# 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.