Statistical power analyses using G∗Power 3.1: tests for correlation and regression analyses

A G*Power post hoc power analysis with an input effect size of 0.10 indicated an achieved power of 0.825, suggesting a high probability of correctly rejecting the null hypothesis.

“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].”

The sample size of 50 participants was chosen to account for up to 20% attrition, so as to obtain at least 40 complete study samples powered to detect a medium effect size (Cohen's d > 0.45) primary outcome difference in pre vs post PHQ9 scores at 0.8 power and alpha 0.05, computed a priori.

“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].”

The study sample (n = 467) was larger than the required sample size (434) to attain an adequate power level (0.80) for detecting small effect sizes.

“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”

Sample size was calculated to require 26 calves per treatment to achieve 80% power with a significance level of α = 0.05, and 30 calves per treatment were included to allow for dropouts.

“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.”

A prior power analysis 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.

“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)).”

An a priori power analysis revealed a required sample size of 108 in total and 36 participants in each group.

“The power analysis revealed a required sample size of 108 in total and 36 participants in each group.”

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% yielded a total sample size of 196.

“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.”

A power calculation with 80% power and α-error probability of 0.05 to detect an effect size of 0.1 resulted in a total sample size of 967 participants.

“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.”

Our sample size of about 2600 subjects included in GWAS analysis 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.

“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.”

A power analysis indicated that the sample of 57 had 80% power to detect a medium-to-large effect for the baseline regressions and a large effect for the logistic regression.

“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.”

A power calculation using G*Power determined that 107 participants were needed to achieve 95% power to detect a medium effect size (f2=0.15) in multiple linear regression with two predictors at an alpha of 0.05.

“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.”

The study had adequate statistical power: with 80% power and an a priori effect size of R2 = .13, a minimum sample of 216 was required.

“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.”

A statistical power analysis was performed using GPower 3.1 to estimate sample size for a comparison of differences between two dependent means (matched pairs).

“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).”

Using G*Power, to detect a similar between-group effect at a 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).

“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 study's target sample size (N=432) was determined with an a priori power analysis using G*Power.

“Wedetermined our target sample size (N=432) with an a priori power analysis using the statistical software G*Power [38, 39].”

The power was recalculated with G*Power assuming SAQOL-39 as primary outcome, effect size 0.3, sample size 30, measurement coefficient 0.654, two repeated measures and two groups, obtaining a final power of 96%.

“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%.”

The target sample size was 30 participants per discipline, based on a G*Power calculation assuming a medium effect size of 0.5, power of 0.8, and type I error probability of 0.05, giving a minimum of 28 per group.

“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].”

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.

“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).”

An a priori power analysis using G*Power with alpha .05, power 0.95, and effect size f = .35 determined a desired total sample size of 109; 120 participants were recruited to allow for 10% data loss.

“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).”

An a priori power analysis in G*power reveals a total sample size of N = 366 needed to detect effect sizes larger than g = 0.34.

“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).”

Sample size was calculated using G*Power with a focus on calf age and plasma glucose; 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 after long-distance transport in a similar previous study; to obtain a power of 0.80 with alpha 0.05, the minimum sample size needed was 31 calves per treatment;

“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”

A post-hoc power analysis on the ANCOVA in subsection V-D using G*Power calculated a power (1-β) of 0.73.

“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.”

Power calculations were carried out a-priori using G*power 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.

“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.”

An a priori power analysis indicated that at least 90 participants were necessary to detect a moderate effect (Cohen's f = 0.25) of miCBT vs. WLC with 95% power at α = 0.05, and the target sample size was increased to 120 to account for a 25% dropout rate.

“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.”

A power analysis using G*Power indicated that, based on 2 groups, 3 repeated measurements, 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.

“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”

An a priori power analysis indicated that a sample of 42 participants was required (ρ H1 = 0.18, α = 0.05, Power = 0.90).

“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).”

The study used G*Power 3.1 power analysis; for an independent-samples t-test with d = 0.30, alpha = 0.05, and power = 0.80, the required sample size was about 176 per condition.

“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.”

The correlation results for PP and CFR from Buchsbaum et al. were used post hoc to calculate statistical power, resulting in a power value of .95.

“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).”

A power analysis was performed using G*Power with parameters taken from previous reports or similar experiments.

“Power analysis was performed using G∗Power (59, 60) with parameters taken from previous reports or similar experiments.”

The sample size was determined by an a priori power analysis using G*Power, assuming power 0.80, alpha 0.05, required N=90 to detect medium-sized effects of d=0.4.

“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.”

Post-hoc calculation of the effect sizes for comparisons between the forest and roadside walks were small (partial η2 less than 0.03), whereas the effect sizes for comparisons among walks and ADL conditions were of medium size (partial η2 greater than 0.06).

“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].”

Anodal and cathodal tDCS result in excitability-enhancing and excitability-reducing plasticity, respectively.

“Similar to the acute membrane polarization effects, anodal and cathodal tDCS result in excitability-enhancing and excitability-reducing plasticity, respectively [16, 20, 21].”

According to G*Power's calculation, a conservative Wilcoxon-Mann-Whitney two-tailed test requires 90 participants per condition to detect medium-sized effects (Cohen's d = 0.5) at alpha = 0.05 with power (1-beta) = 0.90.

“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.”

For the Wilcoxon Signed-rank tests used, the needed sample size was always below the sample size used for the primary studies (1000).

“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.”

Patients are more likely to accept vaccine recommendations from a healthcare provider if the provider uses presumptive statements rather than participatory statements.

“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).”

A priori power analysis indicated a minimum sample size of 108 participants (36 per condition) to detect a medium effect size (0.25) with 80% power at a 0.05 significance level.

“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.”

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.

“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.”

Sample size for the larger study was determined on the basis of primary endpoints of 3 outcomes with Bonferroni's corrected α value, and for this subgroup analysis of participants with IBS-C (n = 43), power was estimated to range from 0.57 to 0.98.

“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”

The sample size was determined by power analysis using G*Power, with effect size 0.30 from a previous study, significance level .05, power 80%, yielding an optimal sample size of approximately 45 dyads per group.

“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].”

A minimum sample size of 90 participants was determined based on a power analysis for fixed effects, omnibus, 1-way ANOVA using G*Power 3.1 software (α = 0.05, power = 0.85, medium effect size f = 0.38).

“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).”

The required sample size for Study 1 to detect a small to medium-sized point biserial correlation between analytic thinking and identification of the deepfake video as fake was determined a priori using G*Power to be 191 (two-tailed, alpha = .05, power = .80, rho = .20).

“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).”

The required sample size to detect a small to medium-sized Pearson correlation between analytic thinking and continuous deepfake identification was 193.

“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).”

The required sample size to detect a small to medium effect of f2 = .10 was at least 432.

“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.”

A post-hoc power analysis was conducted to estimate the sample size needed to detect between-group differences.

“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.”

The sample size was estimated using G*Power.

“The sample size was estimated using G*Power (Faul et al., 2009).”

Sample size estimation indicated that 80 6-person groups were needed to detect a significant effect based on an estimated average small-to-medium effect size of oxytocin effect on social behaviors (d = 0.28).

“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).”

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.

“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 .”

A sample size of 61 participants was needed to detect a moderate correlation between SPE on trust and on interpersonal distance with α = 0.05 and 90% power.

“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).”

We performed power analysis 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.

“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.”

A required sample size was calculated for depressive symptoms assessed by DASS 21; to detect a small effect size (0.25) or more at alpha 0.05 and beta 0.15, the estimated sample size was 289 participants in each group.

“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.”