ = {result.G_critical:.3f}")
    axes[0].axhline(-result.G_critical, color="crimson", linestyle="--")
    axes[0].set_xlabel("replicate")
    axes[0].set_ylabel(r"$(x_i-\bar x)/s$")
    axes[0].set_title("Replicate titration endpoints")
    axes[0].legend()

    n_grid = np.arange(3, 61)
    axes[1].plot(n_grid, [grubbs_critical_value(n, 0.05) for n in n_grid], label=r"$\alpha$ = 0.05")
    axes[1].plot(n_grid, [grubbs_critical_value(n, 0.01) for n in n_grid], label=r"$\alpha$ = 0.01")
    axes[1].set_xlabel("sample size n")
    axes[1].set_ylabel(r"$G_{crit}$")
    axes[1].set_title("Critical value grows with n")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/qtest/images/sphx_glr_plot_02_grubbs_outlier_test_001.png
   :alt: Replicate titration endpoints, Critical value grows with n
   :srcset: /api/gallery/analytical/qtest/images/sphx_glr_plot_02_grubbs_outlier_test_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.593 seconds)


.. _sphx_glr_download_api_gallery_analytical_qtest_plot_02_grubbs_outlier_test.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_grubbs_outlier_test.ipynb <plot_02_grubbs_outlier_test.ipynb>`

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

      :download:`Download Python source code: plot_02_grubbs_outlier_test.py <plot_02_grubbs_outlier_test.py>`

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

      :download:`Download zipped: plot_02_grubbs_outlier_test.zip <plot_02_grubbs_outlier_test.zip>`


.. only:: html

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

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