Introduction to chemCal

Johannes Ranke

2020-05-20

2021-04-08

Source: vignettes/chemCal.Rmd

chemCal.Rmd

@@ -99,25 +99,29 @@ 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)
-})
-massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
-
-m <- lm(y ~ x, w = weights, data = massart97ex3.means)

+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)
+
+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)

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

## $Prediction
 ## [1] 5.865367
 ## 
@@ -129,7 +133,8 @@
 ## 
 ## $`Confidence Limits`
 ## [1] 3.387082 8.343652

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

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

## $Prediction
 ## [1] 44.06025
 ## 
@@ -170,7 +175,7 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
             {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
 \end{equation}\]
 where I interpret \(\frac{{s_s}^2}{w_s}\) as an estimator of the variance at location \(\hat{x_s}\), which can be replaced by a user-specified value using the argument var.s of the function inverse.predict.
-
+
 
 Analytical Methods Committee. 1989. “Robust Statistics — How Not to Reject Outliers. Part 1. Basic Concepts.” The Analyst 114: 1693–7.
 
@@ -202,7 +207,7 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/articles/chemCal_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/articles/chemCal_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 0000000..ca349fd
--- /dev/null
+++ b/docs/articles/chemCal_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty  tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
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
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diff --git a/docs/articles/chemCal_files/header-attrs-2.7/header-attrs.js b/docs/articles/chemCal_files/header-attrs-2.7/header-attrs.js
new file mode 100644
index 0000000..dd57d92
--- /dev/null
+++ b/docs/articles/chemCal_files/header-attrs-2.7/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/articles/index.html b/docs/articles/index.html
index dc6cbba..6373471 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -79,7 +79,7 @@
       
         
   
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-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/authors.html b/docs/authors.html
index ad1c893..1db4904 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -79,7 +79,7 @@
       
         
   
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+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/index.html b/docs/index.html
index 53401d4..e954fa0 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -45,7 +45,7 @@
       
 
   
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@@ -130,7 +130,7 @@


 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/news/index.html b/docs/news/index.html
index 4fc042b..9ea5e1d 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -79,7 +79,7 @@
       
         
   
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@@ -96,7 +96,7 @@
       
         
   
-    
+    
      
   
 
@@ -117,17 +117,18 @@
       Source: NEWS.md


 
-    
+    
 
-chemCal 0.2.2 Unreleased 
+chemCal 0.2.2 Unreleased 
 
 
-Added the cadmium dataset from Rocke and Lorenzato (1995)
+‘calplot’ gains an argument ‘legend_x’ for better control of the legend position
+Added the cadmium dataset from Rocke and Lorenzato (1995)
 
 
-    
+    
 
-chemCal 0.2.1 2018-07-17 
+chemCal 0.2.1 2018-07-17 
 
 
 ‘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
@@ -138,17 +139,17 @@
 Update static documentation
 
 
-    
+    
 
-chemCal 0.1-37 2015-10-08 
+chemCal 0.1-37 2015-10-08 
 
 
 Maintenance release
 
 
-    
+    
 
-chemCal 0.1-34 2014-04-25 
+chemCal 0.1-34 2014-04-25 
 
 
 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.
@@ -172,7 +173,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/pkgdown.css b/docs/pkgdown.css
index c01e592..1273238 100644
--- a/docs/pkgdown.css
+++ b/docs/pkgdown.css
@@ -244,14 +244,14 @@ nav[data-toggle='toc'] .nav .nav > .active:focus > a {
 
 .ref-index th {font-weight: normal;}
 
-.ref-index td {vertical-align: top;}
+.ref-index td {vertical-align: top; min-width: 100px}
 .ref-index .icon {width: 40px;}
 .ref-index .alias {width: 40%;}
 .ref-index-icons .alias {width: calc(40% - 40px);}
 .ref-index .title {width: 60%;}
 
 .ref-arguments th {text-align: right; padding-right: 10px;}
-.ref-arguments th, .ref-arguments td {vertical-align: top;}
+.ref-arguments th, .ref-arguments td {vertical-align: top; min-width: 100px}
 .ref-arguments .name {width: 20%;}
 .ref-arguments .desc {width: 80%;}
 
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index ece837b..f4bc8f6 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,7 +1,7 @@
-pandoc: 2.2.1
-pkgdown: 1.5.1
+pandoc: 2.9.2.1
+pkgdown: 1.6.1
 pkgdown_sha: ~
 articles:
   chemCal: chemCal.html
-last_built: 2020-05-20T06:44Z
+last_built: 2021-04-08T05:16Z
 
diff --git a/docs/reference/Rplot001.png b/docs/reference/Rplot001.png
new file mode 100644
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diff --git a/docs/reference/calplot.lm-1.png b/docs/reference/calplot.lm-1.png
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diff --git a/docs/reference/calplot.lm.html b/docs/reference/calplot.lm.html
index 7822b7e..fb329f6 100644
--- a/docs/reference/calplot.lm.html
+++ b/docs/reference/calplot.lm.html
@@ -81,7 +81,7 @@
       
         
   
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+    
      
   
 
@@ -98,7 +98,7 @@
       
         
   
-    
+    
      
   
 
@@ -125,8 +125,9 @@
   as confidence, and, for unweighted regression, prediction bands.
     
 
-    calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
-    xlab = "Concentration", ylab = "Response", alpha=0.05, varfunc = NULL)
+    calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
+    xlab = "Concentration", ylab = "Response", legend_x = "auto",
+    alpha=0.05, varfunc = NULL)
 
     Arguments
     
@@ -153,6 +154,10 @@
       
+    
+      
+      
+    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 
@@ -181,11 +186,16 @@
 
It is possible to compare the calplot prediction bands with the
   lod values if the lod() alpha and beta parameters are
   half the value of the calplot() alpha parameter.
+    Author
+
+    Johannes Ranke 
+  jranke@uni-bremen.de
 
     Examples
-    data(massart97ex3)
-m <- lm(y ~ x, data = massart97ex3)
-calplot(m)

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

   
   
     
@@ -201,7 +211,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/din32645-1.png b/docs/reference/din32645-1.png
index cee27e9..27914e8 100644
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diff --git a/docs/reference/din32645.html b/docs/reference/din32645.html
index 6af5152..b3ae61c 100644
--- a/docs/reference/din32645.html
+++ b/docs/reference/din32645.html
@@ -80,7 +80,7 @@
       
         
   
-    
+    
      
   
 
@@ -97,7 +97,7 @@
       
         
   
-    
+    
      
   
 
@@ -123,7 +123,7 @@
     Sample dataset to test the package.
     
 
-    data(din32645)
+    data(din32645)
 
 
     Format
@@ -140,35 +140,42 @@
   Analytica Chimica Acta 391, 105 - 126.
 
     Examples
-    m <- lm(y ~ x, data = din32645)
-calplot(m)

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

 ## Prediction of x with confidence interval
-prediction <- inverse.predict(m, 3500, alpha = 0.01)
+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

+round(prediction$Confidence, 5)
+
#> [1] 0.07434

 ## Critical value:
-crit <- lod(m, alpha = 0.01, beta = 0.5)
+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

+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

+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

+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)$x
#> [1] 0.2122306
+3.04 * lod(m, alpha = 0.01, beta = 0.5)$x
+
#> [1] 0.2122306
   
   
     
@@ -184,7 +191,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/index.html b/docs/reference/index.html
index d68dbd9..ea1ff81 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -79,7 +79,7 @@
       
         
   
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-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/inverse.predict.html b/docs/reference/inverse.predict.html
index 3c4c867..0ea86a3 100644
--- a/docs/reference/inverse.predict.html
+++ b/docs/reference/inverse.predict.html
@@ -89,7 +89,7 @@
       
         
   
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@@ -106,7 +106,7 @@
       
         
   
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@@ -141,8 +141,8 @@
   This is elaborated in the package vignette.
     
 
-    inverse.predict(object, newdata, ...,
-  ws, alpha=0.05, var.s = "auto")
+    inverse.predict(object, newdata, ...,
+  ws, alpha=0.05, var.s = "auto")
 
     Arguments
     
@@ -199,8 +199,9 @@
 
     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
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15)        #  6.1 +- 4.9
+
#> $Prediction
 #> [1] 6.09381
 #> 
 #> $`Standard Error`
@@ -211,7 +212,8 @@
 #> 
 #> $`Confidence Limits`
 #> [1]  1.187059 11.000561
-#> 
inverse.predict(m, 90)        # 43.9 +- 4.9
#> $Prediction
+#> 
inverse.predict(m, 90)        # 43.9 +- 4.9
+
#> $Prediction
 #> [1] 43.93983
 #> 
 #> $`Standard Error`
@@ -222,7 +224,8 @@
 #> 
 #> $`Confidence Limits`
 #> [1] 39.03178 48.84788
-#> 
inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
#> $Prediction
+#> 
inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+
#> $Prediction
 #> [1] 43.93983
 #> 
 #> $`Standard Error`
@@ -236,18 +239,19 @@
 #> 

 # 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)
-})
+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)
 
-m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
+m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
 
-inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
#> $Prediction
+inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
+
#> $Prediction
 #> [1] 5.865367
 #> 
 #> $`Standard Error`
@@ -258,7 +262,8 @@
 #> 
 #> $`Confidence Limits`
 #> [1] 3.387082 8.343652
-#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
#> $Prediction
+#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
+
#> $Prediction
 #> [1] 44.06025
 #> 
 #> $`Standard Error`
@@ -286,7 +291,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/lod.html b/docs/reference/lod.html
index e5a1158..f647e8c 100644
--- a/docs/reference/lod.html
+++ b/docs/reference/lod.html
@@ -87,7 +87,7 @@
       
         
   
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+    
      
   
 
@@ -104,7 +104,7 @@
       
         
   
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+    
      
   
 
@@ -137,7 +137,7 @@
   one-sided significance test).
     
 
-    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
     

     
@@ -207,8 +207,9 @@
     Examples for din32645
Examples
-    m <- lm(y ~ x, data = din32645)
-lod(m)
#> $x
+    m <- lm(y ~ x, data = din32645)
+lod(m) 
+
#> $x
 #> [1] 0.08655484
 #> 
 #> $y
@@ -216,7 +217,8 @@
 #> 

 # The critical value (decision limit, German Nachweisgrenze) can be obtained
 # by using beta = 0.5:
-lod(m, alpha = 0.01, beta = 0.5)
#> $x
+lod(m, alpha = 0.01, beta = 0.5)
+
#> $x
 #> [1] 0.0698127
 #> 
 #> $y
@@ -237,7 +239,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/loq.html b/docs/reference/loq.html
index 2c7dc6a..6515e41 100644
--- a/docs/reference/loq.html
+++ b/docs/reference/loq.html
@@ -86,7 +86,7 @@
       
         
   
-    
+    
      
   
 
@@ -103,7 +103,7 @@
       
         
   
-    
+    
      
   
 
@@ -135,8 +135,8 @@
   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
     

 
     
@@ -204,15 +204,17 @@
     Examples for din32645
Examples
-    m <- lm(y ~ x, data = massart97ex1)
-loq(m)
#> $x
+    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
+loq(m, n = 3)
+
#> $x
 #> [1] 9.971963
 #> 
 #> $y
@@ -233,7 +235,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/massart97ex1.html b/docs/reference/massart97ex1.html
index 95e6b3f..60f43ab 100644
--- a/docs/reference/massart97ex1.html
+++ b/docs/reference/massart97ex1.html
@@ -80,7 +80,7 @@
       
         
   
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+    
      
   
 
@@ -97,7 +97,7 @@
       
         
   
-    
+    
      
   
 
@@ -123,7 +123,7 @@
     Sample dataset from p. 175 to test the package.
     
 
-    data(massart97ex1)
+    data(massart97ex1)
 
 
     Format
@@ -150,7 +150,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/massart97ex3.html b/docs/reference/massart97ex3.html
index a1efeba..13e28fd 100644
--- a/docs/reference/massart97ex3.html
+++ b/docs/reference/massart97ex3.html
@@ -80,7 +80,7 @@
       
         
   
-    
+    
      
   
 
@@ -97,7 +97,7 @@
       
         
   
-    
+    
      
   
 
@@ -123,7 +123,7 @@
     Sample dataset from p. 188 to test the package.
     
 
-    massart97ex3
+    massart97ex3
 
 
     Format
@@ -139,19 +139,20 @@
     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)
-})
+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)
 
-m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
+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
+inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
+
#> $Prediction
 #> [1] 5.865367
 #> 
 #> $`Standard Error`
@@ -162,7 +163,8 @@
 #> 
 #> $`Confidence Limits`
 #> [1] 3.387082 8.343652
-#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
#> $Prediction
+#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
+
#> $Prediction
 #> [1] 44.06025
 #> 
 #> $`Standard Error`
@@ -176,15 +178,17 @@
 #> 

 # The LOD is only calculated for models from unweighted regression
 # with this version of chemCal
-m0 <- lm(y ~ x, data = massart97ex3)
-lod(m0)
#> $x
+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
+loq(m0)
+
#> $x
 #> [1] 9.627349
 #> 
 #> $y
@@ -195,14 +199,15 @@
 # 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
+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. 
+#> 
# 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. 
 
   
   
@@ -219,7 +224,7 @@
 
 
 
-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/rl95_cadmium.html b/docs/reference/rl95_cadmium.html
index 509a0ab..c29ebae 100644
--- a/docs/reference/rl95_cadmium.html
+++ b/docs/reference/rl95_cadmium.html
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-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/rl95_toluene.html b/docs/reference/rl95_toluene.html
index f295d6d..9022e1e 100644
--- a/docs/reference/rl95_toluene.html
+++ b/docs/reference/rl95_toluene.html
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-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
diff --git a/docs/reference/utstats14.html b/docs/reference/utstats14.html
index c15f06d..8655c36 100644
--- a/docs/reference/utstats14.html
+++ b/docs/reference/utstats14.html
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-  Site built with pkgdown 1.5.1.
+  Site built with pkgdown 1.6.1.
 
 
       
-- 
cgit v1.2.1

Introduction to chemCal

Johannes Ranke

2020-05-20

2021-04-08

-chemCal 0.2.2 Unreleased +chemCal 0.2.2 Unreleased

-chemCal 0.2.1 2018-07-17 +chemCal 0.2.1 2018-07-17

-chemCal 0.1-37 2015-10-08 +chemCal 0.1-37 2015-10-08

-chemCal 0.1-34 2014-04-25 +chemCal 0.1-34 2014-04-25

Arguments

Author

Examples

Format

Examples

Arguments

Examples

Arguments

Examples

Arguments

Examples

Format

Format

Examples