Power Calculations and Sample Size Determination

• Richard Valliant
• Jill A. Dever
• Frauke Kreuter
Chapter
Part of the Statistics for Social and Behavioral Sciences book series (SSBS, volume 51)

Abstract

In Chap. we calculated sample sizes based on targets for coefficients of variation (CV s), margins of error, and cost constraints. Another method is to determine the sample size needed to detect a particular alternative value when testing a hypothesis. For example, when comparing the means for two groups, one way of determining sample size is through a power calculation. Roughly speaking, power is a measure of how likely you are to recognize a certain size of difference in the means. A sample size is determined that will allow that difference to be detected with high probability (i.e., a detectable difference). Power can also be determined in a one-sample case where a simple hypothesis is being tested versus a simple alternative. Using power to determine sample sizes is especially useful when some important analytic comparisons can be identified in advance of selecting the sample. Although not covered in most books on sample design, most practitioners will inevitably have applications where power calculations are needed.

Keywords

Sample Size Calculation Simple Random Sample Rejection Region Scholastic Aptitude Test Determine Sample Size
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

1. Armitage P., Berry G. (1987). Statistical Methods in Medical Research, 2nd edn. Blackwell, OxfordGoogle Scholar
2. Brown L., Cai T., Das Gupta A. (2001). Interval estimation for a binomial proportion. Statistical Science 16:101–133
3. Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Associates, New Jersey
4. Hedges L.V., Olkin I. (1985). Statistical Methods for Meta-analysis. Academic Press, Orlando
5. Heiberger R.M., Neuwirth E. (2009) R Through Excel: A Spreadsheet Interface for Statistics, Data Analysis, and Graphics. Springer, New York
6. Korn E.L. (1986). Sample size tables for bounding small proportions. Biometrics 42:213–216
7. Lemeshow S., Hosmer D., Klar J., Lwanga S. (1990). Adequacy of Sample Size in Health Studies. John Wiley & Sons, Inc., ChichesterGoogle Scholar
8. R Core Team and contributors worldwide (2012c). stats: R statistical functions. URL http://finzi.psych.upenn.edu/R/library/stats/html/00Index.html
9. Royall R.M. (1986). The effect of sample size on the meaning of significance tests. The American Statistician 40:313–315
10. Rust K.F. (1984). Techniques for estimating variances for sample surveys. PhD thesis, University of Michigan, Ann Arbor MI, unpublishedGoogle Scholar
11. Rust K.F. (1985). Variance estimation for complex estimators in sample surveys. Journal of Official Statistics 1:381–397Google Scholar
12. Schlesselman J. (1982). Case-Control Studies: Design, Conduct, and Analysis. Oxford University Press, New YorkGoogle Scholar
13. Valliant R., Rust K.F. (2010). Degrees of freedom approximations and rules-of-thumb. Journal of Official Statistics 26:585–602Google Scholar
14. Woodward M. (1992). Formulas for sample size, power, and minimum detectable relative risk in medical studies. The Statistician 41:185–196

© Springer Science+Business Media New York 2013

Authors and Affiliations

• Richard Valliant
• 1
• Jill A. Dever
• 2
• Frauke Kreuter
• 3
1. 1.University of MichiganAnn ArborUSA
2. 2.RTI InternationalWashington, DCUSA
3. 3.University of MarylandCollege ParkUSA

Personalised recommendations

Citechapter 