.. _sphx_glr_api_gallery_statistics_hypothesis_tests:

Hypothesis tests
------------------

z-tests, Student's t-tests, chi-square tests (goodness-of-fit and
independence), Fisher's exact test, and one-way ANOVA.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="With only a handful of measurements, the standardized mean t = (\bar x - \mu_0)/(s/\sqrt n) is not normal: estimating the spread from the same small sample gives it heavier tails. Gosset (&quot;Student&quot;, 1908) derived its exact distribution. This example shows the heavy tails, how a normal cutoff misleads for small samples, and the one- and two-sample t-tests built on Student&#x27;s distribution.">

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  .. image:: /api/gallery/statistics/hypothesis_tests/images/thumb/sphx_glr_plot_01_student_t_test_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/hypothesis_tests/plot_01_student_t_test`

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      <div class="sphx-glr-thumbnail-title">Student's t-distribution and the small-sample t-test</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Pearson&#x27;s chi-square statistic applied two ways: testing whether a die&#x27;s observed roll counts match a fair-die model (goodness-of-fit), and testing whether two categorical variables in a contingency table are independent.">

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  .. image:: /api/gallery/statistics/hypothesis_tests/images/thumb/sphx_glr_plot_02_chi_square_tests_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/hypothesis_tests/plot_02_chi_square_tests`

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      <div class="sphx-glr-thumbnail-title">Chi-square goodness-of-fit and independence tests</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Fisher&#x27;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.">

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  .. image:: /api/gallery/statistics/hypothesis_tests/images/thumb/sphx_glr_plot_03_fisher_exact_lady_tea_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/hypothesis_tests/plot_03_fisher_exact_lady_tea`

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      <div class="sphx-glr-thumbnail-title">Fisher's exact test and the lady tasting tea</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Compares three fertilizer treatments&#x27; effect on plant growth, as in Fisher&#x27;s Rothamsted field trials. ANOVA splits the total variability into a between-groups and a within-groups sum of squares; their ratio, the F-statistic, tests all group means for equality in one test.">

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  .. image:: /api/gallery/statistics/hypothesis_tests/images/thumb/sphx_glr_plot_04_one_way_anova_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/hypothesis_tests/plot_04_one_way_anova`

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      <div class="sphx-glr-thumbnail-title">Fisher's one-way analysis of variance</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/statistics/hypothesis_tests/plot_01_student_t_test
   /api/gallery/statistics/hypothesis_tests/plot_02_chi_square_tests
   /api/gallery/statistics/hypothesis_tests/plot_03_fisher_exact_lady_tea
   /api/gallery/statistics/hypothesis_tests/plot_04_one_way_anova