5.8: Additional Resources

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Although there are many experiments in the literature that incorporate external standards, the method of standard additions, or internal standards, the issue of choosing a method standardization is not the experiment’s focus. One experiment designed to consider the issue of selecting a method of standardization is given here.

Harvey, D. T. “External Standards or Standard Additions? Selecting and Validating a Method of Standardization,” J. Chem. Educ. 2002, 79, 613–615.

In addition to the texts listed as suggested readings in Chapter 4, the following text provide additional details on linear regression.

Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd. ed.; Wiley: New York, 1981.

The following articles providing more details about linear regression.

Analytical Methods Committee “Is my calibration linear?” AMC Technical Brief, December 2005.
Analytical Methods Committee “Robust regression: an introduction, “AMCTB 50, 2012.
Badertscher, M.; Pretsch, E. “Bad results from good data,” Trends Anal. Chem. 2006, 25, 1131–1138.
Boqué, R.; Rius, F. X.; Massart, D. L. “Straight Line Calibration: Something More Than Slopes, Intercepts, and Correlation Coefficients,” J. Chem. Educ. 1993, 70, 230–232.
Danzer, K.; Currie, L. A. “Guidelines for Calibration in Analytical Chemistry. Part 1. Fundamentals and Single Component Calibration,” Pure Appl. Chem. 1998, 70, 993–1014.
Henderson, G. “Lecture Graphic Aids for Least-Squares Analysis,” J. Chem. Educ. 1988, 65, 1001–1003.
Logan, S. R. “How to Determine the Best Straight Line,” J. Chem. Educ. 1995, 72, 896–898.
Mashkina, E.; Oldman, K. B. “Linear Regressions to Which the Standard Formulas do not Apply,” ChemTexts, 2015, 1, 1–11.
Miller, J. N. “Basic Statistical Methods for Analytical Chemistry. Part 2. Calibration and Regression Methods,” Analyst 1991, 116, 3–14.
Raposo, F. “Evaluation of analytical calibration based on least-squares linear regression for instrumental techniques: A tutorial review,” Trends Anal. Chem. 2016, 77, 167–185.
Renman, L., Jagner, D. “Asymmetric Distribution of Results in Calibration Curve and Standard Addition Evaluations,” Anal. Chim. Acta 1997, 357, 157–166.
Rodriguez, L. C.; Gamiz-Gracia; Almansa-Lopez, E. M.; Bosque-Sendra, J. M. “Calibration in chemical measurement processes. II. A methodological approach,” Trends Anal. Chem. 2001, 20, 620–636.

Useful papers providing additional details on the method of standard additions are gathered here.

Bader, M. “A Systematic Approach to Standard Addition Methods in Instrumental Analysis,” J. Chem. Educ. 1980, 57, 703–706.
Brown, R. J. C.; Roberts, M. R.; Milton, M. J. T. “Systematic error arising form ‘Sequential’ Standard Addition Calibrations. 2. Determination of Analyte Mass Fraction in Blank Solutions,” Anal. Chim. Acta 2009, 648, 153–156.
Brown, R. J. C.; Roberts, M. R.; Milton, M. J. T. “Systematic error arising form ‘Sequential’ Standard Addition Calibrations: Quantification and correction,” Anal. Chim. Acta 2007, 587, 158–163.
Bruce, G. R.; Gill, P. S. “Estimates of Precision in a Standard Additions Analysis,” J. Chem. Educ. 1999, 76, 805–807.
Kelly, W. R.; MacDonald, B. S.; Guthrie “Gravimetric Approach to the Standard Addition Method in Instrumental Analysis. 1.” Anal. Chem. 2008, 80, 6154–6158.
Meija, J.; Pagliano, E.; Mester, Z. “Coordinate Swapping in Standard Addition Graphs for Analytical Chemistry: A Simplified Path for Uncertainty Calculation in Linear and Nonlinear Plots,” Anal. Chem. 2014, 86, 8563–8567.
Nimura, Y.; Carr, M. R. “Reduction of the Relative Error in the Standard Additions Method,” Analyst 1990, 115, 1589–1595.

Approaches that combine a standard addition with an internal standard are described in the following paper.

Jones, W. B.; Donati, G. L.; Calloway, C. P.; Jones, B. T. “Standard Dilution Analysis,” Anal. Chem. 2015, 87, 2321–2327.

The following papers discusses the importance of weighting experimental data when use linear regression.

Analytical Methods Committee “Why are we weighting?” AMC Technical Brief, June 2007.
Karolczak, M. “To Weight or Not to Weight? An Analyst’s Dilemma,” Current Separations 1995, 13, 98–104.

Algorithms for performing a linear regression with errors in both X and Y are discussed in the following papers. Also included here are papers that address the difficulty of using linear regression to compare two analytical methods.

Irvin, J. A.; Quickenden, T. L. “Linear Least Squares Treatment When There are Errors in Both x and y,” J. Chem. Educ. 1983, 60, 711–712.
Kalantar, A. H. “Kerrich’s Method for y = ax Data When Both y and x Are Uncertain,” J. Chem. Educ. 1991, 68, 368–370.
Macdonald, J. R.; Thompson, W. J. “Least-Squares Fitting When Both Variables Contain Errors: Pitfalls and Possibilities,” Am. J. Phys. 1992, 60, 66–73.
Martin, R. F. “General Deming Regression for Estimating Systematic Bias and Its Confidence Interval in Method-Comparison Studies,” Clin. Chem. 2000, 46, 100–104.
Ogren, P. J.; Norton, J. R. “Applying a Simple Linear Least-Squares Algorithm to Data with Uncertain- ties in Both Variables,” J. Chem. Educ. 1992, 69, A130–A131.
Ripley, B. D.; Thompson, M. “Regression Techniques for the Detection of Analytical Bias,” Analyst 1987, 112, 377–383.
Tellinghuisen, J. “Least Squares in Calibration: Dealing with Uncertainty in x,” Analyst, 2010, 135, 1961–1969.

Outliers present a problem for a linear regression analysis. The following papers discuss the use of robust linear regression techniques.

Glaister, P. “Robust Linear Regression Using Thiel’s Method,” J. Chem. Educ. 2005, 82, 1472–1473.
Glasser, L. “Dealing with Outliers: Robust, Resistant Regression,” J. Chem. Educ. 2007, 84, 533–534.
Ortiz, M. C.; Sarabia, L. A.; Herrero, A. “Robust regression techniques. A useful alternative for the detection of outlier data in chemical analysis,” Talanta 2006, 70, 499–512.

The following papers discusses some of the problems with using linear regression to analyze data that has been mathematically transformed into a linear form, as well as alternative methods of evaluating curvilinear data.

Chong, D. P. “On the Use of Least Squares to Fit Data in Linear Form,” J. Chem. Educ. 1994, 71, 489–490.
Hinshaw, J. V. “Nonlinear Calibration,” LCGC 2002, 20, 350–355.
Lieb, S. G. “Simplex Method of Nonlinear Least-Squares - A Logical Complementary Method to Linear Least-Squares Analysis of Data,” J. Chem. Educ. 1997, 74, 1008–1011.
Zielinski, T. J.; Allendoerfer, R. D. “Least Squares Fitting of Nonlinear Data in the Undergraduate Laboratory,” J. Chem. Educ. 1997, 74, 1001–1007.

More information on multivariate and multiple regression can be found in the following papers.

Danzer, K.; Otto, M.; Currie, L. A. “Guidelines for Calibration in Analytical Chemistry. Part 2. Multispecies Calibration,” Pure Appl. Chem. 2004, 76, 1215–1225.
Escandar, G. M.; Faber, N. M.; Goicoechea, H. C.; de la Pena, A. M.; Olivieri, A.; Poppi, R. J. “Second- and third-order multivariate calibration: data, algorithms and applications,” Trends Anal. Chem. 2007, 26, 752–765.
Kowalski, B. R.; Seasholtz, M. B. “Recent Developments in Multivariate Calibration,” J. Chemometrics 1991, 5, 129–145.
Lang, P. M.; Kalivas, J. H. “A Global Perspective on Multivariate Calibration Methods,” J. Chemomet- rics 1993, 7, 153–164.
Madden, S. P.; Wilson, W.; Dong, A.; Geiger, L.; Mecklin, C. J. “Multiple Linear Regression Using a Graphing Calculator,” J. Chem. Educ. 2004, 81, 903–907.
Olivieri, A. C.; Faber, N. M.; Ferré, J.; Boqué, R.; Kalivas, J. H.; Mark, H. “Uncertainty Estimation and Figures of Merit for Multivariate Calibration,” Pure Appl. Chem. 2006, 78, 633–661.

An additional discussion on method blanks, including the use of the total Youden blank, is found in the fol- lowing papers.

Cardone, M. J. “Detection and Determination of Error in Analytical Methodology. Part II. Correc- tion for Corrigible Systematic Error in the Course of Real Sample Analysis,” J. Assoc. Off. Anal. Chem. 1983, 66, 1283–1294.
Cardone, M. J. “Detection and Determination of Error in Analytical Methodology. Part IIB. Direct Calculational Technique for Making Corrigible Systematic Error Corrections,” J. Assoc. Off. Anal. Chem. 1985, 68, 199–202.
Ferrus, R.; Torrades, F. “Bias-Free Adjustment of Analytical Methods to Laboratory Samples in Routine Analytical Procedures,” Anal. Chem. 1988, 60, 1281–1285.
Vitha, M. F.; Carr, P. W.; Mabbott, G. A. “Appropriate Use of Blanks, Standards, and Controls in Chemical Measurements,” J. Chem. Educ. 2005, 82, 901–902.

There are a variety of computational packages for completing linear regression analyses. These papers provide details on there use in a variety of contexts.

Espinosa-Mansilla, A.; de la Peña, A. M.; González-Gómez, D. “Using Univariate Linear Regression Calibration Software in the MATLAB Environment. Application to Chemistry Laboratory Practices,” Chem. Educator 2005, 10, 1–9.
Harris, D. C. “Nonlinear Least-Squares Curve Fitting with Microsoft Excel Solver,” J. Chem. Educ. 1998, 75, 119–121.
Kim, M. S.; Bukart, M.; Kim, M. H. “A Method Visual Interactive Regression,” J. Chem. Educ. 2006, 83, 1884.
Machuca-Herrera, J. G. “Nonlinear Curve Fitting with Spreadsheets,” J. Chem. Educ. 1997, 74, 448–449.
Smith, E. T.; Belogay, E. A.; Hõim “Linear Regression and Error Analysis for Calibration Curves and Standard Additions: An Excel Spreadsheet Exercise for Undergraduates,” Chem. Educator 2010, 15, 100–102.
Smith, E. T.; Belogay, E. A.; Hõim “Using Multiple Linear Regression to Analyze Mixtures: An Excel Spreadsheet Exercise for Undergraduates,” Chem. Educator 2010, 15, 103–107.
Young, S. H.; Wierzbicki, A. “Mathcad in the Chemistry Curriculum. Linear Least-Squares Regres- sion,” J. Chem. Educ. 2000, 77, 669.
Young, S. H.; Wierzbicki, A. “Mathcad in the Chemistry Curriculum. Non-Linear Least-Squares Re- gression,” J. Chem. Educ. 2000, 77, 669.