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Mean Difference, Standardized Mean Difference (SMD), and Their Use in Meta-Analysis: As Simple as It Gets
Open accessAbstract
In randomized controlled trials (RCTs), endpoint scores, or change scores representing the difference between endpoint and baseline, are values of interest. These values are compared between experimental and control groups, yielding a mean difference between the experimental and control groups for each outcome that is compared. When the mean difference values for a specified outcome, obtained from different RCTs, are all in the same unit (such as when they were all obtained using the same rating instrument), they can be pooled in meta-analysis to yield a summary estimate that is also known as a mean difference (MD). Because pooling of the mean difference from individual RCTs is done after weighting the values for precision, this pooled MD is also known as the weighted mean difference (WMD). Sometimes, different studies use different rating instruments to measure the same outcome; that is, the units of measurement for the outcome of interest are different across studies. In such cases, the mean differences from the different RCTs cannot be pooled. However, these mean differences can be divided by their respective standard deviations (SDs) to yield a statistic known as the standardized mean difference (SMD). The SD that is used as the divisor is usually either the pooled SD or the SD of the control group; in the former instance, the SMD is known as Cohen's d, and in the latter instance, as Glass' delta. SMDs of 0.2, 0.5, and 0.8 are considered small, medium, and large, respectively. SMDs can be pooled in meta-analysis because the unit is uniform across studies. This article presents and explains the different terms and concepts with the help of simple examples.
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InfluentialPhenotypic plasticity in visual opsin gene expression: a meta-analysis in teleost fish
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“Therefore, in this context, SMD and ES were equivalent [40–42].”
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“Effect sizes of 0.2 − 0.5 are considered small, 0.5 − 0.8 moderate, and > 0.8 large in psychopharmacology studies [40].”
BackgroundInfluentialExpanding Affordable Middle Housing Options in Single-Family Neighborhoods
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“SMDs of 0.2, 0.5, and 0.8 are indicative of small, medium, and large differences, respectively (Andrade, 2020).”
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Huang, X., Du, C., Yang, Q., & Fan, D. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2022.938256 · Cited by 10
Robledo, D. A., Prudente, M. S., Aguja, S. E., & Iwata, H. (2023) · Current Research in Toxicology · doi:10.1016/j.crtox.2023.100131 · Cited by 8
Sobeeh, M. G., Hassan, K. A., Silva, A. G., & Bruehl, S. P. (2023) · Pain Medicine · doi:10.1093/pm/pnad144 · Cited by 7
He, B., Wang, X., Liguo, S., Cheng, H., & Zhao, L. (2024) · Biomarkers in Medicine · doi:10.2217/bmm-2023-0605 · Cited by 8
Unoki, Y., Ono, S., Sasabuchi, Y., Hashimoto, Y., Yasunaga, H., & Yokota, I. (2024) · BMC Health Services Research · doi:10.1186/s12913-024-10763-0 · Cited by 8
“Standardized differences were calculated to evaluate differences in baseline characteristics., with a difference within the range of − 0.2 to 0.2 considered negligible [45].”
MethodInfluentialTrends and associated outcomes of fat embolism after trauma surgery
Ali, K., Cho, N. Y., Tran, Z. K., Kim, S., Sakowitz, S., Curry, J., Balian, J., & Benharash, P. (2024) · Surgery · doi:10.1016/j.surg.2024.04.008 · Cited by 8
Malik, M. I., Bilal, M., Anwar, M. Z., Hassan, T., Rashid, M. A., Tarla, D. N., Dunshea, F. R., & Cheng, L. (2024) · Journal of Animal Science · doi:10.1093/jas/skae241 · Cited by 10
“To determine the SMD, the treatment mean was subtracted from the con-trol mean, then the result was divided by the pooled standard deviation (Andrade, 2020).”
MethodCorrea, E., Michelogiannakis, D., Barmak, A. B., Rossouw, P. E., & Javed, F. (2024) · Orthodontics and Craniofacial Research · doi:10.1111/ocr.12868 · Cited by 8
Ali, M., Rosales, R. S., Brogren, E., Waldén, M., Nordenskjöld, J., & Atroshi, I. (2024) · EFORT Open Reviews · doi:10.1530/eor-23-0212 · Cited by 8
“The SMD is used in meta-analyses when the included studies assess an outcome using different outcome measures in order to unify the outcome measures and express the clinical impact of the examined factor (38).”
Tavares, V. D. D. O., Cuthbert, C. A., Teychenne, M. J., Schuch, F. B., Cabral, D. A. R., de Sousa, G. M., Prado, C. M. M., Patten, S. B., Coelho, N. L. G., & Hallgren, M. Å. (2024) · Journal of Psychosocial Oncology · doi:10.1080/07347332.2024.2441693 · Cited by 8
“34 We examined between-study variability for heterogeneity, using the I 2 statistic for quantifying inconsistency.”
Altamimi, R., Alnajjar, D., Salamah, R. A. B., Mandoorah, J., Al-Ghamdi, A. M., Aloteibi, R. E., Almusharaf, L., & Albabtain, B. (2025) · Journal of Clinical Medicine · doi:10.3390/jcm14030679 · Cited by 8
Roncero, D., Moreno‐Fernández, R. D., & Fernández-Moreno, Á. (2025) · Aggression and Violent Behavior · doi:10.1016/j.avb.2025.102034 · Cited by 8
Jazayeri, S. B., Zamarud, A., Derhab, M., Ghozy, S. A., Mirbeyk, M., Heit, J. J., & Kallmes, D. F. (2025) · Journal of NeuroInterventional Surgery · doi:10.1136/jnis-2024-023000 · Cited by 8
“19 Data conversion was done if necessary to calculate means and standard deviation (SD) from other data frames, using the DECoMA tool.”
Li, Y., Liu, M., Yang, J., Liu, Q., Zhou, W., Yu, J., Wang, X., & Wang, C. (2025) · Ageing Research Reviews · doi:10.1016/j.arr.2025.102819 · Cited by 10
Niyazova, G. Z., Duisekeyeva, B., Berdi, D., Usembayeva, I. B., & Миндетбаева, А. А. (2026) · Frontiers in Education · doi:10.3389/feduc.2026.1754080 · Cited by 18
Kast, S., Jakob, F. J., Kohl, M., von Stengel, S., Kerschan‐Schindl, K., Lange, U., Thomasius, F. E., & KEMMLER, W. K. (2022) · Rheumatology Advances in Practice · doi:10.1093/rap/rkad019 · Cited by 9
“8 were considered as small, medium and large effects [24].”
BackgroundA Meta-Analysis of Influencing Factors on the Activity of BiVO4-Based Photocatalysts
Che, R., Zhu, Y., Tu, B., Miao, J., Dong, Z., Liu, M., Wang, Y., Li, J., Chen, S., & Wang, F. (2023) · Nanomaterials · doi:10.3390/nano13162352 · Cited by 8
“model for analysis, the selected trials were measured inconsistently and in different units of measure, so standardized mean difference (SMD) was used to express the results of each test variable between the experimental and control groups [84].”
MethodNeurobehavioral effects of fungicides in zebrafish: a systematic review and meta-analysis
Reis, C. G., Bastos, L. M., Chitolina, R., Gallas‐Lopes, M., Zanona, Q. K., Becker, S. Z., Herrmann, A. P., & Piato, Â. (2023) · Scientific Reports · doi:10.1038/s41598-023-45350-6 · Cited by 10
“We also ran meta-analyses excluding studies containing experiments with atypically high SMD as seen in the forest plots (Andrade, 2020).”
MethodQin, Z., Zizhao, G., & Junsheng, W. (2023) · Disability and Rehabilitation · doi:10.1080/09638288.2023.2288931 · Cited by 8
“The measurement method, exercise time, exercise cycle, and exercise type used for dynamic balance and mobility-related indicators were standardized mean difference (SMD) and 95% confidence interval (CI) as effect values [27].”
Harrington, K. M., Quaden, R. M., Steele, L., Helmer, D. A., Hauser, E. R., Ahmed, S. T., Aslan, M., Radhakrishnan, K., Honerlaw, J. P., Nguyen, X. T., et al. (2024) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph21010072 · Cited by 8
“Given the large sample size of this study, we chose to report SMD as a measure of the magnitude of group differences because large samples render p -values considerably less meaningful [34,35].”
BackgroundInfluentialChen, X., Zhang, W., Cheng, B., Yu, Y.-L., Peng, J.-L., Bao, S.-H., Tong, C.-G., & Zhao, J. (2024) · International Journal of Surgery · doi:10.1097/js9.0000000000001027 · Cited by 8
“An SMD of less than 10% represented a negligible demographic difference [35] .”
Background
Metadata
- Authors
- Andrade, C.
- Affiliations
- National Institute of Mental Health and Neurosciences (IN)
- Corresponding author
- Andrade, Chittaranjan
- Venue
- The Journal of Clinical Psychiatry
- Publisher
- Physicians Postgraduate Press, Inc
- Published
- 2020-09-22
- Volume
- 81
- Issue
- 5
- ISSN
- 0160-6689 (ISSN-L)
- 1555-2101
- OpenAlex
- W3089264828
- Cited by
- 841
- References
- 5
- Citations by year
- 2026: 158 · 2025: 221 · 2024: 199 · 2023: 161 · 2022: 77 · 2021: 25
- FWCI
- 40.09
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Clinical Psychiatry (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Social Sciences › Sociology and Political Science › Delphi Technique in Research
- Keywords
- mean difference, standardized mean difference, Cohen's d, effect size, meta-analysis, change scores, rating instruments, effect size heterogeneity
- MeSH terms
- Data Interpretation, Statistical, Humans, Statistics as Topic, Meta-Analysis as Topic
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