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Statistical power analyses using G∗Power 3.1: tests for correlation and regression analyses
Open accessAbstract
G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.
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“Additionally, a G*Power post hoc power analysis with an input effect size of 0.10 indicated an achieved power of 0.825, a power level that suggested a high probability of correctly rejecting the null hypothesis [54].”
From Internalized Racism and Mental Health: The Moderating Role of Collective Racial Self-Esteem (2024) · cites this paper as [54]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The sample size of 50 participants accounted for up to 20% attrition, so as to obtain at least 40 complete study samples that were powered to detect a statistically meaningful medium effect size (Cohen’s d > 0.45) primary outcome difference in pre vs post comparisons of PHQ9 scores at 0.8 power and alpha level of 0.05, computed a priori [41].”
From Personalized machine learning guided intervention for optimizing lifestyle behaviors in depression: a pilot study (2026) · cites this paper as [41]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“According to sample size and statistical power calculations in multiple regressions, assuming a small effect size ( f 2 = 0.03) for a maximum number of predictors (5) and an alpha level of .05, in order to attain a statistical power level of .80, the required sample size would be 434 (Faul et al., 2009). As indicated, the study sample was composed of 467 students, thus, larger than the required to”
From Romantic myths and cyber dating violence victimization in Spanish adolescents: A moderated mediation model (2023) · cites this paper as Faul et al., 2009
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“We required 26 calves per treatment to achieve 80% power with a significance level of α = 0.05 and chose to include 30 calves per treatment to allow for dropouts.”
From Effects of pre- and post-transport feeding protocols on the metabolism and physiological status of veal calves. (2025) · cites this paper as Faul et al., 2009
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“A prior power analysis conducted in G Power at alpha 0.05 specified a minimum target of 120 participants for a two-group comparison with baseline adjustment, with planned over-recruitment to accommodate attrition and incomplete documentation, using conventional small to medium effect size expectations for educational interventions (Cohen 1992;Faul et al. 2009Faul et al. , 2007)).”
From A Study on the Role of Midjourney, A Generative Artificial Intelligence Tool, in Enhancing Student Creativity in Illustration Design Classes (2026) · cites this paper as Faul et al. 2009
Experimental — accuracy not yet measured
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In the citing paper
“The power analysis revealed a required sample size of 108 in total and 36 participants in each group.”
From Efficacy and mechanisms of mobile application-delivered Acceptance and Commitment Therapy for posttraumatic stress disorder in China: Study protocol for a randomized controlled trial (2022) · cites this paper as Faul et al., 2009
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“An a priori power calculation, targeting an effect of d=0.42 at an alpha level of 5% (one-tailed) and a power of 90%, has yielded a total sample size of 196.”
From Clinical and cost-effectiveness of a guided internet-based Acceptance and Commitment Therapy to improve chronic pain-related disability in green professions (PACT-A): Study protocol of a pragmatic randomised controlled trial (2020) · cites this paper as [49]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“To detect an effect size of 0.1, a power calculation with 80% power and an α-error probability of 0.05 resulted in a total sample size of 967 participants.”
From Effects of five-minute internet-based cognitive behavioral therapy and simplified emotion-focused mindfulness on depressive symptoms: A randomized controlled trial (2017) · cites this paper as [28]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Our sample size of about 2600 subjects included in GWAS analysis has sufficient power to detect small variation; it has 90% power to detect 0.0174 effect size index (f2) at GWS level (α = 5E-08) that corresponds to 1.71% variance (R2) explained by a single SNP.”
From Genome-wide analysis identifies novel loci influencing plasma apolipoprotein E concentration and Alzheimer’s disease risk (2023) · cites this paper as [56]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“A power analysis conducted using G*Power (Faul, Erdfelder, Buchner, & Lang, 2009) indicated that using an alpha of 0.05 the study sample size of 57 had 0.80 power to detect a medium to large effect (f2 = 0.15) for the baseline regression analyses and to detect a large effect (odds ratio = 2.43) for the logistic regression analysis.”
From Intolerance of uncertainty in hoarding disorder (2019) · cites this paper as Faul, Erdfelder, Buchner, & Lang, 2009
The cited source says what the claim attributes to it.
In the citing paper
“Sample size calculations (using G*Power version 3.1 (Faul, Erdfelder, Buchner, & Lang, 2009) determined that 107 participants were needed to provide sufficient power (1-β = 0.95) to detect medium effect size (f 2 = 0.15) associations using multiple linear regression analyses with two presumed predictors (perceived stress and psychological flexibility), and an alpha level of 0.05.”
From Is psychological flexibility a mediator between perceived stress and general anxiety or depression among suspected patients of the 2019 coronavirus disease (COVID-19)? (2021) · cites this paper as Faul, Erdfelder, Buchner, & Lang, 2009
The cited source says what the claim attributes to it.
In the citing paper
“Consistent with findings from previous IP research (Bernard et al., 2017; Cokley et al., 2017), power for moderated regression analyses was set to 80% with an a priori effect size of R2 = .13, which corresponds to a small to medium effect (Cohen, 1988). Using G*Power (Faul et al., 2009), it was determined that a minimum sample size of 216 was necessary to test the study hypotheses.”
From Impostor Phenomenon and Psychological Well-Being: The Moderating Roles of John Henryism and School Racial Composition Among Black College Students (2020) · cites this paper as Faul et al., 2009
The cited source says what the claim attributes to it.
In the citing paper
“A statistical power analysis was performed using GPower 3.1 [72,73] to estimate sample size for a comparison of differences between two dependent means (matched pairs).”
From Walking Green: Developing an Evidence Base for Nature Prescriptions (2019) · cites this paper as [73]
The cited source says what the claim attributes to it.
In the citing paper
“Using the G*Power software [48], it shows that to detect a similar between-group effect at a level significance level of 0.05 with power above 0.80, the total sample size in the current study will need to be larger than 52 (i.e., 26 per group).”
The cited source says what the claim attributes to it.
In the citing paper
“Wedetermined our target sample size (N=432) with an a priori power analysis using the statistical software G*Power [38, 39].”
From "I'm Not Sure, But...": Examining the Impact of Large Language Models' Uncertainty Expression on User Reliance and Trust (2024) · cites this paper as [38]
The cited source says what the claim attributes to it.
In the citing paper
“The power was finally recalculated with the G*Power tool [40] assuming SAQOL-39 as the primary outcome, an effect size of 0.3, a sample size of 30, a calculated measurement coefficient of 0.654, two repeated measures and two groups, obtaining a final power in the study of 96%.”
From Early Occupational Therapy Intervention post-stroke (EOTIPS): A randomized controlled trial (2024) · cites this paper as [40]
The cited source says what the claim attributes to it.
In the citing paper
“The target sample size was calculated to be 30 participants from each discipline (medicine, nursing, and pharmacy) to participate in the pilot evaluation of the VSGs. Sample size targets were based on statistical analysis using G*Power [21].”
The cited source says what the claim attributes to it.
In the citing paper
“Two-tailed two-sample t-tests comparing 84 patients to 44 healthy controls and 29 relapsers to 38 non-relapsers have a power of 0.8 to detect medium (d = 0.52) and large (d = 0.70) group differences, respectively, and a power of 0.95 to detect effects of d = 0.67 and 0.90, respectively (using G*Power 3.153).”
From The relationship between resting-state functional connectivity, antidepressant discontinuation and depression relapse (2020) · cites this paper as [53]
The cited source says what the claim attributes to it.
In the citing paper
“A priori power analysis was conducted, using an alpha of .05, a power of 0.95, and a moderate to large effect size (f = .35) to determine the sample size. According to G∗Power, the desired total sample size was 109. Therefore, 120 participants recruited, allowing for a 10% loss of data (dropping out prior intervention, post-intervention assessment).”
From Application of Artificial Intelligence powered digital writing assistant in higher education: randomized controlled trial (2021) · cites this paper as Faul et al., 2009
The cited source says what the claim attributes to it.
In the citing paper
“Accordingly, an a priori power analysis in G*power (Faul et al., 2009) reveals a total sample size of N = 366 needed to detect effect sizes larger than g = 0.34 (analysis of variance [ANOVA]: main effects and interactions; f = 0.17 [equals g = 0.34]; α = .05; Power = .90; numerator df = 1; number of groups = 4).”
From Do Salient Social Norms Moderate Mortality Salience Effects? A (Challenging) Meta-Analysis of Terror Management Studies (2023) · cites this paper as Faul et al., 2009
The cited source says what the claim attributes to it.
In the citing paper
“Sample size was calculated using the program G*Power [32], with a focus on one of the main treatment factors, calf age, and one of the main outcomes of interest, plasma glucose concentrations. The expected effect size was calculated from mean plasma glucose concentrations of two groups of calves aged 2–3 (3.6 mmol/L) and 5–6 (3.1 mmol/L) weeks, measured after long-distance transport in a similar”
From Effects of age and feeding protocols on the metabolic and physiological condition of unweaned calves during and after long-distance transport (2026) · cites this paper as [32]
The cited source says what the claim attributes to it.
In the citing paper
“We also conducted a post-hoc power analysis on the ANCOVA in subsection V-D using G*Power [33] and calculated a power ( 1 -β ) of 0.73.”
From Dynamic Selection of Reliance Calibration Cues With AI Reliance Model (2023) · cites this paper as [33]
The cited source says what the claim attributes to it.
In the citing paper
“Power calculations were carried out a-priori, G*power (version 3.1) (Faul, Erdfelder, Buchner & Lang, 2009) was used to calculate sample size estimates for correlation analysis to detect medium and large effect sizes, with a power of 0.80 and an alpha of <0.05.”
From Psychosocial adjustment to Mild Cognitive Impairment: The role of illness perceptions, cognitive fusion and cognitive impairment. (2021) · cites this paper as Faul, Erdfelder, Buchner & Lang, 2009
The cited source says what the claim attributes to it.
In the citing paper
“An a priori power analysis was conducted using G*Power (43). Based on previous evidence a moderate effect of miCBT vs. WLC was assumed (9). Thus, with Cohen's f = 0.25 at a power of 1 – β = 0.95 with an α = 0.05, a necessary sample size of at least 90 participants was calculated. Considering a dropout rate of 25%, the target sample size was increased to 120 participants.”
From Efficacy of Cognitive-Behavioral Therapy for the Prophylaxis of Migraine in Adults: A Three-Armed Randomized Controlled Trial (2022) · cites this paper as [43]
The cited source says what the claim attributes to it.
In the citing paper
“A power analysis using G*Power [58] indicated that, based on 2 groups (ie, control vs active treatment), 3 repeated measurements (ie, baseline, midtreatment, posttreatment), a conservative r=.60 correlation among repeated measures, and a small d=0.2 treatment effect size, a sample of n=54 provides 95% power to detect a treatment by time interaction using the most conservative outcome in this study”
From App-Based Mindfulness Meditation for People of Color Who Experience Race-Related Stress: Protocol for a Randomized Controlled Trial (2022) · cites this paper as [58]
The cited source says what the claim attributes to it.
In the citing paper
“An a priori power analysis G*Power 3 (Faul, Erdfelder, Buchner, & Lang, 2009) showed that a sample of 42 participants was required (ρ H1 = 0.18, α = 0.05, Power = 0.90).”
From Challenging anxious cognitions or accepting them? Exploring the efficacy of the cognitive elements of cognitive behaviour therapy and acceptance and commitment therapy in the reduction of children's fear of the dark (2020) · cites this paper as Faul, Erdfelder, Buchner, & Lang, 2009
The cited source says what the claim attributes to it.
In the citing paper
“G*Power 3.1 was used to perform a power analysis (Faul et al., 2009).In a scenario involving an independent-samples t-test of two means, with a small-to-medium effect size (d = 0.30), alpha = 0.05 and power = 0.80, the necessary sample size is about 176 per condition.”
From The Impact of Generative AI on Personalized Content Marketing in E-Commerce (2025) · cites this paper as Faul et al., 2009
The cited source says what the claim attributes to it.
In the citing paper
“The correlation results for PP and CFR (r50 = .62, p < .001) from Buchsbaum et al. (2012) was used posthoc to calculate the statistical power needed to detect an effect using the G*Power calculator resulting in a power value of .95 (Faul et al., 2009).”
From A plausible role of imagination in pretend play, counterfactual reasoning, and executive functions (2023) · cites this paper as Faul et al., 2009
The cited source says what the claim attributes to it.
In the citing paper
“Power analysis was performed using G∗Power (59, 60) with parameters taken from previous reports or similar experiments.”
From Active transport by cytoplasmic dynein sustains dendritic MAP2 localization in developing neurons (2026) · cites this paper as [60]
The cited source says what the claim attributes to it.
In the citing paper
“The sample size for the study was determined by an a priori power analysis using G*Power (Faul et al., 2009). Assuming a power of 1–β = 0.80, and an α-error of 0.05, we calculated a required sample size of 90 participants to be able to consistently detect medium-sized effects of d = 0.4.”
From Check the box! How to deal with automation bias in AI-based personnel selection (2023) · cites this paper as Faul et al., 2009
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Post-hoc calculation of the effect sizes for comparisons between the forest and roadside walks were small (i.e., partial η2 less than 0.03) whereas the effect sizes for comparisons among walks and ADL conditions were of medium size (i.e., partial η2 greater than 0.06) [73,96].”
From Walking Green: Developing an Evidence Base for Nature Prescriptions (2019) · cites this paper as [73]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Similar to the acute membrane polarization effects, anodal and cathodal tDCS result in excitability-enhancing and excitability-reducing plasticity, respectively [16, 20, 21].”
From Investigation of the effect of delayed auditory feedback and transcranial direct current stimulation (DAF-tDCS) treatment for the enhancement of speech fluency in adults who stutter: A randomized controlled trial (2022) · cites this paper as [21]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“According to G*Power's calculation, a conservative WilcoxonMann-Whitney two-tailed test requires 90 participants per condition to detect medium-sized effects (Cohen's d = 0.5) at the significance level of 𝛼 = 0.05 with power (1𝛽 ) = 0.90.”
From "I'm Not Sure, But...": Examining the Impact of Large Language Models' Uncertainty Expression on User Reliance and Trust (2024) · cites this paper as [38]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“For the tests that we used (Wilcoxon Signed-rank test), we found that the needed sample size was always below the sample size we used for our primary studies, viz., 1000.”
From Automatic Semantic Augmentation of Language Model Prompts (for Code Summarization) (2024) · cites this paper as [19]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Patients were more likely to accept vaccine recommendations from a HCP if they used presumptive statements (e.g., “Today you will receive two vaccinations, correct?”) rather than participatory (e.g., “Are we going to vaccinate today?”) (21).”
From Development and evaluation of virtual simulation games to increase the confidence and self-efficacy of healthcare learners in vaccine communication, advocacy, and promotion (2024) · cites this paper as [21]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“The analysis indicated that a minimum sample size of 108 participants (36 per condition) was needed to detect a medium effect size (0.25) with 80% power at a 0.05 significance level.”
From The effects of generative AI agents and scaffolding on enhancing students’ comprehension of visual learning analytics (2025) · cites this paper as Faul, Erdfelder, Buchner, & Lang, 2009
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“For a between group effect size of f = 0.25, alpha 0.05, power 0.80, 0.5 correlation among repeated measures and 1.0 non-sphericity correction, a total sample size of 98 participants is needed for two-sided testing.”
From Eye movement desensitization and reprocessing (EMDR) therapy or supportive counseling prior to exposure therapy in patients with panic disorder: study protocol for a multicenter randomized controlled trial (IMPROVE) (2023) · cites this paper as [56]
Experimental — accuracy not yet measuredIn the citing paper
“Sample size for the larger study was determined on the basis of primary endpoints of 3 outcomes for which Bonferroni’s corrected α value (α = 0.05/3 = 0.0167) was used. Therefore, we calculated that the sample size required for the larger study was N = 80, with previously reported24 effect sizes of f = 0.45, α = 0.0167, and β = 0.2 for repeated-measures analysis of variance and with an assumption”
In the citing paper
“The sample size required to obtain a valid assessment of the effectiveness of the CCPI was determined by power analysis using G*Power version 3.1.9.2 [31].”
From Effects of a Continuity of Preterm Infant Care Program on Parenting outcomes and Service Utilization Rates (2022) · cites this paper as [31]
In the citing paper
“We determined a minimum sample size of 90 participants based on a power analysis for fixed effects, omnibus, 1-way analysis of variance (ANOVA) using G*Power 3.1 software86 (α = 0.05, power = 0.85, medium effect size f = 0.38).”
From Investigating disorder-specific and transdiagnostic alterations in model-based and model-free decision-making (2024) · cites this paper as [86]
In the citing paper
“The number of participants was determined a priori using G*Power (Faul et al., 2009).The required sample size to detect a small to medium-sized point biserial correlation between analytic thinking and the identification of the deepfake video as fake amounted to 191 (two-tailed, given a ¼ .05,power ¼ .80,rho ¼ .20).”
From The detection of political deepfakes (2022) · cites this paper as Faul et al., 2009
In the citing paper
“The required sample size to detect a small to medium-sized Pearson correlation between analytic thinking and our continuous deepfake identification measure amounted to 193 (twotailed, given a ¼ .05,power ¼ .80,rho ¼ .20,G*Power, Faul et al. , 2009).”
From The detection of political deepfakes (2022) · cites this paper as Faul et al., 2009
In the citing paper
“The required sample size to detect a small to medium effect of f 2 ¼ .10 was determined a priori with G*Power (Faul et al., 2009) to be at least 432, given a ¼ .05 and power (1Àb) ¼ .90.”
From The detection of political deepfakes (2022) · cites this paper as Faul et al., 2009
In the citing paper
“Using G*Power 3.1 (Faul et al., 2009), we conducted a post-hoc power analysis to estimate the sample size that would be needed to detect between-group differences.”
From No evidence of differences in cognitive control in children with autism spectrum disorder or obsessive-compulsive disorder: An fMRI study (2019) · cites this paper as Faul et al., 2009
In the citing paper
“The sample size was estimated using G*Power (Faul et al., 2009).”
From A neurobiological association of revenge propensity during intergroup conflict (2020) · cites this paper as Faul et al., 2009
In the citing paper
“Based on an estimated average small-to-medium effect size of oxytocin effect on social behaviors (d = 0.28, Walum et al., 2016), 80 6-person groups were needed to detect a significant effect (α = 0.05, β = 0.85, ANOVA: repeated measures, within-between interaction, G-Power, Faul et al., 2009).”
From Oxytocin promotes coordinated out-group attack during intergroup conflict in humans (2019) · cites this paper as Faul et al., 2009
In the citing paper
“The duration of the fMRI scanning and the post-scan test were carefully controlled within the time frame of the oxytocin peak response in the brain 54 .”
From Oxytocin modulates social value representations in the amygdala (2019) · cites this paper as [54]
In the citing paper
“To detect a moderate correlation (r = 0.4; ref. 37) between SPE on trust and on interpersonal distance with α = 0.05 and 90% power, a sample size of 61 participants was needed (G*Power 3.1; ref .38).”
From Placebo treatment facilitates social trust and approach behavior (2018) · cites this paper as [38]
In the citing paper
“We performed power analysis39 on the 427 meta-analyses of 44 IRFs done in the eight disorders, 318 of them (74%) have sufficient power ( ≥ 0.8), while the rest were under-powered.”
From Inflammation-related biomarkers in major psychiatric disorders: a cross-disorder assessment of reproducibility and specificity in 43 meta-analyses (2019) · cites this paper as [39]
In the citing paper
“To detect a small effect size (i.e., 0.25) or more at an alpha error rate of 0.05 and a beta error rate of 0.15, the estimated sample size was 289 participants in each group.”
From Effect of smartphone-based stress management programs on depression and anxiety of hospital nurses in Vietnam: a three-arm randomized controlled trial (2021) · cites this paper as [41]
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Metadata
- Authors
- Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G.
- Affiliations
- Christian-Albrechts-Universität zu Kiel (DE)
- University of Mannheim (DE)
- Heinrich Heine University Düsseldorf (DE)
- Corresponding author
- Faul, Franz
- Erdfelder, Edgar
- Venue
- Behavior Research Methods
- Published
- 2009-11
- Volume
- 41
- Issue
- 4
- Pages
- 1149-1160
- ISSN
- 1554-351X (ISSN-L)
- 1554-3528
- OpenAlex
- W2072500831
- Cited by
- 37,615
- References
- 38
- Citations by year
- 2026: 5346 · 2025: 5407 · 2024: 4408 · 2023: 3968 · 2022: 3860 · 2021: 3574 · 2020: 2568 · 2019: 1950 · 2018: 1458 · 2017: 1140 · 2016: 1030 · 2015: 914 · 2014: 677 · 2013: 573 · 2012: 380
- FWCI
- 199.20
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Behavior Research Methods (publishedVersion)
- PubMed (publishedVersion)
- MADOC (University of Mannheim) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- statistical power analysis, correlation analysis, regression analysis, tetrachoric correlation, multiple linear regression, logistic regression, Poisson regression, software extension
- MeSH terms
- Algorithms, Data Interpretation, Statistical, Regression Analysis, Software, Linear Models
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