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Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range
Open accessAbstract
The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a statistical technique widely used in evidence-based medicine for analytically combining the findings from independent clinical trials to provide an overall estimation of a treatment effectiveness. The sample mean and standard deviation are two commonly used statistics in meta-analysis but some trials use the median, the minimum and maximum values, or sometimes the first and third quartiles to report the results. Thus, to pool results in a consistent format, researchers need to transform those information back to the sample mean and standard deviation. In this article, we investigate the optimal estimation of the sample mean for meta-analysis from both theoretical and empirical perspectives. A major drawback in the literature is that the sample size, needless to say its importance, is either ignored or used in a stepwise but somewhat arbitrary manner, e.g. the famous method proposed by Hozo et al. We solve this issue by incorporating the sample size in a smoothly changing weight in the estimators to reach the optimal estimation. Our proposed estimators not only improve the existing ones significantly but also share the same virtue of the simplicity. The real data application indicates that our proposed estimators are capable to serve as "rules of thumb" and will be widely applied in evidence-based medicine.
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“When studies reported a median and interquartile range, we estimated the mean and standard deviation (SD) using conventional formulae (Luo et al., 2018;Wan et al., 2014).When both of these were absent, we estimated the standard deviation using prognostic imputation (Ma et al., 2008).”
From Decision making capacity for treatment in psychiatric inpatients: a systematic review and meta-analysis (2024) · cites this paper as Luo et al., 2018
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Citations
Cites
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,417
Measuring inconsistency in meta-analyses
Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003) · BMJ · doi:10.1136/bmj.327.7414.557 · Cited by 63,139 · cited 1×
“ods seem to be close to each other, we found that the I2 indices for heterogeneity between studies are quite different (i.e., 48.54% from Hozo et al.’s method and 34.85% from our method). According to Higgins et al. (2003), the value 48.54% of I2 is very close to moderate heterogeneity level while the value 34.85% is c…”
MethodInfluentialStatistical Power Analysis for the Behavioral Sciences
Cohen, J. (2013) · doi:10.4324/9780203771587 · Cited by 25,373
Wan, X., Wang, W., Liu, J., & Tong, T. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-135 · Cited by 11,735 · cited 3×
“Finally, by plugging the approximation formula (6) into the estimator (4), we propose the estimator for Scenario S1 as XðwÞ 4 4þ n0:75 aþ b 2 þ n 0:75”
BackgroundMethodSelf-citationEstimating the mean and variance from the median, range, and the size of a sample
Hozo, S. P., Djulbegovic, B., & Hozo, I. (2005) · BMC Medical Research Methodology · doi:10.1186/1471-2288-5-13 · Cited by 9,062
Guyatt, G. H. (1992) · JAMA · doi:10.1001/jama.1992.03490170092032 · Cited by 4,577 · cited 4×
“’s method has a change point near n1⁄4 25 (as suggested in (1)), especially for log-normal distribution and exponential distribution.”
BackgroundMethodInfluentialWilkinson, R. J., Llewelyn, M., Toossi, Z., Patel, P., Pasvol, G., Lalvani, A., Wright, D. J., Latif, M., & Davidson, R. N. (2000) · The Lancet · doi:10.1016/s0140-6736(99)02301-6 · Cited by 768
Low serum vitamin D levels and tuberculosis: a systematic review and meta-analysis
Nnoaham, K. E., & Clarke, A. (2008) · International Journal of Epidemiology · doi:10.1093/ije/dym247 · Cited by 682
Relations, Bounds and Approximations for Order Statistics
Arnold, B. C., & Balakrishnan, N. (1989) · Lecture notes in statistics · doi:10.1007/978-1-4612-3644-3 · Cited by 243
Johnson, R. R. (1976) · UCLA Biblioteca de Ingenieria Civil · Cited by 160
Research works printed but not linked: 4
- Davies P, 1987, Eur J Resp Dis, 71, 341
- Davies P, 1988, Int Med J Thailand, 4, 45
- Chan T, 1994, J Trop Med Hygiene, 97, 26
- Sasidharan P, 2002, J Assoc Phys India, 50, 554
Cited by
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Leybourne, D. J., & Aradottir, G. I. (2022) · Scientific Reports · doi:10.1038/s41598-022-20741-3 · Cited by 30
Chen, B.-K., Liu, Y., Chen, C.-C., Chen, Y., Kuo, Y., & Huang, S.-W. (2023) · Journal of Orthopaedic Surgery and Research · doi:10.1186/s13018-023-03516-y · Cited by 26
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Zhang, F., Dai, M., Yang, X., Cheng, Y., Ye, L., Huang, W., Chen, X., Yin, T., & Sha, Y.-W. (2023) · Andrology · doi:10.1111/andr.13448 · Cited by 26
“24,25 The Newcastle–Ottawa Scale (NOS) for quality assessment of retrospective case–control studies was used by two authors (Feng Zhang and Xinyuan Yang) 26 ; the detailed evaluation processes are presented in Table S2.”
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“Medians and ranges or interquartile ranges were converted to means and standard deviations using algorithms described by Luo et al .”
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Lin, W., Wang, J.-X., & Liu, Y.-J. (2024) · Systematic Reviews · doi:10.1186/s13643-024-02460-0 · Cited by 27
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Chen, S., Gao, J., Zhou, Y., Zheng, B., Liu, Y., Cao, M., Huang, H., Su, X., & Chen, J. (2024) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/s12984-024-01462-2 · Cited by 26
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MethodSnoek, M. A. J., van den Berg, V. J., Dahan, A., & Boon, M. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2024.09.020 · Cited by 26
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Shou, S., Maolan, A., Zhang, D., Jiang, X., Liu, F., Li, Y., Zhang, X., Geer, E., Pu, Z., Hua, B., et al. (2025) · Experimental Hematology and Oncology · doi:10.1186/s40164-025-00597-9 · Cited by 29
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Dou, Y., Lin, B., Cheng, H., Wang, C., Zhao, M., Zhang, J., & Wu, J. (2019) · Hypertension in Pregnancy · doi:10.1080/10641955.2019.1581215 · Cited by 26
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Li, J., Peng, L., Cao, D., Gou, H., Li, Y., & Wei, Q. (2020) · The Aging Male · doi:10.1080/13685538.2020.1771552 · Cited by 26
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Wu, C., Su, Y., Wu, K.-S., Wu, T., & Yang, C. (2020) · Journal of Clinical Pharmacy and Therapeutics · doi:10.1111/jcpt.13301 · Cited by 27
Wang, L., Xiang, H., Yan, Y., Deng, Z., Li, H., Li, X., & Liu, J. (2021) · Annals of Hematology · doi:10.1007/s00277-020-04376-w · Cited by 26
Self-citationLi, H., Shen, Q.-H., Zhou, X., & Shen, X. (2021) · Journal of International Medical Research · doi:10.1177/0300060521999568 · Cited by 26
“For continuous data described as the median (range) in studies, we converted these data to the mean and standard deviation according to a previously described protocol.(17,18) P< 0.”
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Li, H., Zhang, Q., Wang, J., Gao, S., Li, C., Wang, J., Zhang, S., & Lin, J. (2021) · Clinical Therapeutics · doi:10.1016/j.clinthera.2021.03.023 · Cited by 26
Ayoub‐Charette, S., Chiavaroli, L., Liu, Q., Khan, T. A., Zurbau, A., Au‐Yeung, F., Cheung, A., Ahmed, A., Lee, D., Choo, V. L., et al. (2021) · Journal of Nutrition · doi:10.1093/jn/nxab144 · Cited by 28
Mo, M.-Q., Huang, Z., Liang, Y., Liao, Y., & Xia, N. (2021) · Digestive and Liver Disease · doi:10.1016/j.dld.2021.08.017 · Cited by 26
Su, L., Qu, H., Cao, Y., Zhu, J., Zhang, S., Wu, J., & Jiao, Y. (2021) · Advances in Nutrition · doi:10.1093/advances/nmab127 · Cited by 28
Deng, J., Zhou, F., Heybati, K., Ali, S. H., Zuo, Q., Hou, W., Dhivagaran, T., Ramaraju, H. B., Chang, O., Wong, C. Y., et al. (2021) · Future Virology · doi:10.2217/fvl-2021-0119 · Cited by 29
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Upadhyay, K. D., Viramgami, A., Bagepally, B. S., & Balachandar, R. (2022) · Scientific Reports · doi:10.1038/s41598-022-05976-4 · Cited by 26
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Yan, L., Hu, X., Chen, R., Pan, M., Han, Y., Gao, M., & Liu, H. (2022) · Journal of Clinical Apheresis · doi:10.1002/jca.22018 · Cited by 26
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Zafar, M. I., Mills, K., Baird, C. D., Jiang, H., & Li, H. (2023) · Drugs · doi:10.1007/s40265-023-01853-0 · Cited by 28
Reyniers, P., van Beek, N., Schrijver, F. D., & Goeminne, S. (2023) · Hand surgery & rehabilitation · doi:10.1016/j.hansur.2023.03.006 · Cited by 26
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Zhou, Y., Zheng, C., Wu, P. C., & Zhou, L. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.121998 · Cited by 26
Iftikhar, S., Sameer, H. M., & Zainab (2023) · Frontiers in Neurology · doi:10.3389/fneur.2023.1265789 · Cited by 27
Systematic review on intentional non-medical fentanyl use among people who use drugs
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Ling, L., Gao, F., Zhang, Q., He, T., Zhao, Y., Xing, Y., Yu, Y., & Ji, K. (2019) · BioMed Research International · doi:10.1155/2019/6723917 · Cited by 26
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Yang, K., Pang, K. H., Fan, S., Li, X., Osman, N. I., Chapple, C. R., Zhou, L., & Li, X. (2023) · BMC Urology · doi:10.1186/s12894-023-01313-7 · Cited by 25
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Self-citationMethylene blue in sepsis and septic shock: a systematic review and meta-analysis
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Wu, K., Wang, Z., Zhang, Y., Yao, J., & Zhang, Z. (2020) · ANZ Journal of Surgery · doi:10.1111/ans.15681 · Cited by 25
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Vors, C., Allaire, J., Mejía, S. B., Khan, T. A., Sievenpiper, J. L., & Lamarche, B. (2020) · Advances in Nutrition · doi:10.1093/advances/nmaa086 · Cited by 27
“(27) and SDs were estimated from IQR using the method described by Wan et al.”
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“Rosen, 202122 28 (25-30) 29 (27-33) 4 2 17 21 14 11 12 13 6 3 NR Taylor, 202017 29 (26-39) 31 (28-38) 6 3 NR 10 5 0 0 0 0 6 (3-12) 5 (2-9) Tonelli, 202116 26 (19-36) 28 (20-37) 6 11 NR 8 14 7 30 5 17 20 (3-41) 24 (3-45) Zang, 202019 NR NR 6 17 3 9 8 4 10 28 8 (4-16) 27 (16-54) Abbreviations: APP: awake prone positioni…”
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“The estimated mean and standard deviation of eligible studies were used for meta-analysis [28, 29].”
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“to calculate the mean and standard deviation [28,29].”
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“Data are presented as median (min–max) or median (IQR) and were transformed into mean±SD according to Luo et al [18] and Wan et al [19].”
Partitioning of Persistent Organic Pollutants between Adipose Tissue and Serum in Human Studies
Moriceau, M.-A., Cano-Sancho, G., Kim, M. J., Coumoul, X., Emond, C., Arrebola, J. P., Antignac, J., Audouze, K., & Rousselle, C. (2022) · Toxics · doi:10.3390/toxics11010041 · Cited by 25
“Meta-estimates were appraised using a random-effect meta-analysis approach implemented with the metamean function in the “meta” R package [37,38].”
Zhang, L., Wang, Y., Ye, Y., Gao, J., Zhu, F., & Min, L. (2023) · International Journal of COPD · doi:10.2147/copd.s402506 · Cited by 29
“If means and SD were not provided, we were estimated according to methods from Luo and Wan.17,18 Heterogeneity between studies was evaluated using the χ²-based Q test and quantified by using the I² test, with a significance value of at P<0.10 or I²≥50% respectively.19 If there was no significant heterogeneity, a fixed…”
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Viderman, D., Aubakirova, M., Nabidollayeva, F., Yegembayeva, N., Bilotta, F., Badenes, R., & Abdildin, Y. G. (2023) · Journal of Clinical Medicine · doi:10.3390/jcm12134314 · Cited by 26
“Whenever needed, we used mathematical methods for estimating the sample mean and standard deviation [15,16].”
MethodHeterogeneity in defining multiple trauma: a systematic review of randomized controlled trials
Jeanmougin, T., Cole, E. M., Duceau, B., Raux, M., & James, A. (2023) · Critical Care · doi:10.1186/s13054-023-04637-w · Cited by 25
“When the mean value was not available in full-text article, we use a method developed by Luo et al. to estimate the mean and standard deviation from median and quantiles [18].”
MethodWu, B., Fang, L., Sun, G., & Wang, S. (2023) · Frontiers in Neurology · doi:10.3389/fneur.2023.1118563 · Cited by 25
Soe, K. K., Krikeerati, T., Pheerapanyawaranun, C., Niyomnaitham, S., Phinyo, P., & Thongngarm, T. (2023) · Frontiers in Pharmacology · doi:10.3389/fphar.2023.1184552 · Cited by 25
Du, C., Li, Y., Yin, C.-Y., Luo, X., & Pan, X. (2024) · Andrology · doi:10.1111/andr.13583 · Cited by 24
Kuang, H., Jiang, N., Jia, X., Cui, Z., & Zhao, M. (2024) · Autoimmunity Reviews · doi:10.1016/j.autrev.2024.103531 · Cited by 24
Park, J. Y., Fernandes, A., Park, S. Y., Lim, H., Sayudo, I. F., Leibovitch, L., Machinski, E., & Ha, J. (2024) · European Journal of Orthopaedic Surgery & Traumatology · doi:10.1007/s00590-024-03984-w · Cited by 24
“In cases of missing mean and standard deviation (SD), calculations were derived from the median, minimum, and maximum, following the approach outlined by Luo et al. [12].”
MethodAamir, A. B., Kumari, R., Latif, R., Ahmad, S., Rafique, N., Salem, A. M., Asoom, L. I. A., Alsunni, A. A., Alabdulhadi, A. S., & Chander, S. (2024) · Obesity Reviews · doi:10.1111/obr.13838 · Cited by 24
“If the median and IQR were reported, they were converted to mean and SD, as previously described by Luo et al. 23 and Wan et al., 24 respectively.”
Nocturia in CPAP-Treated Obstructive Sleep Apnea Patients: a Systematic Review and Meta-Analysis
Papadopoulos, V. P., Apergis, N., & Filippou, D. K. (2020) · SN Comprehensive Clinical Medicine · doi:10.1007/s42399-020-00584-7 · Cited by 24
Seo, S. H. B., Carson, D. A., Bhat, S., Varghese, C., Wells, C. I., Bissett, I. P., & O’Grady, G. (2021) · Colorectal Disease · doi:10.1111/codi.15969 · Cited by 25
“Continuous data originally presented as the median and interquartile range (IQR) or range were converted to the mean and SD [19,20].”
MethodNi, H.-J., Hsu, T., Chen, L., Chou, H., Tung, H., Chow, L., & Chen, Y. (2021) · Archives of Gerontology and Geriatrics · doi:10.1016/j.archger.2021.104605 · Cited by 25
Sampsonas, F., Karamouzos, V., Karampitsakos, Τ., Παπαϊωάννου, Ο., Katsaras, M., Lagadinou, M., Zarkadi, E., Malakounidou, E., Velissaris, D., Stratakos, G., et al. (2022) · Frontiers in Medicine · doi:10.3389/fmed.2022.815799 · Cited by 24
Fernández‐de‐las‐Peñas, C., Navarro‐Santana, M. J., Curiel-Montero, F., Plaza‐Manzano, G., Alburquerque‐Sendín, F., & Rodrigues‐de‐Souza, D. P. (2022) · Cephalalgia · doi:10.1177/03331024221084217 · Cited by 24
“Non-parametric data, if provided, were also converted to means and standard deviations (22).”
MethodXie, S., Li, Q., Luk, A. O. Y., Lan, H. Y., Chan, P. K. S., Bayés‐Genís, A., Chan, F. K. L., & Fung, E. (2022) · Biomolecules · doi:10.3390/biom12070934 · Cited by 24
Sharma, D., & Bhaskar, S. M. M. (2022) · Journal of Central Nervous System Disease · doi:10.1177/11795735221110373 · Cited by 24
Salih, S. H., Abdelsalam, S., Hamdan, M., Abdelmaboud, A., Hamzah, M., Hilal, A. M., & Motwakel, A. (2022) · IEEE Access · doi:10.1109/access.2022.3202954 · Cited by 24
“It reflects the hypothetical mean of the study, and accordingly, the average of the phrase that exceeds the hypothetical mean (3) [71] signifies the approval of the sample members on the phrase.”
BackgroundMarčec, R., Dodig, V. M., Radanović, I., & Likić, R. (2022) · Reviews in Medical Virology · doi:10.1002/rmv.2397 · Cited by 23
“If a study reported median and interquartile range (IQR) values, the mean and SD values were estimated by an online calculator (https://tinyurl.com/2p9db7mk) using methods described by Luo et al.15 and Wan et al.16 One author (IR) conducted the risk of bias assessment using the RoB‐217 tool for randomised studies and…”
MethodHowell, M. J., Avidan, A. Y., Foldvary‐Schaefer, N., Malkani, R. G., During, E., Roland, J. P., McCarter, S. J., Zak, R., Carandang, G., Kazmi, U., et al. (2022) · Journal of Clinical Sleep Medicine · doi:10.5664/jcsm.10426 · Cited by 24
Gupta, R., Mahmoudi, E., Behnoush, A. H., Khalaji, A., Malik, A. H., Sood, A., Bandyopadhyay, D., Zaid, S., Goel, A., Sreenivasan, J., et al. (2023) · Progress in Cardiovascular Diseases · doi:10.1016/j.pcad.2022.12.006 · Cited by 24
Comparison of dexmedetomidine and propofol for sedation in awake craniotomy: A meta-analysis
Viderman, D., Nabidollayeva, F., Bilotta, F., & Abdildin, Y. G. (2023) · Clinical Neurology and Neurosurgery · doi:10.1016/j.clineuro.2023.107623 · Cited by 24
Grasmann, J., Almenräder, F., Voracek, M., & Tran, U. S. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms24054445 · Cited by 26
Monteiro, E. B., Ajackson, M., Stockler‐Pinto, M. B., Guebre‐Egziabher, F., Daleprane, J. B., & Soulage, C. O. (2023) · Life Sciences · doi:10.1016/j.lfs.2023.121664 · Cited by 24
Fijan, S., Kolč, N., Hrašovec, M., Jamtvedt, G., Pogačar, M. Š., Turk, D. M., & Maver, U. (2023) · Pharmaceutics · doi:10.3390/pharmaceutics15041256 · Cited by 28
High-intensity laser therapy in low back pain management: a systematic review with meta-analysis
Abdildin, Y. G., Tapinova, K., Jyeniskhan, N., & Viderman, D. (2023) · Lasers in Medical Science · doi:10.1007/s10103-023-03827-w · Cited by 28
“When necessary, some statistics were estimated using the existing methods [18, 19].”
Chi, M., Nie, Y., Su, Y., Wang, N., Li, A., Ma, T., & Hou, Y. (2023) · European Journal of Preventive Cardiology · doi:10.1093/eurjpc/zwad284 · Cited by 26
Pradeilles, R., Norris, T., Sellem, L., & Markey, O. (2023) · Advances in Nutrition · doi:10.1016/j.advnut.2023.09.003 · Cited by 24
“…data (timepoint or not presented as mean (cid:5) SD) were obtained either by contacting the authors of the original full-text articles [31,32], by converting SEs to SDs [33], or by closest approximation of mean and SD from median and interquartile range values, using previous guidance [34,35].”
MethodZhang, Y., Peng, M., Wei, J., Huang, J., Ma, W., & Li, Y. (2023) · BMJ Open · doi:10.1136/bmjopen-2022-071253 · Cited by 24
Metadata
- Authors
- Luo, D., Wan, X., Liu, J., & Tong, T.
- Affiliations
- Hong Kong Baptist University (HK)
- Corresponding author
- Wan, Xiang
- Venue
- Statistical Methods in Medical Research
- Publisher
- SAGE Publications
- Published
- 2016-09-27
- Volume
- 27
- Issue
- 6
- Pages
- 1785-1805
- ISSN
- 0962-2802 (ISSN-L)
- 1477-0334
- OpenAlex
- W1534181333
- Cited by
- 4,066
- References
- 21
- Citations by year
- 2026: 789 · 2025: 833 · 2024: 700 · 2023: 601 · 2022: 462 · 2021: 379 · 2020: 188 · 2019: 91 · 2018: 20 · 2017: 1
- FWCI
- 34.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Methods in Medical Research (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Hong Kong Baptist University (FRG2/14-15/077, FRG1/14-15/084, FRG2/15-16/019)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- sample mean estimation, meta-analysis, median, sample size, standard deviation estimation, optimal estimators, evidence-based medicine
- MeSH terms
- Algorithms, Sampling Studies, Meta-Analysis as Topic, Sample Size, Evidence-Based Medicine
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