How Appropriate are Popular Sample Size Formulas?

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Abstract
One concern in the early stages of study planning and design is the minimum sample size needed to provide statistically credible results. This minimum sample size is usually determined via the use of simple formulas or, equivalently, from tables. The more popular formulas, however, involve large-sample approximations and hence may underestimate required sample sizes. This article provides empirical evidence indicating that this underestimation phenomenon is extreme for certain sample size formulas based on confidence interval width. Common sample size formulas that consider statistical power are also discussed; these are shown to perform quite well, even for small sample size situations. In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.