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  • Explain the basic information needed to calculate sample size

  • Describe additional considerations that may need to be addressed before calculating a sample size

  • Identify examples of available software for power and sample size calculation

  • Demonstrate how to calculate sample size requirements for basic study designs

  • Differentiate between sample size calculations based on precision analysis and power analysis

  • Explain the limitations associated with retrospective power analysis


  • α

  • β

  • Cohen’s d

  • Effect size

  • One-sided test

  • Power

  • Power analysis

  • Precision analysis

  • Retrospective power analysis

  • Standardized effect size

  • Two-sided test

  • Type I error

  • Type II error


In the conduct of research, resources are often limited. Furthermore, ethical standards with respect to research with human subjects require that researchers minimize the number of individuals who are exposed to a research protocol to the number that is needed to accomplish a particular purpose. On the other hand, studies that are smaller than necessary run the risk of generating invalid scientific knowledge while exposing subjects to risks and burdens, which is also considered unethical.1 Thus, it is imperative for researchers to consider sample size needs when planning a project: studies that are too large waste resources and may unnecessarily expose subjects to risks, inconveniences, and burdens with limited additional societal benefit,2 while studies that are too small are underpowered leading to findings that may be invalid, misinterpreted, or never disseminated.

The basic principles of statistics can be used to calculate a justifiable sample size for a study. In addition to obtaining an appropriate and defensible estimate of the number of subjects needed, this process is important for several reasons. It requires researchers, often in collaboration with a statistician, to consider the availability of existing information, the data analysis plan, and the magnitude of the treatment effect considered to be important. Although the final sample size for a study is often affected by the availability of subjects, financial resources, and ethical considerations, sample size calculation is a necessary first step to balance statistical needs with issues of feasibility.

The purpose of this chapter is to introduce the statistical principles underlying sample size calculation. It begins with a few examples of such calculations from the biomedical literature that will be used to subsequently illustrate certain concepts. General principles necessary for understanding sample size estimation are then reviewed, followed by a discussion of needed information when using the method of sample size determination referred to as power analysis. After a brief review of some available software, a few worked examples from basic designs are conducted using a free software program. This chapter concludes with a discussion of some other considerations when estimating sample size for a study.


Many articles in the biomedical literature include information justifying the sample size used in ...

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