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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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“There were no differences in HbA1c levels in pediatric T2DM patients with NAFLD vs. those without NAFLD (87).”
The use of small-arms stability measures in combat shooting assessments
Coleman, J. L., Davey, P. C., McClelland, J. A., & Middleton, K. J. (2024) · Applied Ergonomics · doi:10.1016/j.apergo.2024.104385 · Cited by 5
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“…between cases and controls were small, as indicated by standardized mean difference (SMD) values according to the criteria described by Andrade [37]: SMD values between 0.2 and 0.5 were defined as small values, those between 0.5 and 0.8 as medium values, and those greater than 0.8 as large…”
InfluentialMeta-analyses of executive function deficits in chemotherapy-treated rodent models
Chen, W., & Johnston, I. N. (2025) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2025.106131 · Cited by 6
“Because different studies use different behavioural parameters and units of measurement, we used SMD as the effect size, calculated by dividing the mean differences obtained from individual experiments by their respective SDs (Andrade, 2020).”
Hsiao, C.-C., Chen, M., Liu, C. Y., Chan, C.-Y., Fang, Y.-W., Liou, H., & Tsai, M. (2025) · Clinical Kidney Journal · doi:10.1093/ckj/sfaf172 · Cited by 9
“An SMD value 0.1 was considered to indicate a negligible difference be-tween groups, ensuring comparability [17 , 18 ].”
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“The mean SMD was subsequently derived, with thresholds of > 0.5 and > 0.2 indicating moderate-to-large and small differences, respectively [10].”
InfluentialFavez, L., Simon, M., Bleijlevens, M. H. C., Serdaly, C., & Zúñiga, F. (2022) · Journal of the American Geriatrics Society · doi:10.1111/jgs.17798 · Cited by 5
“8 large.(33) We used boxplots to illustrate the differences in staff opinion levels between the “above-average” units and the “average” units.”
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“In order to combine the measurements for outcomes of interest across different studies, the standardized mean difference (SMD) and 95% confidence interval (95% CI) were employed [18].”
MethodDemography and movement patterns of a freshwater ciliate: The influence of oxygen availability
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Enhanced Outcomes in Type 2 Diabetes Patients With Acute Kidney Disease Through Thiazolidinedione
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“The median follow-up durations were 19.1 months (IQR: 11.3–49.9 months) in the immune cell group and 67.7 months (IQR: 36.8–103.4 months) in the control group.”
InfluentialSingh, S., Sharma, R., Singh, J., Jain, K., & Paul, D. (2021) · Journal of Pediatric Hematology/Oncology · doi:10.1097/mph.0000000000002264 · Cited by 5
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“29 from the test for subgroup differences) (Andrade, 2020).”
BackgroundInfluentialHung, J., Chen, J., & Chen, O. (2023) · PLoS ONE · doi:10.1371/journal.pone.0279278 · Cited by 5
“When building forest plots, the effect size was measured by the standardised mean difference—the difference between the sample means divided by the standard deviation of the outcome [26, 27].”
MethodEffects of Physical Activity on Reducing Depression and Menopausal Symptoms: A Meta-Analysis
Park, S., Han, K. S., & Jang, Y. J. (2023) · Journal of Korean Academy of Psychiatric and Mental Health Nursing · doi:10.12934/jkpmhn.2023.32.3.325 · Cited by 5
“8 was categorized as a large effect size.[26].”
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“In contrast, this meta-analysis emphasizes comparing means and standard deviations before and after interventions, following Andrade ’ s (2020) (Andrade, 2020) methodology for more accurate pre-and post-intervention comparisons within and between groups.”
InfluentialTan, J., Zhang, D., Cheng, L., Liu, N., Jamali, M., Jamloo, H., Farjaminejad, R., Lei, C., Saedisomeolia, A., & Jamilian, A. (2024) · Nutrition Reviews · doi:10.1093/nutrit/nuae190 · Cited by 7
Cardiovascular Health at the Intersection of Race and Gender in Medicare Fee for Service
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Zheng, J., Chen, R., Wang, S., Chen, J., & Lin, X. (2025) · Frontiers in Physiology · doi:10.3389/fphys.2025.1681272 · Cited by 4
“Due to variations in intervention protocols and measurement units among the included studies, all outcome measures were synthesized using a random-effects model and expressed as standardized mean differences (SMD) with 95% confidence intervals (CI) (Borenstein et al., 2010; Andrade, 2020).”
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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