# Sample Size Calculation and Sample Size Justification

**Sample size calculation** is concerned with how much data we require to make a correct decision on particular research. If we have more data, then our decision will be more accurate and there will be less error of the parameter estimate. This doesn't necessarily mean that more is always best in sample size calculation. A statistician with expertise in sample size calculation will need to apply statistical techniques and formulas in order to find the correct sample size calculation accurately.

There are some basics formulas for sample size calculation, although sample size calculation differs from technique to technique. For example, when we are comparing the means of two populations, if the sample size is less than 30, then we use the t-test. If the sample size is greater than 30, then we use the z-test. If the population size is small, than we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the smaller population. Sample size calculation will also differ with different margins of error.

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Statistical consulting provides a priori sample size calculation, to tell you how many participants you need, and sample size justification, to justify the sample you can obtain. Knowing the appropriate number of participants for your particular study and being able to justify your sample size is important to meet your power and effect size requirements. Using the appropriate power and establishing the effect size will tell you how many people you need to find statistically significant results. Power and effect size measurements are also important to lending credibility to your study and are easily calculated by the experts at Statistics Solutions. Sample size justification is as important as the sample size calculation. If the sample size cannot be accurately justified, the researcher will not be able to make a valid inference. Statistics Solutions can assist with determining the sample size / power analysis for your research study. To learn more, visit our webpage on sample size / power analysis, or contact us today.

**Tools to Calculate Sample Size and Power Analysis**

Statistics Solutions offers tools to calculate sample size for populations and power analysis for your dissertation or research study. Our sample size for populations calculator is available for free with signup at our Basic Membership webpage. The Sample Size/Power Analysis Calculator with Write-up is a tool for anyone struggling with power analysis. Simply identify the test to be conducted and the degrees of freedom where applicable (explained in the document), and the sample size/power analysis calculator will calculate your sample size for a power of .80 of an alpha of .05 for small, medium and large effect sizes. The sample size/power analysis calculator then presents the write-up with references which can easily be integrated in your dissertation document. Click here for a sample. For questions about these or any of our products and services, please email info@statisticssolutions.com or call 877-437-8622.

**Additional Resource Pages Related to Sample Size Calculation and Sample Size Justification:**

- Sample Size / Power Analysis
- Statistical Power Analysis
- Sampling
- Resampling
- Monte Carlo Methods
- Sample Size Formula
- Standard Error

**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.