The DOI matches its Crossref record; 51 of the 52 references it cites were found in a registry or an index.
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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“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
In the citing paper
“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]
In the citing paper
“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
In the citing paper
“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
In the citing paper
“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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“intervention studies with a control group, Hedges’ gb was calculated as the difference of the mean scores of the treatment and the control group at the respective follow-up divided by their pooled standard deviation [21,38].”
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“…(the area of application motiving the study) seen in practice (Hedges & Hedberg, 2007).11 Population values for regression coefficients were based on eta squared and then converted to Cohen’s d as outlined in Fritz, Morris, and Richler (2012) and are presented in Table 3 for ease of interpretation.”
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“Study of effect size has become a major focus of statistical science (Batterham and Hopkins, 2006; Nakagawa and Cuthill, 2007; Ellis, 2010; Stang et al., 2010; Fritz et al., 2012).”
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“…represent the proportion of total variation attributable to the independent variable after partialling out the contribution of the other variables under investigation. h2p values of 0.01 indicate small effects, 0.06 represent medium effects, and 0.14 constitute large effects (Fritz et al., 2012).”
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“…in power analysis and meta-analysis which emphasize the standard metric (i.e., having a M 0 and a SD 1), effect sizes for research reporting could be also be standardized, as emphasized by many authors (e.g., Fritz et al., 2012; Henson, 2006; Kashy et al., 2009; Kirk, 2013; Lakens, 2013).”
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“We also discuss our results in terms of effect size because a statistically significant effect does not entail that it is practically significant (Fritz et al., 2012).”
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“Nonetheless quite easy methods based on estimation of ES variance can be found and have been shown to work properly up to mild sized effects as is for Cohen’s d (Example 6) (25).”
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“From the resulting z-values the effect sizes (r) were calculated: r = abs( z √ N ), with N= 50 (Fritz et al., 2012).”
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“1, a small effect [24, 25].”
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“overestimate the true population effect size (Fritz et al. 2012).”
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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].”
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“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
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“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).”
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“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).”
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“…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…”
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“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).”
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“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).”
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“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).”
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“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].”
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“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]).”
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“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
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“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
“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 163
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
“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
Narcissism and Social Networking Behavior: A Meta‐Analysis
Gnambs, T., & Appel, M. (2017) · Journal of Personality · doi:10.1111/jopy.12305 · Cited by 156
Magnitud del efecto, una guía rápida
Domínguez-Lara, S. (2017) · Educación Médica · doi:10.1016/j.edumed.2017.07.002 · Cited by 269
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
“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 148
“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 139
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
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
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 138
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
Banda, H. J., & Nzabahimana, J. (2022) · Journal of Science Education and Technology · doi:10.1007/s10956-022-10010-3 · Cited by 255
“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 136
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
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
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
“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 127
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
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
Magnini, V. P., & Kim, S. (2015) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2015.11.001 · Cited by 118
“Fritz et al. 2012) acknowledge that observed effects sought in most expermental research are likely to be small.”
Background
Metadata
- 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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