.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/statistics/plot_02_horwitz_trumpet.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_statistics_plot_02_horwitz_trumpet.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_statistics_plot_02_horwitz_trumpet.py:


The Horwitz trumpet: interlaboratory precision vs. concentration
==================================================================

:func:`~chemistrykit.analytical.horwitz_rsd` gives Horwitz's empirical
expected between-laboratory RSD, :math:`2^{1-0.5\log_{10}C}`, which
doubles for every 100-fold drop in concentration. Plotted as
:math:`\pm\text{RSD}` against concentration it opens like a trumpet.
:func:`~chemistrykit.analytical.horrat` scores a method's observed RSD
against it.

.. GENERATED FROM PYTHON SOURCE LINES 14-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import horrat, horwitz_rsd

    for label, C in [("pure substance", 1.0), ("1 %", 1e-2), ("1 ppm", 1e-6), ("1 ppb", 1e-9)]:
        print(f"{label:15s}: predicted RSD_R = {horwitz_rsd(C):5.1f} %")





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

 .. code-block:: none

    pure substance : predicted RSD_R =   2.0 %
    1 %            : predicted RSD_R =   4.0 %
    1 ppm          : predicted RSD_R =  16.0 %
    1 ppb          : predicted RSD_R =  45.3 %




.. GENERATED FROM PYTHON SOURCE LINES 23-24

Hypothetical collaborative-study results: (mass fraction, observed RSD %)

.. GENERATED FROM PYTHON SOURCE LINES 24-29

.. code-block:: Python

    studies = {"protein in feed": (0.2, 2.1), "pesticide residue": (5e-8, 30.0), "aflatoxin (poor method)": (5e-9, 110.0), "Na in serum": (3e-3, 2.0)}
    print()
    for name, (C, rsd) in studies.items():
        print(f"{name:24s}: observed {rsd:5.1f} %, Horwitz {horwitz_rsd(C):5.1f} %, HorRat = {horrat(rsd, C):.2f}")





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

 .. code-block:: none


    protein in feed         : observed   2.1 %, Horwitz   2.5 %, HorRat = 0.82
    pesticide residue       : observed  30.0 %, Horwitz  25.1 %, HorRat = 1.19
    aflatoxin (poor method) : observed 110.0 %, Horwitz  35.5 %, HorRat = 3.10
    Na in serum             : observed   2.0 %, Horwitz   4.8 %, HorRat = 0.42




.. GENERATED FROM PYTHON SOURCE LINES 30-44

.. code-block:: Python

    C = np.logspace(-10, 0, 300)
    fig, ax = plt.subplots(figsize=(7, 4.5))
    ax.plot(C, horwitz_rsd(C), color="black", label=r"$+\mathrm{RSD}_R$")
    ax.plot(C, -horwitz_rsd(C), color="black", label=r"$-\mathrm{RSD}_R$")
    ax.fill_between(C, -horwitz_rsd(C), horwitz_rsd(C), color="gray", alpha=0.15)
    for name, (Cs, rsd) in studies.items():
        ax.plot([Cs], [rsd], "o", label=f"{name} (HorRat {horrat(rsd, Cs):.1f})")
    ax.set_xscale("log")
    ax.set_xlabel("concentration (mass fraction)")
    ax.set_ylabel("between-laboratory RSD (%)")
    ax.set_title("The Horwitz trumpet")
    ax.legend(fontsize=8)
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/statistics/images/sphx_glr_plot_02_horwitz_trumpet_001.png
   :alt: The Horwitz trumpet
   :srcset: /api/gallery/analytical/statistics/images/sphx_glr_plot_02_horwitz_trumpet_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.061 seconds)


.. _sphx_glr_download_api_gallery_analytical_statistics_plot_02_horwitz_trumpet.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_horwitz_trumpet.ipynb <plot_02_horwitz_trumpet.ipynb>`

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

      :download:`Download Python source code: plot_02_horwitz_trumpet.py <plot_02_horwitz_trumpet.py>`

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

      :download:`Download zipped: plot_02_horwitz_trumpet.zip <plot_02_horwitz_trumpet.zip>`


.. only:: html

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

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