# Sample Size / Power Analysis

At Statistics Solutions, we look at the type of statistical analysis you are conducting and select the appropriate sample size.  Below is an explanation of how sample size is related to statistical power, effect size, and significance level.

Power Analysis

Each of these four components  of your study (sample size, statistical power, effect size, and significance level) are a function of the other three, meaning that altering one causes changes in the others.

It is not uncommon for researchers to take an inappropriate “one-size-fits-all” approach in determining these components of your study.  At Statistics Solutions, our professional statisticians will determine the sample size for your study and justify that sample size.  In addition, we will determine the appropriate effect size, power, and significance level for your study.

Sample Size

Sample size is critical to ensuring the validity of your study.  Ideally, your sample size will be determined a priori. With our experience and expertise gained from completing thousands of dissertations and theses, it is possible for us to justify “less-than-ideal” sample sizes and still make your dissertation, thesis, or research worth while.

Effect Size

The effect size of your study is critical to sample size, power, and significance level.  This unique measurement will tell you the strength or importance of a particular relationship.  The professional statisticians at Statistics Solutions will ensure that an appropriate effect size is chosen for your study a priori or determined in post hoc analysis.

Power

Power is the probability of not making a type II error, while beta is the probability of making a type II error.  Restated, beta is the probability of not finding a relationship that actually exists in your research.  While there are general guidelines as to what is appropriate (typically .80), the a priori power is unique to every study.

Significance Level

The alpha or significance level of your study is the probability of committing a Type I error.   More simply stated, it is your probability of finding a relationship that does not exist. Generally, committing a Type I error is considered more severe than committing a Type II error.  The significance level measurement is unique to your study.  The significance level for a study involving airbag deployment failures would not be the same as the significance level for a study involving the satisfaction of five-year-old children with a particular brand of red crayon.  At Statistics Solutions we will determine the appropriate significance level for your study, ensuring meaningful, defendable results that are easy to understand.

Contact Statistics Solutions today for a free dissertation consultation.

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. View

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.