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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“, 2011), while standardized mean differences (SMD) were used in metaanalyses, as different instruments were adopted by different studies (Andrade, 2020) and aimed to summarize the effects of different S&C training programs.”
MethodChabert, J., Allauze, E., Pereira, B., Chassain, C., de Chazeron, I., Rotgé, J., Fossati, P., Llorca, P., & Samalin, L. (2022) · International Journal of Molecular Sciences · doi:10.3390/ijms23168974 · Cited by 29 · see citing works
Panchal, H., Athalye‐Jape, G., Rao, S. C., & Patole, S. (2023) · European Journal of Clinical Nutrition · doi:10.1038/s41430-023-01270-2 · Cited by 29 · see citing works
Jing, Y., & Lin, L. (2024) · JBI Evidence Synthesis · doi:10.11124/jbies-23-00368 · Cited by 32 · see citing works
“6 Readers seeking more in-depth information may refer to the review articles by Andrade, 6 Lin and Aloe, 16 and Chapter 6.5 of the Cochrane Handbook, 11 which provide detailed explorations and examples about various SMD estimators.”
BackgroundMethodInfluentialThe efficacy of curcumin in relieving osteoarthritis: A meta‐analysis of meta‐analyses
Bideshki, M. V., Jourabchi‐Ghadim, N., Radkhah, N., Behzadi, M., Asemani, S., Jamilian, P., & Zarezadeh, M. (2024) · Phytotherapy Research · doi:10.1002/ptr.8153 · Cited by 29 · see citing works
“This larger effect size was expected because WMD is dependent on the importance and magnitude of each study (Andrade, 2020).”
BackgroundInfluentialRisk of Glaucoma in Patients without Diabetes Using a Glucagon-Like Peptide 1 Receptor Agonist
Vasu, P., Dorairaj, E. A., Weinreb, R. N., Huang, A. S., & Dorairaj, S. K. (2025) · Ophthalmology · doi:10.1016/j.ophtha.2025.02.011 · Cited by 28 · see citing works
Xie, G., Wang, T., Deng, L., Zhou, L., Zheng, X., Zhao, C., Li, L., Sun, H., Liao, J., & Yuan, K. (2025) · Systematic Reviews · doi:10.1186/s13643-025-02794-3 · Cited by 28 · see citing works
“According to Cochrane guidelines and literature [32, 33], the SMD should be used to evaluate overall effects in specific scenarios to mitigate the impact of inter-study variability on results.”
Zhi-zhong, Y., Ni, J., Teng, Y., Su, M., Wei, M., Li, T., Fan, D., Lü, T., Xie, H., Zhang, W., et al. (2022) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2022.1017882 · Cited by 28 · see citing works
“Before standardization, mean values were multiplied by −1 from some sets of studies to ensure that all scales pointed in the same direction, in which a positive SMD indicated a greater effect of hearing aid use on cognition (Andrade, 2020).”
MethodChen, X., You, J., Ma, H., Zhou, M., & Huang, C. (2023) · BMJ Open · doi:10.1136/bmjopen-2022-062322 · Cited by 30 · see citing works
Lan, H., Wen, J., Mao, Y., Huang, H., Chen, G., & Lin, W. (2022) · Clinical Endocrinology · doi:10.1111/cen.14742 · Cited by 26 · see citing works
“If the 95% CI for the SMD included 0, the SMD is not statistically significant.(21) In addition, the risk ratio (RR) was reported for the data on preference and subjective cardiovascular symptoms.”
BackgroundEvangelista, G., Dono, F., Consoli, S., Lanzone, J., Corniello, C., Russo, M., Anzellotti, F., ONOFRJ, M. C., Vollono, C., & Sensi, S. L. (2023) · European Journal of Neurology · doi:10.1111/ene.15792 · Cited by 27 · see citing works
Bahreiny, S. S., Bastani, M., Dabbagh, M. R., Ghorbani, H., Aghaei, M., Zahedian, M., & Fard, R. M. (2024) · Middle East Fertility Society Journal · doi:10.1186/s43043-023-00162-6 · Cited by 27 · see citing works
“Standardized mean differences (SMD) and 95% confidence intervals (CI) were calculated to assess the effect sizes of semen quality outcomes, including semen volume, sperm count, sperm concentration, total motility, and progressive motility, before and after exposure to air pollution [27, 28].”
MethodBarker, T. G., O’Higgins, A., Fonagy, P., & Gardner, F. E. M. (2024) · Journal of Affective Disorders · doi:10.1016/j.jad.2023.12.080 · Cited by 28 · see citing works
Casanova‐Rodríguez, D., Ranchal‐Sánchez, A., Rodríguez, R. B., & Jurado‐Castro, J. M. (2025) · European Journal of Pain · doi:10.1002/ejp.4783 · Cited by 36 · see citing works
“Forest plots with mean differences (MD) and 95% confidence intervals (CI) were used to present the results of the meta-analysis, instead of standardised mean difference (SMD), due to the results of the intervention, which could be normalised (C. Andrade 2020; Tufanaru et al. 2015).”
Sharp, K. J., Sherar, L. B., Kettle, V. E., Sanders, J. P., & Daley, A. (2022) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-022-01379-w · Cited by 31 · see citing works
Wang, M., Xie, X., Zhao, S., Ma, X., Wang, Z., & Zhang, Y. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1136343 · Cited by 27 · see citing works
Stella, F., Chiappella, A., Casadei, B., Bramanti, S., Ljevar, S., Chiusolo, P., Rocco, A. D., Tisi, M. C., Carrabba, M. G., Cutini, I., et al. (2024) · Blood Cancer Discovery · doi:10.1158/2643-3230.bcd-24-0052 · Cited by 26 · see citing works
“The differences in characteristics between the two treatment groups are expressed in standardized mean differences, which are able to detect treatment unbalances (46).”
Wang, C.-A., Lai, H.-W., Chen, J., Wang, W.-J., Lin, L.-C., Chiu, Y., Cheng, C., & Wu, V. (2025) · Nature Communications · doi:10.1038/s41467-025-64640-3 · Cited by 28 · see citing works
“Adequate balance between the matched groups was considered achieved when the standardized difference was less than 0.1, indicating minimal differences 48 .”
InfluentialBasso, I. B., Gonçalves, F. M., Martins, A. A., Schröder, Â. G. D., Taveira, K. V. M., Stechman‐Neto, J., Santos, R. S., Filho, O. G., & de Araújo, C. M. (2021) · Clinical Oral Investigations · doi:10.1007/s00784-021-04304-w · Cited by 26 · see citing works
“8 were considered large effect size[15].”
Pulse Wave Velocity and Sarcopenia in Older Persons—A Systematic Review and Meta-Analysis
Piotrowicz, K., Klich‐Rączka, A., Skalska, A., Gryglewska, B., Grodzicki, T. K., & Gąsowski, J. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19116477 · Cited by 26 · see citing works
“In order to overcome the variability of measurement methods, we used the standardized mean differences that present the between-group differences as the standard deviation units [51].”
MethodSingh, A., Molina‐García, P., Hussain, S., Paul, A. K., Das, S. K., Leung, Y.-Y., Hill, C. L., Danda, D., Samuels, J., & Antony, B. (2022) · Clinical Rheumatology · doi:10.1007/s10067-022-06402-w · Cited by 26 · see citing works
“[36] Limited evidence was reported assessing the effect of colchicine on biochemical markers [14, 15, 35] and imaging markers [14, 15] in knee OA patients.”
BackgroundKarimi, M., Pirzad, S., Shirsalimi, N., Ahmadizad, S., Hashemi, S. M., Karami, S., Kazemi, K., Shahir-Roudi, E., & Aminzadeh, A. (2024) · Nutrition & Metabolism · doi:10.1186/s12986-024-00847-3 · Cited by 25 · see citing works
“The effect size for the outcomes was evaluated using the mean difference (MD) along with 95% confidence intervals (CI) to quantify the impact of chia seed supplementation on cardiometabolic indices [24].”
Zhang, Y., Ding, Y., Chen, X., Li, Y., Li, J., & Hu, X. (2023) · Worldviews on Evidence-Based Nursing · doi:10.1111/wvn.12652 · Cited by 26 · see citing works
Li, T., Jiang, Q., Zhong, W., Zhu, T., Lu, Z., & Ding, Y. (2024) · Journal of Orthopaedic Surgery and Research · doi:10.1186/s13018-024-04743-7 · Cited by 25 · see citing works
“According to Cohen’s criteria, an SMD ≤ 0.2 indicates a slight difference in covariate balance [17].”
MethodInfluentialLai, H.-W., See, C. Y., Chen, J.-Y., & Wu, V.-C. (2024) · Cardiovascular Diabetology · doi:10.1186/s12933-024-02364-2 · Cited by 25 · see citing works
“The equilibrium of baseline characteristics in the propensity score-matched populations was gauged using absolute standardized mean differences, whereby a value 0.1 indicated a negligible difference [23].”
MethodInfluentialXiang, X.-N., Wang, Z., Hu, J., Zhang, J.-Y., Li, K., Chen, Q.-X., Xu, F., Zhang, Y.-W., He, H., He, C., et al. (2024) · Journal of Medical Internet Research · doi:10.2196/54876 · Cited by 28 · see citing works
“A P value .05 was deemed statistically significant [35].”
- 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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