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102 Modern Analytical Chemistry

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question? (d) Assuming that X and s are good distributed? (e) It has been reported that this method for
2
approximations for mand s , what percentage of all preparing copper sulfide results in a nonstoichiometric
experimentally determined Cu/S ratios will be greater than 2? compound with a Cu/S ratio of less than 2. Determine if the
How does this compare with the experimental data? Does this mean value for these data is significantly less than 2 at a
support your conclusion about whether the data are normally significance level of a= 0.01.

4L SUGGESTED READINGS

A more comprehensive discussion of the analysis of data, covering Mitschele, J. “Small Sample Statistics,” J. Chem. Educ. 1991, 68,
all topics considered in this chapter as well as additional material, 470–473.
can be found in any textbook on statistics or data analysis; The following papers provide additional information on error and
following are several such texts. uncertainty, including the propagation of uncertainty.
Anderson, R. L. Practical Statistics for Analytical Chemists. Van Andraos, J. “On the Propagation of Statistical Errors for a
Nostrand Reinhold: New York, 1987. Function of Several Variables,” J. Chem. Educ. 1996, 73,
Graham, R. C. Data Analysis for the Chemical Sciences. VCH 150–154.
Publishers: New York, 1993. Donato, H.; Metz, C. “A Direct Method for the Propagation of
Mark, H.; Workman, J. Statistics in Spectroscopy. Academic Press: Error Using a Personal Computer Spreadsheet Program,”
Boston, 1991. J. Chem. Educ. 1988, 65, 867–868.
Mason, R. L.; Gunst, R. F.; Hess, J. L. Statistical Design and Gordon, R.; Pickering, M.; Bisson, D. “Uncertainty Analysis by the
Analysis of Experiments. Wiley: New York, 1989. ‘Worst Case’ Method,” J. Chem. Educ. 1984, 61, 780–781.
Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, 3rd ed. Guare, C. J. “Error, Precision and Uncertainty,” J. Chem. Educ.
Ellis Horwood PTR Prentice-Hall: New York, 1993. 1991, 68, 649–652.
Sharaf, M. H.; Illman, D. L.; Kowalski, B. R. Chemometrics. Wiley- Guedens, W. J.; Yperman, J.; Mullens, J.; et al. “Statistical Analysis
Interscience: New York, 1986. of Errors: A Practical Approach for an Undergraduate
The difference between precision and accuracy and a discussion of Chemistry Lab,” Part 1. The Concept, J. Chem. Educ. 1993, 70,
indeterminate and determinate sources of error 776–779; Part 2. Some Worked Examples, J. Chem. Educ. 1993,
is covered in the following paper. 70, 838–841.
Treptow, R. S. “Precision and Accuracy in Measurements,” Heydorn, K. “Detecting Errors in Micro and Trace Analysis by
J. Chem. Educ. 1998, 75, 992–995. Using Statistics,” Anal. Chim. Acta 1993, 283, 494–499.
The detection of outliers, particularly when working with a small Taylor, B. N.; Kuyatt, C. E. “Guidelines for Evaluating and
number of samples, is discussed in the following papers. Expressing the Uncertainty of NIST Measurement Results,”
NIST Technical Note 1297, 1994.
Efstathiou, C. “Stochastic Calculation of Critical Q-Test Values for
the Detection of Outliers in Measurements,” J. Chem. Educ. A further discussion of detection limits is found in
1992, 69, 773–736. Currie, L. A., ed. Detection in Analytical Chemistry: Importance,
Kelly, P. C. “Outlier Detection in Collaborative Studies,” Anal. Theory and Practice. American Chemical Society: Washington,
Chem. 1990, 73, 58–64. DC, 1988.

4 M REFERENCES

1. Goedhart, M. J.; Verdonk, A. H. J. Chem. Educ. 1991, 68, 1005–1009. 9. Marecek, V.; Janchenova, H.; Brezina, M.; et al. Anal. Chim. Acta
2. Rousseeuw, P. J. J. Chemom. 1991, 5, 1–20. 1991, 244, 15–19.
3. Ellison, S.; Wegscheider, W.; Williams, A. Anal. Chem. 1997, 69, 10. Rorabacher, D. B. Anal. Chem. 1991, 63, 139–146.
607A–613A. 11. Deming, W. E. Statistical Adjustment of Data. Wiley: New York, 1943
4. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in (republished by Dover: New York, 1961); p. 171.
Physical Chemistry, 5th ed. McGraw-Hill: New York, 1989, pp. 55–63. 12. Richardson, T. H. J. Chem. Educ. 1991, 68, 310–311.
5. Lam, R. B.; Isenhour, T. L. Anal. Chem. 1980, 52, 1158–1161. 13. Kirchner, C. J. “Estimation of Detection Limits for Environmental
6. Mark, H.; Workman, J. Spectroscopy, 1988, 3(1), 44–48. Analytical Procedures,” In Currie, L. A., ed. Detection in Analytical
Chemistry: Importance, Theory and Practice. American Chemical
7. Winn, R. L. Statistics for Scientists and Engineers, Prentice-Hall:
Englewood Cliffs, NJ, 1964; pp. 165–174. Society: Washington, DC, 1988.
14. Long, G. L.; Winefordner, J. D. Anal. Chem. 1983, 55, 712A–724A.
8. Mark, H.; Workman, J. Spectroscopy, 1989, 4(3), 56–58.