The professionals at Statistics Solutions are sample size and statistical power experts. We look at the type of data analysis you are conducting and select the appropriate sample size for your statistical tests. 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. The complex synergy of this relationship has been the focus of numerous scholarly articles, authored by some of the brightest minds in the field of statistical analysis. At Statistics Solutions, our professional statisticians understand this relationship and know how to help you understand this relationship.
It is not uncommon for statistics consultants 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 ideal 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, ensuring a smooth transition from theory to practice.
Sample Size
Sample size is critical to ensuring the validity of your study. Ideally, your sample size will be determined a priori; however, the professional statisticians at Statistics Solutions can work with and justify your data to help you make meaningful inferences. 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 or thesis great.
Effect Size
The effect size of your study is critical in the synergy of 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
This measurement is your probability of committing a Type II error. Restated, it is the probability of not finding a relationship that exists in your analysis. While there are general guidelines as to what is appropriate, the a priori power is unique to you and every study conducted. The professional statisticians at Statistics Solutions will determine the appropriate power, as well as conduct post hoc analysis to determine the power after the fact.
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. The professional statisticians at Statistics Solutions will determine the appropriate significance level for your study, ensuring meaningful, defendable results that are easy to write about and easy to understand.
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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.
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.
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.
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.
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.
