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authorJohannes Ranke <jranke@uni-bremen.de>2022-03-31 19:21:03 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2022-03-31 19:59:10 +0200
commit08465d77a6ca5a9656ac86047c6008f1e7f3e9c7 (patch)
treef27a775e146748881eb6526ed57298f4bdc40c2f /docs/reference
parentf4fcef8228ebd5a1a73bc6edc47b5efa259c2e20 (diff)
Fix URLs in README, convert to roxygenv0.2.3
- The roxygen conversion was done using Rd2roxygen - Also edit _pkgdown.yml to group the reference - Use markdown bullet lists for lod and loq docs
Diffstat (limited to 'docs/reference')
-rw-r--r--docs/reference/calplot-1.pngbin0 -> 71932 bytes
-rw-r--r--docs/reference/calplot.html154
-rw-r--r--docs/reference/din32645.html23
-rw-r--r--docs/reference/index.html27
-rw-r--r--docs/reference/inverse.predict.html103
-rw-r--r--docs/reference/lod.html101
-rw-r--r--docs/reference/loq.html99
-rw-r--r--docs/reference/massart97ex1.html11
-rw-r--r--docs/reference/massart97ex3.html19
-rw-r--r--docs/reference/rl95_cadmium.html17
-rw-r--r--docs/reference/rl95_toluene.html18
-rw-r--r--docs/reference/utstats14.html21
12 files changed, 390 insertions, 203 deletions
diff --git a/docs/reference/calplot-1.png b/docs/reference/calplot-1.png
new file mode 100644
index 0000000..c2deae8
--- /dev/null
+++ b/docs/reference/calplot-1.png
Binary files differ
diff --git a/docs/reference/calplot.html b/docs/reference/calplot.html
new file mode 100644
index 0000000..88321b1
--- /dev/null
+++ b/docs/reference/calplot.html
@@ -0,0 +1,154 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Plot calibration graphs from univariate linear models — calplot • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Plot calibration graphs from univariate linear models — calplot"><meta property="og:description" content="Produce graphics of calibration data, the fitted model as well as
+confidence, and, for unweighted regression, prediction bands."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+
+
+ <div class="container template-reference-topic">
+ <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
+ <div class="container">
+ <div class="navbar-header">
+ <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
+ <span class="sr-only">Toggle navigation</span>
+ <span class="icon-bar"></span>
+ <span class="icon-bar"></span>
+ <span class="icon-bar"></span>
+ </button>
+ <span class="navbar-brand">
+ <a class="navbar-link" href="../index.html">chemCal</a>
+ <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.3</span>
+ </span>
+ </div>
+
+ <div id="navbar" class="navbar-collapse collapse">
+ <ul class="nav navbar-nav"><li>
+ <a href="../articles/chemCal.html">Get started</a>
+</li>
+<li>
+ <a href="../reference/index.html">Reference</a>
+</li>
+<li>
+ <a href="../news/index.html">Changelog</a>
+</li>
+ </ul><ul class="nav navbar-nav navbar-right"><li>
+ <a href="https://github.com/jranke/chemCal/" class="external-link">
+ <span class="fab fa-github fa-lg"></span>
+
+ </a>
+</li>
+ </ul></div><!--/.nav-collapse -->
+ </div><!--/.container -->
+</div><!--/.navbar -->
+
+
+
+ </header><div class="row">
+ <div class="col-md-9 contents">
+ <div class="page-header">
+ <h1>Plot calibration graphs from univariate linear models</h1>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/calplot.R" class="external-link"><code>R/calplot.R</code></a></small>
+ <div class="hidden name"><code>calplot.Rd</code></div>
+ </div>
+
+ <div class="ref-description">
+ <p>Produce graphics of calibration data, the fitted model as well as
+confidence, and, for unweighted regression, prediction bands.</p>
+ </div>
+
+ <div id="ref-usage">
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">calplot</span><span class="op">(</span>
+ <span class="va">object</span>,
+ xlim <span class="op">=</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="st">"auto"</span>, <span class="st">"auto"</span><span class="op">)</span>,
+ ylim <span class="op">=</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="st">"auto"</span>, <span class="st">"auto"</span><span class="op">)</span>,
+ xlab <span class="op">=</span> <span class="st">"Concentration"</span>,
+ ylab <span class="op">=</span> <span class="st">"Response"</span>,
+ legend_x <span class="op">=</span> <span class="st">"auto"</span>,
+ alpha <span class="op">=</span> <span class="fl">0.05</span>,
+ varfunc <span class="op">=</span> <span class="cn">NULL</span>
+<span class="op">)</span></code></pre></div>
+ </div>
+
+ <div id="arguments">
+ <h2>Arguments</h2>
+ <dl><dt>object</dt>
+<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
+<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x -
+1</code>.</p></dd>
+<dt>xlim</dt>
+<dd><p>The limits of the plot on the x axis.</p></dd>
+<dt>ylim</dt>
+<dd><p>The limits of the plot on the y axis.</p></dd>
+<dt>xlab</dt>
+<dd><p>The label of the x axis.</p></dd>
+<dt>ylab</dt>
+<dd><p>The label of the y axis.</p></dd>
+<dt>legend_x</dt>
+<dd><p>An optional numeric value for adjusting the x coordinate of
+the legend.</p></dd>
+<dt>alpha</dt>
+<dd><p>The error tolerance level for the confidence and prediction
+bands. Note that this includes both tails of the Gaussian distribution,
+unlike the alpha and beta parameters used in <code><a href="lod.html">lod</a></code> (see note
+below).</p></dd>
+<dt>varfunc</dt>
+<dd><p>The variance function for generating the weights in the
+model. Currently, this argument is ignored (see note below).</p></dd>
+</dl></div>
+ <div id="value">
+ <h2>Value</h2>
+ <p>A plot of the calibration data, of your fitted model as well as
+lines showing the confidence limits. Prediction limits are only shown for
+models from unweighted regression.</p>
+ </div>
+ <div id="note">
+ <h2>Note</h2>
+ <p>Prediction bands for models from weighted linear regression require
+weights for the data, for which responses should be predicted. Prediction
+intervals using weights e.g. from a variance function are currently not
+supported by the internally used function <code><a href="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code>,
+therefore, <code>calplot</code> does not draw prediction bands for such models.</p>
+<p>It is possible to compare the <code>calplot</code> prediction bands with
+the <code><a href="lod.html">lod</a></code> values if the <code><a href="lod.html">lod()</a></code> alpha and beta parameters
+are half the value of the <code>calplot()</code> alpha parameter.</p>
+ </div>
+ <div id="author">
+ <h2>Author</h2>
+ <p>Johannes Ranke</p>
+ </div>
+
+ <div id="ref-examples">
+ <h2>Examples</h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">massart97ex3</span><span class="op">)</span></span>
+<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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>
+<span class="r-in"><span class="fu">calplot</span><span class="op">(</span><span class="va">m</span><span class="op">)</span></span>
+<span class="r-plt img"><img src="calplot-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"></span>
+</code></pre></div>
+ </div>
+ </div>
+ <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+ <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+ </nav></div>
+</div>
+
+
+ <footer><div class="copyright">
+ <p></p><p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+ <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+</div>
+
+ </footer></div>
+
+
+
+
+
+
+ </body></html>
+
diff --git a/docs/reference/din32645.html b/docs/reference/din32645.html
index 1c02f36..ba6246a 100644
--- a/docs/reference/din32645.html
+++ b/docs/reference/din32645.html
@@ -47,7 +47,7 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Calibration data from DIN 32645</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>din32645.Rd</code></div>
</div>
@@ -55,9 +55,6 @@
<p>Sample dataset to test the package.</p>
</div>
- <div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">din32645</span><span class="op">)</span></code></pre></div>
- </div>
<div id="format">
<h2>Format</h2>
@@ -66,18 +63,19 @@
<div id="references">
<h2>References</h2>
<p>DIN 32645 (equivalent to ISO 11843), Beuth Verlag, Berlin, 1994</p>
-<p>Dintest. Plugin for MS Excel for evaluations of calibration data. Written
- by Georg Schmitt, University of Heidelberg. Formerly available from
- the Website of the University of Heidelberg.</p>
-<p>Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
- detection and quantification capabilities (IUPAC Recommendations 1995).
- Analytica Chimica Acta 391, 105 - 126.</p>
+<p>Dintest. Plugin for MS Excel for evaluations of calibration data. Written by
+Georg Schmitt, University of Heidelberg. Formerly available from the Website
+of the University of Heidelberg.</p>
+<p>Currie, L. A. (1997) Nomenclature in evaluation of analytical methods
+including detection and quantification capabilities (IUPAC Recommendations
+1995). Analytica Chimica Acta 391, 105 - 126.</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">din32645</span><span class="op">)</span></span>
-<span class="r-in"><span class="fu"><a href="calplot.lm.html">calplot</a></span><span class="op">(</span><span class="va">m</span><span class="op">)</span></span>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">din32645</span><span class="op">)</span></span>
+<span class="r-in"><span class="fu"><a href="calplot.html">calplot</a></span><span class="op">(</span><span class="va">m</span><span class="op">)</span></span>
<span class="r-plt img"><img src="din32645-1.png" alt="" width="700" height="433"></span>
<span class="r-in"></span>
<span class="r-in"><span class="co">## Prediction of x with confidence interval</span></span>
@@ -118,6 +116,7 @@
<span class="r-in"><span class="co"># LQ = 3.04 * LC (Currie 1999, p. 120)</span></span>
<span class="r-in"><span class="fl">3.04</span> <span class="op">*</span> <span class="fu"><a href="lod.html">lod</a></span><span class="op">(</span><span class="va">m</span>, alpha <span class="op">=</span> <span class="fl">0.01</span>, beta <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span><span class="op">$</span><span class="va">x</span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.2122306</span>
+<span class="r-in"></span>
</code></pre></div>
</div>
</div>
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 3685007..9812256 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -50,22 +50,14 @@
</div>
<table class="ref-index"><colgroup><col class="alias"><col class="title"></colgroup><tbody><tr><th colspan="2">
- <h2 id="all-functions">All functions <a href="#all-functions" class="anchor" aria-hidden="true"></a></h2>
+ <h2 id="main-functions">Main functions <a href="#main-functions" class="anchor" aria-hidden="true"></a></h2>
<p class="section-desc"></p>
</th>
</tr></tbody><tbody><tr><td>
- <p><code><a href="calplot.lm.html">calplot()</a></code> </p>
+ <p><code><a href="calplot.html">calplot()</a></code> </p>
</td>
<td><p>Plot calibration graphs from univariate linear models</p></td>
</tr><tr><td>
- <p><code><a href="din32645.html">din32645</a></code> </p>
- </td>
- <td><p>Calibration data from DIN 32645</p></td>
- </tr><tr><td>
- <p><code><a href="inverse.predict.html">inverse.predict()</a></code> </p>
- </td>
- <td><p>Predict x from y for a linear calibration</p></td>
- </tr><tr><td>
<p><code><a href="lod.html">lod()</a></code> </p>
</td>
<td><p>Estimate a limit of detection (LOD)</p></td>
@@ -74,6 +66,18 @@
</td>
<td><p>Estimate a limit of quantification (LOQ)</p></td>
</tr><tr><td>
+ <p><code><a href="inverse.predict.html">inverse.predict()</a></code> </p>
+ </td>
+ <td><p>Predict x from y for a linear calibration</p></td>
+ </tr></tbody><tbody><tr><th colspan="2">
+ <h2 id="datasets">Datasets <a href="#datasets" class="anchor" aria-hidden="true"></a></h2>
+ <p class="section-desc"></p>
+ </th>
+ </tr></tbody><tbody><tr><td>
+ <p><code><a href="din32645.html">din32645</a></code> </p>
+ </td>
+ <td><p>Calibration data from DIN 32645</p></td>
+ </tr><tr><td>
<p><code><a href="massart97ex1.html">massart97ex1</a></code> </p>
</td>
<td><p>Calibration data from Massart et al. (1997), example 1</p></td>
@@ -84,7 +88,8 @@
</tr><tr><td>
<p><code><a href="rl95_cadmium.html">rl95_cadmium</a></code> </p>
</td>
- <td><p>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)</p></td>
+ <td><p>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995)</p></td>
</tr><tr><td>
<p><code><a href="rl95_toluene.html">rl95_toluene</a></code> </p>
</td>
diff --git a/docs/reference/inverse.predict.html b/docs/reference/inverse.predict.html
index cb9fe98..6fe081e 100644
--- a/docs/reference/inverse.predict.html
+++ b/docs/reference/inverse.predict.html
@@ -1,14 +1,14 @@
<!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Predict x from y for a linear calibration — inverse.predict • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Predict x from y for a linear calibration — inverse.predict"><meta property="og:description" content="This function predicts x values using a univariate linear model that has been
- generated for the purpose of calibrating a measurement method. Prediction
- intervals are given at the specified confidence level.
- The calculation method was taken from Massart et al. (1997). In particular,
- Equations 8.26 and 8.28 were combined in order to yield a general treatment
- of inverse prediction for univariate linear models, taking into account
- weights that have been used to create the linear model, and at the same
- time providing the possibility to specify a precision in sample measurements
- differing from the precision in standard samples used for the calibration.
- This is elaborated in the package vignette."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Predict x from y for a linear calibration — inverse.predict • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Predict x from y for a linear calibration — inverse.predict"><meta property="og:description" content="This function predicts x values using a univariate linear model that has
+been generated for the purpose of calibrating a measurement method.
+Prediction intervals are given at the specified confidence level. The
+calculation method was taken from Massart et al. (1997). In particular,
+Equations 8.26 and 8.28 were combined in order to yield a general treatment
+of inverse prediction for univariate linear models, taking into account
+weights that have been used to create the linear model, and at the same time
+providing the possibility to specify a precision in sample measurements
+differing from the precision in standard samples used for the calibration.
+This is elaborated in the package vignette."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -56,73 +56,87 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Predict x from y for a linear calibration</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/inverse.predict.lm.R" class="external-link"><code>R/inverse.predict.lm.R</code></a></small>
<div class="hidden name"><code>inverse.predict.Rd</code></div>
</div>
<div class="ref-description">
- <p>This function predicts x values using a univariate linear model that has been
- generated for the purpose of calibrating a measurement method. Prediction
- intervals are given at the specified confidence level.
- The calculation method was taken from Massart et al. (1997). In particular,
- Equations 8.26 and 8.28 were combined in order to yield a general treatment
- of inverse prediction for univariate linear models, taking into account
- weights that have been used to create the linear model, and at the same
- time providing the possibility to specify a precision in sample measurements
- differing from the precision in standard samples used for the calibration.
- This is elaborated in the package vignette.</p>
+ <p>This function predicts x values using a univariate linear model that has
+been generated for the purpose of calibrating a measurement method.
+Prediction intervals are given at the specified confidence level. The
+calculation method was taken from Massart et al. (1997). In particular,
+Equations 8.26 and 8.28 were combined in order to yield a general treatment
+of inverse prediction for univariate linear models, taking into account
+weights that have been used to create the linear model, and at the same time
+providing the possibility to specify a precision in sample measurements
+differing from the precision in standard samples used for the calibration.
+This is elaborated in the package vignette.</p>
</div>
<div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">object</span>, <span class="va">newdata</span>, <span class="va">...</span>,
- <span class="va">ws</span>, alpha<span class="op">=</span><span class="fl">0.05</span>, var.s <span class="op">=</span> <span class="st">"auto"</span><span class="op">)</span></code></pre></div>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">inverse.predict</span><span class="op">(</span>
+ <span class="va">object</span>,
+ <span class="va">newdata</span>,
+ <span class="va">...</span>,
+ ws <span class="op">=</span> <span class="st">"auto"</span>,
+ alpha <span class="op">=</span> <span class="fl">0.05</span>,
+ var.s <span class="op">=</span> <span class="st">"auto"</span>
+<span class="op">)</span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
-<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
- <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code>
- with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.</p></dd>
+<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
+<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x -
+1</code>.</p></dd>
<dt>newdata</dt>
<dd><p>A vector of observed y values for one sample.</p></dd>
<dt>...</dt>
-<dd><p>Placeholder for further arguments that might be needed by
- future implementations.</p></dd>
+<dd><p>Placeholder for further arguments that might be needed by
+future implementations.</p></dd>
<dt>ws</dt>
<dd><p>The weight attributed to the sample. This argument is obligatory
- if <code>object</code> has weights.</p></dd>
+if <code>object</code> has weights.</p></dd>
<dt>alpha</dt>
-<dd><p>The error tolerance level for the confidence interval to be reported.</p></dd>
+<dd><p>The error tolerance level for the confidence interval to be
+reported.</p></dd>
<dt>var.s</dt>
-<dd><p>The estimated variance of the sample measurements. The default is to take
- the residual standard error from the calibration and to adjust it
- using <code>ws</code>, if applicable. This means that <code>var.s</code>
- overrides <code>ws</code>.</p></dd>
+<dd><p>The estimated variance of the sample measurements. The default
+is to take the residual standard error from the calibration and to adjust it
+using <code>ws</code>, if applicable. This means that <code>var.s</code> overrides
+<code>ws</code>.</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
<p>A list containing the predicted x value, its standard error and a
- confidence interval.</p>
+confidence interval.</p>
+ </div>
+ <div id="details">
+ <h2>Details</h2>
+ <p>This is an implementation of Equation (8.28) in the Handbook of Chemometrics
+and Qualimetrics, Part A, Massart et al (1997), page 200, validated with
+Example 8 on the same page, extended as specified in the package vignette</p>
</div>
<div id="note">
<h2>Note</h2>
- <p>The function was validated with examples 7 and 8 from Massart et al. (1997).
- Note that the behaviour of inverse.predict changed with chemCal version
- 0.2.1. Confidence intervals for x values obtained from calibrations with
- replicate measurements did not take the variation about the means into account.
- Please refer to the vignette for details.</p>
+ <p>The function was validated with examples 7 and 8 from Massart et al.
+(1997). Note that the behaviour of inverse.predict changed with chemCal
+version 0.2.1. Confidence intervals for x values obtained from calibrations
+with replicate measurements did not take the variation about the means into
+account. Please refer to the vignette for details.</p>
</div>
<div id="references">
<h2>References</h2>
- <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
- Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
- p. 200</p>
+ <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong,
+S., Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
+Qualimetrics: Part A, p. 200</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="co"># This is example 7 from Chapter 8 in Massart et al. (1997)</span></span>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="co"># This is example 7 from Chapter 8 in Massart et al. (1997)</span></span>
<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">massart97ex1</span><span class="op">)</span></span>
<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m</span>, <span class="fl">15</span><span class="op">)</span> <span class="co"># 6.1 +- 4.9</span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
@@ -204,6 +218,7 @@
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 36.20523 51.91526</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-in"></span>
+<span class="r-in"></span>
</code></pre></div>
</div>
</div>
diff --git a/docs/reference/lod.html b/docs/reference/lod.html
index a2d66ce..1fbae76 100644
--- a/docs/reference/lod.html
+++ b/docs/reference/lod.html
@@ -1,12 +1,12 @@
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Estimate a limit of detection (LOD) — lod • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate a limit of detection (LOD) — lod"><meta property="og:description" content="The decision limit (German: Nachweisgrenze) is defined as the signal or
- analyte concentration that is significantly different from the blank signal
- with a first order error alpha (one-sided significance test).
- The detection limit, or more precise, the minimum detectable value
- (German: Erfassungsgrenze), is then defined as the signal or analyte
- concentration where the probability that the signal is not detected although
- the analyte is present (type II or false negative error), is beta (also a
- one-sided significance test)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+analyte concentration that is significantly different from the blank signal
+with a first order error alpha (one-sided significance test). The detection
+limit, or more precise, the minimum detectable value (German:
+Erfassungsgrenze), is then defined as the signal or analyte concentration
+where the probability that the signal is not detected although the analyte
+is present (type II or false negative error), is beta (also a one-sided
+significance test)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -54,76 +54,81 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Estimate a limit of detection (LOD)</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/lod.R" class="external-link"><code>R/lod.R</code></a></small>
<div class="hidden name"><code>lod.Rd</code></div>
</div>
<div class="ref-description">
<p>The decision limit (German: Nachweisgrenze) is defined as the signal or
- analyte concentration that is significantly different from the blank signal
- with a first order error alpha (one-sided significance test).
- The detection limit, or more precise, the minimum detectable value
- (German: Erfassungsgrenze), is then defined as the signal or analyte
- concentration where the probability that the signal is not detected although
- the analyte is present (type II or false negative error), is beta (also a
- one-sided significance test).</p>
+analyte concentration that is significantly different from the blank signal
+with a first order error alpha (one-sided significance test). The detection
+limit, or more precise, the minimum detectable value (German:
+Erfassungsgrenze), is then defined as the signal or analyte concentration
+where the probability that the signal is not detected although the analyte
+is present (type II or false negative error), is beta (also a one-sided
+significance test).</p>
</div>
<div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">lod</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span>, alpha <span class="op">=</span> <span class="fl">0.05</span>, beta <span class="op">=</span> <span class="fl">0.05</span>, method <span class="op">=</span> <span class="st">"default"</span>, tol <span class="op">=</span> <span class="st">"default"</span><span class="op">)</span></code></pre></div>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">lod</span><span class="op">(</span>
+ <span class="va">object</span>,
+ <span class="va">...</span>,
+ alpha <span class="op">=</span> <span class="fl">0.05</span>,
+ beta <span class="op">=</span> <span class="fl">0.05</span>,
+ method <span class="op">=</span> <span class="st">"default"</span>,
+ tol <span class="op">=</span> <span class="st">"default"</span>
+<span class="op">)</span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
-<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
- <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code>
- with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>,
- optionally from a weighted regression.</p></dd>
+<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
+<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x -
+1</code>, optionally from a weighted regression.</p></dd>
<dt>...</dt>
-<dd><p>Placeholder for further arguments that might be needed by
- future implementations.</p></dd>
+<dd><p>Placeholder for further arguments that might be needed by
+future implementations.</p></dd>
<dt>alpha</dt>
<dd><p>The error tolerance for the decision limit (critical value).</p></dd>
<dt>beta</dt>
<dd><p>The error tolerance beta for the detection limit.</p></dd>
<dt>method</dt>
-<dd><p>The “default” method uses a prediction interval at the LOD
- for the estimation of the LOD, which obviously requires
- iteration. This is described for example in Massart, p. 432 ff.
- The “din” method uses the prediction interval at
- x = 0 as an approximation.</p></dd>
+<dd><p>The “default” method uses a prediction interval at the
+LOD for the estimation of the LOD, which obviously requires iteration. This
+is described for example in Massart, p. 432 ff. The “din” method
+uses the prediction interval at x = 0 as an approximation.</p></dd>
<dt>tol</dt>
<dd><p>When the “default” method is used, the default tolerance
- for the LOD on the x scale is the value of the smallest non-zero standard
- divided by 1000. Can be set to a numeric value to override this.</p></dd>
+for the LOD on the x scale is the value of the smallest non-zero standard
+divided by 1000. Can be set to a numeric value to override this.</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
- <p>A list containig the corresponding x and y values of the estimated limit of
- detection of a model used for calibration.</p>
+ <p>A list containig the corresponding x and y values of the estimated
+limit of detection of a model used for calibration.</p>
</div>
<div id="note">
<h2>Note</h2>
- <p>- The default values for alpha and beta are the ones recommended by IUPAC.
- - The estimation of the LOD in terms of the analyte amount/concentration
- xD from the LOD in the signal domain SD is done by simply inverting the
- calibration function (i.e. assuming a known calibration function).
- - The calculation of a LOD from weighted calibration models requires
- a weights argument for the internally used <code><a href="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code>
- function, which is currently not supported in R.</p>
+ <p>* The default values for alpha and beta are the ones recommended by IUPAC.
+* The estimation of the LOD in terms of the analyte amount/concentration xD
+from the LOD in the signal domain SD is done by simply inverting the
+calibration function (i.e. assuming a known calibration function).
+* The calculation of a LOD from weighted calibration models requires a
+weights argument for the internally used <code><a href="https://rdrr.io/r/stats/predict.lm.html" class="external-link">predict.lm</a></code>
+function, which is currently not supported in R.</p>
</div>
<div id="references">
<h2>References</h2>
- <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
- Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
- Chapter 13.7.8</p>
+ <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong,
+S., Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
+Qualimetrics: Part A, Chapter 13.7.8</p>
<p>J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and
- Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
- Web edition.</p>
-<p>Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
- detection and quantification capabilities (IUPAC Recommendations 1995).
- Analytica Chimica Acta 391, 105 - 126.</p>
+Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
+Web edition.</p>
+<p>Currie, L. A. (1997) Nomenclature in evaluation of analytical methods
+including detection and quantification capabilities (IUPAC Recommendations
+1995). Analytica Chimica Acta 391, 105 - 126.</p>
</div>
<div id="see-also">
<h2>See also</h2>
@@ -132,7 +137,8 @@
<div id="ref-examples">
<h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">din32645</span><span class="op">)</span></span>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">din32645</span><span class="op">)</span></span>
<span class="r-in"><span class="fu">lod</span><span class="op">(</span><span class="va">m</span><span class="op">)</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $x</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.08655484</span>
@@ -150,6 +156,7 @@
<span class="r-out co"><span class="r-pr">#&gt;</span> $y</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 3155.393</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"></span>
</code></pre></div>
</div>
</div>
diff --git a/docs/reference/loq.html b/docs/reference/loq.html
index 0960251..86c8f43 100644
--- a/docs/reference/loq.html
+++ b/docs/reference/loq.html
@@ -1,11 +1,10 @@
<!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Estimate a limit of quantification (LOQ) — loq • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate a limit of quantification (LOQ) — loq"><meta property="og:description" content="The limit of quantification is the x value, where the relative error
- of the quantification given the calibration model reaches a prespecified
- value 1/k. Thus, it is the solution of the equation
- $$L = k c(L)$$
- where c(L) is half of the length of the confidence interval at the limit L
- (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
- inverse.predict, and L is obtained by iteration."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Estimate a limit of quantification (LOQ) — loq • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate a limit of quantification (LOQ) — loq"><meta property="og:description" content="The limit of quantification is the x value, where the relative error of the
+quantification given the calibration model reaches a prespecified value 1/k.
+Thus, it is the solution of the equation $$L = k c(L)$$
+where c(L) is half of the length of the confidence interval at the limit L
+(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
+inverse.predict, and L is obtained by iteration."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -53,69 +52,75 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Estimate a limit of quantification (LOQ)</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/loq.R" class="external-link"><code>R/loq.R</code></a></small>
<div class="hidden name"><code>loq.Rd</code></div>
</div>
<div class="ref-description">
- <p>The limit of quantification is the x value, where the relative error
- of the quantification given the calibration model reaches a prespecified
- value 1/k. Thus, it is the solution of the equation
- $$L = k c(L)$$
- where c(L) is half of the length of the confidence interval at the limit L
- (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
- <code><a href="inverse.predict.html">inverse.predict</a></code>, and L is obtained by iteration.</p>
+ <p>The limit of quantification is the x value, where the relative error of the
+quantification given the calibration model reaches a prespecified value 1/k.
+Thus, it is the solution of the equation $$L = k c(L)$$
+where c(L) is half of the length of the confidence interval at the limit L
+(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
+<code><a href="inverse.predict.html">inverse.predict</a></code>, and L is obtained by iteration.</p>
</div>
<div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">loq</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span>, alpha <span class="op">=</span> <span class="fl">0.05</span>, k <span class="op">=</span> <span class="fl">3</span>, n <span class="op">=</span> <span class="fl">1</span>, w.loq <span class="op">=</span> <span class="st">"auto"</span>,
- var.loq <span class="op">=</span> <span class="st">"auto"</span>, tol <span class="op">=</span> <span class="st">"default"</span><span class="op">)</span></code></pre></div>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">loq</span><span class="op">(</span>
+ <span class="va">object</span>,
+ <span class="va">...</span>,
+ alpha <span class="op">=</span> <span class="fl">0.05</span>,
+ k <span class="op">=</span> <span class="fl">3</span>,
+ n <span class="op">=</span> <span class="fl">1</span>,
+ w.loq <span class="op">=</span> <span class="st">"auto"</span>,
+ var.loq <span class="op">=</span> <span class="st">"auto"</span>,
+ tol <span class="op">=</span> <span class="st">"default"</span>
+<span class="op">)</span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
-<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
- <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code>
- with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>,
- optionally from a weighted regression. If weights are specified
- in the model, either <code>w.loq</code> or <code>var.loq</code> have to
- be specified.</p></dd>
-<dt>alpha</dt>
-<dd><p>The error tolerance for the prediction of x values in the calculation.</p></dd>
+<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
+<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x -
+1</code>, optionally from a weighted regression. If weights are specified in the
+model, either <code>w.loq</code> or <code>var.loq</code> have to be specified.</p></dd>
<dt>...</dt>
-<dd><p>Placeholder for further arguments that might be needed by
- future implementations.</p></dd>
+<dd><p>Placeholder for further arguments that might be needed by
+future implementations.</p></dd>
+<dt>alpha</dt>
+<dd><p>The error tolerance for the prediction of x values in the
+calculation.</p></dd>
<dt>k</dt>
-<dd><p>The inverse of the maximum relative error tolerated at the
- desired LOQ.</p></dd>
+<dd><p>The inverse of the maximum relative error tolerated at the desired
+LOQ.</p></dd>
<dt>n</dt>
<dd><p>The number of replicate measurements for which the LOQ should be
- specified.</p></dd>
+specified.</p></dd>
<dt>w.loq</dt>
-<dd><p>The weight that should be attributed to the LOQ. Defaults
- to one for unweighted regression, and to the mean of the weights
- for weighted regression. See <code><a href="massart97ex3.html">massart97ex3</a></code> for
- an example how to take advantage of knowledge about the
- variance function.</p></dd>
+<dd><p>The weight that should be attributed to the LOQ. Defaults to
+one for unweighted regression, and to the mean of the weights for weighted
+regression. See <code><a href="massart97ex3.html">massart97ex3</a></code> for an example how to take
+advantage of knowledge about the variance function.</p></dd>
<dt>var.loq</dt>
-<dd><p>The approximate variance at the LOQ. The default value is
- calculated from the model.</p></dd>
+<dd><p>The approximate variance at the LOQ. The default value is
+calculated from the model.</p></dd>
<dt>tol</dt>
-<dd><p>The default tolerance for the LOQ on the x scale is the value of the
- smallest non-zero standard divided by 1000. Can be set to a
- numeric value to override this.</p></dd>
+<dd><p>The default tolerance for the LOQ on the x scale is the value of
+the smallest non-zero standard divided by 1000. Can be set to a numeric
+value to override this.</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
- <p>The estimated limit of quantification for a model used for calibration.</p>
+ <p>The estimated limit of quantification for a model used for
+calibration.</p>
</div>
<div id="note">
<h2>Note</h2>
- <p>- IUPAC recommends to base the LOQ on the standard deviation of the signal
- where x = 0.
- - The calculation of a LOQ based on weighted regression is non-standard
- and therefore not tested. Feedback is welcome.</p>
+ <p>* IUPAC recommends to base the LOQ on the standard deviation of the
+signal where x = 0.
+* The calculation of a LOQ based on weighted regression is non-standard and
+therefore not tested. Feedback is welcome.</p>
</div>
<div id="see-also">
<h2>See also</h2>
@@ -124,7 +129,8 @@
<div id="ref-examples">
<h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">massart97ex1</span><span class="op">)</span></span>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</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">massart97ex1</span><span class="op">)</span></span>
<span class="r-in"><span class="fu">loq</span><span class="op">(</span><span class="va">m</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $x</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 13.97764</span>
@@ -141,6 +147,7 @@
<span class="r-out co"><span class="r-pr">#&gt;</span> $y</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 22.68539</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"></span>
</code></pre></div>
</div>
</div>
diff --git a/docs/reference/massart97ex1.html b/docs/reference/massart97ex1.html
index e5dd85a..a02dfe0 100644
--- a/docs/reference/massart97ex1.html
+++ b/docs/reference/massart97ex1.html
@@ -47,7 +47,7 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Calibration data from Massart et al. (1997), example 1</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>massart97ex1.Rd</code></div>
</div>
@@ -55,9 +55,6 @@
<p>Sample dataset from p. 175 to test the package.</p>
</div>
- <div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">massart97ex1</span><span class="op">)</span></code></pre></div>
- </div>
<div id="format">
<h2>Format</h2>
@@ -65,9 +62,9 @@
</div>
<div id="source">
<h2>Source</h2>
- <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
- Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
- Chapter 8.</p>
+ <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S.,
+Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
+Qualimetrics: Part A, Chapter 8.</p>
</div>
</div>
diff --git a/docs/reference/massart97ex3.html b/docs/reference/massart97ex3.html
index 4196882..5cbdbd6 100644
--- a/docs/reference/massart97ex3.html
+++ b/docs/reference/massart97ex3.html
@@ -47,7 +47,7 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Calibration data from Massart et al. (1997), example 3</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>massart97ex3.Rd</code></div>
</div>
@@ -55,25 +55,23 @@
<p>Sample dataset from p. 188 to test the package.</p>
</div>
- <div id="ref-usage">
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="va">massart97ex3</span></code></pre></div>
- </div>
<div id="format">
<h2>Format</h2>
- <p>A dataframe containing 6 levels of x values with 5
- observations of y for each level.</p>
+ <p>A dataframe containing 6 levels of x values with 5 observations of y
+for each level.</p>
</div>
<div id="source">
<h2>Source</h2>
- <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
- Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
- Chapter 8.</p>
+ <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S.,
+Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
+Qualimetrics: Part A, Chapter 8.</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
- <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="co"># For reproducing the results for replicate standard measurements in example 8,</span></span>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
+<span class="r-in"><span class="co"># For reproducing the results for replicate standard measurements in example 8,</span></span>
<span class="r-in"><span class="co"># we need to do the calibration on the means when using chemCal &gt; 0.2</span></span>
<span class="r-in"><span class="va">weights</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/with.html" class="external-link">with</a></span><span class="op">(</span><span class="va">massart97ex3</span>, <span class="op">{</span></span>
<span class="r-in"> <span class="va">yx</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/split.html" class="external-link">split</a></span><span class="op">(</span><span class="va">y</span>, <span class="va">x</span><span class="op">)</span></span>
@@ -149,6 +147,7 @@
<span class="r-in"><span class="co"># The weight for the loq should therefore be derived at x = 7.3 instead</span></span>
<span class="r-in"><span class="co"># of 15, but the graphical procedure of Massart (p. 201) to derive the </span></span>
<span class="r-in"><span class="co"># variances on which the weights are based is quite inaccurate anyway. </span></span>
+<span class="r-in"></span>
</code></pre></div>
</div>
</div>
diff --git a/docs/reference/rl95_cadmium.html b/docs/reference/rl95_cadmium.html
index da9294d..4ddb8e4 100644
--- a/docs/reference/rl95_cadmium.html
+++ b/docs/reference/rl95_cadmium.html
@@ -1,5 +1,7 @@
<!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995) — rl95_cadmium • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995) — rl95_cadmium"><meta property="og:description" content="Dataset reproduced from Table 1 in Rocke and Lorenzato (1995)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995) — rl95_cadmium • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995) — rl95_cadmium"><meta property="og:description" content="Dataset reproduced from Table 1 in Rocke and Lorenzato (1995)."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -46,8 +48,9 @@
</header><div class="row">
<div class="col-md-9 contents">
<div class="page-header">
- <h1>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)</h1>
-
+ <h1>Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995)</h1>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>rl95_cadmium.Rd</code></div>
</div>
@@ -58,13 +61,13 @@
<div id="format">
<h2>Format</h2>
- <p>A dataframe containing four replicate observations for each
- of the six calibration standards.</p>
+ <p>A dataframe containing four replicate observations for each of the
+six calibration standards.</p>
</div>
<div id="source">
<h2>Source</h2>
- <p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
- measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
+ <p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
+for measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
</div>
</div>
diff --git a/docs/reference/rl95_toluene.html b/docs/reference/rl95_toluene.html
index fb071e1..4c8c7d2 100644
--- a/docs/reference/rl95_toluene.html
+++ b/docs/reference/rl95_toluene.html
@@ -1,7 +1,7 @@
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995) — rl95_toluene • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995) — rl95_toluene"><meta property="og:description" content="Dataset reproduced from Table 4 in Rocke and Lorenzato (1995). The toluene
- amount in the calibration samples is given in picograms per 100 µL.
- Presumably this is the volume that was injected into the instrument."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+amount in the calibration samples is given in picograms per 100 µL.
+Presumably this is the volume that was injected into the instrument."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -49,26 +49,26 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995)</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>rl95_toluene.Rd</code></div>
</div>
<div class="ref-description">
<p>Dataset reproduced from Table 4 in Rocke and Lorenzato (1995). The toluene
- amount in the calibration samples is given in picograms per 100 µL.
- Presumably this is the volume that was injected into the instrument.</p>
+amount in the calibration samples is given in picograms per 100 µL.
+Presumably this is the volume that was injected into the instrument.</p>
</div>
<div id="format">
<h2>Format</h2>
- <p>A dataframe containing four replicate observations for each
- of the six calibration standards.</p>
+ <p>A dataframe containing four replicate observations for each of the
+six calibration standards.</p>
</div>
<div id="source">
<h2>Source</h2>
- <p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
- measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
+ <p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
+for measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
</div>
</div>
diff --git a/docs/reference/utstats14.html b/docs/reference/utstats14.html
index 78d2604..1ffc224 100644
--- a/docs/reference/utstats14.html
+++ b/docs/reference/utstats14.html
@@ -1,6 +1,6 @@
<!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Example data for calibration with replicates from University of Toronto — utstats14 • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Example data for calibration with replicates from University of Toronto — utstats14"><meta property="og:description" content="Dataset read into R from
- https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Example data for calibration with replicates from University of Toronto — utstats14 • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Example data for calibration with replicates from University of Toronto — utstats14"><meta property="og:description" content="Dataset read into R from
+https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -48,26 +48,27 @@
<div class="col-md-9 contents">
<div class="page-header">
<h1>Example data for calibration with replicates from University of Toronto</h1>
-
+ <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>utstats14.Rd</code></div>
</div>
<div class="ref-description">
- <p>Dataset read into R from
- <a href="https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls" class="external-link">https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls</a>.</p>
+ <p>Dataset read into R from
+<a href="https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls" class="external-link">https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls</a>.</p>
</div>
<div id="format">
<h2>Format</h2>
- <p>A tibble containing three replicate observations of the response for five
- calibration concentrations.</p>
+ <p>A tibble containing three replicate observations of the response for
+five calibration concentrations.</p>
</div>
<div id="source">
<h2>Source</h2>
- <p>David Stone and Jon Ellis (2011) Statistics in Analytical Chemistry. Tutorial website
- maintained by the Departments of Chemistry, University of Toronto.
- <a href="https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html" class="external-link">https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html</a></p>
+ <p>David Stone and Jon Ellis (2011) Statistics in Analytical Chemistry.
+Tutorial website maintained by the Departments of Chemistry, University of
+Toronto.
+<a href="https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html" class="external-link">https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html</a></p>
</div>
</div>

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