Sampling Theory

Contents of this page:

• General
• Lower Bound of the Confidence Interval
• Messy Data, Outliers, and Nonresponse
• Populations with Many Zero Values
• Stratification
  

This page lists articles and books related to sampling and the derivation of formulas useful in a wide range of statistical applications. This includes derivations of formulas and empricial tests. This list is selected from the thousands of books and articles related to sampling. These refrerences include a mix of theory and applications. Sampling applications in specific domains, such as auditing and accounting, are cited on other web pages on this web site. Some items are cited on more than one web page in this web site.

Related Web pages at this Web site:

• Auditing
• Data Mining
• Evidence and Expert Testimony
• Forensic Economics Sites
• Sampling in Financial and Internal Audits
• Sampling for Medicare and Other Claims
• Sampling in Sales and Use Tax Audits
• Sampling for Sales and Use Tax Audits - Bibliography of Review Articles
• Statistical Evidence in Litigation
• Statistical Education and Software
• Will Yancey's Home Page

Disclaimer: Inclusion in this list does not imply the reference is or was a reliable authority or relevant to any particular set of facts.  Omission from this list does not imply the item was not reliable.

Maintained by Will Yancey. Please e-mail your suggestions for additions and changes to will@willyancey.com

General

• Arkin, Herbert, Handbook of Sampling for Auditing and Accounting , 3rd edition, (McGraw-Hill, 1984).
• Bartlett, J. E., II, Kotrlik, J. W., & Higgins, C. (2001). "Organizational research: Determining appropriate sample size for survey research", 19(1) Information Technology, Learning, and Performance Journal 43 (2001), http://www.osra.org/itlpj/bartlettkotrlikhiggins.pdf
• Batcher, Mary K., Yan Liu, and Wendy Rotz, "Application of the Hypergeometric Distribution in the Estimation of Rare Events," 2001 Proceedings of the American Statistical Association Section on Survey Research Methods, (2001).
• Benedetto, John J., and Paulo J. S. G. Ferreira, Modern Sampling Theory: Mathematics and Applications, (Birkhauser Boston, 2000).
• Bernstein, Peter L., Against the Gods: The Remarkable Story of Risk, (Wiley, 1996).
• Berry, Michael J. A., and Gordon Linoff, Data Mining Techniques for Marketing, Sales, and Customer Support, (Wiley, 1997).
• Brewer, K. R. W., and M. Hanif, Sampling with Unequal Probabilities, (Springer-Verlag, 1983).
• Browne, Richard H., "On the Use of a Pilot Sample for Sample Size Determination", 14 Statistics in Medicine 1933 (1995).
• Campbell, Donald T., and Julian C. Stanley, Experimental and Quasi-Experimental Designs for Research, (Houghton Mifflin Company, 1963).
• Cochran, William Gemell, Sampling Techniques, 2nd edition, (Wiley, 1963).
• Cochran, William Gemell, Sampling Techniques, 3rd edition, (Wiley, 1977).
• Cohen, S. B., "An Evaluation of Alternative PC-Based Software Packages Developed for the Analysis of Complex Survey Data",  51 The American Statistician 285 (1997).
• Cook, Thomas D., and Donald T. Campbell, Quasi-experimentation: Design and analysis for field settings, (Rand McNally, 1979).
• Cornfield, J., "The determination of sample size", 41 American Journal of Public Health 654 (1951).
• David, I. P., and Sukhatme, B. V., "On the bias and mean square error of the ratio estimator", 69 Journal of the American Statistical Association 464 (1974).
• Deming, William Edwards, Some Theory of Sampling, (Wiley, 1950;  reprinted Dover, 1966).
• Deming, William Edwards, Sample Design in Business Research, (Wiley, 1960; reprinted Wiley Classics, 1990).
• Deming, William Edwards, Statistical Adjustment of Data, (Wiley, 1943;  reprinted Dover, 1964).
• Dutka, Solomon, Notes on Statistical Sampling for Surveys, (Audits & Surveys, 1982).
• Finkelstein, Michael O., and Bruce Levin, Statistics for Lawyers, (Springer-Verlag, 1st edition 1990, 2nd edition 2001).
• Fleiss, Joseph L., Statistical Methods for Rates and Proportions, 2nd edition, (Wiley, 1981).
• Fleiss, Joseph L., Bruce Levin, and Myunghee Cho Paik, Statistical Methods for Rates and Proportions, 3rd edition, (Wiley, 2003).
• Freund, John E., and Frank J. Williams, Dictionary/Outline of Basic Statistics, (reprinted Dover, 1991).
• Glass, Gene, Introduction to Quantitative Methods: A Basic Statistics Course
• Gregoire, Timothy J., "Sampling-skewed biological populations: behavior of confidence intervals for the population total", Ecology  (April 1999).
• Groves, R. M., Survey Errors and Survey Costs, (Wiley, 1989).
• Gunning, Patricia, Jane Horgan, and William Yancey, "Geometric Stratification of Accounting Data", Contaduría y Administración, 11 (September-December 2004). Published by Universidad Nacional Autonoma de Mexico (UNAM).
• Hajek, J., Sampling from a Finite Population, (Marcel Dekker, 1981).
• Hald, A., Statistical Theory of Sampling Inspection by Attributes, (Academic Press, 1981).
• Hansen, Morris H., William N. Hurwitz, and William G. Madow, Sample Survey Methods and Theory, 2 volumes (Wiley, 1953, reprinted in 1993).
• Hedayat, A., and K. S. Bekas, Design and Inference in Finite Population Sampling, (Wiley, 1991).
• Hoerl, Roger, and Ronald Snee, Statistical Thinking: Improving Business Performance, (Duxbury, 2002).
• Intriligator, Michael D., Ronald G. Bodkin, and Cheng Hsiao, Econometric Models, Techniques, and Applications, 2nd ed., (Prentice-Hall, 1996).
• John, J. A. (Nye), David Whitaker, and David G. Johnson, Statistical Thinking in Business, Second Edition, (Chapman & Hall / CRC, 2006).
• Johnson, P. O., and M. S. Rao, Modern Sampling Methods, (University of Minnesota Press, 1959).
• Kalton, Graham, Introduction to Survey Sampling, (Sage Publications, 1983).
• Kaye, David H., and David A. Freedman, "Reference Guide on Statistics", Reference Manual on Scientific Evidence, 1st ed., (Federal Judicial Center, 1994), pages 333-414, www.fjc.gov
• Kaye, David H., and David A. Freedman, "Reference Guide on Statistics", Reference Manual on Scientific Evidence, 2nd ed., (Federal Judicial Center, 2000), pages 83-178,  www.fjc.gov
• Kish, Leslie F., "Some Statistical Problems in Research Design", 24(3) American Sociological Review 328 (1959).
• Kish, Leslie F., Survey Sampling, (Wiley, 1967; paperback 1995).
• Kish, Leslie F., Statistical Design for Research, (Wiley, 1987).
• Koller, Glenn R., Risk Modeling for Determining Value and Decision Making, (Chapman & Hall/CRC Press, 2000).
• Korn, Edward L., and Barry I. Graubard, Analysis of Health Surveys, (Wiley, 1999).
• Kowalewski, Milton J., and Josh B. Tye, editors, Statistical Sampling: Past, Present, and Future Theoretical and Practical, Papers presented at a symposium on statistical sampling, held in Philadelphia on April 2, 1990, (ASTM, 1990).
• Krishnaiah, P. R. and C. R. Rao, editors, Handbook of Statistics: Volume 6, Sampling, (Elsevier Science Publishing, 1988).
• Kvanli, Alan H., Janet Fowler, James E. Foster, "Warning! Some Misleading Statistical Sampling Formulas,"  41 The Government Accountants Journal 49 (Winter 1992).
• Lehtonen, Risto & Erkki J. Pahkinen, Practical Methods for Design and Analysis of Complex Surveys, (Wiley, 1995).
• Lessler, Judith T., and William D. Kalsbeek, Nonsampling Error in Surveys, (Wiley, 1992).
• Levy, Paul S., and Stanley Lemeshow, Sampling of Populations: Methods and Applications, 3rd edition, (Wiley, 1999).
• Lindgren, B., Statistical Theory, 4th edition, (Chapman & Hall, 1993).
• Little, Roderick J. A., and Donald B. Rubin, Statistical Analysis with Missing Data, 2nd edition, (Wiley 2002).
• Lohr, Sharon L., Sampling: Design and Analysis, (Duxbury Press, 1999).
• Marsaglia, George, "DIEHARD: a battery of tests for random number generators", http://stat.fsu.edu/~geo/
• Miaoulis, G., and R. D. Michner, An Introduction to Sampling, (Kendall/Hunt, 1976).
• Moore, D. S., Statistics: Concepts and Controversies, (W. H. Freeman, 1985).
• Moser, C.A. & Graham Kalton, Graham, Survey Methods in Social Investigation, 2nd edition. (Heinemann, 1971).
• Neter, John, and William Waserman, Fundamental Statistics For Business and Economics, 3rd edition, (Allyn and Bacon, 1966).
• Neyman, J., and E. S. Pearson, "On the use and interpretation of certain test criteria for purposes of statistical inference", Part I. 20A Biometrika 175 (1928).
• Ostle, B., and R.W. Mensing, Statistics in Research, 3rd edition, (Iowa State University Press, 1975).
• Panel on Nonstandard Mixtures of Distributions, "Statistical Models and Analysis in Auditing", 4 Statistical Science 2 (1989). Report of a distinguished panel of statisticians sponsored by the National Research Council.
• Raj, Des, Sampling Theory, (McGraw-Hill, 1968).
• RAND, A Million Random Digits with 100,000 Normal Deviates, (Free Press, 1955).
• Ripley, B. D., Pattern Recognition and Neural Networks, (Cambridge University Press, 1996).
• Rotz, Wendy, Eric Falk, Daniel Wood, and Jeri Mulrow, "A Comparison of Random Number Generators Used in Business", Proceedings of the American Statistical Association, (August 2001).
• Rotz, Wendy, Eric Falk, and Archana Joshee, "A Comparison of Random Number Generators Used in Business - 2004 Update", 2004 Proceedings of the American Statistical Association Section on Business & Economics Statistics 1316, (JSM 2004).
• Rubinfield, Daniel L. "Reference Guide on Multiple Regression", Reference Manual on Scientific Evidence, 2nd edition, (Federal Judicial Center, 2000), pages 179-227,  http://air.fjc.gov/public/fjcweb.nsf/pages/16
• Sampath, S., Sampling Theory and Methods, (CRC Press, 2001).
• Sarndal, Carl-Erik, Bengt Swensson, and Jan Wretman, Model Assisted Survey Sampling, (Springer-Verlag, 1992).
• Scheaffer, Richard L., William Mendenhall, and Lyman Ott, Elementary Survey Sampling, 5th edition, (Duxbury Press, 1996).
• Shao, I., and D. Tu, The Jacknife and Bootstrap, (Springer-Verlag, 1995).
• Siegel, Sidney, and N. John Castellan, Jr., Nonparametric Statistics for the Behavioral Sciences, 2nd edition, (McGraw-Hill, 1988).
• Slonim, M. J., Sampling, (Simon and Schuster, 1960).
• Snedecor, George W., and William Gemmell Cochran, Statistical Methods, 8th edition, (Iowa State University Press, 1989).
• Som, R. K., Practical Sampling Techniques, 2nd edition, (M. Dekker, 1996).
• Statistics Canada, Statistics Canada Quality Guidelines, www.statcan.ca/english/freepub/12-539-XIE/index.htm
• Statsoft, Electronic Statistics Textbook, www.statsoft.com/textbook/stathome.html, (StatSoft, 1999).
• Stuart, Alan, Basic Ideas of Scientific Sampling, 1st edition, (Charles Griffin & Company Limited, London, 1962).
• Stuart, Alan, Basic Ideas of Scientific Sampling, 2nd edition, (Charles Griffin & Company Limited, London, 1976).
• Stuart, Alan, The Ideas of Sampling, (Oxford University Press, 1984).
• Sudman, S., Applied Sampling, (Academic Press, 1976).
• Tal, Joseph, Reading Between the Numbers: Statistical Thinking in Everyday Life, (McGraw-Hill, 2001).
• Thompson, M. E., Theory of Sample Surveys, (Chapman & Hall, 1997).
• Thompson, Steven K., Sampling, (Wiley, 1992).
• Thompson, Steven K., and George A. F. Seber, Adaptive Sampling, (Wiley, 1996).
• Tryfos, Peter, Sampling Methods for Applied Research: Text and Cases, (Wiley, 1996).
• Williams, Frederick, Reasoning with Statistics: How to Read Quantitative Research, 4th edition, (Harcourt Brace, 1992).
• Winger, M. E., Principles of Statistical Sampling, (University of North Dakota).
• Wolter, K. M., Introduction to Variance Estimation, (Springer-Verlag, 1985).
• Wright, Tommy, Exact Confidence Bounds When Sampling from Small Finite Universes: An Easy Reference Based on the Hypergeometric Distribution, Lecture Notes in Statistics, (Springer, 1991).
• Yamane, Taro, Elementary Sampling Theory, (Prentice-Hall, 1967).
• Yates, F., Sampling Methods for Censuses and Surveys, 4th ed., (Macmillan/Griffin, 1981).

Lower Bound of the Confidence Interval

• Bright, Joseph C., Jr., Joseph B. Kadane, and Daniel S. Nagin, "Statistical Sampling in Tax Audits", 13 Law & Social Inquiry 305 (Spring 1988).
• Edwards, Don, Gail Ward-Besser, Jennifer Lasecki, Brenda Parker, Kristin Wieduwil, Fuming Wu, and Philip Moorhead, "The Minimum Sum Method: A Distribution-Free Sampling Procedure for Medicare Fraud Investigations", 4 Health Services and Outcomes Research Methodology 241 (December 2003). [Online at http://springerlink.com
• Panel on Nonstandard Mixtures of Distributions, "Statistical Models and Analysis in Auditing", 4 Statistical Science 2 (1989). Report of a distinguished panel of statisticians sponsored by the National Research Council.
• Solomon, Herbert, "Confidence Intervals in Legal Settings," In Morris H. DeGroot, Stephen E. Fienberg, and Joseph B. Kadane, editors, Statistics and the Law, (Wiley, 1986, reprinted 1994), pp. 457-458.

Messy Data, Outliers, and Nonresponse

• Barnett, Vic, and Toby Lewis, Outliers in Statistical Data, 3rd edition, (Wiley, 1994).
• Fomby, Thomas, Messy Data - Missing Observations, Outliers, and Mixed-Frequency Data, (1998).
• Kalton, Graham, Compensating for Missing Survey Data, (University of Michigan Institute for Social Research, 1983).
• Kok, Johan J., On Data Snooping and Multiple Outlier Testing, (U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, 1984).
• Kruskal, William H., "Some Remarks on Wild Observations", Technometrics, (February 1960), http://www.tufts.edu/~gdallal/out.htm
• Madow, W. G., I. Olkin, and D. B. Rubin, editors, Incomplete Data in Sample Surveys, (Academic Press, 1983).
• Rubin, Donald B., Multiple Imputation for Nonresponse in Surveys, (Wiley, 1987).

Populations with Many Zero Values

• Chen, Jiahua, Shun-Yi Chen, and J. N. K. Rao, "Empirical Likelihood Confidence Intervals for the Mean of a Population Containing Many Zero Values", 31 Canadian Journal of Statistics 53 (2003).
• Cox, D. R., and E. J. Snell, "On Sampling and the Estimation of Rare Errors", 66 Biometrika 1 (1979).
• Kalton, Graham, and D. W. Anderson, "Sampling Rare Populations", 149 Journal of the Royal Statistical Society, Series A 65 (1986).
• Korn, Edward L., and Barry I. Graubard, "Confidence Intervals for Proportions with Small Expected Number of Positive Counts Estimated From Survey Data", 24 Survey Methodology 193, (December 1998).
• Kvanli, Alan H., Y. K. Shen, and L. Y. Deng, "Construction of Confidence Intervals for the Mean of a Population Containing Many Zero Values", 16 Journal of Business & Economic Statistics 362 (1998).

Stratification

• Chatterjee, S., "A study of optimal allocation in multivariate stratified surveys", 55 Skand. Akt. 73 (1972).
• Cochran, William Gemell, "Comparison of methods for determining stratum boundaries", 38 Bulletin of the International Statistical Insitute 345 (1961 (2)).
• Dalenius, Tore, and Joesph L. Hodges, Jr., "Minimum Variance Stratification", 54 Journal of the American Statistical Association 88 (March 1959). [Presented method now known of the Cumulative Square Root of the Frequency Method for setting stratification boundaries.]
• Evans, W. D., "On stratification and optimal allocation", 46 Journal of the American Statistical Association 95 (1951).
• Schneeberger, H., "Some comments on sampling optimization", 208 Jahrbücher für Nationalökonomie und Statistik 67 (1991).