Cited by 842Meta-analysis and systematic reviewsStatistical Methods in Clinical TrialsDelphi Technique in Research

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Mean Difference, Standardized Mean Difference (SMD), and Their Use in Meta-Analysis: As Simple as It Gets

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Andrade, Chittaranjan·2020·The Journal of Clinical Psychiatry

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Abstract

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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Implementing Oral Antibiotics for Bone and Joint Infections: Lessons Learned and Opportunities for Improvement
Hawkins, M. R., Thottacherry, E. D., Juthani, P. V., Aronson, J., Chang, A., Amanatullah, D. F., Kittle, J. T., Shen, S., Holubar, M. K., Andrews, J. R., et al. (2024) · Open Forum Infectious Diseases · doi:10.1093/ofid/ofae683 · Cited by 17
“An SMD of 0.2 to 0.5 indicated a small imbalance, 0.5 to 0.8 medium, and > 0.8 large [10].”
Influential
Duration of untreated or undiagnosed bipolar disorder and clinical characteristics and outcomes: systematic review and meta-analysis
Keramatian, K., Pinto, J. V., Tsang, V. W. L., Chakrabarty, T., & Yatham, L. N. (2025) · The British Journal of Psychiatry · doi:10.1192/bjp.2025.63 · Cited by 17
“27 The significance level was set at 0.05.”
Influential
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The Effectiveness of Physical Exercise After Lumbar Fusion Surgery: A Systematic Review and Meta-Analysis
Özden, F. (2022) · World Neurosurgery · doi:10.1016/j.wneu.2022.03.143 · Cited by 17
Effectiveness of prone position in acute respiratory distress syndrome and moderating factors of obesity class and treatment durations for COVID-19 patients: A meta-analysis
Ashra, F., Chen, R., Kang, X. L., Chiang, K., Pien, L., Jen, H., Liu, D., Hsiao, S. S., & Chou, K. (2022) · Intensive and Critical Care Nursing · doi:10.1016/j.iccn.2022.103257 · Cited by 17
“…session Length of therapy: 1 day Total time: 16 hours Intervention time from admission: NA PEEP Ventilator PaO2/ FiO2 Baseline and 16 h after prone 2 Avdeev et al., 2021 Prospective cohort study Russia NonICU 22 Age: Mean = 48.5 Range = 39.8–62.8 Gender: M = 16 F = 6 Mean BMI: 28.7 Comorbidities:…”
Influential
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Effectiveness of respiratory rehabilitation in patients with COVID ‐19: A meta‐analysis
Ashra, F., Jen, H., Liu, D., Lee, T., Pien, L., Chen, R., Lin, H., & Chou, K. (2023) · Journal of Clinical Nursing · doi:10.1111/jocn.16692 · Cited by 18
Circulating Pulmonary-Originated Epithelial Biomarkers for Acute Respiratory Distress Syndrome: A Systematic Review and Meta-Analysis
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“SMD is the quotient of the difference between the two means and the pooled standard deviation, which eliminates the effect of different units in the analysis [36].”
Background
Effectiveness of electrophysical agents in subjects with frozen shoulder: a systematic review and meta-analysis
Brindisino, F., Girardi, G., Crestani, M., Fiore, A., Giovannico, G., Garzonio, F., Venturin, D., & Struyf, F. (2023) · Disability and Rehabilitation · doi:10.1080/09638288.2023.2251880 · Cited by 17
“SMD values of 0.2–0.5 could be considered as small, values of 0.5–0.8 as medium, and values >0.8 as large [36].”
Influential
The Kynurenine Pathway in Attention-Deficit/Hyperactivity Disorder: A Systematic Review and Meta-Analysis of Blood Concentrations of Tryptophan and Its Catabolites
Cavaleri, D., Crocamo, C., Morello, P., Bartoli, F., & Carrà, G. (2024) · Journal of Clinical Medicine · doi:10.3390/jcm13020583 · Cited by 17
“Effect sizes were evaluated according to standard cut-offs for SMDs (0.2: small; 0.5: medium; 0.8: large effect) [33].”
MethodInfluential
Efficacy and safety of esketamine for perioperative depression in patients undergoing elective surgery: A meta-analysis of randomized controlled trials
Lou, X.-J., Qiu, D., Ren, Z.-Y., Hashimoto, K., Zhang, G.-F., & Yang, J. (2024) · Asian Journal of Psychiatry · doi:10.1016/j.ajp.2024.103997 · Cited by 17
Efficacy of deep brain stimulation for Tourette syndrome and its comorbidities: A meta-analysis
Zhang, A., Liu, T., Xu, J., Zhao, Q., Wang, X., Jiang, Z., Liang, S., Cui, Y., & Li, Y. (2024) · Neurotherapeutics · doi:10.1016/j.neurot.2024.e00360 · Cited by 17
“For the secondary outcomes, the mean improvement in the severity of OCB, depression symptoms, or anxiety symptoms was measured using the standardized mean difference (SMD) [19].”
Method
Effect of zinc supplementation on glycemic biomarkers: an umbrella of interventional meta-analyses
Daneshvar, M., Ghaheri, M., Safarzadeh, D., Karimi, F., Adib-Hajbagheri, P., Ahmadzade, M., & Haedi, A. R. (2024) · Diabetology & Metabolic Syndrome · doi:10.1186/s13098-024-01366-0 · Cited by 17
“Since SMD adjusts results based on SD, in some analyzes results from WMD differed from SMD, which could be due to wide SD range [32].”
Risk of Incident Atrial Fibrillation in Women With a History of Hypertensive Disorders of Pregnancy: A Population-Based Retrospective Cohort Study
Johnston, A., Petrcich, W., Smith, G. N., Fell, D. B., Tanuseputro, P., Coutinho, T. A., & Edwards, J. D. (2025) · Circulation · doi:10.1161/circulationaha.124.072418 · Cited by 18
“37 In this study, ASDs >10% were considered indicative of potentially meaningful differences; however, in line with best practices in causal inference, statistical measures such as the magnitude of ASDs should not be used to classify a variable as a confounder.”
Extracorporeal shock wave therapy shows comparative results with other modalities for the management of plantar fasciitis: A systematic review and meta-analysis
Tung, W. S., Daher, M., Covarrubias, O., Herber, A., & Gianakos, A. L. (2024) · Foot and Ankle Surgery · doi:10.1016/j.fas.2024.11.005 · Cited by 16
Effectiveness of Astaxanthin as a Feed Supplement to Improve Growth Performance and Feed Utilization in Aquaculture Animals: A Meta-Analysis
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“This study employed standardized mean difference (SMD) effect sizes using Hedges’ g with 95% CI to evaluate differences between intervention and control groups, a metric suitable for integrating continuous variables with inconsistent measurement units across studies [29].”
Effects of aquatic exercises on physical fitness and quality of life in postmenopausal women: an updated systematic review and meta-analysis
Zhou, W.-S., Mao, S., Zhang, S., Xu, H., & Li, W.-L. (2023) · Frontiers in Public Health · doi:10.3389/fpubh.2023.1126126 · Cited by 22
“Standardized mean difference (SMD) was employed if there were different outcome measures (49).”
Method
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Fakontis, C., Iakovidis, P., Kasimis, K., Lytras, D., Koutras, G., Fetlis, A., & Algiounidis, I. (2023) · Physical Therapy in Sport · doi:10.1016/j.ptsp.2023.09.009 · Cited by 16
Impact of Varicocele on Testicular Oxidative Stress and Sperm Parameters in Experimental Animals: A Systematic Review and Meta-Analysis
Russo, G. I., Saleh, R. A., Finocchi, F., Juma, A. R., Durairajanayagam, D., Kahraman, O., Söğütdelen, E., Sokolakis, I., Vishwakarma, R. B., Bahar, F., et al. (2024) · The World Journal of Men s Health · doi:10.5534/wjmh.230260 · Cited by 16
“The standardized mean difference (SMD) was chosen as the effect size for statistical comparison between cases and controls to allow comparison between studies that measured the outcome using different instruments [14].”
Influence of nitrous oxide added to general anaesthesia on postoperative mortality and morbidity: a systematic review and meta-analysis
Kampman, J. M., Plasmans, K. Y. Q., Hermanides, J., Hollmann, M. W., Repping, S., & Weiland, N. H. S. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2024.02.011 · Cited by 16
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Yan, Y., Chan, L. M. L., Wang, M. P., Kwok, J. Y. Y., Anderson, C. S., & Lee, J. J. (2024) · npj Digital Medicine · doi:10.1038/s41746-024-01067-y · Cited by 20
“In this review, a negative g indicates the intervention group mean is lower than the control mean 52 , with the absolute value of g = 0.2, 0.5, and 0.8 for small, medium, and large effects, respectively 53 .”
BackgroundInfluential
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Lu, Q., Liang, Q., & Xi, Y. (2024) · Frontiers in Nutrition · doi:10.3389/fnut.2024.1419747 · Cited by 16
Enhanced renoprotective effects of combined glucagon‐like peptide‐1 receptor agonists and sodium‐glucose cotransporter 2 inhibitors in type 2 diabetes mellitus: Real‐world evidence
Jhu, J., Fang, Y., Huang, C., Liou, H., Chen, M., & Tsai, M. (2024) · Journal of Diabetes Investigation · doi:10.1111/jdi.14361 · Cited by 17
“Standardized mean differences (SMD) were also assessed, with a SMD of 0.1 indicating a minor difference between groups 24,25 .”
Influential
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“MD was computed instead of standardized mean differences, as all FMD data across studies used the same unit of percent 19 .”
Method
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Zhu, M., Wong, S. Y. S., Zhong, C. C., Zeng, Y., Xie, L., Lee, E. K. P., Chung, V. C., & Sit, R. W. S. (2025) · Journal of Psychosomatic Research · doi:10.1016/j.jpsychores.2025.112061 · Cited by 16
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“The inverse variance method using a ﬁxed-eﬀects model was applied to calculate the mean diﬀer-ence (MD) and the standardised mean diﬀerence (SMD), since the same outcomes were assessed using diﬀerent tools in the included studies [37].”
Glucagon-Like Peptide-1 Receptor Agonists and Age-Related Macular Degeneration.
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“…experimental group and the mean of the control group; SMD is the MD divided by the standard deviations; RR is the ratio of the incidence of events in the experimental group to the incidence of events in the control group; I2 is a percentage to reflect heterogeneity between studies) [Andrade, 2020].”
Result
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“Standardized mean difference (SMD, Cohen’s d) [27] was calculated for pooling of studies with either PANSS-N or SANS scale measurement after iTBS treatment using the inverse variance random effects model in Review Manager 5.4.”
MethodInfluential
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Ieong, C., Chen, T., Chen, S., Gao, X., Yan, K., He, W., Hong, H., Gu, Y., Chen, X., & Yuan, G. (2024) · BMC Geriatrics · doi:10.1186/s12877-024-05197-6 · Cited by 14
“Since different ADB scales were used in each study to calculate ADB, the SMD could eliminate the effect of absolute magnitude and the effect of the metric on the outcome [35].”
Method
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“However,itislargely unknownhowto leveragetheTTEand FLframeworkstoestimatereal-worldtreatmenteffectsusingthedistributed siteswithoutsharingpatient-levelinformation.”
The association between preoperative anxiety and chronic post-surgical pain after general anaesthesia, a systematic review and meta-analysis
Bakker-Bons, M., Hijmering, R. M. J., Soer, R., & Wolff, A. P. (2025) · BJA Open · doi:10.1016/j.bjao.2025.100487 · Cited by 18
“32 For both odds ratio and correlation ( r ), the formulas described by Borenstein and colleagues 29 and Chinn 33 were used.”
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“Considering that the measurements for the same outcome of interest were different across studies, we calculated the standard mean differences (SMDs) to pool the effect size, along with their respective 95% confidence intervals (CI) (Andrade, 2020).”
Method
Effects of high-intensity interval training on vascular function in patients with cardiovascular disease: a systematic review and meta-analysis
Fuertes-Kenneally, L., Blasco‐Peris, C., Casanova‐Lizón, A., Baladzhaeva, S., Climent, V. E., Sarabia, J. M., & Manresa‐Rocamora, A. (2023) · Frontiers in Physiology · doi:10.3389/fphys.2023.1196665 · Cited by 17
“The mean difference (MD) with its 95% confidence interval (CI) was used as the effect size (ES) index, as the eligible studies had to measure relative changes in brachial FMD (inclusion criteria) (Andrade, 2020).”
Method

Authors: Andrade, C.
Affiliations: National Institute of Mental Health and Neurosciences (IN)
Corresponding author: Andrade, Chittaranjan
ORCID: 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
DOI: 10.4088/jcp.20f13681
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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Mean Difference, Standardized Mean Difference (SMD), and Their Use in Meta-Analysis: As Simple as It Gets

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