.. _sphx_glr_api_gallery_analytical_statistics:

Statistics of replicate measurements
--------------------------------------

Student's `t` confidence interval for a mean of a few replicates, and the
Horwitz function for expected interlaboratory precision.


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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 n replicates the standard deviation s is itself uncertain, so the interval \bar x\pm t\,s/\sqrt n from t_confidence_interval uses Student&#x27;s t instead of the normal 1.96. We simulate many triplicate analyses and show that the t interval covers the true value 95% of the time, while the naive \pm1.96\,s/\sqrt n interval falls well short.">

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  .. image:: /api/gallery/analytical/statistics/images/thumb/sphx_glr_plot_01_student_t_confidence_interval_thumb.png
    :alt:

  :doc:`/api/gallery/analytical/statistics/plot_01_student_t_confidence_interval`

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      <div class="sphx-glr-thumbnail-title">Student's t: confidence intervals from a few replicates</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="horwitz_rsd gives Horwitz&#x27;s empirical expected between-laboratory RSD, 2^{1-0.5\log_{10}C}, which doubles for every 100-fold drop in concentration. Plotted as \pm\text{RSD} against concentration it opens like a trumpet. horrat scores a method&#x27;s observed RSD against it.">

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  .. image:: /api/gallery/analytical/statistics/images/thumb/sphx_glr_plot_02_horwitz_trumpet_thumb.png
    :alt:

  :doc:`/api/gallery/analytical/statistics/plot_02_horwitz_trumpet`

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      <div class="sphx-glr-thumbnail-title">The Horwitz trumpet: interlaboratory precision vs. concentration</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/analytical/statistics/plot_01_student_t_confidence_interval
   /api/gallery/analytical/statistics/plot_02_horwitz_trumpet