The Importance of Beta, the Type II Error and Sample Size in the Design and Interpretation of the Randomized Control Trial: Survey of 71 Negative Trials
Abstract
Seventy-one "negative" randomized control trials were re-examined to determine if the investigators had studied large enough samples to give a high probability (greater than 0.90) of detecting a 25 per cent and 50 per cent therapeutic improvement in the response. Sixty-seven of the trials had a greater than 10 per cent risk of missing a true 25 per cent therapeutic improvement, and with the same risk, 50 of the trials could have missed a 50 per cent improvement. Estimates of 90 per cent confidence intervals for the true improvement in each trial showed that in 57 of these "negative" trials, a potential 25 per cent improvement was possible, and 34 of the trials showed a potential 50 per cent improvement. Many of the therapies labeled as "no different from control" in trials using inadequate samples have not received a fair test. Concern for the probability of missing an important therapeutic improvement because of small sample sizes deserves more attention in the planning of clinical trials.
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Considering limited resources and budget, sample size calculation and power analysis may require a trade-off between cost-effectiveness and power.
“For this reason, considering limited resources and budget, sample size calculation and power analysis may require a trade-off between cost-effectiveness and power [3,4].”
From Sample size determination and power analysis using the G*Power software (2021) · cites this paper as [4]
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- Authors
- Freiman, J. A., Chalmers, T. C., Smith, H., & Kuebler, R. R.
- ORCID
- Smith, Harry
- Venue
- New England Journal of Medicine
- Publisher
- Massachusetts Medical Society
- Published
- 1978-09-28
- Volume
- 299
- Issue
- 13
- Pages
- 690-694
- ISSN
- 0028-4793 (ISSN-L)
- 1533-4406
- OpenAlex
- W1970046651
- Cited by
- 1,628
- References
- 5
- Citations by year
- 2026: 8 · 2025: 11 · 2024: 14 · 2023: 14 · 2022: 13 · 2021: 30 · 2020: 14 · 2019: 22 · 2018: 52 · 2017: 22 · 2016: 25 · 2015: 24 · 2014: 22 · 2013: 30 · 2012: 30
- FWCI
- 61.86
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- New England Journal of Medicine (publishedVersion)
- PubMed (publishedVersion)
- DigitalGeorgetown (Georgetown University Library) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- type II error, sample size, randomized controlled trials, negative trial results, statistical power, confidence intervals, clinical trial design, trial interpretation
- MeSH terms
- Clinical Trials as Topic, Humans, Probability, Research, Research Design, Therapeutics
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.
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