Effect size estimates: Current use, calculations, and interpretation.
Abstract
The Publication Manual of the American Psychological Association (American Psychological Association, 2001, American Psychological Association, 2010) calls for the reporting of effect sizes and their confidence intervals. Estimates of effect size are useful for determining the practical or theoretical importance of an effect, the relative contributions of factors, and the power of an analysis. We surveyed articles published in 2009 and 2010 in the Journal of Experimental Psychology: General, noting the statistical analyses reported and the associated reporting of effect size estimates. Effect sizes were reported for fewer than half of the analyses; no article reported a confidence interval for an effect size. The most often reported analysis was analysis of variance, and almost half of these reports were not accompanied by effect sizes. Partial η2 was the most commonly reported effect size estimate for analysis of variance. For t tests, 2/3 of the articles did not report an associated effect size estimate; Cohen's d was the most often reported. We provide a straightforward guide to understanding, selecting, calculating, and interpreting effect sizes for many types of data and to methods for calculating effect size confidence intervals and power analysis.
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Restricting sampling to a narrow range of the population tends to lower effect sizes because variability is reduced.
“A common property of statistics holds that sampling from restricted ranges of the total population usually biases ES downward, due to reduced variability (Bobko, Roth, & Bobko, 2001;Fritz, Morris, & Richler, 2012).”
From Improving fluid intelligence with training on working memory: a meta-analysis (2015) · cites this paper as Fritz, Morris, & Richler, 2012
Small-sample studies are generally more prone to bias, and their relatively large confidence intervals suggest high uncertainty around point estimates.
“Small-sample studies are generally more prone to bias, and the relatively large confidence intervals presented in these studies suggest high uncertainty around the point estimates [47, 48].”
From Depression, anxiety, PTSD, and OCD after stillbirth: a systematic review (2021) · cites this paper as [47]
Reporting the effect size and its confidence intervals continues to be uncommon.
“Nevertheless, reporting the effect size and its confidence intervals continues to be uncommon (Frias-Navarro et al., 2012; Fritz et al., 2012; Peng et al., 2013).”
From Misconceptions of the p-value among Chilean and Italian Academic Psychologists (2016) · cites this paper as Fritz et al., 2012
There are several websites that offer routines/programs for computing general or specific effect size estimators and their confidence intervals.
“There are several websites that offer routines/programs for computing general or specific effect size estimators and their confidence intervals (Fritz et al., 2012; Peng et al., 2013).”
From Misconceptions of the p-value among Chilean and Italian Academic Psychologists (2016) · cites this paper as Fritz et al., 2012
The gender ratio in included studies does not reflect the typical demographic profile of the SCI population, where males often comprise 70-80% of individuals affected, which hinders the generalizability of the review findings to this population.
“This ratio does not reflect the typical demographic profile of the SCI population, where males often comprise 70-80% of individuals affected, which hinders the generalizability of the review findings to this population [43].”
From Mindfulness- and acceptance-based interventions for people with spinal cord injury: a scoping review. (2025) · cites this paper as [43]
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“In order to determine the practical and theoretical relevance of an effect as well as the power of the analyses, effect sizes were estimated for each analysis [93].”
Alimoradi, Z., Jafari, E., Broström, A., Ohayon, M. M., Lin, C., Griffiths, M. D., Blom, K., Jernelöv, S., Kaldo, V., & Pakpour, A. H. (2022) · Sleep Medicine Reviews · doi:10.1016/j.smrv.2022.101646 · Cited by 178 · see citing works
“SMD effect size of 0.2 e 0.5 is considered as small effect size; 0.5 e 0.8 is considered as medium effect size; and greater than 0.8 is interpreted as large effect size [51].”
InfluentialEffect sizes for nonparametric tests
Peres, F. F. (2025) · Biochemia Medica · doi:10.11613/bm.2026.010101 · Cited by 241 · see citing works
“The absolute value of r is commonly classified as small (≥ 0.1), medium (≥ 0.3), or large (≥ 0.5), following Cohen’s thresholds (7,17).”
InfluentialA Systematic Review of Teacher-Delivered Behavior-Specific Praise on K–12 Student Performance
Royer, D. J., Lane, K. L., Dunlap, K. D., & Ennis, R. P. (2018) · Remedial and Special Education · doi:10.1177/0741932517751054 · Cited by 175 · see citing works
“BC-SMD effect sizes can be interpreted following other standardized mean difference effect size interpretation (e.g., Fritz, Morris, & Richler, 2012): small (0.20–0.50), medium (0.50–0.80), large ( (cid:116) 0.80).”
InfluentialRoberts, H., Lissa, C. J. V., Hagedoorn, P., Kellar, I., & Helbich, M. (2019) · Environmental Research · doi:10.1016/j.envres.2019.108606 · Cited by 164 · see citing works
Do we click in the right way? A meta-analytic review of clicker-integrated instruction
Chien, Y., Chang, Y.-H., & Chang, C. (2015) · Educational Research Review · doi:10.1016/j.edurev.2015.10.003 · Cited by 166 · see citing works
“…Hedges, Higgins, & Rothstein, 2009; de Boer, Donker, & van der Werf, 2014; Donker, de Boer, Kostons, Dignath van Ewijk, & van der Werf, 2014; Fritz et al., 2012; Scammacca, Roberts, & Stuebing, 2014). g ¼ 1 3 4 n1 þ n2ð Þ 9 d (2) The standardized effect sizes presented in this meta-analysis…”
Arning, K., Offermann-van Heek, J., Linzenich, A., Kaetelhoen, A., Sternberg, A., Bardow, A., & Ziefle, M. (2019) · Energy Policy · doi:10.1016/j.enpol.2018.10.039 · Cited by 165 · see citing works
Graduate Theses and Dissertations
Davis, M., Davis, K. J., & Dunagan, M. M. (2012) · Elsevier eBooks · doi:10.1016/b978-0-12-384727-0.00006-9 · Cited by 165 · see citing works
Diverse motives for human curiosity
Kobayashi, K., Ravaioli, S., Baranès, A., Woodford, M., & Gottlieb, J. P. (2019) · Nature Human Behaviour · doi:10.1038/s41562-019-0589-3 · Cited by 157 · see citing works
Reduced empathic concern leads to utilitarian moral judgments in trait alexithymia
Patil, I., & Silani, G. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.00501 · Cited by 156 · see citing works
“Also, for inter- and intra-group comparisons, Mann-Whitney U test and Wilcoxon Signed Rank test were used and effect size (r) for these tests was computed as r = Z/√n, where Z is the standardized statistic and n is the sample size (Fritz et al., 2012).”
BackgroundMethodPatterson, M., Geis, G. L., LeMaster, T., & Wears, R. L. (2012) · BMJ Quality & Safety · doi:10.1136/bmjqs-2012-000951 · Cited by 156 · see citing works
Aging Affects Dopaminergic Neural Mechanisms of Cognitive Flexibility
Berry, A. S., Shah, V. D., Baker, S. L., Vogel, J. W., O’Neil, J. P., Janabi, M., Schwimmer, H., Marks, S. M., & Jagust, W. J. (2016) · Journal of Neuroscience · doi:10.1523/jneurosci.0626-16.2016 · Cited by 155 · see citing works
“Effect sizes for repeated-measures ANOVA are reported using G 2 (Bakeman, 2005), which gives smaller values than the frequently used P 2, but is preferable as it reduces error when comparing across studies (Fritz et al., 2012).”
MethodCognitive fatigue: A Time-based Resource-sharing account
Borragán, G., Slama, H., Bartolomei, M., & Peigneux, P. (2017) · Cortex · doi:10.1016/j.cortex.2017.01.023 · Cited by 151 · see citing works
Fascia thickness, aging and flexibility: is there an association?
Wilke, J., Macchi, V., De, R., & Stecco, C. (2018) · Journal of Anatomy · doi:10.1111/joa.12902 · Cited by 153 · see citing works
“In case of significance, effect sizes were calculated using the formula r = z/√n and interpreted as small (0.1–0.3), medium (0.3–0.5) or large (> 0.5; Fritz et al. 2012).”
MethodInfluentialCloître, M., Hyland, P., Prins, A., & Shevlin, M. E. (2021) · European Journal of Psychotraumatology · doi:10.1080/20008198.2021.1930961 · Cited by 153 · see citing works
Palmas, W., March, D., Darakjy, S., Findley, S. E., Teresi, J., Carrasquillo, O., & Luchsinger, J. A. (2015) · Journal of General Internal Medicine · doi:10.1007/s11606-015-3247-0 · Cited by 164 · see citing works
The diminishing criterion model for metacognitive regulation of time investment.
Ackerman, R. (2014) · Journal of Experimental Psychology: General · doi:10.1037/a0035098 · Cited by 152 · see citing works
Thibaut, A., Wannez, S., Donneau, A., Chatelle, C., Gosseries, O., Bruno, M., & Laureys, S. (2017) · Brain Injury · doi:10.1080/02699052.2016.1274776 · Cited by 147 · see citing works
“The effect size was calculated using the following expression r = z/√2n where z is the statistics obtained from the Wilcoxon signed-rank test [36].”
MethodEggmann, S., Verra, M. L., Luder, G., Takala, J. A., & Jakob, S. M. (2018) · PLoS ONE · doi:10.1371/journal.pone.0207428 · Cited by 145 · see citing works
“Effect sizes were calculated with Cohen’s d for normally distributed data and with Cohen’s r for WilcoxonMann-Whitney test statistic in case of non-normal data (using appropriate z value as in [35]).”
MethodPelsser, L. M., Frankena, K., Toorman, J., & Rodrigues Pereira, R. (2017) · PLOS ONE · doi:10.1371/journal.pone.0169277 · Cited by 145 · see citing works
Krägeloh, C. U., Czuba, K., Billington, D. R., Kersten, P., & Siegert, R. J. (2014) · Psychiatric Services · doi:10.1176/appi.ps.201400141 · Cited by 142 · see citing works
Psychosocial Factors and Community College Student Success
Fong, C. J., Davis, C., Kim, Y., Kim, Y. W., Marriott, L., & Kim, S. (2016) · Review of Educational Research · doi:10.3102/0034654316653479 · Cited by 150 · see citing works
Effects of Nintendo Wii‐Fit <sup>®</sup> video games on balance in children with mild cerebral palsy
Tarakci, D., Ersoz Huseyinsinoglu, B., Tarakci, E., & Razak Ozdincler, A. (2016) · Pediatrics International · doi:10.1111/ped.12942 · Cited by 138 · see citing works
Refinement and revalidation of the demoralization scale: The DS‐II—external validity
Robinson, S., Kissane, D. W., Brooker, J., Hempton, C., Michael, N. G., Fischer, J., Franco, M. E., Sulistio, M., Clarke, D. M., Özmen, M., et al. (2016) · Cancer · doi:10.1002/cncr.30012 · Cited by 137 · see citing works
Clemente, F. M., Mendes, B., Nikolaidis, P. Τ., Calvete, F., Carriço, S., & Owen, A. L. (2017) · Physiology & Behavior · doi:10.1016/j.physbeh.2017.06.021 · Cited by 136 · see citing works
“ES can be interpreted as the magnitude of a study’s findings and complement the interpretation of statistical significance (27).”
MethodTowards understanding and detecting fake reviews in app stores
Martens, D., & Maalej, W. (2019) · Empirical Software Engineering · doi:10.1007/s10664-019-09706-9 · Cited by 137 · see citing works
“For Wilcoxon tests we calculated the r value, dividing the z distribution by the square root of the number of samples (Fritz et al., 2012).”
BackgroundMethodThe views of teachers in England on an action-oriented climate change curriculum
Howard‐Jones, P. A., Sands, D., Dillon, J. S., & Fenton-Jones, F. (2021) · Environmental Education Research · doi:10.1080/13504622.2021.1937576 · Cited by 148 · see citing works
“A teacher’s resources are considered to significantly impact on engagement with their professional work (Hakanen, Bakker, and Schaufeli 2006) and so we included the statement from the NPR/IPSOS poll (2019): “I have the resources I need to answer students’ questions about climate change” to provide…”
BackgroundSchneider, S., Nebel, S., Beege, M., & Rey, G. D. (2018) · Learning and Instruction · doi:10.1016/j.learninstruc.2018.06.006 · Cited by 145 · see citing works
Eliasson, A., Krumlinde‐Sundholm, L., Gordon, A. M., Feys, H., Klingels, K., Aarts, P. B. M., Rameckers, E. A. A., Autti‐Rämö, I., & Hoare, B. (2013) · Developmental Medicine & Child Neurology · doi:10.1111/dmcn.12273 · Cited by 135 · see citing works
“However, depending on the statistical method used, effect size can also be reported using Pearson’s r, the coefficient of determination (r(2)), eta squared (g(2)), or omega squared (x(2)).(73) In general, the larger the difference and the smaller the variability between groups, the larger the effect size.”
MethodUndeutsch hypothesis and Criteria Based Content Analysis: A meta-analytic review
Amado, B. G., Fernández, R. A., & Rivera, F. F. (2015) · The European Journal of Psychology Applied to Legal Context · doi:10.1016/j.ejpal.2014.11.002 · Cited by 135 · see citing works
Narcissism and Social Networking Behavior: A Meta‐Analysis
Gnambs, T., & Appel, M. (2017) · Journal of Personality · doi:10.1111/jopy.12305 · Cited by 135 · see citing works
Magnitud del efecto, una guía rápida
Domínguez-Lara, S. (2017) · Educación Médica · doi:10.1016/j.edumed.2017.07.002 · Cited by 132 · see citing works
Differential mosquito attraction to humans is associated with skin-derived carboxylic acid levels
Obaldia, M. E. D., Morita, T., Dedmon, L. C., Boehmler, D. J., Jiang, C. S., Zeledon, E. V., Cross, J. R., & Vosshall, L. B. (2022) · Cell · doi:10.1016/j.cell.2022.09.034 · Cited by 134 · see citing works
“Nonparametric effect size (ES) was calculated as ES= Z/sqrt(N) where N is the number of observations (Figure 1E) (Fritz et al., 2012).”
Depression, anxiety, PTSD, and OCD after stillbirth: a systematic review
Westby, C. L., Erlandsen, A. R., Nilsen, S. A., Visted, E., & Thimm, J. C. (2021) · BMC Pregnancy and Childbirth · doi:10.1186/s12884-021-04254-x · Cited by 130 · see citing works
“Small-sample studies are generally more prone to bias, and the relatively large confidence intervals presented in these studies suggest high uncertainty around the point estimates [47, 48].”
BackgroundDay, L. J. (2018) · Anatomical Sciences Education · doi:10.1002/ase.1772 · Cited by 130 · see citing works
Is Omega Squared Less Biased? a Comparison of Three Major Effect Size Indices in One-Way Anova
Okada, K. (2013) · Behaviormetrika · doi:10.2333/bhmk.40.129 · Cited by 128 · see citing works
To adjust or not adjust: Nonparametric effect sizes, confidence intervals, and real-world meaning
Ivarsson, A., Andersen, M. B., Johnson, U., & Lindwall, M. (2012) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2012.07.007 · Cited by 125 · see citing works
On the relationship between positive and negative affect: Their correlation and their co-occurrence.
Larsen, J. T., Ersner-Hershfield, H., Stastny, B. J., & Hester, N. (2016) · Emotion · doi:10.1037/emo0000231 · Cited by 127 · see citing works
Different cognitive abilities displayed by action video gamers and non-gamers
Kowal, M., Toth, A. J., Exton, C., & Campbell, M. J. (2018) · Computers in Human Behavior · doi:10.1016/j.chb.2018.07.010 · Cited by 126 · see citing works
Banda, H. J., & Nzabahimana, J. (2022) · Journal of Science Education and Technology · doi:10.1007/s10956-022-10010-3 · Cited by 124 · see citing works
“14 indicates the experimental group’s mean at the 86 percentiles of the control group (Fritz et al., 2012; Rosnow & Rosenthal, 1996).”
BackgroundClemente‐Suárez, V. J., García, J. P. F., Marcos, R. D. L. V., & Patiño, M. J. M. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.01985 · Cited by 124 · see citing works
Non‐Motor Symptoms in Parkinson's Disease are Reduced by Nabilone
Peball, M., Krismer, F., Knaus, H., Djamshidian, A., Werkmann, M., Carbone, F., Ellmerer, P., Heim, B., Marini, K., Valent, D., et al. (2020) · Annals of Neurology · doi:10.1002/ana.25864 · Cited by 123 · see citing works
Meta-analysis of mindfulness training on teacher well-being.
Zarate, K., Maggin, D. M., & Passmore, A. (2019) · Psychology in the Schools · doi:10.1002/pits.22308 · Cited by 119 · see citing works
McEwen, S. E., Polatajko, H. J., Baum, C. M., Rios, J., Cirone, D., Doherty, M., & Wolf, T. (2014) · Neurorehabilitation and neural repair · doi:10.1177/1545968314558602 · Cited by 122 · see citing works
“For nonnormally distributed data, medians were determined, and a nonparametric effect size r was calculated using the formula r(2) = z(2)/N.(34) CO-OP therapist logs and institutional patient records were reviewed to establish which self-selected activities were trained during the outpatient rehabilitation program.”
MethodMind wandering simultaneously prolongs reactions and promotes creative incubation
Leszczyński, M., Chaieb, L., Reber, T. P., Derner, M., Axmacher, N., & Fell, J. (2017) · Scientific Reports · doi:10.1038/s41598-017-10616-3 · Cited by 120 · see citing works
Eljaiek, R., Cavayas, Y. A., Rodrigue, É., Desjardins, G., Lamarche, Y., Toupin, F., Denault, A. Y., & Beaubien‐Souligny, W. (2018) · British Journal of Anaesthesia · doi:10.1016/j.bja.2018.09.028 · Cited by 120 · see citing works
Adam‐Troian, J., Wagner‐Egger, P., Motyl, M. S., Arciszewski, T., Imhoff, R., Zimmer, F., Klein, O., Babińska, M., Bangerter, A., Bilewicz, M., et al. (2020) · Political Psychology · doi:10.1111/pops.12716 · Cited by 119 · see citing works
Magnini, V. P., & Kim, S. (2015) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2015.11.001 · Cited by 118 · see citing works
“Fritz et al. 2012) acknowledge that observed effects sought in most expermental research are likely to be small.”
Background
- Authors
- Fritz, C. O., Morris, P. E., & Richler, J. J.
- Affiliations
- Lancaster University (GB)
- ORCID
- Richler, Jennifer J.
- Venue
- Journal of Experimental Psychology: General
- Published
- 2012
- Volume
- 141
- Issue
- 1
- Pages
- 2-18
- ISSN
- 0096-3445 (ISSN-L)
- 1939-2222
- OpenAlex
- W2148540129
- Cited by
- 5,199
- References
- 52
- Citations by year
- 2026: 484 · 2025: 626 · 2024: 516 · 2023: 502 · 2022: 581 · 2021: 607 · 2020: 491 · 2019: 339 · 2018: 293 · 2017: 239 · 2016: 198 · 2015: 138 · 2014: 86 · 2013: 67 · 2012: 21
- FWCI
- 61.22
- Type
- journal article
- Language
- en
- Update notices
- correction (2011-10-24)
- Open access
- closed
- Locations
- Journal of Experimental Psychology General (publishedVersion)
- PubMed (publishedVersion)
- Lancaster EPrints (Lancaster University) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- effect size, effect size reporting, confidence intervals, power analysis, partial eta squared, Cohen's d, analysis of variance, t-test, statistical reporting
- MeSH terms
- Data Interpretation, Statistical, Humans, Research Design, Statistics as Topic, Sample Size
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