# Sample Size / Power Analysis

Every study needs data, the question is how much data are needed. The sample size determination using a power analysis is the process of figuring that question out and will be of particular interest to both your committee for Proposal and IRB approval. Details below briefly examine how a power analysis calculates sample size, before going into how to use free resources to determine your study’s sample size in just a few minutes.

** Power Analysis.** For a given statistical test, the sample size is calculated from statistical power, effect size, and significance level. That is, each of these four components of your study—namely, sample size, statistical power, effect size, and significance level—are a function of the other three. Specifically, the effect size of your study tells you the strength or importance of a particular relationship. The power, typically .80, is the probability of not making a type II error, which differs from beta, or the probability of making a type II error. The

** Free Resources.** To facilitate sample size determination, our team has calculated the sample size for a large variety of statistical tests for small, medium and large effect sizes. You can simply sign-up for the toolbox, then click the analysis you plan on using.

If you have trouble with the toolbox or would like more assistance, you can contact us for a free dissertation consultation. For additional assistance with your proposal, call (877-437-8622) or email us at [email protected].

**Power Analysis Resources**

Abraham, W. T., & Russell, D. W. (2008). Statistical power analysis in psychological research. *Social and Personality Psychology Compass, 2*(1), 283-301.

Bausell, R. B., & Li, Y. -F. (2002). *Power analysis for experimental research: A practical guide for the biological, medical and social sciences. *Cambridge, UK: Cambridge University Press.

Bonett, D. G., & Seier, E. (2002). A test of normality with high uniform power. *Computational Statistics & Data Analysis*,* 40*(3), 435-445.

Cohen, J. (1969). *Statistical power analysis for the behavioral sciences*. Hillsdale, NJ: Lawrence Erlbaum Associates. View

Goodman, S. N. & Berlin, J. A. (1994). The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. *Annals of Internal Medicine, 121*(3), 200-206.

Jones, A., & Sommerlund, B. (2007). A critical discussion of null hypothesis significance testing and statistical power analysis within psychological research. *Nordic Psychology, 59*(3), 223-230.

Lipsey, M. W. (1990). *Design sensitivity: Statistical power for experimental research*. Newbury Park, CA: Sage Publications. View

MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. *Psychological Methods, 11*(1), 19-35.

Murphy, K. R., & Myors, B. (2004). *Statistical power analysis: A simple and general model for traditional and modern hypothesis tests* (2nd ed.).Mahwah, NJ: Lawrence Erlbaum Associates. View

Murphy, K. R., Myors, B., & Wolach, A. (2008). *Statistical power analysis: A simple and general model for traditional and modern hypothesis tests* (3rd ed.).Mahwah, NJ: Lawrence Erlbaum Associates. View

Sahai, H., & Khurshid, A. (1996). Formulas and tables for the determination of sample sizes and power in clinical trials involving the difference of two populations: A review. *Statistics in Medicine**, 15*(1), 1-21.