Introduction to Sample Size Choice for Confidence Intervals Based on t Statistics

Abstract

Sample size can be chosen to achieve a specified width in a confidence interval. The probability of obtaining a narrow width given that the confidence interval includes the population parameter is defined as the power of the confidence interval, a concept unfamiliar to many practitioners. This article shows how to utilize the Statistical Analysis System (SAS) proc power procedure to determine an appropriate sample size and achieve sufficient power for a specified confidence interval. Two examples in sport and exercise science are used to illustrate sample size determination for confidence intervals in the dependent and independent t tests. The relevant SAS code and output are provided with detailed annotations. As the use of confidence intervals becomes a more integral part of studies in sport and exercise science, the reporting and analysis of their power should be considered much like that of hypothesis tests.

Keywords:

• sample size
• confidence interval
• SAS