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How Big is a Big Odds Ratio? Interpreting the Magnitudes of Odds Ratios in Epidemiological Studies
Abstract
The odds ratio (OR) is probably the most widely used index of effect size in epidemiological studies. The difficulty of interpreting the OR has troubled many clinical researchers and epidemiologists for a long time. We propose a new method for interpreting the size of the OR by relating it to differences in a normal standard deviate. Our calculations indicate that OR = 1.68, 3.47, and 6.71 are equivalent to Cohen's d = 0.2 (small), 0.5 (medium), and 0.8 (large), respectively, when disease rate is 1% in the nonexposed group; Cohen's d < 0.2 when OR <1.5, and Cohen's d > 0.8 when OR > 5.
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“Although the effect sizes of Hedges g and OR can be difficult to compare, outcomes based on continuous data and reported as Hedges g, appeared to generate larger effect sizes compared with dichotomous scoring, reported as OR [91].”
From The psychological subtype of intimate partner violence and its effect on mental health: a systematic review with meta-analyses (2022) · cites this paper as [91]
In the citing paper
“The mentoring structures and outcomes of the students in our study differed based on their gender and race/ethnicity, although the sizes of these differences were small (Cohen, 1992; Chen et al., 2010).”
From Race and Gender Differences in Undergraduate Research Mentoring Structures and Research Outcomes (2017) · cites this paper as Chen et al., 2010
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“According to recent guidelines, these effects should be interpreted as small in size, except for medium-sized effect for gender (Chen et al., 2010).”
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“The odds ratio for choosing the tournament was 4.25, a value which corresponds to an effect size between medium and large (Chen et al., 2010)12.”
BackgroundInfluentialAndrews, N. E., Ireland, D., Vijayakumar, P., Burvill, L., Hay, E., Westerman, D., Rose, T., Schlumpf, M., Strong, J., & Claus, A. P. (2023) · JMIR Formative Research · doi:10.2196/47267 · Cited by 18
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“Odds ratios (ORs) and 95% CIs were used to represent statistical significance and effect sizes of the variables in the logistic regression analysis [71].”
MethodReimer, N. K., Hughes, J., Blaylock, D., Donnelly, C., Wölfer, R., & Hewstone, M. (2021) · Developmental Psychology · doi:10.1037/dev0001274 · Cited by 19
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“risk factors is so complex that traditional measures like odds ratios (ORs), which are hard to communicate even for risk factor main effects [9,10], might be of very limited use in this context.”
BackgroundGazing Past the Gaps: A Growth-Based Assessment of the Mathematics Achievement of Black Girls
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“However, from a pure statistical perspective, the long-term consequences are small (Chen et al., 2010).”
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“05) to detect at least a 2-fold increased odds [moderate effect size (35)] of better healthrelated QoL among those who engaged in LTPA compared with No LTPA, we would need at least 402 participants.”
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“We interpret small effects as Hedges’ g and Cox’s d value of 0.2–0.49, and large effects as values >0.8, with medium effect sizes in between these values (Chen et al., 2010).”
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“Correlation coefficient values of ≤ 0.3, 0.4 to 0.6, and ≥ 0.7, and OR values of ≤ 1.68, 1.69 to 3.47, and ≥ 6.7 were interpreted as weak, moderate and strong, respectively [42,43].”
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“To test hypotheses using social behaviors as outcome variables (see Sections 3.2 and 3.4), it was estimated that sample sizes of 34 and 21 per group were adequately powered to detect medium and large effects, respectively, using standards outlined by Chen, Cohen, and Chen (2010).”
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Child maltreatment severity, chronic substance abuse, and disability status.
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“The effect sizes for attitudes toward CCRC and wellbeing were large (Chen et al., 2010), whereas the effect size for subjective future health was medium (Chen et al.”
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“The targeted odds ratio corresponds to a small-to-medium effect of Cohen d [48] and was selected because we consider that this will be an effect size that contributes a meaningful explanation of variance in the logistic regression.”
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“4 risk ratios (aRRs), with practically meaningful differences identified using Chen’s criteria for at least a small effect, which varies based on predictor prevalence (Chen et al., 2010), and statistical significance defined with a Bonferroni-corrected p-value of <.”
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Self-citationWong, J. M., Volkman, H. R., Adams, L. E., García, C. O., Martinez-Quiñones, A., Pérez‐Padilla, J., Bertrán‐Pasarell, J., de la Peña, D. S., Tosado-Acevedo, R., Santiago, G. A., et al. (2022) · American Journal of Tropical Medicine and Hygiene · doi:10.4269/ajtmh.22-0149 · Cited by 16
“01) Neurologic Disoriented or confused 38 (14) 13 (22) 1.”
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“As a point of reference, we used Chen et al. (2010) thresholds for interpretation of effect size for logistic regression: for odds less than 1, 0.60, 0.29, and 0.15 indicate small, medium, and large effects, respectively; and for odds greater than 1, 1.68, 3.47, and 6.71 indicate small, medium, and…”
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“The effect size for each feature was measured using the odds ratio (OR; small: 1.68/0.60; medium: 3.47/0.29; large: 6.71/0.15 [50]).”
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“In fact, based on Chen (2010), the effect size (odds ratio; OR ) for this contrast is very small (1/ OR = 1.16, 95% CI [1.03, 1.30]).”
BackgroundInfluentialLiu, C.-C., Ling, J., Zahry, N. R., Liu, C., Ammigan, R., & Kaur, L. (2024) · PLoS ONE · doi:10.1371/journal.pone.0293130 · Cited by 16
“Using the G * Power program, we assumed a small effect size with an odds ratio (OR) of 1.68 [18], 50% probability of not being fully vaccinated [2] and a significance level of 0.05, a sample size of 133 was needed to achieve at least an 80% study power when using logistic regression models to…”
InfluentialPawlak, M., Schmidtler, H., & Kopala‐Sibley, D. C. (2024) · Development and Psychopathology · doi:10.1017/s0954579424000130 · Cited by 21
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“A priori power analysis showed that a minimum sample size of 54 participants (G*Power, Version 3.1, University of Dusseldorf, Germany) was needed to detect a moderate effect size for logistic regression (OR = 3.5), with a power of 0.80 and type 1 error of 0.05 [13, 14].”
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“The odds ratio for both comparisons only corresponds to a small effect size [13].”
Are valence and social avoidance associated with the memory conformity effect?
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“between binary outcomes was adapted from the study by Chen et al. (2010). The effect size thresholds of the absolute lnθ lnθ were 0.”
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Andreas, S., Schulz, H., Volkert, J., Lüdemann, J., Dehoust, M. C., Sehner, S., Suling, A. I., Wegscheider, K., Ausín, B., Canuto, A., et al. (2021) · Australian & New Zealand Journal of Psychiatry · doi:10.1177/00048674211025711 · Cited by 16
“Based on the study by Chen et al. (2010), we used the following ranges to interpret the odds ratio (OR) as an effect size: OR < 1.5 = small effect; OR = 1.5–4.9 medium effect and OR > 5 = large effect.”
MethodInfluentialTayfur, S. N., Prior, S., Roy, A. S., Fitzpatrick, L. I., & Forsyth, K. (2021) · Educational Research Review · doi:10.1016/j.edurev.2021.100404 · Cited by 16
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“We considered OR = 1.68 to be a small effect, OR = 3.47 to be a medium effect, and OR = 6.71 a large effect (Chen et al., 2010).”
BackgroundInfluentialExploring the association between character strengths and moral functioning
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“Cohen’s D exceeds .2 as an indicator for a small effect, .5 as a medium effect, and .8 as a large effect (Chen et al., 2010).”
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Comorbidity of Airway Inflammatory Diseases in Chemical and Building-Related Intolerance
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“0 as large.(38) On the basis of these cutoffs, the increased risk for nonallergic asthma can be considered as small to medium in both CI and BRI, and large for the other five inflammatory diseases.”
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“…and the outcome (here make =1), one can refer to Table 2 where we provide a statistical framework for assessing the effect size of the log of odds ratio in terms of Cohen’s d for its easier interpretation based on a widely-accepted method in statistics and health sciences (Chen et al., 2010).”
BackgroundMethodInfluentialSelf-citationWarach, B., Bornstein, R. F., Gorman, B. S., & Moyer, A. E. (2024) · Personal Relationships · doi:10.1111/pere.12571 · Cited by 21
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Heise, K.-F., Rueda‐Delgado, L. M., Chalavi, S., King, B. R., Monteiro, T. S., Edden, R. A. E., Mantini, D., & Swinnen, S. P. (2022) · Communications Biology · doi:10.1038/s42003-022-03378-w · Cited by 15
Erentaitė, R., Vosylis, R., Sevalneva, D., Melnikė, E., Raižienė, S., & Daukantaité, D. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.820247 · Cited by 19
McConkie‐Rosell, A., Spillmann, R. C., Schoch, K., Sullivan, J. A., Walley, N., McDonald, M., Undiagnosed Diseases Network, Hooper, S. R., & Shashi, V. (2023) · Journal of Genetic Counseling · doi:10.1002/jgc4.1707 · Cited by 15
“Additionally, geographic location accounted for the majority of the variance with an odds ratio of 6.56 (Chen et al., 2010 ).”
InfluentialYu, Z., Qu, W., & Ge, Y. (2023) · Journal of Risk Research · doi:10.1080/13669877.2023.2270669 · Cited by 15
“Neuroticism negatively predicts crashes, but the odds ratio is small (Chen, Cohen, and Chen 2010).”
BackgroundTaheri, N., Pirboveiri, R., Sayyah, M., Bijanzadeh, M., & Ghandil, P. (2023) · BMC Psychiatry · doi:10.1186/s12888-023-05292-9 · Cited by 15
“According to Chen et al., 2010 [36] effect size in logistic regression can be classified as follows: • Odds Ratio 1.68 -”
BackgroundInfluentialKeding, A., Boehnke, J. R., Croudace, T. J., Richmond, S. J., & MacPherson, H. (2015) · BMC Medical Research Methodology · doi:10.1186/s12874-015-0054-6 · Cited by 16
“98) was only weak [66], and the effect size in terms of pseudo R(2) [67] was negligible.”
BackgroundChoi, B., DiNitto, D. M., Marti, C., & Choi, N. G. (2016) · Western Journal of Emergency Medicine · doi:10.5811/westjem.2016.1.28310 · Cited by 15
Quality of life in HIV-infected Chinese women and their family caregivers:an intervention study
Chen, W., Shiu, C. A., Yang, J. P., Wang, K., Zhang, L., Zhang, J., Reynolds, N. R., Kennedy, H. P., Khoshnood, K., Chen, L., et al. (2018) · AIDS Care · doi:10.1080/09540121.2018.1510095 · Cited by 15
Broadly sampled assessment reduces ethnicity‐related differences in clinical grades
van Andel, C. E. E., Born, M. P., Themmen, A. P. N., & Stegers‐Jager, K. M. (2019) · Medical Education · doi:10.1111/medu.13790 · Cited by 15
Aarabi, G., Valdez, R., Spinler, K., Walther, C., Seedorf, U., Heydecke, G., König, H., & Hajek, A. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16183344 · Cited by 15
“, Chen, 2010) translating OR into indices of effect size, the ORs reported in our study are classified as small [21].”
BackgroundPredictors of Overweight and Obesity in Childhood Cancer Survivors
Gance‐Cleveland, B., Linton, A., Arbet, J., Stiller, D., & Sylvain, G. (2020) · Journal of Pediatric Oncology Nursing · doi:10.1177/1043454219897102 · Cited by 15
Kaboré, J., Saïdi, H., Dassieu, L., Choinière, M., & Pagé, M. G. (2020) · Pain Practice · doi:10.1111/papr.12883 · Cited by 15
“Our study identified few predictors and reported ORs indicating a small effect size and a weak association for those that were identified.(71) In addition, the predictive model showed a low sensitivity and a low accuracy, highlighting the difficulty in predicting which patients will experience improved pain outcomes.”
ResultIs All Dating Violence Equal? Gender and Severity Differences in Predictors of Perpetration
Ontiveros, G., Cantos, A. L., Chen, P., Charak, R., & O’Leary, K. D. (2020) · Behavioral Sciences · doi:10.3390/bs10070118 · Cited by 15
“Given the results presented in Tables 6 through 9, most odds ratios of the significant study variables indicated medium to large effects (odd ratios > 3.47, according to the criteria proposed by Chen et al., 2010) [66].”
MethodResultInfluentialHirota, T., Paksarian, D., He, J., Înoue, S., Stapp, E. K., Meter, A. V., & Merikangas, K. R. (2021) · Journal of Clinical Child & Adolescent Psychology · doi:10.1080/15374416.2021.1875326 · Cited by 15
“Third, although the magnitude of ORs is interpreted with respect to the scale of the corresponding variable, our results generally indicated small to medium effect sizes for the social capital factors (Chen et al., 2010).”
ResultBarger, B. D., Rice, C. E., Benevides, T. W., Salmon, A., Sanchez-Alvarez, S., & Crimmins, D. (2021) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-021-04943-8 · Cited by 15
Middleton, A. E., Farris, E. A., Ring, J. J., & Odegard, T. N. (2021) · Journal of Learning Disabilities · doi:10.1177/00222194211047633 · Cited by 15
“Chen et al. (2010) relate ORs of 1.68, 3.47, and 6.71 as respective equivalents to standardized mean differences of d = 0.2, 0.5, and 0.8.”
BackgroundInfluentialDriving while under the influence of hallucinogens: Prevalence, correlates, and risk profiles
Salas‐Wright, C. P., Cano, M. N., Hodges, J. C., Oh, S., Hai, A. H., & Vaughn, M. G. (2021) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2021.109055 · Cited by 15
Yang, X., Ding, N., Tu, X., Zhao, C., Xu, H., Lai, X., & Zhang, G. (2021) · Addictive Behaviors · doi:10.1016/j.addbeh.2021.107233 · Cited by 15
Nutor, J. J., Gyamerah, A. O., Alhassan, R. K., Duah, H. O., Thompson, R., Wilson, N., Harris, O., Gutierrez, J., Hoffmann, T. J., Getahun, M., et al. (2023) · AIDS Research and Therapy · doi:10.1186/s12981-023-00538-8 · Cited by 15
“1, equivalent to an approximately medium effect size [29].”
BackgroundMayne, D. J., Morgan, G. G., Jalaludin, B. B., & Bauman, A. E. (2018) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph15020275 · Cited by 15
“All variables were statistically significant and important in univariate models with small to medium effect sizes [90].”
BackgroundDeutschlander, D. (2019) · Educational Evaluation and Policy Analysis · doi:10.3102/0162373719845653 · Cited by 15
Metadata
- Authors
- Chen, H., Cohen, P., & Chen, S.
- Affiliations
- Winthrop-University Hospital (US)
- New York State Psychiatric Institute (US)
- Health Canada (CA)
- Corresponding author
- Chen, Henian
- Venue
- Communications in Statistics - Simulation and Computation
- Publisher
- Informa UK Limited
- Published
- 2010-03-31
- Volume
- 39
- Issue
- 4
- Pages
- 860-864
- ISSN
- 0361-0918 (ISSN-L)
- 1532-4141
- OpenAlex
- W2029059557
- Cited by
- 1,952
- References
- 20
- Citations by year
- 2026: 170 · 2025: 201 · 2024: 259 · 2023: 234 · 2022: 254 · 2021: 242 · 2020: 196 · 2019: 123 · 2018: 93 · 2017: 65 · 2016: 44 · 2015: 31 · 2014: 18 · 2013: 11 · 2012: 4
- FWCI
- 5.45
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Communications in Statistics - Simulation and Computation (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- odds ratio, effect size interpretation, Cohen's d, standardized mean difference, disease incidence
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