.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/qtest/plot_01_dixon_q_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_01_dixon_q_test.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_qtest_plot_01_dixon_q_test.py:


Dixon's Q-test for outlier rejection
========================================

:func:`~chemistrykit.analytical.systems.qtest.dixon_q_test` compares the
gap between a suspect value and its nearest neighbor, relative to the
full data range, against a tabulated critical value
(:data:`~chemistrykit.analytical.systems.qtest.Q_CRITICAL_TABLE`) that
depends on sample size and confidence level.

.. GENERATED FROM PYTHON SOURCE LINES 13-15

.. code-block:: Python

    from chemistrykit.analytical.systems.qtest import Q_CRITICAL_TABLE, dixon_q_test








.. GENERATED FROM PYTHON SOURCE LINES 16-17

Five replicate titration endpoints (mL), one of them clearly off:

.. GENERATED FROM PYTHON SOURCE LINES 17-24

.. code-block:: Python

    replicates = [24.51, 24.55, 24.48, 24.53, 25.10]

    for confidence in (0.90, 0.95, 0.99):
        result = dixon_q_test(replicates, confidence=confidence)
        verdict = "REJECT" if result.reject else "retain"
        print(f"confidence={confidence:.0%}: suspect={result.suspect_value}, Q={result.Q_statistic:.4f}, Q_crit={result.Q_critical:.4f} -> {verdict}")





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

 .. code-block:: none

    confidence=90%: suspect=25.1, Q=0.8871, Q_crit=0.6420 -> REJECT
    confidence=95%: suspect=25.1, Q=0.8871, Q_crit=0.7100 -> REJECT
    confidence=99%: suspect=25.1, Q=0.8871, Q_crit=0.8210 -> REJECT




.. GENERATED FROM PYTHON SOURCE LINES 25-28

The critical value grows with confidence level (harder to reject at
higher confidence) and shrinks with sample size (more data makes a
single outlier easier to identify):

.. GENERATED FROM PYTHON SOURCE LINES 28-32

.. code-block:: Python

    print("\nQ_crit(n, 95%) for n=3..10:")
    for n in range(3, 11):
        print(f"  n={n}: {Q_CRITICAL_TABLE[n][0.95]}")





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

 .. code-block:: none


    Q_crit(n, 95%) for n=3..10:
      n=3: 0.97
      n=4: 0.829
      n=5: 0.71
      n=6: 0.625
      n=7: 0.568
      n=8: 0.526
      n=9: 0.493
      n=10: 0.466




.. GENERATED FROM PYTHON SOURCE LINES 33-35

If the suspect value were retained instead (a smaller, more plausible
deviation), the Q-test would not reject it even at 90% confidence:

.. GENERATED FROM PYTHON SOURCE LINES 35-38

.. code-block:: Python

    close_replicates = [24.51, 24.55, 24.48, 24.53, 24.62]
    result = dixon_q_test(close_replicates, confidence=0.90)
    print(f"\nCloser data set: Q={result.Q_statistic:.4f}, Q_crit={result.Q_critical:.4f}, reject={result.reject}")




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

 .. code-block:: none


    Closer data set: Q=0.5000, Q_crit=0.6420, reject=False





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

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


.. _sphx_glr_download_api_gallery_analytical_qtest_plot_01_dixon_q_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_01_dixon_q_test.ipynb <plot_01_dixon_q_test.ipynb>`

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

      :download:`Download Python source code: plot_01_dixon_q_test.py <plot_01_dixon_q_test.py>`

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

      :download:`Download zipped: plot_01_dixon_q_test.zip <plot_01_dixon_q_test.zip>`


.. only:: html

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

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