4.10: Additional Resources

The following experiments provide useful introductions to the statistical analysis of data in the analytical chemistry laboratory.

• Bularzik, J. “The Penny Experiment Revisited: An Illustration of Significant Figures, Accuracy, Precision, and Data Analysis,” J. Chem. Educ. 2007, 84, 1456–1458.
• Columbia, M. R. “The Statistics of Coffee: 1. Evaluation of Trace Metals for Establishing a Coffee’s Country of Origin Based on a Means Comparison,” Chem. Educator 2007, 12, 260–262.
• Cunningham, C. C.; Brown, G. R.; St Pierre, L. E. “Evaluation of Experimental Data,” J. Chem. Educ. 1981, 58, 509–511.
• Edminston, P. L.; Williams, T. R. “An Analytical Laboratory Experiment in Error Analysis: Repeated Determination of Glucose Using Commercial Glucometers,” J. Chem. Educ. 2000, 77, 377–379.
• Gordus, A. A. “Statistical Evaluation of Class Data for Two Buret Readings,” J. Chem. Educ. 1987, 64, 376–377.
• Harvey, D. T. “Statistical Evaluation of Acid/Base Indicators,” J. Chem. Educ. 1991, 68, 329–331.
• Hibbert, D. B. “Teaching modern data analysis with The Royal Austrian Chemical Institute’s titration competition,” Aust. J. Ed. Chem. 2006, 66, 5–11.
• Johll, M. E.; Poister, D.; Ferguson, J. “Statistical Comparison of Multiple Methods for the Determination of Dissolved Oxygen Levels in Natural Water,” Chem. Educator 2002, 7, 146–148.
• Jordon, A. D. “Which Method is Most Precise; Which is Most Accurate?,” J. Chem. Educ. 2007, 84, 1459–1460.
• Olsen, R. J. “Using Pooled Data and Data Visualization To Introduce Statistical Concepts in the General Chemistry Laboratory,” J. Chem. Educ. 2008, 85, 544–545.
• O’Reilley, J. E. “The Length of a Pestle,” J. Chem. Educ. 1986, 63, 894–896.
• Overway, K. “Population versus Sampling Statistics: A Spreadsheet Exercise,” J. Chem. Educ. 2008 85, 749.
• Paselk, R. A. “An Experiment for Introducing Statistics to Students of Analytical and Clinical Chem- istry,” J. Chem. Educ. 1985, 62, 536.
• Puignou, L.; Llauradó, M. “An Experimental Introduction to Interlaboratory Exercises in Analytical Chemistry,” J. Chem. Educ. 2005, 82, 1079–1081.
• Quintar, S. E.; Santagata, J. P.; Villegas, O. I.; Cortinez, V. A. “Detection of Method Effects on Quality of Analytical Data,” J. Chem. Educ. 2003, 80, 326–329.
• Richardson, T. H. “Reproducible Bad Data for Instruction in Statistical Methods,” J. Chem. Educ. 1991, 68, 310–311.
• Salzsieder, J. C. “Statistical Analysis Experiment for Freshman Chemistry Lab,” J. Chem. Educ. 1995, 72, 623.
• Samide, M. J. “Statistical Comparison of Data in the Analytical Laboratory,” J. Chem. Educ. 2004, 81, 1641–1643.
• Sheeran, D. “Copper Content in Synthetic Copper Carbonate: A Statistical Comparison of Experimental and Expected Results,” J. Chem. Educ. 1998, 75, 453–456.
• Spencer, R. D. “The Dependence of Strength in Plastics upon Polymer Chain Length and Chain Orientation,” J. Chem. Educ. 1984, 61, 555–563.
• Stolzberg, R. J. “Do New Pennies Lose Their Shells? Hypothesis Testing in the Sophomore Analytical Chemistry Laboratory,” J. Chem. Educ. 1998, 75, 1453–1455.
• Stone, C. A.; Mumaw, L. D. “Practical Experiments in Statistics,” J. Chem. Educ. 1995, 72, 518– 524.
• Thomasson, K.; Lofthus-Merschman, S.; Humbert, M.; Kulevsky, N. “Applying Statistics in the Undergraduate Chemistry Laboratory: Experiments with Food Dyes,” J. Chem. Educ. 1998, 75, 231–233.
• Vitha, M. F.; Carr, P. W. “A Laboratory Exercise in Statistical Analysis of Data,” J. Chem. Educ. 1997, 74, 998–1000.

A more comprehensive discussion of the analysis of data, which includes all topics considered in this chapter as well as additional material, are found in many textbook on statistics or data analysis; several such texts are listed here.

• Anderson, R. L. Practical Statistics for Analytical Chemists, Van Nostrand Reinhold: New York; 1987.
• Graham, R. C. Data Analysis for the Chemical Sciences, VCH Publishers: New York; 1993.
• Mark, H.; Workman, J. Statistics in Spectroscopy, Academic Press: Boston; 1991.
• Mason, R. L.; Gunst, R. F.; Hess, J. L. Statistical Design and Analysis of Experiments; Wiley: New York, 1989.
• Massart, D. L.; Vandeginste, B. G. M.; Buydens, L. M. C.; De Jong, S.; Lewi, P. J.; Smeyers-Verbeke, J. Handbook of Chemometrics and Qualimetrics, Elsevier: Amsterdam, 1997.
• Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, Ellis Horwood PTR Prentice-Hall: New York; 3rd Edition, 1993.
• NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006.
• Sharaf, M. H.; Illman, D. L.; Kowalski, B. R. Chemometrics, Wiley-Interscience: New York; 1986.

The importance of defining statistical terms is covered in the following papers.

• Analytical Methods Committee “Terminology—the key to understanding analytical science. Part 1: Accuracy, precision and uncertainty,” AMC Technical Brief No. 13, Sept. 2003.
• Goedart, M. J.; Verdonk, A. H. “The Development of Statistical Concepts in a Design-Oriented Laboratory Course in Scientific Measuring,” J. Chem. Educ. 1991, 68, 1005–1009.
• Sánchez, J. M. “Teaching Basic Applied Statistics in University Chemistry Courses: Students’ Misconceptions,” Chem. Educator 2006, 11, 1–4.
• Thompson, M. “Towards a unified model of errors in analytical measurements,” Analyst 2000, 125, 2020–2025.
• Treptow, R. S. “Precision and Accuracy in Measurements,” J. Chem. Educ. 1998, 75, 992–995.

The detection of outliers, particularly when working with a small number of samples, is discussed in the following papers.

• Analytical Methods Committee “Robust Statistics—How Not To Reject Outliers Part 1. Basic Concepts,” Analyst 1989, 114, 1693–1697.
• Analytical Methods Committee “Robust Statistics—How Not to Reject Outliers Part 2. Inter-laboratory Trials,” Analyst 1989, 114, 1699–1702.
• Analytical Methods Committee “Rogues and Suspects: How to Tackle Outliers,” AMCTB 39, 2009.
• Analytical Methods Committee “Robust statistics: a method of coping with outliers,” AMCTB 6, 2001.
• Analytical Methods Committee “Using the Grubbs and Cochran tests to identify outliers,” Anal. Meth- ods, 2015, 7, 7948–7950.
• Efstathiou, C. “Stochastic Calculation of Critical Q-Test Values for the Detection of Outliers in Measurements,” J. Chem. Educ. 1992, 69, 773–736.
• Efstathiou, C. “Estimation of type 1 error probability from experimental Dixon’s Q parameter on testing for outliers within small data sets,” Talanta 2006, 69, 1068–1071.
• Kelly, P. C. “Outlier Detection in Collaborative Studies,” Anal. Chem. 1990, 73, 58–64.
• Mitschele, J. “Small Sample Statistics,” J. Chem. Educ. 1991, 68, 470–473.

The following papers provide additional information on error and uncertainty, including the propagation of uncertainty.

• Analytical Methods Committee “Optimizing your uncertainty—a case study,” AMCTB 32, 2008.
• Analytical Methods Committee “Dark Uncertainty,” AMCTB 53, 2012.
• Analytical Methods Committee “What causes most errors in chemical analysis?” AMCTB 56, 2013.
• Andraos, J. “On the Propagation of Statistical Errors for a Function of Several Variables,” J. Chem. Educ. 1996, 73, 150–154.
• Donato, H.; Metz, C. “A Direct Method for the Propagation of Error Using a Personal Computer Spreadsheet Program,” J. Chem. Educ. 1988, 65, 867–868.
• Gordon, R.; Pickering, M.; Bisson, D. “Uncertainty Analysis by the ‘Worst Case’ Method,” J. Chem. Educ. 1984, 61, 780–781.
• Guare, C. J. “Error, Precision and Uncertainty,” J. Chem. Educ. 1991, 68, 649–652.
• Guedens, W. J.; Yperman, J.; Mullens, J.; Van Poucke, L. C.; Pauwels, E. J. “Statistical Analysis of Errors: A Practical Approach for an Undergraduate Chemistry Lab Part 1. The Concept,” J. Chem. Educ. 1993, 70, 776–779
• Guedens, W. J.; Yperman, J.; Mullens, J.; Van Poucke, L. C.; Pauwels, E. J. “Statistical Analysis of Errors: A Practical Approach for an Undergraduate Chemistry Lab Part 2. Some Worked Examples,” J. Chem. Educ. 1993, 70, 838–841.
• Heydorn, K. “Detecting Errors in Micro and Trace Analysis by Using Statistics,” Anal. Chim. Acta 1993, 283, 494–499.
• Hund, E.; Massart, D. L.; Smeyers-Verbeke, J. “Operational definitions of uncertainty,” Trends Anal. Chem. 2001, 20, 394–406.
• Kragten, J. “Calculating Standard Deviations and Confidence Intervals with a Universally Applicable Spreadsheet Technique,” Analyst 1994, 119, 2161–2165.
• Taylor, B. N.; Kuyatt, C. E. “Guidelines for Evaluating and Expressing the Uncertainty of NIST Mea- surement Results,” NIST Technical Note 1297, 1994.
• Van Bramer, S. E. “A Brief Introduction to the Gaussian Distribution, Sample Statistics, and the Student’s t Statistic,” J. Chem. Educ. 2007, 84, 1231.
• Yates, P. C. “A Simple Method for Illustrating Uncertainty Analysis,” J. Chem. Educ. 2001, 78, 770–771.

Consult the following resources for a further discussion of detection limits.

• Boumans, P. W. J. M. “Detection Limits and Spectral Interferences in Atomic Emission Spectrometry,” Anal. Chem. 1984, 66, 459A–467A.
• Currie, L. A. “Limits for Qualitative Detection and Quantitative Determination: Application to Radiochemistry,” Anal. Chem. 1968, 40, 586–593.
• Currie, L. A. (ed.) Detection in Analytical Chemistry: Importance, Theory and Practice, American Chemical Society: Washington, D. C., 1988.
• Ferrus, R.; Egea, M. R. “Limit of discrimination, limit of detection and sensitivity in analytical systems,” Anal. Chim. Acta 1994, 287, 119–145.
• Fonollosa, J.; Vergara, A; Huerta, R.; Marco, S. “Estimation of the limit of detection using information theory measures,” Anal. Chim. Acta 2014, 810, 1–9.
• Glaser, J. A.; Foerst, D. L.; McKee, G. D.; Quave, S. A.; Budde, W. L. “Trace analyses for wastewaters,” Environ. Sci. Technol. 1981, 15, 1426–1435.
• Kimbrough, D. E.; Wakakuwa, J. “Quality Control Level: An Introduction to Detection Levels,” Environ. Sci. Technol. 1994, 28, 338–345.

The following articles provide thoughts on the limitations of statistical analysis based on significance testing.

• Analytical Methods Committee “Significance, importance, and power,” AMCTB 38, 2009.
• Analytical Methods Committee “An introduction to non-parametric statistics,” AMCTB 57, 2013.
• Berger, J. O.; Berry, D. A. “Statistical Analysis and the Illusion of Objectivity,” Am. Sci. 1988, 76, 159–165.
• Kryzwinski, M. “Importance of being uncertain,” Nat. Methods 2013, 10, 809–810.
• Kryzwinski, M. “Significance, P values, and t-tests,” Nat. Methods 2013, 10, 1041–1042.
• Kryzwinski, M. “Power and sample size,” Nat. Methods 2013, 10, 1139–1140.
• Leek, J. T.; Peng, R. D. “What is the question?,” Science 2015, 347, 1314–1315.

The following resources provide additional information on using Excel, including reports of errors in its handling of some statistical procedures.

• McCollough, B. D.; Wilson, B. “On the accuracy of statistical procedures in Microsoft Excel 2000 and Excel XP,” Comput. Statist. Data Anal. 2002, 40, 713–721.
• Morgon, S. L.; Deming, S. N. “Guide to Microsoft Excel for calculations, statistics, and plotting data,”
• (http://www.chem.sc.edu/faculty/morga...ide_Morgan.pdf ).
• Kelling, K. B.; Pavur, R. J. “A Comparative Study of the Reliability of Nine Statistical Software Pack-ages,” Comput. Statist. Data Anal. 2007, 51, 3811–3831.

To learn more about using R, consult the following resources.

• Chambers, J. M. Software for Data Analysis: Programming with R, Springer: New York, 2008.
• Maindonald, J.; Braun, J. Data Analysis and Graphics Using R, Cambridge University Press: Cambridge, UK, 2003.
• Sarkar, D. Lattice: Multivariate Data Visualization With R, Springer: New York, 2008.

The following papers provide insight into visualizing data.

• Analytical Methods Committee “Representing data distributions with kernel density estimates,” AMC Technical Brief, March 2006.
• Frigge, M.; Hoaglin, D. C.; Iglewicz, B. “Some Implementations of the Boxplot,” The American Statistician 1989, 43, 50–54.