The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Optimally estimating the sample standard deviation from the five‐number summary
Open accessAbstract
When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. For these studies, when included in a meta‐analysis, it is often desired to convert the five‐number summary back to the sample mean and SD. For this purpose, several methods have been proposed in the recent literature and they are increasingly used nowadays. In this article, we propose to further advance the literature by developing a smoothly weighted estimator for the sample SD that fully utilizes the sample size information. For ease of implementation, we also derive an approximation formula for the optimal weight, as well as a shortcut formula for the sample SD. Numerical results show that our new estimator provides a more accurate estimate for normal data and also performs favorably for non‐normal data. Together with the optimal sample mean estimator in Luo et al., our new methods have dramatically improved the existing methods for data transformation, and they are capable to serve as “rules of thumb” in meta‐analysis for studies reported with the five‐number summary. Finally for practical use, an Excel spreadsheet and an online calculator are also provided for implementing our optimal estimators.
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Cites
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Self-citationBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2021) · doi:10.1002/9781119558378 · Cited by 9,799
Luo, D., Wan, X., Liu, J., & Tong, T. (2018) · Statistical Methods in Medical Research · doi:10.1177/0962280216669183 · Cited by 4,066 · cited 2×
“To have an approximation formula for the optimal weight, we numerically compute the true values of J(n) and wopt(n) for different values of n using formulas (7) and (8).”
BackgroundMethodSelf-citationQuantitative Synthesis in Systematic Reviews
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“Note that the new estimator is a weighted combination of estimators (2) and (3).”
BackgroundMethodInfluential
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Cited by
Danopoulos, E., Jenner, L. C., Twiddy, M., & Rotchell, J. M. (2020) · Environmental Health Perspectives · doi:10.1289/ehp7171 · Cited by 302
“When needed, the conversion of the fi ve-number summary (sample minimum and maximum, median, lower and upper quartile) to the quantities needed for this review, was made using the methods and calculator developed by Shi et al. (2020).”
Falz, R., Bischoff, C., Thieme, R., Lässing, J., Mehdorn, M., Stelzner, S., Busse, M., & Gockel, I. (2022) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-022-04088-w · Cited by 104
Protein intake and physical function in older adults: A systematic review and meta-analysis
Coelho-Júnior, H. J., Calvani, R., Tosato, M., Landi, F., Picca, A., & Marzetti, E. (2022) · Ageing Research Reviews · doi:10.1016/j.arr.2022.101731 · Cited by 86
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Liao, Y., Chiu, H., Huang, F., Chang, Y., Huang, Y., Wei, P., Wang, W., Hung, C., & Tung, H. (2025) · Journal of the American Geriatrics Society · doi:10.1111/jgs.19425 · Cited by 34
Metadata
- Authors
- Shi, J., Luo, D., Weng, H., Zeng, X., Lin, L., Chu, H., & Tong, T.
- Venue
- Research Synthesis Methods
- Publisher
- Wiley
- Published
- 2020-07-25
- Volume
- 11
- Issue
- 5
- Pages
- 641-654
- ISSN
- 1759-2879 (ISSN-L)
- 1759-2887
- OpenAlex
- W3036368019
- Cited by
- 611
- References
- 6
- FWCI
- 35.04
- Type
- journal article
- Language
- en
- Open access
- green
- Funders
- General Research Fund of Shanghai Normal University (HKBU12303918)
- National Natural Science Foundation of China (11671338, 11971265)
- Hong Kong Baptist University
- U.S. National Library of Medicine (R01LM012982)
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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