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Power and Sample Size

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Part of the Methods in Molecular Biology™ book series (MIMB,volume 404)


In this chapter, we discuss the concept of statistical power and show how the sample size can be chosen to ensure a desired power. Power is the probability of rejecting the null hypothesis when the null hypothesis is false, that is the probability of saying there is a difference when a difference actually exists. An underpowered study does not have a sufficiently large sample size to answer the research question of interest. An overpowered study has too large a sample size and wastes resources. We will show how the power and required sample size can be calculated for several common types of studies, mention software that can be used for the necessary calculations, and discuss additional considerations.

Key Words

  • Clinically meaningful effect
  • hypothesis test
  • power
  • sample size
  • type I error
  • type II error

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  1. Cohen, J. (1988) Statistical Power Analysis for the Behavioral Science, 2nd ed. Hillsdale, Lawrence Erlbaum Associates.

    Google Scholar 

  2. Kraemer, H. C., and Thiemann, S. (1987) How Many Subjects? Statistical Power Analysis in Research. Newbury Park, SAGE Publications.

    Google Scholar 

  3. Murphy, K. R., and Myors, B. (1998) Statistical Power Analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests. Mahwah, Lawrence Erlbaum Associates.

    Google Scholar 

  4. Chow, S-C., Shao, J., and Wang, H. (2003) Sample Size Calculations in Clinical Research. New York, Marcel Dekker.

    Google Scholar 

  5. Fleiss, J. L. (1981) Statistical Methods for Rates and Proportions, 2nd ed. New York, John Wiley & Sons.

    Google Scholar 

  6. Peace, K. E. (1988) Letter to the editor: some thoughts on one-tailed tests. Controlled Clinical Trials 9, 383–384.

    PubMed  CrossRef  CAS  Google Scholar 

  7. Dudewicz, E. J. (1972) Confidence intervals for power, with special reference to medical trials. Aust. J. Stat. 14, 211–216.

    CrossRef  Google Scholar 

  8. Shiffler, R. E., and Adams, A. J. (1987) A correction for biasing effects of pilot sample size on sample size determination. Journal of Marketing Research 24, 319–321.

    CrossRef  Google Scholar 

  9. Browne, R. H. (1995) On the use of a pilot sample for sample size determination. Stat. Med. 14, 1933–1940; 1995.

    Google Scholar 

  10. Lee, S. J., and Zelen, M. (2000) Clinical trials and sample size considerations: another perspective. Stat. Sci. 15(2), 95–103.

    Google Scholar 

  11. O’Brien, R. G., and Castelloe, J. (2006) Sample-Size Analysis for Traditional Hypothesis Testing: Concepts and Issues, in Pharmaceutical Statistics. (D’Agostino, R., Dmitrienko, A., and Chuang-Stein, C., eds.) Cary, SAS Press, SAS Institute.

    Google Scholar 

  12. Wittes, J. (2002) Sample size calculations for randomized controlled trials. Epidemiol. Rev. 24, 39–53.

    PubMed  CrossRef  Google Scholar 

  13. Lenth, R. V. (2001) Some practical guidelines for effective sample-size determination. Am. Stat. 55, 187–193.

    CrossRef  Google Scholar 

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© 2007 Humana Press Inc., Totowa, NJ

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Case, L.D., Ambrosius, W.T. (2007). Power and Sample Size. In: Ambrosius, W.T. (eds) Topics in Biostatistics. Methods in Molecular Biology™, vol 404. Humana Press.

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  • Publisher Name: Humana Press

  • Print ISBN: 978-1-58829-531-6

  • Online ISBN: 978-1-59745-530-5

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