G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences

An a priori sample-size estimate indicated at least 30 participants per group were needed to allow for a 20% dropout rate.

“The estimate was that we needed at least 30 participants per group to account for a 20% dropout rate.”

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).”

A minimum sample size of n = 1145 was needed to detect a small effect size (f2 = 0.02) for the eight-predictor Comprehensive School Survey difference-in-difference regression models, based on alpha = 0.05 and power = 0.95.

“According to G*Power v3.1.97(Faul et al., 2007), a minimum sample size of n = 1145 was needed to detect a small effect size (f 2 = 0.02) for our eight-predictor Comprehensive School Survey (CSS) difference-in-difference (DiD) regression models, based on α = 0.05 and, conservatively, power = 0.95.”

A minimum sample size of eight individuals was determined at power 0.80 (two-tailed α = 0.05) and effect size for enjoyment equal to 1.0.

“At a power equal to 0.80 (two-tailed α = 0.05) and effect size for enjoyment equal to 1.0, a minimum sample size of eight individuals was determined [26] which is similar to a previous study [12].”

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.”

A sample size estimation established that nine participants per group were needed (f = 0.25, actual power = 80.70%) to detect differences with an assumed Type I error of 0.05 and statistical power of 80%.

“The results established a need for nine participants per group (f = 0.25 and actual power = 80.70%) to detect differences with an assumed Type I error of 0.05 and a Type II error rate of 0.20 (statistical power = 80%).”

The sample size was calculated using G*Power ver. 3.1.9.7 with α=.05 and power=.80, assuming an effect size of Cohen's d=0.85, yielding a minimum required sample size of 22 participants per group.

“The sample size was calculated using G*Power ver. 3.1.9.7 (Heinrich-Heine-Universität Düsseldorf) with a significance level of α=.05 and statistical power of .80. Assuming an effect size of Cohen’s d=0.85, the minimum required sample size was 22 participants per group [23].”

The minimum required sample size for each group was determined to be 26 individuals for a two-tail test of the difference between two independent means, with a 1:1 allocation, power of 0.80, significance level of 0.05, and effect size of 0.80.

“For a two-tail test of the difference between two independent means (two groups), with a 1:1 allocation, a power of 0.80, a significance level of 0.05, and an effect size of 0.80, the minimum required sample size for each group was determined to be 26 individuals.”

The study's sample size was justified by a G-Power calculation with eight predictors, power 0.95, and effect size 0.15, indicating a minimum of 160 respondents.

“The sample size was estimated using G-Power 3.1 software with eight predictors, a power of 0.95, and an effect size of 0.15. The smallest number of samples that needed to be analyzed with sufficient power was 160 [74].”

A sample of 73 subjects per group is adequate to detect a minimum effect size of f2 = 0.15 with power 0.90, 7 predictors, and α = 0.05.

“Taking into account a power of 0.90, 7 predictors (i.e., the maximum number of predictors included in multiple linear regression), and α = 0.05, a sample of 73 subjects for each group is adequate to detect a minimum effect size of f2 = 0.15, which is considered a medium effect [59].”

An a priori power analysis using G*Power indicated that 77 participants were needed to detect a medium effect size with three predictors, .05 alpha, and .8 power.

“To detect a medium effect size with three predictors, and .05alpha level, and a .8/80%power which is often considered to be sufficient for a medium effect size (Cohen, 1988), this necessitated 77 participants.”

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)).”

The sample size was calculated using G-Power software version 3.1 for a moderate effect size set at 0.5, an expected power of 0.8 and an alpha error probability of 0.05.

“The sample size was calculated using the G-Power software version 3.1 [64] for a moderate effect size set at 0.5, an expected power of 0.8 and an alpha error probability of 0.05.”

A priori power analysis for phase 2 of the CovSocial project, using G*Power with α = 0.05, power = 0.80, three groups, two measurements, and effect sizes r = 0.39 and f = 0.10, yielded a required sample size of 297 individuals.

“Key parameters included α = 0.05, power = 0.80, three groups, and two measurements, with effect sizes denoted by r = 0.39 and f = 0.10. These calculations yielded a required sample size of 297 individuals.”

The sample size was calculated to be 287 for linear multiple regression with an effect size of 0.10, 13 independent variables, a significance level of 0.05, and 95% power.

“considering an effect size of 0.10, 13 independent variables associated with sleep quality based on the relevant published studies [26–28], a significant level (P) of 0.05, and 95% power, the sample size was calculated to be 287.”

Sample size was calculated using G*Power 3.1 with alpha 0.05, power 0.80, two-tailed t-test, and effect size 0.60, requiring 90 participants (45 per condition).

“To calculate the sample size, we used the G*Power 3.1 software (30), taking into account an alpha of 0.05 and a statistical power of 0.80 on a two-tailed t-test. We need a sample size of 90 participants (45 participants per condition) to reach an effect size of 0.60 for meaning in life.”

An a-priori power calculation at 0.8, medium effect size f = 0.25 recommends a sample size of 28.

“(using the G∗Power3.1 power analysis program, an a-priori power calculation at 0.8, medium effect size f = 0.25 recommends a sample size of 28; Faul et al., 2007).”

Power analysis indicated a total sample size of 154 to reach an effect of f=0.25 and 80% power, two-tailed alpha of 0.05, two groups and three measurement points.

“To reach an effect of f =0.25 and 80% Power, a two-tailed alpha of 0.05, two groups and three points of measurement where entered and resulted in a total sample size of 154.”

For the nested RCT, assuming a participation rate of 80% and a correlation of 0.5 among repeated measures, the study will have sufficient power (1-β > 0.99) to detect medium effect sizes (f = 0.25).

“Given a maximum of 15 bodily interventions and 15 control interventions per person and assuming a participation rate in daily interventions of 80% (which is a rather conservative estimate, as compared to the previously observed 96% participation rate in an earlier study [51]), we expect on average a total of 24 completed smartphone-triggered interventions per participant. Assuming a correlation of”

With alpha 0.05, power 0.9, and effect size f=0.25, a total sample size of 46 participants (23 per group) would be needed.

“With an alpha of 0.05, a power of 0.9, and an effect size of f = 0.25, a total sample size of 46 participants would be needed (i.e., 23 per group).”

Sample size was calculated based on recent research evaluating telemedical-based treatment of posttraumatic stress symptoms, assuming a moderate between-group effect at T1 (Cohen's d = 0.5), significance level α = 0.05, power 1-β = 0.90, yielding optimal n = 140; expecting 40% dropout, n = 94 additional, yielding ideal baseline n = 234.

“Anticipated sample size was calculated based on recent research evaluating the efficacy of telemedical-based treatment of posttraumatic stress symptoms [20, 21, 38].”

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.”

Sample size has been calculated for a 3 (between) × 4 (within) ANOVA using G*Power software, setting alpha to 0.05, power to 0.80, and possible dropout, a total sample of 90 is considered enough to detect a small effect size (f = 0.20).

“Sample size has been calculated for a 3 (between) × 4 (within) ANOVA using G*Power software (release 3.1.3) [50]. Setting alpha to 0.05, power to 0.80, and possible dropout, a total sample of 90 is considered enough to detect a small effect size (f = 0.20).”

Post hoc sample size calculations on the primary outcome (AAQ-ABI) indicate a total sample size of 58 (ES partial η2=.17, power=.80) is required to establish a significant interaction effect from pre to post intervention.

“Post hoc sample size calculations on the primary outcome in this study (AAQ-ABI), indicates a total sample size of 58 ( ES Partial η2 = .17, Power = .80), is required to establish a significant interaction effect from pre to post intervention (Faul, Erdfelder, Lang, & Buchner, 2007).”

The sample size and power were estimated by a priori or criterion calculation using G*Power software.

“The sample size and power were estimated by A priori or Criterion calculation using G*Power software (Version 3.1.9.7, RRID:SCR_013726) (Faul et al. 2007).”

An a priori power analysis indicated a minimum sample size of 22 subjects with actual power 0.96.

“Results of the power analysis indicated a minimum of 22 subjects with an actual power of 0.96.”

A minimum sample size of 52 nursing students was calculated based on a significance level of 0.05, an effect size (d) of 0.8, and 80% power.

“A minimum sample size of 52 nursing students was calculated based on a significance level of 0.05, an effect size (d) of 0.8, and 80% power [33].”

The study was underpowered to detect between-group differences in YBOCS change, with observed power of .49.

“An observed (post-hoc) power analysis using G*Power (Faul et al., 2007) with 𝛼 = .05, observed effect size of d = .369, n = 34 for sexual minorities and n = 157 for heterosexual individuals, indicated that observed power was .49 to detect between-group differences in YBOCS change.”

An a priori power analysis indicated that a sample size of 114 was needed to detect the model's significance at alpha = .05, power = .80, effect size f2 = 0.15, with 9 predictors; therefore, the sample size of 292 was sufficient.

“An a priori analysis was conducted using G*power analysis (version 3.1; Faul et al., 2007), which indicated that a sample size of 114 was needed to detect the model's significance at α = .05,power (1 -β error probability) = 0.80, effect size f 2 = 0.15 (medium), with the number of predictors = 9.Therefore, this study's sample size of 292 people was sufficient.”

A power analysis using G*Power indicated that a sample of 93 OCD patients would be sufficient to detect within-factors interaction with power >95% to test a small-medium effect size with α<.05.

“A power analysis using G*Power [51] indicated that a sample of 93 OCD patients would be sufficient to detect within- factors interaction with power > 95 % to test a small-medium effect size (based on our pilot study [49]) with a Type I error α < .05.”

A sensitivity analysis showed the OCI-R subsample of 83 participants allows detecting effect sizes η2 ≥ 0.08 for OCD symptom severity on alerting benefits and η2 ≥ 0.025 for OCD symptom severity on reduction in Simon/Flanker costs with a warning cue; smaller effects could be missed.

“A sensitivity analysis (Faul et al., 2007) showed that with alpha set to 0.05 and power set to 0.80, the OCI-R subsample of 83 participants allows detecting the effect of OCD symptom severity on alerting benefits of size η 2 ≥ 0.08, and the effect of OCD symptom severity on the reduction in Simon/Flanker costs on trials that start with a warning cue of size η 2 ≥ 0.025. Smaller effects could be”

A sensitivity analysis showed the matched sample of 80 participants allows detecting effect sizes η2 ≥ 0.09 for OCD on alerting benefits and η2 ≥ 0.024 for OCD on reductions in Simon/Flanker costs with a warning cue; smaller effects could be missed.

“However, a sensitivity analysis (Faul et al., 2007) showed that with alpha set to 0.05 and power set to 0.80, the matched sample of 80 participants allows detecting the effect of OCD on alerting benefits of size η 2 ≥ 0.09, and the effect of OCD on reductions in Simon/Flanker costs on trials that start with a warning cue of size η 2 ≥ 0.024. Smaller effects could be missed.”

The authors planned to collect data from at least 261 participants, computed using G*Power for an ANOVA with main effects and interactions, specifying an effect size of 0.25, a significance threshold of 0.0045, a desired power of 0.8, 24 groups, and respective degrees of freedom.

“We planned to collect data from at least 261 participants.We computed the required sample size using the software G*Power [34] for an ANOVA with main efects and interactions; specifying the default efect size of 0.25, a signifcance threshold of = 0.05 = 0.0045 (i.e., due to testing multiple hy-11 potheses; see Section 4.2.6), a desired power of 0.8, 24 groups, and the respective degrees of freedom”

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 study's sample of N=110 provides sufficient statistical power to detect within-group and interaction effects of d=0.20 and between-group effects of d=0.46 or larger, and is sufficiently powered to address its primary aims.

“Power analysis with G*Power (v3.1; 109) based on traditional NHST, with alpha=.05, power=.80, 3 groups, and 8 measurements (the 4 tasks described above, with 2 variables from each task in each model) indicates that our N=110 can reliably detect within-group and interaction effects of d=0.20, and between-group effects of d=0.46 or larger. Thus, the study is sufficiently powered to address its prima”

Study 3 sample size was determined by G*Power analysis, requiring at least 172 participants to detect a medium effect size (f = 0.25) for a between-subjects design with power 0.90 (α = 0.05).

“According to G*Power analysis [67], at least 172 participants were needed to detect a medium effect size (f = 0.25) for a between-subjects design with power 0.90 (α = 0.05).”

A G*Power analysis indicated that at least 256 participants were needed to detect a medium effect size (ηp2 = 0.03) for a between-subject design with power 0.80 and α = 0.05.

“A G*Power analysis [67] showed that at least 256 participants were needed to detect a medium effect size (ηp2 = 0.03) for a between-subject design with a power of 0.80 (α = 0.05).”

A post-hoc sensitivity power analysis showed a sample of 21 participants would be sensitive to effects of ρ = 0.57, assuming 80% power, alpha 0.05.

“Using an exact two-sided test, a sample of 21 participants (the number for whom we obtained personality data) would be sensitive to effects of ρ = 0.57, assuming 80% power, an alpha level of 0.05, and a null hypothesis correlation of 0.”

An a priori power analysis was used to detect a medium-to-large effect f = 0.30 with power preset at 0.8.

“An a priori power analysis, calculated using G*Power (Faul et al., 2007), was used.A MANCOVA model was used, with between-and within-group factors, to detect a medium-to-large effect, f = 0.30.This effect size was determined based on the calculated effect size in an exercise study examining sCort outcomes with similar experimental design (Hill et al., 2008).Power was preset at 0.8.”

A full-scale randomised controlled trial needs a total sample size of 128 participants to detect a true between-group difference, assuming 80% power, a type I error probability of 0.05, a two-tailed test, and an effect size of r = 0.5; including a 20% attrition rate, a total sample size of 160 participants is required.

“Utilising G*Power version 3.1.9.7 [61], with an assumed power of 80%, a type I error probability of 0.05, a two-tailed test, and effect size of r = 0.5 (SPL effect sizes mean), a total sample size of 128 participants is needed to detect a true between-group difference. Including a 20% attrition rate, a total sample size of 160 participants is required.”

The sample size was computed using G*Power 3 with 10 predictors, an effect size of 0.15, an alpha error probability of 0.05, and a power of 0.95, yielding a target sample size of 172 participants.

“The sample size for this study was computed using G*Power 3, a statistical power analysis program for social and medical sciences (33). We set the sample size computation based on 10 predictors, an effect size of 0.15, an alpha error probability of 0.05, and a power of 0.95. The computed target sample size was 172 participants.”

The required sample size obtained with G*Power was 128 participants (64 per group).

“For the analysis, the software G*Power (version 3.1.6 [54]) was used, and a required sample size of 128 participants was obtained (64 per group).”

To determine the required sample size, a power estimation was carried out with G*Power: ANOVA with repeated measures and within-between interactions, 2 groups and 3 measurement times, small expected effect 0.1, desired power 0.80, p = 0.01 (4 outcome variables), correlation among repeated measures 0.7 results in a total sample size of N = 142.

“To determine the required sample size, a power estimation was carried out with G*Power [38]: ANOVA with repeated measures and within-between interactions, 2 groups and 3 measurement times, small expected effect 0.1, desired power of 0.80 (1-β), p = 0.01 (4 outcome variables), correlation among repeated measures 0.7 results in a total sample size of N = 142.”

An a priori power analysis revealed a required sample size of 152 participants to detect at least a small effect size (f = 0.10) for the interaction between time (five assessment points) and group (intervention vs. CAU), assuming power 0.80, alpha 0.05, and 20% drop-out.

“an a priori power analysis with G*Power [181] using repeated measures analyses of variance (ANOVA, within-between-interaction), an assumed power of 0.80, an alpha-level of 0.05, and an expected drop-out rate of 20% [98], revealed a required sample size of 152 participants.”

Power analyses were conducted using G-Power to determine the most appropriate sample size for the pilot randomized controlled trial.

“Power analyses were conducted using G-Power [71] to determine the most appropriate sample size for the pilot randomized controlled trial.”

Using G*Power 3 and previous meta-analyses of the effect size of mindfulness interventions on anxiety, the authors estimated that a sample size of 290 cases was needed.

“Using the G*Power 3 [19] software and previous meta-analyses of the effect size of mindfulness interventions on anxiety [20], we estimated that we would need a sample size of 290 cases for the study.”

A post hoc power analysis indicated that with 10 predictors, 87 participants, and a critical α of .05, the study had sufficient power (exceeding .99) to detect a large effect size (f2=.60).

“A post hoc power analysis was conducted using G*Power3 (Faul et al., 2007); with 10 predictors, 87 participants, and a critical α of .05, the study had sufficient power (exceeding .99) to detect a large effect size (f 2 = .60).”

Sample size was calculated using G*Power considering repeated measure ANOVAs with a medium effect size of 0.25, power of 0.80, two groups, and four time measurements, with an addition of an estimated 30% drop-out rate.

“The sample size was calculated using G*Power [34] and considering our main statistical analyses (repeated measure ANOVAs with a medium effect size of 0.25, power of 0.80, two groups, and four time measurements), with an addition of an estimated 30% drop-out rate.”

A power analysis with the software G*Power resulted in a target sample size of N = 103 to detect a medium-sized effect (f = 0.28) with α = 0.05 and a power of 0.80 for an ANCOVA.

“A power analysis with the software G*Power [29] resulted in a target sample size of N = 103 to detect a medium-sized effect (f = 0.28) with α = 0.05 and a power of 0.80 for an ANCOVA.”

The sample size was calculated as 52 subjects for the paired t-test using G*Power with α=0.05, effect size d=0.80, and power β=0.80.

“The sample size was determined using G * Power software,version 3.1.9.4; Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Ger-many) [27] and derived from the insertion of the α (two-tailed) (0.05), effect size d (0.80), and power β (0.80) and ultimately calculated as 52 subjects for the paired t-test.”

A minimum of 316 university students was deemed necessary to have enough statistical power according to G-power software (multiple regression; R2 deviation from zero), based on a 5% risk of error, 80% power, f2 = 2.5% and 10 factors to be entered in the multivariable analysis.

“A minimum of 316 university students was deemed necessary to have enough statistical power according to the G-power software (multiple regression; R2 deviation from zero) [52], based on a 5% risk of error, 80% power, f2 = 2.5% and 10 factors to be entered in the multivariable analysis.”

An a priori power analysis showed that a total sample of 140 was required to achieve a power of 0.80 for detecting a medium effect size (d = 0.50) with an alpha of 0.05.

“An a priori power analysis was performed using G*Power3 [22] to examine the difference between the means of two independent groups on the CERQ scales, with a medium effect size (d = 0.50) and an alpha of 0.05. The results showed that a total sample of 140 was required to achieve a power of 0.80.”

The estimated sample size necessary to detect a small to medium effect size at an alpha rate of 0.05 (two-tailed) was 104 participants.

“Based on previous RCT studies of ACT interventions in HCPs [24, 29], we estimated a small to medium effect size (f = 0.22). The estimated sample size necessary to detect a small to medium effect size at an alpha rate of 0.05 (two-tailed) using the G* Power 3 programme [37], was 104 participants.”

Study power was estimated using different effect sizes from the literature and G*Power 3.1, and published in the study protocol.

“Different effect sizes found in the literature based on the transdiagnostic perspective of EDs were considered to estimate the study power in this study. These calculations were performed with the software program G*Power 3.1 [59] and published in the study protocol [58].”

A sample size of N = 70 is calculated to detect a medium to large effect size of d = 0.80 with alpha level 0.05 and power 0.80.

“To detect a medium to large effect size of d = 0.80, with an alpha level of α = 0.05 and a power of 0.80, G*Power [66] calculated a sample size of N = 70.”

The proposed sample size of 50 would leave 22 women per group (assuming 12% attrition) to provide outcome data and yield 80% power for a smallest detectable effect size of .87.

“The proposed sample size of 50 would leave 22 women per group (assuming 12% attrition) to provide outcome data and yield 80% power for a smallest detectable effect size of .87 (G*Power 3.1.9.4) [24].”

The required sample size was computed for an analysis of variance (ANOVA) with 2 groups (between variable; ACT + TAU vs. TAU) × 2 times (within variable; Time 0/Time 1).

“The required sample size was computed for an analysis of variance (ANOVA) with 2 groups (between variable; ACT + TAU vs. TAU) × 2 times (within variable; Time 0/Time 1).”

A minimum of 64 participants per arm is required to detect a moderate effect size (Cohen's d = 0.5) as statistically significant in a two-tailed test at alpha = 0.05 with 80% power.

“Therefore, to capture an effect size 0.5 as statistically significant in a two-tailed test at alpha = 0.05 and a power of (1-Beta) = 0.80, a minimum of 64 participants per Arm will be required, as computed by G*Power 3.0.10 (Faul et al., 2007).”

A G*Power analysis with power 0.8, alpha 0.05, and a priori moderate effect size d=0.5 indicated that a one-way univariate repeated-measures ANOVA requires 28 participants.

“A G*Power analysis (Faul et al., 2007) was conducted with power selected at 0.8, alpha at 0.05 and with an a priori moderate effect size of d = 0.5 (ηp2=0.06) selected (based on the criteria of Cohen (1988)).”

Statistical power analysis using G*Power indicates that with an alpha level of 0.05 and a beta level of 0.10, total sample size 206 is needed to detect moderate to medium effect size f = 0.25 in main and interaction effects with one-two-way ANOVA.

“Statistical power analysis using G*Power [43] indicates that with an α-level at 0.05 and, a β-level at 0.10, the total sample size in a design like this should be 206 to detect differences in the main and interaction effects of a moderate to medium effect size, f = 0.25, with a one-two-way analysis of variance (ANOVA).”

Power analyses with G*Power for detection of small effects (Cohen's f = 0.12) for interaction between time and treatment condition resulted in a sample size of 123 patients.

“Power analyses with G*Power (Faul et al. 2007) for the detection of small effects (Cohen’s f = 0.12) for the interaction between time (pre, mid-5, mid-15, post) and treatment condition (TAU-M versus TAU-PMR versus TAU) (ANOVA repeated measures, within-between-interaction, α = 0.05, power = 0.80, number of groups = 3, number of measurements = 4, pre-post correlation r = 0.05, nonsphericity correc”

A priori power analysis using G-Power was conducted to estimate a statistically sufficient sample size.

“To estimate a statistically sufficient sample size for the study, a priori power analysis using G‐Power (Faul et al., 2007) was conducted.”

A power analysis was conducted using G*Power based on effect sizes from McCracken et al. (2013).

“Based on these effect sizes, a power analysis was conducted using G* Power (Faul, Erdfelder, Lang, & Buchner, 2007).”

A power analysis indicated a detectable effect size of r = 0.15 in a sample of 66 participants (power = 0.80, alpha = 0.05).

“A power analysis in the software program G*Power (Faul et al., 2007) indicated a detectable effect size of r = 0.15 in a sample of 66 participants (power = 0.80, Cronbach ' s α = 0.05).”

A power analysis for a dependent sample t-test was conducted using G*Power to determine a sufficient sample size using alpha 0.05, power 0.80, a large effect size (dz=2.9), and two tails.

“Based on the effect size observed between NIRS devices during isometric exercise at 50% MVC, a power analysis for a dependant sample t -test was conducted using G*Power to determine a sufficient sample size using an alpha of 0.05, a power of 0.80, a large effect size ( dz ¼ 2.9 ), and two tails. 30”

Sample size was calculated using pain during arm elevation with no load as the primary outcome, with alpha 0.05 and power 80% for between-group analysis.

“Sample size was calculated (G*Power 3.1, Christian-Albrechts-Universitat, Kiel, Germany) using pain during arm elevation (no load) as the primary outcome, α = 0.05, and power of 80% for between-group analysis [24].”

The Experiment 1 sample size of 660 was chosen based on prior work and sensitivity power analyses showing at least 80% power to detect a minimum effect size of = .113 for mixed ANOVAs and d = 0.28 for follow-up independent samples t-tests.

“This sample size was chosen on the basis of prior work on the bias blind spot (Mandel et al., 2022) with sensitivity power analyses using G*Power (Faul et al., 2007) revealing that this sample provided at least 80% power to detect a minimum effect size of = .113 for the conducted mixed ANOVAs and d = 0.28 for follow-up independent samples t-tests.”

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.”

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.”

The rare APOE variant L28P is in complete linkage disequilibrium with the APOE*4 allele.

“due to the complete linkage disequilibrium of L28P with APOE*4 (C112R)”

In 1999, two groups independently identified a novel and rare missense mutation in the APOE gene (L28P; rs769452) in which leucine is replaced by proline at codon 28.

“In 1999, two groups independently identified a novel and rare missense mutation in the APOE gene [9, 10] in which the leucine residue is replaced by proline at codon 28 (L28P; rs769452).”

A priori power calculations indicated that a total sample size of 55 would be appropriate for main behavioural analyses in each tandem group.

“A priori power calculations were conducted using G∗Power 3.142 and indicated that a total sample size of 55 would be appropriate for our main behavioural analyses (e.g., linear regressions with 6 predictors) in each tandem group (effect size f2 = 0.15, power = 0.80, α = 0.05).”

Power calculation for the sample set was performed on G*Power, and for a total sample size of 60 spread equally across 3 groups, assuming a large effect size (f = 0.4) and β/α = 1, the power of the statistical test (1-β) was 88.1%.

“Power calculation for the sample set was performed on G*Power (v.3.1.9.7) [28]. We performed a “compromise power analysis” for one-way ANOVA (F-tests) for a total sample size of 60 spread equally across 3 groups. The calculations were performed assuming a large effect size (f = 0.4) and the ratio of type II to type I error (β/α) equals 1. The power of the statistical test (1-β) was thus determined”

A minimum of 98 participants were required for this study.

“According to Cohen’s sample size recommendation [30] and using G*Power [31] and the 10 times rule of thumb, a minimum of 98 participants were required for this study.”

To detect an effect size of d = 0.28 with power 1-β = 0.80, a sample size of at least 202 per group is needed.

“In order to detect such an effect with power 1-β = 0.80, future researchers should use a sample size of at least 202 per group (Faul, Erdfelder, Lang, & Buchner, 2007).”

A G*Power analysis showed that 787 participants were needed to detect a small effect size (Cohen's f = .10) with 80% power and alpha = .05.

“A G*Power analysis, a commonly used software for power analysis in the social and behavioral sciences [17,30], showed that 787 participants were needed to detect a small effect size (Cohen's 𝑓 = .10)with 80% power and 𝛼 = .05.”

Sample size was calculated using G*Power with effect size 0.8 and power 0.8, yielding an estimated sample size of 15.

“Our initial sample size was calculated using the G*Power tool (Faul et al., 2007). Based in other effects described in the literature, the effect size considered is 0.8 (the mean difference is 0.8 standard deviations). In these conditions, for power of 0.8 the estimated sample size is 15.”

Based on a power analysis using G*Power, given α = 0.05, power of 0.80 and effect size of 0.24 (as per a meta-analysis of dual n-back training studies), for a repeated measures, within-between interaction, a minimum of 139 individuals would be required for analysis.

“Based on a power analysis using G*Power [61], given α = 0.05, power of 0.80 and effect size of 0.24 (as per a meta-analysis of dual n-back training studies [14]) for a repeated measures, within-between interaction, a minimum of 139 individuals would be required for analysis.”

Sample size was justified by power calculation (G*power3, α=0.05; 1−β=0.80; based on observed data).

“Following study approval from the University of Hertfordshire Life and Medical Sciences Ethics Committee (LMS/SF/UH/00011), and power calculation assessment for sample size (G*power3, Dusseldorf [34]; using α = 0.05; 1 − β = 0.80; based on observed data [9,14])”

The statistical power of each study was assessed by comparing sample sizes against a power calculation conducted with G*Power.

“Finally, the statistical power of each study included in the review was assessed by comparing the sample sizes in these studies against that recommended by a power calculation conducted with G*Power (Faul et al., 2007).”

An initial power analysis targeted detection of medium effects (d = 0.5, α = 0.05, 1 − β = 0.80) and suggested a sample size of n = 34.

“An initial power analysis in G*Power 3.0 (ref.51) targeted on the detection of medium effects (d = 0.5, α = 0.05 and 1 − β = 0.80) suggested a sample size of n = 34.”

A power analysis indicated that a sample size of 18 would achieve 90% power for a repeated measures design, given a large effect size (partial η2=0.14) and α=0.05.

“A power analysis using G*Power software45 indicated that a sample size of 18 would achieve 90% power for a repeated measures design, given a large effect size (partial η2=0.14) and α=0.05.”

A power analysis conducted with G*Power indicated that between subjects studies should have at least 64 participants in each group and within subjects studies should have at least 34 participants to have 80% power to detect a moderate effect.

“According to the power analysis conducted with G*Power (Faul et al., 2007), between subjects studies should have at least 64 participants in each group and within subjects studies should have at least 34 participants, to have 80% power to detect a moderate effect.”

Sample size was calculated a priori with G*Power, expecting moderate between-group differences, with 80% power, alpha 0.05, Cohen's d of 0.5, yielding 50 participants needed per condition.

“Sample size was calculated a priori with the statistical software G*Power [49] considering previous studies on complications of pain treatments [30,50].”

The sample size of 123 was powered to detect effects of Cohen's d = 0.45.

“The sample size of 123 was powered (with power = 0.8, alpha = 0.05, calculated with GPower [40]) to detect the effects of Cohen’s d = 0.45.”

Power analysis using G*Power 3 indicated that a sample size of N = 98 with both pretest and posttest data would yield power of .80 to detect a medium effect size (Cohen's f = .25).

“Power analysis conducted using G*Power 3 software (Faul, Erdfelder, Lang, & Buchner, 2007) indicated that a sample size of N = 98 with both pretest and posttest data would yield power of .80 to detect a medium effect size (Cohen’s f = .25).”

Prior to data collection, a power analysis for split-half reliability suggested a sample size of N = 138.

“For the main sample, prior to data collection, a power analysis concerning sample size for split-half reliability (bivariate correlation, two tailed) was performed by means of G-power [36], resulting in a suggested sample size of N = 138.”

The target sample size was 104 participants, calculated to provide 80% power at 5% significance, assuming a medium effect size of 0.25 and 25% loss to follow-up after 12 months.

“To provide 80% power (5% level of significance) and assuming a medium effect size of 0.25 and a loss to follow-up of 25% after 12 months, the target sample size was 104 participants [9].”