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<title>Calibration Functions for Analytical Chemistry • chemCal</title>
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<script src="pkgdown.js"></script><meta property="og:title" content="Calibration Functions for Analytical Chemistry">
<meta property="og:description" content="Simple functions for plotting linear
calibration functions and estimating standard errors for measurements
according to the Handbook of Chemometrics and Qualimetrics: Part A
by Massart et al. (1997) There are also functions estimating the limit
of detection (LOD) and limit of quantification (LOQ).
The functions work on model objects from - optionally weighted - linear
regression (lm) or robust linear regression (rlm from the MASS package).">
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<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.3.9000</span>
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<div class="section level1">
<div class="page-header"><h1 id="chemcal---calibration-functions-for-analytical-chemistry">chemCal - Calibration functions for analytical chemistry<a class="anchor" aria-label="anchor" href="#chemcal---calibration-functions-for-analytical-chemistry"></a>
</h1></div>
<!-- badges: start -->
<div class="section level2">
<h2 id="overview">Overview<a class="anchor" aria-label="anchor" href="#overview"></a>
</h2>
<p>chemCal is an R package providing some basic functions for conveniently working with linear calibration curves with one explanatory variable.</p>
</div>
<div class="section level2">
<h2 id="installation">Installation<a class="anchor" aria-label="anchor" href="#installation"></a>
</h2>
<p>From within <a href="https://www.r-project.org/" class="external-link">R</a>, get the official chemCal release using</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html" class="external-link">install.packages</a></span><span class="op">(</span><span class="st">"chemCal"</span><span class="op">)</span></code></pre></div>
</div>
<div class="section level2">
<h2 id="usage">Usage<a class="anchor" aria-label="anchor" href="#usage"></a>
</h2>
<p>chemCal works with univariate linear models of class <code>lm</code>. Working with one of the datasets coming with chemCal, we can produce a calibration plot using the <code>calplot</code> function:</p>
<div class="section level3">
<h3 id="plotting-a-calibration">Plotting a calibration<a class="anchor" aria-label="anchor" href="#plotting-a-calibration"></a>
</h3>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/chemCal/" class="external-link">chemCal</a></span><span class="op">)</span>
<span class="va">m0</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">massart97ex3</span><span class="op">)</span>
<span class="fu"><a href="reference/calplot.html">calplot</a></span><span class="op">(</span><span class="va">m0</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-calplot-1.png"><!-- --></p>
</div>
<div class="section level3">
<h3 id="lod-and-loq">LOD and LOQ<a class="anchor" aria-label="anchor" href="#lod-and-loq"></a>
</h3>
<p>If you use unweighted regression, as in the above example, we can calculate a Limit Of Detection (LOD) from the calibration data.</p>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/lod.html">lod</a></span><span class="op">(</span><span class="va">m0</span><span class="op">)</span>
<span class="co">#> $x</span>
<span class="co">#> [1] 5.407085</span>
<span class="co">#> </span>
<span class="co">#> $y</span>
<span class="co">#> [1] 13.63911</span></code></pre></div>
<p>This is the minimum detectable value (German: Erfassungsgrenze), i.e. the value where the probability that the signal is not detected although the analyte is present is below a specified error tolerance beta (default is 0.05 following the IUPAC recommendation).</p>
<p>You can also calculate the decision limit (German: Nachweisgrenze), i.e. the value that is significantly different from the blank signal with an error tolerance alpha (default is 0.05, again following IUPAC recommendations) by setting beta to 0.5.</p>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/lod.html">lod</a></span><span class="op">(</span><span class="va">m0</span>, beta <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span>
<span class="co">#> $x</span>
<span class="co">#> [1] 2.720388</span>
<span class="co">#> </span>
<span class="co">#> $y</span>
<span class="co">#> [1] 8.314841</span></code></pre></div>
<p>Furthermore, you can calculate the Limit Of Quantification (LOQ), being defined as the value where the relative error of the quantification given the calibration model reaches a prespecified value (default is 1/3).</p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/loq.html">loq</a></span><span class="op">(</span><span class="va">m0</span><span class="op">)</span>
<span class="co">#> $x</span>
<span class="co">#> [1] 9.627349</span>
<span class="co">#> </span>
<span class="co">#> $y</span>
<span class="co">#> [1] 22.00246</span></code></pre></div>
</div>
<div class="section level3">
<h3 id="confidence-intervals-for-measured-values">Confidence intervals for measured values<a class="anchor" aria-label="anchor" href="#confidence-intervals-for-measured-values"></a>
</h3>
<p>Finally, you can get a confidence interval for the values measured using the calibration curve, i.e. for the inverse predictions using the function <code>inverse.predict</code>.</p>
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/inverse.predict.html">inverse.predict</a></span><span class="op">(</span><span class="va">m0</span>, <span class="fl">90</span><span class="op">)</span>
<span class="co">#> $Prediction</span>
<span class="co">#> [1] 43.93983</span>
<span class="co">#> </span>
<span class="co">#> $`Standard Error`</span>
<span class="co">#> [1] 1.576985</span>
<span class="co">#> </span>
<span class="co">#> $Confidence</span>
<span class="co">#> [1] 3.230307</span>
<span class="co">#> </span>
<span class="co">#> $`Confidence Limits`</span>
<span class="co">#> [1] 40.70952 47.17014</span></code></pre></div>
<p>If you have replicate measurements of the same sample, you can also give a vector of numbers.</p>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/inverse.predict.html">inverse.predict</a></span><span class="op">(</span><span class="va">m0</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">91</span>, <span class="fl">89</span>, <span class="fl">87</span>, <span class="fl">93</span>, <span class="fl">90</span><span class="op">)</span><span class="op">)</span>
<span class="co">#> $Prediction</span>
<span class="co">#> [1] 43.93983</span>
<span class="co">#> </span>
<span class="co">#> $`Standard Error`</span>
<span class="co">#> [1] 0.796884</span>
<span class="co">#> </span>
<span class="co">#> $Confidence</span>
<span class="co">#> [1] 1.632343</span>
<span class="co">#> </span>
<span class="co">#> $`Confidence Limits`</span>
<span class="co">#> [1] 42.30749 45.57217</span></code></pre></div>
</div>
</div>
<div class="section level2">
<h2 id="reference">Reference<a class="anchor" aria-label="anchor" href="#reference"></a>
</h2>
<p>You can use the R help system to view documentation, or you can have a look at the <a href="https://pkgdown.jrwb.de/chemCal/" class="external-link">online documentation</a>.</p>
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<h2 data-toc-skip>Links</h2>
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<li><a href="https://cloud.r-project.org/package=chemCal" class="external-link">View on CRAN</a></li>
<li><a href="https://github.com/jranke/chemCal/" class="external-link">Browse source code</a></li>
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<h2 data-toc-skip>License</h2>
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<li>GPL (>= 2)</li>
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<li><a href="authors.html#citation">Citing chemCal</a></li>
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<h2 data-toc-skip>Developers</h2>
<ul class="list-unstyled">
<li>Johannes Ranke <br><small class="roles"> Author, maintainer, copyright holder </small> <a href="https://orcid.org/0000-0003-4371-6538" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
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<h2 data-toc-skip>Dev status</h2>
<ul class="list-unstyled">
<li><a href="https://cran.r-project.org/package=chemCal" class="external-link"><img src="https://www.r-pkg.org/badges/version/chemCal"></a></li>
<li><a href="https://app.travis-ci.com/github/jranke/chemCal" class="external-link"><img src="https://travis-ci.com/jranke/chemCal.svg?branch=master" alt="Build Status"></a></li>
<li><a href="https://codecov.io/github/jranke/chemCal" class="external-link"><img src="https://codecov.io/github/jranke/chemCal/branch/master/graphs/badge.svg" alt="codecov"></a></li>
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