Variability: One Statistician’s View

 

Robert Gould

Department of Statistics, UCLA

rgould@stat.ucla.edu

 

GILLIAN A. LANCASTER

University of Liverpool

g.lancaster@liv.ac.uk

                                                                                       

SUMMARY

 

Although variability is of fundamental concern and interest to statisticians, often this does not get communicated to students who are taught instead to view variability as a nuisance parameter. A brief survey of a few case studies, as well as a recounting of some history, shows that variability is worthy of study in its own right, and examination of variability leads to insights that might have been missed had we focused all of our attention on the “trend” of the data. As one of the key components of statistical thinking, variability deserves more prominence in the classroom.

 

Keywords: Variability; Education; Statistical thinking

 

 

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Statistics Education Research Journal, 3(2), 7-16, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), November, 2004

 

 

 

REFERENCES

 

Chatfield, C. (1988). Problem solving: A statistician’s guide. London: Chapman and Hall.

Coen, I. B. (1984). Florence Nightingale. Scientific American 250, 128–137.

DeVeaux, R., Velleman, P., & Bock, D. (2004). Intro Stats. New York: Addison Wesley.

Gigerenzer, G., Switjtink, Z., Porter, T., Daston, L., Beatty, J., & Kruger, L. (1997). The empire of chance: How probability changed science and every day life. Cambridge, UK: Cambridge University Press.

Laird, N. M., & Ware, H. (1982). Random Effects Models for Longitudinal Data. Biometrics, 38, 963–974.

Moore, A., Gould, R., Reuben, D., Greendale, G., Carter, K., Zhou, K., & Karlamangla, A. (2005). Do Adults Drink Less as They Age? Longitudinal Patterns of Alcohol Consumption in the U.S. Accepted for publication in American Journal of Public Health, March 2005.

Moore, D. (1997). Probability and statistics in the core curriculum. In J. Dossey (Ed.), Confronting the core curriculum (pp. 92–97). USA: Mathematical Association of America.

Moore, D. (1990). Uncertainty. In L. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–138). Washington, DC: National Academy Press.

Morton, D. E., Saah, A. J., Silberg, S. L., Owens, W. L., Roberts, M. A., & Saah, M. D. (1982). Lead absorption in children of employees in a lead-related industry. American Journal of Epidemiology, 115, 549–555.

National Center for Health Statistics. Plan and operation of the National Health and Nutrition Examination Survey, United States. 1971-73. Vital Health Stat [1]. 1973;10a. DHEW publication PHS 79-1310.

National Center for Health Statistics. Plan and operation of the National Health and Nutrition Examination Survey, United States. 1971-73. Vital Health Stat [1]. 1973;10b. DHEW publication PHS 79-1310.

National Center for Health Statistics. Plan and operation of the NHANES I Epidemiologic Follow-up Study 1982-84. Vital Health Stat [1]. 1987;22. DHHS publication PHS 87-1324.

National Center for Health Statistics. Plan and operation of the NHANES I Epidemiologic Follow-up Study 1986. Vital Health Stat [1]. 1990;25. DHHS publication PHS 90-1307.

National Center for Health Statistics. Plan and operation of the NHANES I Epidemiologic Follow-up Study 1987. Vital Health Stat [1]. 1992;27. DHHS publication PHS 92-1303.

National Center for Health Statistics. Statistical Issues in Analyzing the NHANES I Epidemiologic Followup Study. Vital and Health Statistics, Series 2: Data Evaluation and Methods Research No. 121. Hyattsville MD: National Center for Health Statistics, 1994. DHHS Publication No. (PHS) 94–1395.

Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge, UK: Cambridge University Press.

Searle, S. R., Casella, G., & McCulloch, C. E. (1992). Variance components. New York: John Wiley & Sons.

Snee, R. D. (1990). Statistical thinking and its contribution to quality. The American Statistician, 44, 116–121.

Thomas, K. (2002). Effects of habitat fragmentation on montane small mammal populations in the Mojave National Preserve. Unpublished report for UCLA OBEE 297A, UCLA, USA, 2002.

Trumbo, B. (2001). Learning statistics with real data. San Francisco: Duxbury Press.

Wild, C. J., & Phannkuch, M. (1999). Statistical Thinking in Empirical Enquiry. International Statistical Review, 67(3), 223–265.

Robert Gould

Dept. of Statistics

8130 Math Science Building

MC 155404

UCLA

Los Angeles, CA 90095-1554, USA