.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/calibration/plot_02_limits_of_detection_and_quantitation.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_calibration_plot_02_limits_of_detection_and_quantitation.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_calibration_plot_02_limits_of_detection_and_quantitation.py:


Limits of detection and quantitation from a calibration curve
================================================================

Long and Winefordner argued that a detection limit should be tied to the
calibration's own residual scatter :math:`s_{y/x}` and slope `m`.
:meth:`~chemistrykit.analytical.LinearCalibration.lod` and
:meth:`~chemistrykit.analytical.LinearCalibration.loq` use the widely
adopted calibration-based convention :math:`\text{LOD}=3.3\,s_{y/x}/m`
and :math:`\text{LOQ}=10\,s_{y/x}/m`. A noisier method has
proportionally higher limits.

.. GENERATED FROM PYTHON SOURCE LINES 15-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import fit_calibration
    from chemistrykit.analytical.visualizers.analytical_plots import plot_calibration_curve

    rng = np.random.default_rng(7)
    concentration = np.array([0.0, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0])  # ppm
    slope, intercept = 12.4, 0.8

    calibrations = {}
    for noise in (1.5, 6.0):
        signal = slope * concentration + intercept + rng.normal(scale=noise, size=concentration.shape)
        cal = fit_calibration(concentration, signal)
        calibrations[noise] = (signal, cal)
        print(f"noise sigma={noise}: s_y/x={cal.residual_std_error:.3f}, LOD={cal.lod():.3f} ppm, LOQ={cal.loq():.3f} ppm, LOQ/LOD={cal.loq() / cal.lod():.4f}")





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

 .. code-block:: none

    noise sigma=1.5: s_y/x=0.801, LOD=0.213 ppm, LOQ=0.646 ppm, LOQ/LOD=3.0303
    noise sigma=6.0: s_y/x=4.432, LOD=1.220 ppm, LOQ=3.696 ppm, LOQ/LOD=3.0303




.. GENERATED FROM PYTHON SOURCE LINES 33-35

The signal levels corresponding to the two limits sit 3.3 and 10
residual standard deviations above the fitted blank (the intercept):

.. GENERATED FROM PYTHON SOURCE LINES 35-40

.. code-block:: Python

    signal_lo, cal_lo = calibrations[1.5]
    print(f"\nBlank (intercept): {cal_lo.intercept:.3f}")
    print(f"Signal at LOD: {cal_lo.predict_signal(cal_lo.lod()):.3f} = blank + 3.3 s_y/x")
    print(f"Signal at LOQ: {cal_lo.predict_signal(cal_lo.loq()):.3f} = blank + 10 s_y/x")





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

 .. code-block:: none


    Blank (intercept): 0.337
    Signal at LOD: 2.980 = blank + 3.3 s_y/x
    Signal at LOQ: 8.347 = blank + 10 s_y/x




.. GENERATED FROM PYTHON SOURCE LINES 41-49

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    for ax, (noise, (signal, cal)) in zip(axes, calibrations.items()):
        plot_calibration_curve(concentration, signal, calibration=cal, lod=cal.lod(), ax=ax)
        ax.axvline(cal.loq(), color="darkorange", linestyle=":", label=f"LOQ = {cal.loq():.2f} ppm")
        ax.set_title(f"noise sigma = {noise}: LOD = {cal.lod():.2f} ppm")
        ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/calibration/images/sphx_glr_plot_02_limits_of_detection_and_quantitation_001.png
   :alt: noise sigma = 1.5: LOD = 0.21 ppm, noise sigma = 6.0: LOD = 1.22 ppm
   :srcset: /api/gallery/analytical/calibration/images/sphx_glr_plot_02_limits_of_detection_and_quantitation_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.085 seconds)


.. _sphx_glr_download_api_gallery_analytical_calibration_plot_02_limits_of_detection_and_quantitation.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_limits_of_detection_and_quantitation.ipynb <plot_02_limits_of_detection_and_quantitation.ipynb>`

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

      :download:`Download Python source code: plot_02_limits_of_detection_and_quantitation.py <plot_02_limits_of_detection_and_quantitation.py>`

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

      :download:`Download zipped: plot_02_limits_of_detection_and_quantitation.zip <plot_02_limits_of_detection_and_quantitation.zip>`


.. only:: html

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

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