How Appropriate are Popular Sample Size Formulas?
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.
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A sample size estimation was carried out with the R Package MBESS to identify a sample from the reference corpus for further analysis.
“Due to time limitations and the large number of relevant articles in the population, a sample size estimation was carried out with the R Package MBESS (Kelley, Lai, Lai, & Suggests, 2018), to identify a sample from this reference corpus for further analysis (Kupper & Hafner, 1989).”
From Facilitating student engagement through educational technology in higher education: A systematic review in the field of arts and humanities (2020) · cites this paper as Kupper & Hafner, 1989
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BINOMIAL AND POISSON CONFIDENCE INTERVALS AND ITS VARIANTS: A BIBLIOGRAPHY
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Shieh, G. (2017) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2017.10.015 · Cited by 7 · see citing works
- Authors
- Kupper, L. L., & Hafner, K. B.
- Affiliations
- University of North Carolina at Chapel Hill (US)
- ORCID
- Kupper, Lawrence L.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1989-05
- Volume
- 43
- Issue
- 2
- Pages
- 101-105
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2087486280
- Cited by
- 196
- References
- 18
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 7 · 2023: 7 · 2022: 3 · 2021: 2 · 2020: 7 · 2019: 4 · 2018: 5 · 2017: 4 · 2016: 5 · 2015: 3 · 2014: 7 · 2013: 12 · 2012: 8
- FWCI
- 6.14
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The American Statistician (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- sample size determination, sample size formula, large sample approximation, confidence interval width, statistical power, research design, small sample size
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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