-Basic calibration functions

Basic calibration functions +

The chemCal package was first designed in the course of a lecture and lab course on “Analytics of Organic Trace Contaminants” at the University of Bremen from October to December 2004. In the fall 2005, an email exchange with Ron Wehrens led to the belief that it would be desirable to implement the inverse prediction method given in Massart et al. (1997) since it also covers the case of weighted regression. Studies of the IUPAC orange book and of DIN 32645 (equivalent to ISO 11843), publications by Currie (1997) and the Analytical Method Committee of the Royal Society of Chemistry (Analytical Methods Committee 1989) and a nice paper by Castells and Castillo (Castells and Castillo 2000) provided some further understanding of the matter.

At the moment, the package consists of four functions (calplot, lod, loq and inverse.predict), working on univariate linear models of class lm or rlm, plus several datasets for validation.

A bug report and the following e-mail exchange on the r-devel mailing list about prediction intervals from weighted regression entailed some further studies on this subject. However, I did not encounter any proof or explanation of the formula cited below yet, so I can’t really confirm that Massart’s method is correct.

At the moment, the package consists of four functions (calplot, lod, loq and inverse.predict), working on univariate linear models of class lm or rlm, plus several datasets for validation.

In fact, in June 2018 I was made aware of the fact that the inverse prediction method implemented in chemCal version 0.1.37 and before did not take the variance of replicate calibration standards about their means into account, nor the number of replicates when calculating the degrees of freedom. Thanks to PhD student Anna Burniol Figols for reporting this issue!

As a consequence, I rewrote inverse.predict not to automatically work with the mean responses for each calibration standard any more. The example calculations from Massart et al. (1997) can still be reproduced when the regression model is calculated using the means of the calibration data as shown below.

-Usage

Usage +

When calibrating an analytical method, the first task is to generate a suitable model. If we want to use the chemCal functions, we have to restrict ourselves to univariate, possibly weighted, linear regression so far.

Once such a model has been created, the calibration can be graphically shown by using the calplot function:

-library(chemCal)
-m0 <- lm(y ~ x, data = massart97ex3)
-calplot(m0)

library(chemCal)
+m0 <- lm(y ~ x, data = massart97ex3)
+calplot(m0)

As we can see, the scatter increases with increasing x. This is also illustrated by one of the diagnostic plots for linear models provided by R:

-plot(m0, which=3)

+plot(m0, which=3)

Therefore, in Example 8 in Massart et al. (1997), weighted regression is proposed which can be reproduced by the following code. Note that we are building the model on the mean values for each standard in order to be able to reproduce the results given in the book with the current version of chemCal.

-weights <- with(massart97ex3, {
-  yx <- split(y, x)
-  ybar <- sapply(yx, mean)
-  s <- round(sapply(yx, sd), digits = 2)
-  w <- round(1 / (s^2), digits = 3)
+weights <- with(massart97ex3, {
+  yx <- split(y, x)
+  ybar <- sapply(yx, mean)
+  s <- round(sapply(yx, sd), digits = 2)
+  w <- round(1 / (s^2), digits = 3)
 })
-massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
+massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
 
-m <- lm(y ~ x, w = weights, data = massart97ex3.means)


+m <- lm(y ~ x, w = weights, data = massart97ex3.means)

If we now want to predict a new x value from measured y values, we use the inverse.predict function:

 inverse.predict(m, 15, ws=1.67)

## $Prediction
-## [1] 5.865367
-## 
-## $`Standard Error`
-## [1] 0.8926109
-## 
-## $Confidence
-## [1] 2.478285
-## 
-## $`Confidence Limits`
-## [1] 3.387082 8.343652

## $Prediction
+## [1] 5.865367
+## 
+## $`Standard Error`
+## [1] 0.8926109
+## 
+## $Confidence
+## [1] 2.478285
+## 
+## $`Confidence Limits`
+## [1] 3.387082 8.343652

 inverse.predict(m, 90, ws = 0.145)

## $Prediction
-## [1] 44.06025
-## 
-## $`Standard Error`
-## [1] 2.829162
-## 
-## $Confidence
-## [1] 7.855012
-## 
-## $`Confidence Limits`
-## [1] 36.20523 51.91526

## $Prediction
+## [1] 44.06025
+## 
+## $`Standard Error`
+## [1] 2.829162
+## 
+## $Confidence
+## [1] 7.855012
+## 
+## $`Confidence Limits`
+## [1] 36.20523 51.91526

The weight ws assigned to the measured y value has to be given by the user in the case of weighted regression, or alternatively, the approximate variance var.s at this location.

-Background for `inverse.predict` -

Background for `inverse.predict` +

Equation 8.28 in Massart et al. (1997) gives a general equation for predicting the standard error $s_{\hat{x_s}}$ for an $x$ value predicted from measurements of $y$ according to the linear calibration function $y = b_0 + b_1 \cdot x$:

\[\begin{equation} s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} + @@ -203,11 +198,13 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +

@@ -216,5 +213,7 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} + + + diff --git a/docs/articles/chemCal_files/figure-html/unnamed-chunk-1-1.png b/docs/articles/chemCal_files/figure-html/unnamed-chunk-1-1.png index fc76c68..51f854a 100644 Binary files a/docs/articles/chemCal_files/figure-html/unnamed-chunk-1-1.png and b/docs/articles/chemCal_files/figure-html/unnamed-chunk-1-1.png differ diff --git a/docs/articles/chemCal_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/chemCal_files/figure-html/unnamed-chunk-2-1.png index 605137b..f30d115 100644 Binary files a/docs/articles/chemCal_files/figure-html/unnamed-chunk-2-1.png and b/docs/articles/chemCal_files/figure-html/unnamed-chunk-2-1.png differ diff --git a/docs/articles/index.html b/docs/articles/index.html index 48a4eca..3e53fde 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -1,66 +1,12 @@ - - - - - - - -Articles • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Articles • chemCal + + - - - - -

- -

Introduction to chemCal: +

- - + + diff --git a/docs/authors.html b/docs/authors.html index 476cf5e..694eb5b 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -1,66 +1,12 @@ - - - - - - - -Authors • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Authors and Citation • chemCal - - + + - - - -

- -

Authors

+ + + +

+
Johannes Ranke. Author, maintainer, copyright holder. +
+

Citation

+ Source: DESCRIPTION +

-
Johannes Ranke. Author, maintainer, copyright holder. -
-

+ +

Ranke J (2022). +chemCal: Calibration Functions for Analytical Chemistry. +https://pkgdown.jrwb.de/chemCal/, https://cgit.jrwb.de/chemCal/about. +

@Manual{,
+  title = {chemCal: Calibration Functions for Analytical Chemistry},
+  author = {Johannes Ranke},
+  year = {2022},
+  note = {https://pkgdown.jrwb.de/chemCal/, https://cgit.jrwb.de/chemCal/about},
+}

@@ -129,22 +81,20 @@ -

- - + + diff --git a/docs/index.html b/docs/index.html index a724173..4019484 100644 --- a/docs/index.html +++ b/docs/index.html @@ -25,6 +25,8 @@ + +

- +

+ -

Static documentation of this R package can be found at https://pkgdown.jrwb.de/chemCal

Overview +

chemCal is an R package providing some basic functions for conveniently working with linear calibration curves with one explanatory variable.

Installation +

From within R, get the official chemCal release using

+install.packages("chemCal")

Usage +

chemCal works with univariate linear models of class lm. Working with one of the datasets coming with chemCal, we can produce a calibration plot using the calplot function:

Plotting a calibration +

+library(chemCal)
+m0 <- lm(y ~ x, data = massart97ex3)
+calplot(m0)

LOD and LOQ +

If you use unweighted regression, as in the above example, we can calculate a Limit Of Detection (LOD) from the calibration data.

+lod(m0)
+#> $x
+#> [1] 5.407085
+#> 
+#> $y
+#> [1] 13.63911

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).

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.

+lod(m0, beta = 0.5)
+#> $x
+#> [1] 2.720388
+#> 
+#> $y
+#> [1] 8.314841

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).

+loq(m0)
+#> $x
+#> [1] 9.627349
+#> 
+#> $y
+#> [1] 22.00246

Confidence intervals for measured values +

Finally, you can get a confidence interval for the values measured using the calibration curve, i.e. for the inverse predictions using the function inverse.predict.

+inverse.predict(m0, 90)
+#> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 1.576985
+#> 
+#> $Confidence
+#> [1] 3.230307
+#> 
+#> $`Confidence Limits`
+#> [1] 40.70952 47.17014

If you have replicate measurements of the same sample, you can also give a vector of numbers.

+inverse.predict(m0, c(91, 89, 87, 93, 90))
+#> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 0.796884
+#> 
+#> $Confidence
+#> [1] 1.632343
+#> 
+#> $`Confidence Limits`
+#> [1] 42.30749 45.57217

Reference +

You can use the R help system to view documentation, or you can have a look at the online documentation.

License

GPL (>= 2)

Developers

+ + +

Citation

Johannes Ranke
Author, maintainer, copyright holder
Citing chemCal

Dev status

Developers

Johannes Ranke
Author, maintainer, copyright holder

+ +

Dev status

+ +

@@ -138,5 +235,7 @@ + + diff --git a/docs/news/index.html b/docs/news/index.html index d3ddaa8..f422331 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -1,66 +1,12 @@ - - - - - - - -Changelog • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Changelog • chemCal - - + + - - -

- -

‘calplot’ gains an argument ‘legend_x’ for better control of the legend position

+ +

Make the use of the ‘investr’ package conditional in testthat tests, update maintainer e-mail address

+ +

‘calplot’ gains an argument ‘legend_x’ for better control of the legend position
Added the cadmium dataset from Rocke and Lorenzato (1995)
Suggest: rmarkdown as it is not a dependency of knitr any more, as pointed out by Kurt Hornik

- -

‘inverse.predict’: Do not work on the means of the calibration standards any more, as this ignores the variability of y values about the means. Thanks to Anna Burniol Figols for pointing out this issue

+ +

‘inverse.predict’: Do not work on the means of the calibration standards any more, as this ignores the variability of y values about the means. Thanks to Anna Burniol Figols for pointing out this issue
Use testthat for tests to simplify development. Adapt the tests using data with replicate standard measurements to work on the means in order to show the relation to ‘inverse.predict’ from earlier versions. Include comparisons with investr::calibrate(method = ‘Wald’) for unweighted regressions. Include tests with more precision to check for changes in numerical output across versions.
‘lod’ and ‘loq’: In the lists that are returned, return the list component ‘y’ without names, because we always only have a single element in ‘y’ (previously the name ‘1’ was returned).
Convert vignette to html and explain the changes to ‘inverse.predict’
Add two example dataset, one from an online course at the University of Toronto, one from Rocke and Lorenzato (1995)
Update static documentation

- -

Maintenance release

- -

Bugfix in lod() and loq(): In the case of small absolute x values (e.g. on the order of 1e-4 and smaller), the lod or loq calculated using the default method could produce inaccurate results as the default tolerance that was used in the internal call to optimize is inappropriate in such cases. Now a reasonable default is used which can be overriden by the user. Thanks to Jérôme Ambroise for reporting the bug.

For a detailed list of changes to the chemCal source please consult the commit history on https://cgit.jrwb.de/chemCal

+ +

Maintenance release

+ +

Bugfix in lod() and loq(): In the case of small absolute x values (e.g. on the order of 1e-4 and smaller), the lod or loq calculated using the default method could produce inaccurate results as the default tolerance that was used in the internal call to optimize is inappropriate in such cases. Now a reasonable default is used which can be overriden by the user. Thanks to Jérôme Ambroise for reporting the bug.

For a detailed list of changes to the chemCal source please consult the commit history on https://cgit.jrwb.de/chemCal

- - + + diff --git a/docs/pkgdown.css b/docs/pkgdown.css index 1273238..80ea5b8 100644 --- a/docs/pkgdown.css +++ b/docs/pkgdown.css @@ -56,8 +56,10 @@ img.icon { float: right; } -img { +/* Ensure in-page images don't run outside their container */ +.contents img { max-width: 100%; + height: auto; } /* Fix bug in bootstrap (only seen in firefox) */ @@ -78,11 +80,10 @@ dd { /* Section anchors ---------------------------------*/ a.anchor { - margin-left: -30px; - display:inline-block; - width: 30px; - height: 30px; - visibility: hidden; + display: none; + margin-left: 5px; + width: 20px; + height: 20px; background-image: url(./link.svg); background-repeat: no-repeat; @@ -90,17 +91,15 @@ a.anchor { background-position: center center; } -.hasAnchor:hover a.anchor { - visibility: visible; -} - -@media (max-width: 767px) { - .hasAnchor:hover a.anchor { - visibility: hidden; - } +h1:hover .anchor, +h2:hover .anchor, +h3:hover .anchor, +h4:hover .anchor, +h5:hover .anchor, +h6:hover .anchor { + display: inline-block; } - /* Fixes for fixed navbar --------------------------*/ .contents h1, .contents h2, .contents h3, .contents h4 { @@ -264,31 +263,26 @@ table { /* Syntax highlighting ---------------------------------------------------- */ -pre { - word-wrap: normal; - word-break: normal; - border: 1px solid #eee; -} - -pre, code { +pre, code, pre code { background-color: #f8f8f8; color: #333; } +pre, pre code { + white-space: pre-wrap; + word-break: break-all; + overflow-wrap: break-word; +} -pre code { - overflow: auto; - word-wrap: normal; - white-space: pre; +pre { + border: 1px solid #eee; } -pre .img { +pre .img, pre .r-plt { margin: 5px 0; } -pre .img img { +pre .img img, pre .r-plt img { background-color: #fff; - display: block; - height: auto; } code a, pre a { @@ -305,9 +299,8 @@ a.sourceLine:hover { .kw {color: #264D66;} /* keyword */ .co {color: #888888;} /* comment */ -.message { color: black; font-weight: bolder;} -.error { color: orange; font-weight: bolder;} -.warning { color: #6A0366; font-weight: bolder;} +.error {font-weight: bolder;} +.warning {font-weight: bolder;} /* Clipboard --------------------------*/ @@ -365,3 +358,27 @@ mark { content: ""; } } + +/* Section anchors --------------------------------- + Added in pandoc 2.11: https://github.com/jgm/pandoc-templates/commit/9904bf71 +*/ + +div.csl-bib-body { } +div.csl-entry { + clear: both; +} +.hanging-indent div.csl-entry { + margin-left:2em; + text-indent:-2em; +} +div.csl-left-margin { + min-width:2em; + float:left; +} +div.csl-right-inline { + margin-left:2em; + padding-left:1em; +} +div.csl-indent { + margin-left: 2em; +} diff --git a/docs/pkgdown.js b/docs/pkgdown.js index 7e7048f..6f0eee4 100644 --- a/docs/pkgdown.js +++ b/docs/pkgdown.js @@ -80,7 +80,7 @@ $(document).ready(function() { var copyButton = ""; - $(".examples, div.sourceCode").addClass("hasCopyButton"); + $("div.sourceCode").addClass("hasCopyButton"); // Insert copy buttons: $(copyButton).prependTo(".hasCopyButton"); @@ -91,7 +91,7 @@ // Initialize clipboard: var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', { text: function(trigger) { - return trigger.parentNode.textContent; + return trigger.parentNode.textContent.replace(/\n#>[^\n]*/g, ""); } }); diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index 6279661..dc4cced 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -1,7 +1,7 @@ pandoc: 2.9.2.1 -pkgdown: 1.6.1 +pkgdown: 2.0.2 pkgdown_sha: ~ articles: chemCal: chemCal.html -last_built: 2021-04-17T05:19Z +last_built: 2022-03-31T16:32Z diff --git a/docs/reference/calplot.lm-1.png b/docs/reference/calplot.lm-1.png index 5d4c4d9..c2deae8 100644 Binary files a/docs/reference/calplot.lm-1.png and b/docs/reference/calplot.lm-1.png differ diff --git a/docs/reference/calplot.lm.html b/docs/reference/calplot.lm.html index b041a8d..7865a66 100644 --- a/docs/reference/calplot.lm.html +++ b/docs/reference/calplot.lm.html @@ -1,68 +1,13 @@ - - - - - - - -Plot calibration graphs from univariate linear models — calplot • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Plot calibration graphs from univariate linear models — calplot • chemCal - - - - + + -

- -

calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
-    xlab = "Concentration", ylab = "Response", legend_x = "auto",
-    alpha=0.05, varfunc = NULL)

- -

Arguments

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

object	A univariate model object of class `lm` or - `rlm` - with model formula `y ~ x` or `y ~ x - 1`.
xlim	The limits of the plot on the x axis.
ylim	The limits of the plot on the y axis.
xlab	The label of the x axis.
ylab	The label of the y axis.
legend_x	An optional numeric value for adjusting the x coordinate of the legend.
alpha	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 `lod` (see note below).
varfunc	The variance function for generating the weights in the model. - Currently, this argument is ignored (see note below).

- -

Value

calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
+    xlab = "Concentration", ylab = "Response", legend_x = "auto",
+    alpha=0.05, varfunc = NULL)

Arguments

object: A univariate model object of class lm or + rlm + with model formula y ~ x or y ~ x - 1.
xlim: The limits of the plot on the x axis.
ylim: The limits of the plot on the y axis.
xlab: The label of the x axis.
ylab: The label of the y axis.
legend_x: An optional numeric value for adjusting the x coordinate of the legend.
alpha: 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 lod (see note below).
varfunc: The variance function for generating the weights in the model. + Currently, this argument is ignored (see note below).

Value

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.

Note

- +

Note

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 predict.lm, therefore, + the internally used function predict.lm, therefore, calplot does not draw prediction bands for such models.

It is possible to compare the calplot prediction bands with the - lod values if the lod() alpha and beta parameters are + lod values if the lod() alpha and beta parameters are half the value of the calplot() alpha parameter.

Author

- +

Author

Johannes Ranke - jranke@uni-bremen.de

+ jranke@uni-bremen.de

Examples

data(massart97ex3)
-m <- lm(y ~ x, data = massart97ex3)
-calplot(m)
-

Examples

data(massart97ex3)
+m <- lm(y ~ x, data = massart97ex3)
+calplot(m)
+
+

- - + + diff --git a/docs/reference/din32645-1.png b/docs/reference/din32645-1.png index 27914e8..170a9ae 100644 Binary files a/docs/reference/din32645-1.png and b/docs/reference/din32645-1.png differ diff --git a/docs/reference/din32645.html b/docs/reference/din32645.html index b46103c..1c02f36 100644 --- a/docs/reference/din32645.html +++ b/docs/reference/din32645.html @@ -1,67 +1,12 @@ - - - - - - - -Calibration data from DIN 32645 — din32645 • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Calibration data from DIN 32645 — din32645 • chemCal - - - - + + -

- -

data(din32645)

- - -

Format

data(din32645)

Format

A dataframe containing 10 rows of x and y values.

References

- +

References

DIN 32645 (equivalent to ISO 11843), Beuth Verlag, Berlin, 1994

Dintest. Plugin for MS Excel for evaluations of calibration data. Written by Georg Schmitt, University of Heidelberg. Formerly available from @@ -138,69 +72,75 @@

Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105 - 126.

Examples

m <- lm(y ~ x, data = din32645)
-calplot(m)
-

-## Prediction of x with confidence interval
-prediction <- inverse.predict(m, 3500, alpha = 0.01)
-
-# This should give 0.07434 according to test data from Dintest, which 
-# was collected from Procontrol 3.1 (isomehr GmbH) in this case
-round(prediction$Confidence, 5)
-
#> [1] 0.07434

-## Critical value:
-crit <- lod(m, alpha = 0.01, beta = 0.5)
-
-# According to DIN 32645, we should get 0.07 for the critical value
-# (decision limit, "Nachweisgrenze")
-round(crit$x, 2)
-
#> [1] 0.07
# and according to Dintest test data, we should get 0.0698 from
-round(crit$x, 4)
-
#> [1] 0.0698

-## Limit of detection (smallest detectable value given alpha and beta)
-# In German, the smallest detectable value is the "Erfassungsgrenze", and we
-# should get 0.14 according to DIN, which we achieve by using the method 
-# described in it:
-lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
-round(lod.din$x, 2)
-
#> [1] 0.14

-## Limit of quantification
-# This accords to the test data coming with the test data from Dintest again, 
-# except for the last digits of the value cited for Procontrol 3.1 (0.2121)
-loq <- loq(m, alpha = 0.01)
-round(loq$x, 4)
-
#> [1] 0.212

-# A similar value is obtained using the approximation 
-# LQ = 3.04 * LC (Currie 1999, p. 120)
-3.04 * lod(m, alpha = 0.01, beta = 0.5)$x
-
#> [1] 0.2122306

Examples

m <- lm(y ~ x, data = din32645)
+calplot(m)
+
+
+## Prediction of x with confidence interval
+prediction <- inverse.predict(m, 3500, alpha = 0.01)
+
+# This should give 0.07434 according to test data from Dintest, which 
+# was collected from Procontrol 3.1 (isomehr GmbH) in this case
+round(prediction$Confidence, 5)
+#> [1] 0.07434
+
+## Critical value:
+crit <- lod(m, alpha = 0.01, beta = 0.5)
+
+# According to DIN 32645, we should get 0.07 for the critical value
+# (decision limit, "Nachweisgrenze")
+round(crit$x, 2)
+#> [1] 0.07
+# and according to Dintest test data, we should get 0.0698 from
+round(crit$x, 4)
+#> [1] 0.0698
+
+## Limit of detection (smallest detectable value given alpha and beta)
+# In German, the smallest detectable value is the "Erfassungsgrenze", and we
+# should get 0.14 according to DIN, which we achieve by using the method 
+# described in it:
+lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
+round(lod.din$x, 2)
+#> [1] 0.14
+
+## Limit of quantification
+# This accords to the test data coming with the test data from Dintest again, 
+# except for the last digits of the value cited for Procontrol 3.1 (0.2121)
+loq <- loq(m, alpha = 0.01)
+round(loq$x, 4)
+#> [1] 0.212
+
+# A similar value is obtained using the approximation 
+# LQ = 3.04 * LC (Currie 1999, p. 120)
+3.04 * lod(m, alpha = 0.01, beta = 0.5)$x
+#> [1] 0.2122306
+

- - + + diff --git a/docs/reference/figures/README-calplot-1.png b/docs/reference/figures/README-calplot-1.png new file mode 100644 index 0000000..b71d326 Binary files /dev/null and b/docs/reference/figures/README-calplot-1.png differ diff --git a/docs/reference/index.html b/docs/reference/index.html index 8549a1d..3685007 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -1,66 +1,12 @@ - - - - - - - -Function reference • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Function reference • chemCal - - + + - - -

- -

- - - - - - - - - - -

All functions

+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

+ All functions
+
`calplot()`	Plot calibration graphs from univariate linear models
+
`din32645`	Calibration data from DIN 32645
+
`inverse.predict()`	Predict x from y for a linear calibration
+
`lod()`	Estimate a limit of detection (LOD)
+
`loq()`	Estimate a limit of quantification (LOQ)
+
`massart97ex1`	Calibration data from Massart et al. (1997), example 1
+
`massart97ex3`	Calibration data from Massart et al. (1997), example 3
+
`rl95_cadmium`	Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)
+
`rl95_toluene`	Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995)
+
`utstats14`	Example data for calibration with replicates from University of Toronto

- +

- - + + diff --git a/docs/reference/inverse.predict.html b/docs/reference/inverse.predict.html index aece430..cb9fe98 100644 --- a/docs/reference/inverse.predict.html +++ b/docs/reference/inverse.predict.html @@ -1,46 +1,5 @@ - - - - - - - -Predict x from y for a linear calibration — inverse.predict • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Predict x from y for a linear calibration — inverse.predict • chemCal - - - - - - - - - - - - - + + -

- -

inverse.predict(object, newdata, ...,
-  ws, alpha=0.05, var.s = "auto")

inverse.predict(object, newdata, ...,
+  ws, alpha=0.05, var.s = "auto")

Arguments

- - - - - - - - - - - - - - - - - - - - - - - - - - -

object	A univariate model object of class `lm` or - `rlm` - with model formula `y ~ x` or `y ~ x - 1`.
newdata	A vector of observed y values for one sample.
...	Placeholder for further arguments that might be needed by - future implementations.
ws	The weight attributed to the sample. This argument is obligatory - if `object` has weights.
alpha	The error tolerance level for the confidence interval to be reported.
var.s	The estimated variance of the sample measurements. The default is to take + + Arguments + object + A univariate model object of class `lm` or + `rlm` + with model formula `y ~ x` or `y ~ x - 1`. + newdata + A vector of observed y values for one sample. + ... + Placeholder for further arguments that might be needed by + future implementations. + ws + The weight attributed to the sample. This argument is obligatory + if `object` has weights. + alpha + The error tolerance level for the confidence interval to be reported. + var.s + The estimated variance of the sample measurements. The default is to take the residual standard error from the calibration and to adjust it using `ws`, if applicable. This means that `var.s` - overrides `ws`.

- -

Value

- + overrides ws.

Value

A list containing the predicted x value, its standard error and a confidence interval.

Note

- +

Note

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.

References

- +

References

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

Examples

# This is example 7 from Chapter 8 in Massart et al. (1997)
-m <- lm(y ~ x, data = massart97ex1)
-inverse.predict(m, 15)        #  6.1 +- 4.9
-
#> $Prediction
-#> [1] 6.09381
-#> 
-#> $`Standard Error`
-#> [1] 1.767278
-#> 
-#> $Confidence
-#> [1] 4.906751
-#> 
-#> $`Confidence Limits`
-#> [1]  1.187059 11.000561
-#> 
inverse.predict(m, 90)        # 43.9 +- 4.9
-
#> $Prediction
-#> [1] 43.93983
-#> 
-#> $`Standard Error`
-#> [1] 1.767747
-#> 
-#> $Confidence
-#> [1] 4.908053
-#> 
-#> $`Confidence Limits`
-#> [1] 39.03178 48.84788
-#> 
inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
-
#> $Prediction
-#> [1] 43.93983
-#> 
-#> $`Standard Error`
-#> [1] 1.141204
-#> 
-#> $Confidence
-#> [1] 3.168489
-#> 
-#> $`Confidence Limits`
-#> [1] 40.77134 47.10832
-#> 

-# For reproducing the results for replicate standard measurements in example 8,
-# we need to do the calibration on the means when using chemCal > 0.2
-weights <- with(massart97ex3, {
-  yx <- split(y, x)
-  ybar <- sapply(yx, mean)
-  s <- round(sapply(yx, sd), digits = 2)
-  w <- round(1 / (s^2), digits = 3)
-})
-
-massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
-
-m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
-
-inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
-
#> $Prediction
-#> [1] 5.865367
-#> 
-#> $`Standard Error`
-#> [1] 0.8926109
-#> 
-#> $Confidence
-#> [1] 2.478285
-#> 
-#> $`Confidence Limits`
-#> [1] 3.387082 8.343652
-#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
-
#> $Prediction
-#> [1] 44.06025
-#> 
-#> $`Standard Error`
-#> [1] 2.829162
-#> 
-#> $Confidence
-#> [1] 7.855012
-#> 
-#> $`Confidence Limits`
-#> [1] 36.20523 51.91526
-#> 

-

Examples

# This is example 7 from Chapter 8 in Massart et al. (1997)
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15)        #  6.1 +- 4.9
+#> $Prediction
+#> [1] 6.09381
+#> 
+#> $`Standard Error`
+#> [1] 1.767278
+#> 
+#> $Confidence
+#> [1] 4.906751
+#> 
+#> $`Confidence Limits`
+#> [1]  1.187059 11.000561
+#> 
+inverse.predict(m, 90)        # 43.9 +- 4.9
+#> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 1.767747
+#> 
+#> $Confidence
+#> [1] 4.908053
+#> 
+#> $`Confidence Limits`
+#> [1] 39.03178 48.84788
+#> 
+inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+#> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 1.141204
+#> 
+#> $Confidence
+#> [1] 3.168489
+#> 
+#> $`Confidence Limits`
+#> [1] 40.77134 47.10832
+#> 
+
+# For reproducing the results for replicate standard measurements in example 8,
+# we need to do the calibration on the means when using chemCal > 0.2
+weights <- with(massart97ex3, {
+  yx <- split(y, x)
+  ybar <- sapply(yx, mean)
+  s <- round(sapply(yx, sd), digits = 2)
+  w <- round(1 / (s^2), digits = 3)
+})
+
+massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
+
+m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
+
+inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
+#> $Prediction
+#> [1] 5.865367
+#> 
+#> $`Standard Error`
+#> [1] 0.8926109
+#> 
+#> $Confidence
+#> [1] 2.478285
+#> 
+#> $`Confidence Limits`
+#> [1] 3.387082 8.343652
+#> 
+inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
+#> $Prediction
+#> [1] 44.06025
+#> 
+#> $`Standard Error`
+#> [1] 2.829162
+#> 
+#> $Confidence
+#> [1] 7.855012
+#> 
+#> $`Confidence Limits`
+#> [1] 36.20523 51.91526
+#> 
+
+

- - + + diff --git a/docs/reference/lod.html b/docs/reference/lod.html index 42fc533..a2d66ce 100644 --- a/docs/reference/lod.html +++ b/docs/reference/lod.html @@ -1,74 +1,19 @@ - - - - - - - -Estimate a limit of detection (LOD) — lod • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Estimate a limit of detection (LOD) — lod • chemCal - - - - - - - - - - - - - + + -

- -

lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")

lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")

Arguments

- - - - - - - - - - - - - - - - - - - - - - - - - - -

object	A univariate model object of class `lm` or - `rlm` + + Arguments + object + A univariate model object of class `lm` or + `rlm` with model formula `y ~ x` or `y ~ x - 1`, - optionally from a weighted regression.
...	Placeholder for further arguments that might be needed by - future implementations.
alpha	The error tolerance for the decision limit (critical value).
beta	The error tolerance beta for the detection limit.
method	The “default” method uses a prediction interval at the LOD + optionally from a weighted regression. + ... + Placeholder for further arguments that might be needed by + future implementations. + alpha + The error tolerance for the decision limit (critical value). + beta + The error tolerance beta for the detection limit. + method + 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.
tol	When the “default” method is used, the default tolerance + The “din” method uses the prediction interval at + x = 0 as an approximation. + tol + 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.

- -

Value

- + divided by 1000. Can be set to a numeric value to override this.

Value

A list containig the corresponding x and y values of the estimated limit of detection of a model used for calibration.

Note

- +

Note

- 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 predict.lm + a weights argument for the internally used predict.lm function, which is currently not supported in R.

References

- +

References

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

@@ -202,53 +124,55 @@

Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105 - 126.

Examples

m <- lm(y ~ x, data = din32645)
-lod(m) 
-
#> $x
-#> [1] 0.08655484
-#> 
-#> $y
-#> [1] 3317.154
-#> 

-# The critical value (decision limit, German Nachweisgrenze) can be obtained
-# by using beta = 0.5:
-lod(m, alpha = 0.01, beta = 0.5)
-
#> $x
-#> [1] 0.0698127
-#> 
-#> $y
-#> [1] 3155.393
-#>

Examples

m <- lm(y ~ x, data = din32645)
+lod(m) 
+#> $x
+#> [1] 0.08655484
+#> 
+#> $y
+#> [1] 3317.154
+#> 
+
+# The critical value (decision limit, German Nachweisgrenze) can be obtained
+# by using beta = 0.5:
+lod(m, alpha = 0.01, beta = 0.5)
+#> $x
+#> [1] 0.0698127
+#> 
+#> $y
+#> [1] 3155.393
+#> 
+

- - + + diff --git a/docs/reference/loq.html b/docs/reference/loq.html index 973b1ff..0960251 100644 --- a/docs/reference/loq.html +++ b/docs/reference/loq.html @@ -1,73 +1,18 @@ - - - - - - - -Estimate a limit of quantification (LOQ) — loq • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Estimate a limit of quantification (LOQ) — loq • chemCal - - - - - - - - - - - - - + + -

- -

Estimate a limit of quantification (LOQ)

@@ -132,119 +64,106 @@ $$L = k c(L)$$ 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.

+ inverse.predict, and L is obtained by iteration.

loq(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
-    var.loq = "auto", tol = "default")

loq(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
+    var.loq = "auto", tol = "default")

Arguments

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

object	A univariate model object of class `lm` or - `rlm` + + Arguments + object + A univariate model object of class `lm` or + `rlm` with model formula `y ~ x` or `y ~ x - 1`, optionally from a weighted regression. If weights are specified in the model, either `w.loq` or `var.loq` have to - be specified.
alpha	The error tolerance for the prediction of x values in the calculation.
...	Placeholder for further arguments that might be needed by - future implementations.
k	The inverse of the maximum relative error tolerated at the - desired LOQ.
n	The number of replicate measurements for which the LOQ should be - specified.
w.loq	The weight that should be attributed to the LOQ. Defaults + be specified. + alpha + The error tolerance for the prediction of x values in the calculation. + ... + Placeholder for further arguments that might be needed by + future implementations. + k + The inverse of the maximum relative error tolerated at the + desired LOQ. + n + The number of replicate measurements for which the LOQ should be + specified. + w.loq + 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 `massart97ex3` for + for weighted regression. See `massart97ex3` for an example how to take advantage of knowledge about the - variance function.
var.loq	The approximate variance at the LOQ. The default value is - calculated from the model.
tol	The default tolerance for the LOQ on the x scale is the value of the + variance function. + var.loq + The approximate variance at the LOQ. The default value is + calculated from the model. + tol + 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.

- -

Value

- + numeric value to override this.

Value

The estimated limit of quantification for a model used for calibration.

Note

- +

Note

- 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.

Examples

m <- lm(y ~ x, data = massart97ex1)
-loq(m)
-
#> $x
-#> [1] 13.97764
-#> 
-#> $y
-#> [1] 30.6235
-#> 

-# We can get better by using replicate measurements
-loq(m, n = 3)
-
#> $x
-#> [1] 9.971963
-#> 
-#> $y
-#> [1] 22.68539
-#>

Examples

m <- lm(y ~ x, data = massart97ex1)
+loq(m)
+#> $x
+#> [1] 13.97764
+#> 
+#> $y
+#> [1] 30.6235
+#> 
+
+# We can get better by using replicate measurements
+loq(m, n = 3)
+#> $x
+#> [1] 9.971963
+#> 
+#> $y
+#> [1] 22.68539
+#> 
+

- - + + diff --git a/docs/reference/massart97ex1.html b/docs/reference/massart97ex1.html index c82bf6f..e5dd85a 100644 --- a/docs/reference/massart97ex1.html +++ b/docs/reference/massart97ex1.html @@ -1,67 +1,12 @@ - - - - - - - -Calibration data from Massart et al. (1997), example 1 — massart97ex1 • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Calibration data from Massart et al. (1997), example 1 — massart97ex1 • chemCal - - - - + + -

- -

data(massart97ex1)

- - -

Format

data(massart97ex1)

Format

A dataframe containing 6 observations of x and y data.

Source

- +

Source

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.

- - + + diff --git a/docs/reference/massart97ex3.html b/docs/reference/massart97ex3.html index 4cbf7ce..4196882 100644 --- a/docs/reference/massart97ex3.html +++ b/docs/reference/massart97ex3.html @@ -1,67 +1,12 @@ - - - - - - - -Calibration data from Massart et al. (1997), example 3 — massart97ex3 • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Calibration data from Massart et al. (1997), example 3 — massart97ex3 • chemCal - - - - + + -

- -

massart97ex3

- - -

Format

massart97ex3

Format

A dataframe containing 6 levels of x values with 5 observations of y for each level.

Source

- +

Source

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.

Examples

# For reproducing the results for replicate standard measurements in example 8,
-# we need to do the calibration on the means when using chemCal > 0.2
-weights <- with(massart97ex3, {
-  yx <- split(y, x)
-  ybar <- sapply(yx, mean)
-  s <- round(sapply(yx, sd), digits = 2)
-  w <- round(1 / (s^2), digits = 3)
-})
-
-massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
-
-m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
-
-# The following concords with the book p. 200
-inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
-
#> $Prediction
-#> [1] 5.865367
-#> 
-#> $`Standard Error`
-#> [1] 0.8926109
-#> 
-#> $Confidence
-#> [1] 2.478285
-#> 
-#> $`Confidence Limits`
-#> [1] 3.387082 8.343652
-#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
-
#> $Prediction
-#> [1] 44.06025
-#> 
-#> $`Standard Error`
-#> [1] 2.829162
-#> 
-#> $Confidence
-#> [1] 7.855012
-#> 
-#> $`Confidence Limits`
-#> [1] 36.20523 51.91526
-#> 

-# The LOD is only calculated for models from unweighted regression
-# with this version of chemCal
-m0 <- lm(y ~ x, data = massart97ex3) 
-lod(m0)
-
#> $x
-#> [1] 5.407085
-#> 
-#> $y
-#> [1] 13.63911
-#> 

-# Limit of quantification from unweighted regression
-loq(m0)
-
#> $x
-#> [1] 9.627349
-#> 
-#> $y
-#> [1] 22.00246
-#> 

-# For calculating the limit of quantification from a model from weighted
-# regression, we need to supply weights, internally used for inverse.predict
-# If we are not using a variance function, we can use the weight from
-# the above example as a first approximation (x = 15 is close to our
-# loq approx 14 from above).
-loq(m3.means, w.loq = 1.67)
-
#> $x
-#> [1] 7.346195
-#> 
-#> $y
-#> [1] 17.90777
-#> 
# The weight for the loq should therefore be derived at x = 7.3 instead
-# of 15, but the graphical procedure of Massart (p. 201) to derive the 
-# variances on which the weights are based is quite inaccurate anyway. 
-

Examples

# For reproducing the results for replicate standard measurements in example 8,
+# we need to do the calibration on the means when using chemCal > 0.2
+weights <- with(massart97ex3, {
+  yx <- split(y, x)
+  ybar <- sapply(yx, mean)
+  s <- round(sapply(yx, sd), digits = 2)
+  w <- round(1 / (s^2), digits = 3)
+})
+
+massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
+
+m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
+
+# The following concords with the book p. 200
+inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
+#> $Prediction
+#> [1] 5.865367
+#> 
+#> $`Standard Error`
+#> [1] 0.8926109
+#> 
+#> $Confidence
+#> [1] 2.478285
+#> 
+#> $`Confidence Limits`
+#> [1] 3.387082 8.343652
+#> 
+inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
+#> $Prediction
+#> [1] 44.06025
+#> 
+#> $`Standard Error`
+#> [1] 2.829162
+#> 
+#> $Confidence
+#> [1] 7.855012
+#> 
+#> $`Confidence Limits`
+#> [1] 36.20523 51.91526
+#> 
+
+# The LOD is only calculated for models from unweighted regression
+# with this version of chemCal
+m0 <- lm(y ~ x, data = massart97ex3) 
+lod(m0)
+#> $x
+#> [1] 5.407085
+#> 
+#> $y
+#> [1] 13.63911
+#> 
+
+# Limit of quantification from unweighted regression
+loq(m0)
+#> $x
+#> [1] 9.627349
+#> 
+#> $y
+#> [1] 22.00246
+#> 
+
+# For calculating the limit of quantification from a model from weighted
+# regression, we need to supply weights, internally used for inverse.predict
+# If we are not using a variance function, we can use the weight from
+# the above example as a first approximation (x = 15 is close to our
+# loq approx 14 from above).
+loq(m3.means, w.loq = 1.67)
+#> $x
+#> [1] 7.346195
+#> 
+#> $y
+#> [1] 17.90777
+#> 
+# The weight for the loq should therefore be derived at x = 7.3 instead
+# of 15, but the graphical procedure of Massart (p. 201) to derive the 
+# variances on which the weights are based is quite inaccurate anyway. 
+

- - + + diff --git a/docs/reference/rl95_cadmium.html b/docs/reference/rl95_cadmium.html index 3b311ec..da9294d 100644 --- a/docs/reference/rl95_cadmium.html +++ b/docs/reference/rl95_cadmium.html @@ -1,67 +1,12 @@ - - - - - - - -Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995) — rl95_cadmium • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995) — rl95_cadmium • chemCal - - - - + + -

- -

Format

- +

Format

A dataframe containing four replicate observations for each of the six calibration standards.

Source

- +

Source

Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for measurement error in analytical chemistry. Technometrics 37(2), 176-184.

- - + + diff --git a/docs/reference/rl95_toluene.html b/docs/reference/rl95_toluene.html index 6b2542b..fb071e1 100644 --- a/docs/reference/rl95_toluene.html +++ b/docs/reference/rl95_toluene.html @@ -1,69 +1,14 @@ - - - - - - - -Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995) — rl95_toluene • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995) — rl95_toluene • chemCal - - - - - - - - - - - - - + + -

- -

Format

- +

Format

A dataframe containing four replicate observations for each of the six calibration standards.

Source

- +

Source

Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for measurement error in analytical chemistry. Technometrics 37(2), 176-184.

- - + + diff --git a/docs/reference/utstats14.html b/docs/reference/utstats14.html index a2822fc..78d2604 100644 --- a/docs/reference/utstats14.html +++ b/docs/reference/utstats14.html @@ -1,68 +1,13 @@ - - - - - - - -Example data for calibration with replicates from University of Toronto — utstats14 • chemCal - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Example data for calibration with replicates from University of Toronto — utstats14 • chemCal - - - - + + -

- -

Example data for calibration with replicates from University of Toronto

@@ -122,46 +54,43 @@

Dataset read into R from - https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls.

+ https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls.

- -

Format

- +

Format

A tibble containing three replicate observations of the response for five calibration concentrations.

Source

- +

Source

David Stone and Jon Ellis (2011) Statistics in Analytical Chemistry. Tutorial website maintained by the Departments of Chemistry, University of Toronto. - https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html

+ https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html

- - + + diff --git a/docs/sitemap.xml b/docs/sitemap.xml new file mode 100644 index 0000000..5d588da --- /dev/null +++ b/docs/sitemap.xml @@ -0,0 +1,57 @@ + + + + /404.html + + + /articles/chemCal.html + + + /articles/index.html + + + /authors.html + + + /index.html + + + /news/index.html + + + /reference/calplot.lm.html + + + /reference/chemCal-package.html + + + /reference/din32645.html + + + /reference/index.html + + + /reference/inverse.predict.html + + + /reference/lod.html + + + /reference/loq.html + + + /reference/massart97ex1.html + + + /reference/massart97ex3.html + + + /reference/rl95_cadmium.html + + + /reference/rl95_toluene.html + + + /reference/utstats14.html + + -- cgit v1.2.1

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Introduction to chemCal

Johannes Ranke

Johannes Ranke

2021-04-17

2022-03-31

-Basic calibration functions