{"id":33,"date":"2024-04-04T00:39:47","date_gmt":"2024-04-03T21:39:47","guid":{"rendered":"https:\/\/sisu.ut.ee\/lcms_method_validation\/32-experiment-setup-and-evaluation-data\/"},"modified":"2026-01-13T10:55:44","modified_gmt":"2026-01-13T08:55:44","slug":"32-experiment-setup-and-evaluation-data","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/lcms_method_validation\/32-experiment-setup-and-evaluation-data\/","title":{"rendered":"3.2. Experiment setup and evaluation of the data"},"content":{"rendered":"<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">Experiment planning for evaluation of linearity<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23307\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23307<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=PdLsxDExgV0\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=PdLsxDExgV0<\/a><\/h5>\n<p><strong>1) Type of calibration samples<\/strong><\/p>\n<p>When choosing the proper quantitation method, we can choose between calibration samples (calibration standards, calibrants) containing matrix and calibration samples that are matrix free. In case of LC-MS analysis, we should prefer samples containing matrix, in order to take into account possible matrix influence on the ionization of the analyte. Blank matrix extracts of\u00a0as similar as possible matrix type as the sample\u00a0are suitable for this.<\/p>\n<p>If the sample to be analysed is diluted prior to the analysis, the matrix concentration in the matrix-matched calibration standards should be diluted proportionately\u00a0so that the matrix amount in each analyzed sample is constant.<\/p>\n<p>If calibration solutions in solvent\u00a0are used, a comparison of calibration graphs in matrix and in solvent should be carried out.\u00a0<a href=\"#\" data-bs-toggle=\"modal\" data-bs-target=\"#popup-modal\" data-title=\"(1)\" data-content=\"(1) Both standard (in solvent) and matrix\u2014matched calibration curves should be constructed. If the matrix does not interfere with the analysis and the use of a standard (in solution) calibration curve is justified, the slopes of these two graphs should not differ statistically. This can be shown using a t-test. In order to do so, the residual variances of the two graphs should be equal. This can be confirmed by using an F-test.&lt;\/p&gt;\n&lt;p&gt;Here is an example where the slopes of the two graphs do not differ statistically and the use of a standard calibration graph is justified: H. Sun, F. Wang, L. Ai, C. Guo, R. Chen, Validated method for determination of eight banned nitroimidazole residues in natural casings by LC\/MS\/MS with solid-phase extraction, J. AOAC Int. 92 (2009) 612\u2013621.&lt;\/p&gt;\n&lt;p&gt;Here is an example where the matrix interferes with the analysis and a matrix matched calibration is used: R.P. Lopes, D.V. Augusti, L.F. de Souza, F.A. Santos, J.A. Lima, E.A. Vargas, R. Augusti, Development and validation (according to the 2002\/657\/EC regulation) of a method to quantify sulfonamides in porcine liver by fast partition at very low temperature and LC\u2013MS\/MS, Anal. Methods 3 (2011) 606\u2013613.\u00a0\">(1)<\/a>\u00a0<\/p>\n<p><strong>2) Concentrations of calibration samples<\/strong><\/p>\n<p>The highest and lowest concentrations of the calibration samples\u00a0should be appropriate for the method, keeping in mind the predicted variation of the analyte concentration levels in the samples. As a minimum, 6 different concentrations are necessary according to most validation guidelines. This is also acceptable for statistical tests carried out later for linearity evaluation, where 4 degrees of freedom is considered minimal. However, as we do not know the span of the linear range at this step of the validation, some concentrations might fall out of the linear range. Therefore, using 10 concentration levels encompassing the expected linear range is recommended. Moreover, concentrations should be approximately evenly spaced over the chosen concentration range, to ensure that the different parts of a calibration graph are covered with approximately the same density of data points.\u00a0<\/p>\n<p><strong>3) Measurement protocol<\/strong><\/p>\n<p>For LC-MS, the order of measuring the solutions in the series and the number of replicate measurements with every solution, is important due to the possible drift or contamination of the instrument. Consequently, the analysis order of calibration samples should be random.<br>It is useful to analyze calibration solutions\u00a0in a manner as similar as possible to the unknown samples, i.e. calibration samples should be in random\u00a0order\u00a0and placed between unknown samples in the analytical run. Calibration samples should be analyzed at least twice (and average values should be\u00a0used in linearity calculations).<br>In the following video, the preparation of matrix matched calibration samples on an example of pesticide analysis in tomato is shown.<\/p>\n<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">Carrying out the experiment for linearity evaluation<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23480\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23480<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=x8KaQ7aC_mI\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=x8KaQ7aC_mI<\/a><br>\u00a0<\/h5>\n<h2>Evaluation of linearity from the experimental data\u00a0<\/h2>\n<p>For quantitative analysis, the calibration data is plotted on a calibration graph, where the concentrations are on the x-axis and the signals are on the y-axis.\u00a0<a href=\"#\" data-bs-toggle=\"modal\" data-bs-target=\"#popup-modal\" data-title=\"(2)\" data-content=\"(2) Calibration curve definition by VIM &amp;#8211; the expression of the relation between indication and corresponding measured quantity value. \u201cThe term &amp;#8220;curve&amp;#8221; implies that the line is not straight. However, the best (parts of) calibration lines are linear and, therefore, the general term &amp;#8220;graph&amp;#8221; is preferred.\u201d \">(2)<\/a><\/p>\n<p>From this plotted graph we can have the first evaluation of the linearity by using the visual evaluation approach. In addition, calculation of\u00a0the residuals can also be useful,\u00a0due to the fact that the residuals show a more clear picture if the applied linear model actually fits the data.<\/p>\n<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">Evaluation of linearity\u00a0<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23351\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23351<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=4c3EMRpFDf0&amp;t=29s\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=4c3EMRpFDf0&amp;t=29s<\/a><br>\u00a0<\/h5>\n<p>Absolute residuals are found as the difference between the\u00a0experimental (<em>y<\/em><sub>i<\/sub>) and calculated (<em>\u0177<\/em><sub>i<\/sub>) signal values: \u00a0<em>y<\/em><sub>i<\/sub>\u2013 <em>\u0177<\/em><sub>i<\/sub>. In addition, relative residuals can be used (Eq 1).<\/p>\n<h6 style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"120\" height=\"54\" class=\"alignnone wp-image-357\" title=\"image006.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/image006.png\" alt=\"image006.png\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Eq 1)<\/h6>\n<p>For more complex cases, where a\u00a0linearity cannot be confirmed by neither a visual evaluation nor residuals, statistical approaches can be of help.\u00a0<\/p>\n<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">Statistical approaches for evaluation of linearity <a href=\"#\" data-bs-toggle=\"modal\" data-bs-target=\"#popup-modal\" data-title=\"*Note 1\" data-content=\"&lt;em&gt;Please see comments in the Mandel&amp;#8217;s test section below on the simplification in the video. The Lack-of-fit equation in this video should be understood the same way as (Eq 2) in the Lack-of-fit section below.&lt;\/em&gt;\">*Note 1<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a style=\"text-align: center; font-family: inherit; font-weight: 600; background-color: #ffffff;\" href=\"http:\/\/www.uttv.ee\/naita?id=23683\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23683<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QFNuo-Jk2Ws\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=QFNuo-Jk2Ws<\/a><\/h5>\n<p style=\"text-align: center;\"><em>*Note 1:\u00a0Please see comments in the Mandel\u2019s test section below on the simplification in the video. The Lack-of-fit equation in this video should be understood the same way as (Eq 2) in the Lack-of-fit section below.<\/em><\/p>\n<p>Different expressions of signal values are used for statistical approaches:<\/p>\n<p><em>y<\/em><sub>ij<\/sub> is the experimental signal value at the concentration level i for replicate measurement j,<\/p>\n<p><i>\u0233<\/i><sub>i<\/sub> is the average value of the experimental signals from <em>p<\/em> replicate measurements at the concentration level i,<\/p>\n<p><em>\u0177<\/em><sub>i <\/sub>is the signal value at the concentration level i, calculated using the calibration function.<\/p>\n<p>In addition, n is the number of concentration levels and <em>p<\/em> is the number of replicate measurements at each concentration level.<\/p>\n<p>Tabulated <em>F<\/em>-values can be found here: <a href=\"http:\/\/www.itl.nist.gov\/div898\/handbook\/eda\/section3\/eda3673.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/www.itl.nist.gov\/div898\/handbook\/eda\/section3\/eda3673.htm<\/a><\/p>\n<p>The <em>F<\/em><sub>tabulated<\/sub> can also be found in excel using the following function:<br>=F.INV.RT(<i>\u03b1<\/i>;DoF1;DoF2),<br>where:<br><i>\u03b1<\/i> is the probability of the F distribution (on 95% confidence interval <i>\u03b1<\/i>=0.05*),<br>DoF1 is the number of degrees of freedom of the numerator <em>MSS<\/em><sub>LoF<\/sub> (<em>n<\/em>-2),<br>DoF2 is the number of degrees of freedom of the denominator <em>MSS<\/em><sub>error<\/sub> (<em>n<\/em>*(<em>p<\/em>-1)).<\/p>\n<p>As a generalisation, the number of degrees of freedom is equal to the number of data points minus the number of parameters calculated from the data. Example: In simple linear regression of the type <i>y<\/i> = <i>b<\/i><sub>0<\/sub> + <i>b<\/i><sub>1<\/sub> \u00b7 <i>x<\/i> DoF is typically <i>n<\/i> \u2013 2, where <i>n<\/i> is the number of data points. The \u201e2\u201c means that two parameters are found: slope and intercept. If the intercept is forced to zero, i.e. if the regression has the form <i>y<\/i> = <i>b<\/i><sub>1<\/sub> \u00b7 <i>x<\/i> then DoF = <i>n<\/i> \u2013 1, because only one parameter is found.<\/p>\n<p>*The 0.05 is found from 95% as follows: (100% \u2013 95%) \/ 100% = 0.05.<\/p>\n<h2>Lack-of-fit test<\/h2>\n<p>IUPAC validation guideline suggests using the lack-of-fit test. The extent of deviation of the points from the line caused by the random scatter of the points is estimated from the replicate measurements (mean sum of squares of random error (<em>MSS<\/em><sub>error<\/sub>)).<\/p>\n<p>This is compared to the extent of deviation of the points from the line caused by the mismatch of the calibration model (mean sum of squares due to lack of fit <em>MSS<\/em><sub>LOF<\/sub>).<\/p>\n<h6 style=\"text-align: center;\">\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" width=\"1053\" height=\"148\" class=\"alignnone wp-image-365\" style=\"width: 450px; height: 63px;\" title=\"lackoffit_f_correct.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lackoffit_f_correct.png\" alt=\"Fcorerct\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lackoffit_f_correct.png 1053w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lackoffit_f_correct-300x42.png 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lackoffit_f_correct-1024x144.png 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lackoffit_f_correct-768x108.png 768w\" sizes=\"auto, (max-width: 1053px) 100vw, 1053px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Eq 2)<\/h6>\n<p>If the <em>F<\/em><sub>calculated<\/sub> is higher than the\u00a0<em>F<\/em><sub>tabulated<\/sub>, the model cannot be considered fit for the data,\u00a0because the unexplained variance in the model is too big.<\/p>\n<h2>Goodness-of-fit test<\/h2>\n<p>The goodness-of-fit test uses the mean sum of squares of the factors (MSS<sub>factor<\/sub>) describing the variance described by the model and the mean sum of squares of the residuals (MSS<sub>residuals<\/sub>).<\/p>\n<h6 style=\"text-align: center;\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-359\" title=\"image008.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/image008.png\" alt=\"image008.png\" width=\"313\" height=\"108\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/image008.png 401w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/image008-300x103.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Eq 3)<\/h6>\n<p>If the <em>F<\/em><sub>calculated<\/sub> is higher than the\u00a0<em>F<\/em><sub>tabulated<\/sub>, the model differs systematically from the data.<\/p>\n<h2>Mandel\u2019s fitting test\u00a0<\/h2>\n<p>This test compares the fit of two models: the fit of a linear model (<i>S<sub>y<\/sub><\/i><sub>1<\/sub>) with the\u00a0fit of a nonlinear model \u00a0(<i>S<sub>y<\/sub><\/i><sub>2<\/sub>). In this case a three-parameter model,\u00a0parabola, is used. Three-parameter model is suitable for almost all cases. For both of the models, the residual standard deviation is found using this equation:<\/p>\n<h6 style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-369\" title=\"mandels_fit_eq4_01.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq4_01.png\" alt=\"EQ4\" width=\"390\" height=\"63\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq4_01.png 1208w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq4_01-300x48.png 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq4_01-1024x165.png 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq4_01-768x124.png 768w\" sizes=\"auto, (max-width: 390px) 100vw, 390px\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Eq 4)<\/h6>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"background: white;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">, where <i>n<\/i> is the number of calibration points (assuming one point per calibration level, i.e. <i>p<\/i> = 1). <\/span><\/span><span style=\"background: white;\">In case <i>p<\/i> &gt; 1, it is assumed that all concentration levels have the same number of replicates. In many materials <i>n<\/i>\u00b7<i>p<\/i> is denoted by <i>N<\/i>.<\/span><\/span><\/p>\n<p>The <em>F<\/em><sub>calculated<\/sub> is found:\u00a0<\/p>\n<h6 style=\"text-align: center;\">\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-370\" title=\"mandels_fit_eq5_01.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq5_01.png\" alt=\"Eq5\" width=\"286\" height=\"61\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq5_01.png 764w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/mandels_fit_eq5_01-300x64.png 300w\" sizes=\"auto, (max-width: 286px) 100vw, 286px\">\u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0 (Eq 5)<\/h6>\n<p>If the <em>F<\/em><sub>calculated<\/sub> is higher than the\u00a0<em>F<\/em><sub>tabulated<\/sub>, the linear model cannot be applied.<\/p>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"background: white;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">Please note that in different materials the Mandel\u2019s fitting test is presented at different level of rigor. In the video, a simplified version is presented, assuming that <i>p<\/i> is always 1 and disregarding the difference of degrees of freedom between linear and nonlinear model, using <i>n<\/i> \u2013 2 in both cases. A more rigorous version, presented here. In practical application, the differences between the two are not big.<\/span><\/span><\/span><\/p>\n<h2>Intercept<\/h2>\n<p>One important issue concerning the calibration graph is how to handle the intercept. As usually the linear calibration graph model is used, the model has two parameters: a slope and an intercept. A slope gives us the estimation of the sensitivity of our method (signal per one concentration unit, see section 3.4), while an intercept shows the estimate of the signal for a blank sample.<\/p>\n<p>For most of the HPLC detectors, including the MS, it is fair to assume that the sample without an analyte gives no signal. Also for most detectors, intercept is not consistent with the physical model behind the calibration principle. For example in the case of HPLC-UV\/Vis, the calibration model should follow the Beer\u00b4s law:<\/p>\n<h6 style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"80\" height=\"28\" class=\"alignnone wp-image-362\" title=\"image006.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/image006-1.png\" alt=\"image006.png\"><em>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/em>(Eq 6)<\/h6>\n<p>where <em>A<\/em> is the\u00a0measured absorbance, <em>c<\/em> is an analyte concentration, <em>l<\/em> is the\u00a0optical path length and <em>e<\/em> is the\u00a0molar absorption coefficient. Therefore, as the physics behind the HPLC-UV\/Vis signal does not contain an intercept, it is worth checking if the intercept is statistically significant at all.<\/p>\n<p>The statistical way to evaluate the importance of an intercept would be via a\u00a0<em>t<\/em>-test. In order to carry out a\u00a0<em>t<\/em>-test, the linear regression is run with an intercept, i.e. in the form LINEST(Y1:Y2; X1:X2; 1; 1), and the obtained intercept value is compared to zero taking into account the standard deviation of the intercept and the number of points on the calibration graph. However, a simpler method can be used that is based on the assumption of normal distribution and also assuming that there is a sufficient number of points on the calibration graph. In this case, the<em> t<\/em>-value is substituted with 2 (referring to the 95% confidence level in normal distribution).<\/p>\n<p>If<\/p>\n<p>Intercept &lt; 2 \u00b7 Stdev_intercept<\/p>\n<p>then it can be assumed with 95% confidence that the\u00a0intercept is insignificant and can be disregarded in the calibration model. The following form of the LINEST spreadsheet function is used in this case: LINEST(Y1:Y2; X1:X2; 0; 1). Setting the third parameter in the function to zero forces the intercept to zero.<\/p>\n<p>If an intercept, however, is statistically significant, but a physical model behind the detection does not contain an intercept, it may be an indication of\u00a0problems. Most commonly:<\/p>\n<ul>\n<li>a linear model is fitted to\u00a0data that are in fact nonlinear (e.g. saturation of signal at higher concentrations);<\/li>\n<li>blank samples produce signal because of a carryover, contamination, etc.<\/li>\n<\/ul>\n<p>Both of these should be carefully studied and if possible, removed.<\/p>\n<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">\u00a0Evaluation of linearity (visual evaluation, residuals)\u00a0<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=24974\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=24974<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a title=\"https:\/\/youtu.be\/A7hsHZXMsbY?si=Qikjm-e_LoMpDbDg\" href=\"https:\/\/youtu.be\/A7hsHZXMsbY?si=Qikjm-e_LoMpDbDg\" target=\"_blank\" rel=\"noopener\" data-url=\"https:\/\/youtu.be\/A7hsHZXMsbY?si=Qikjm-e_LoMpDbDg\">https:\/\/youtu.be\/A7hsHZXMsbY?si=Qikjm-e_LoMpDbDg<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a style=\"font-weight: normal; background-color: #ffffff;\" href=\"https:\/\/www.youtube.com\/watch?v=l-AXgA31xRY&amp;feature=youtu.be\" target=\"_blank\" rel=\"noopener\">\u00a0<\/a><\/h5>\n<p style=\"text-align: center;\"><\/p><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>\n<h5 style=\"text-align: center;\">Evaluation of linearity (lack-of-fit test)\u00a0\u00a0<\/h5>\n<h5 style=\"text-align: center;\"><a title=\"\" href=\"https:\/\/www.uttv.ee\/naita?id=32138\" target=\"_blank\" rel=\"noopener\" data-url=\"https:\/\/www.uttv.ee\/naita?id=32138\">http:\/\/www.uttv.ee\/naita?id=32138<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/youtu.be\/l07_KulyYoc\">https:\/\/youtu.be\/l07_KulyYoc<\/a><\/h5>\n<p>***<\/p>\n<p>(1) Both standard (in solvent) and matrix\u2014matched calibration curves should be constructed. If the matrix does not interfere with the analysis and the use of a standard (in solution) calibration curve is justified, the slopes of these two graphs should not differ statistically. This can be shown using a <em>t<\/em>-test. In order to do so, the residual variances of the two graphs should be equal. This can be confirmed by using an <em>F<\/em>-test.<\/p>\n<p>An example where the slopes of the two graphs do not differ statistically and the use of a standard calibration graph is justified can be found in ref 53.<\/p>\n<p>An example where the matrix interferes with the analysis and a matrix matched calibration is used can be found in ref 54.<\/p>\n<p>(2) Calibration curve definition by VIM \u2013 the expression of the relation between indication and corresponding measured quantity value. \u201cThe term \u201ccurve\u201d implies that the line is not straight. However, the best (parts of) calibration lines are linear and, therefore, the general term \u201cgraph\u201d is preferred.\u201d [<a href=\"http:\/\/www.fao.org\/docrep\/w7295e\/w7295e09.htm#TopOfPage\" target=\"_blank\" rel=\"noopener\" data-url=\"http:\/\/www.fao.org\/docrep\/w7295e\/w7295e09.htm#TopOfPage\">http:\/\/www.fao.org\/docrep\/w7295e\/w7295e09.htm#TopOfPage<\/a>]<\/p>\n\n\n<div class=\"wp-block-group attached-files-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-2350ba72-736d-454f-a0d1-f69963f621c0\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/copy_of_linearity_example_lack_of_fit_corr_211221.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">linearity_example_lack_of_fit.xlsx _corr<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-7db280b2-ba7d-4416-b999-c1fc557f5b31\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/linearity_evaluation_2023_unsolved.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">linearity_evaluation_2023_unsolved<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>To view third-party content, please accept cookies. Change consent Experiment planning for evaluation of linearity http:\/\/www.uttv.ee\/naita?id=23307 https:\/\/www.youtube.com\/watch?v=PdLsxDExgV0 1) Type of calibration samples When choosing the proper quantitation method, we can choose between calibration samples (calibration standards, calibrants) containing matrix and &#8230;<\/p>\n","protected":false},"author":60,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-33","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/users\/60"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":5,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/33\/revisions"}],"predecessor-version":[{"id":1655,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/33\/revisions\/1655"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/media?parent=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}