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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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“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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Metadata
- 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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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