Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses
Behavior Research MethodsPublished 1 November 2009Open access
Franz Faul, Edgar Erdfelder, Axel Buchner, Albert-Georg Lang
Citations36,027
SJR quartileQ1
SJR score2.46
SNIP3.13
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
In the new version, procedures to analyze the power of tests based on single-sample tetrachoric correlations, comparisons of dependent correlations, bivariate linear regression, multiple linear regression based on the random predictor model, logistic regression, and Poisson regression are added.
Abstract
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.
Keywords
MathematicsAgricultural and Biological Sciences
Computers Environment and Urban SystemsStatistical power analysis for the behavioral sciences
65,645 Citations1990
Behavior Research MethodsG*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences
64,098 Citations2007Franz Faul, Edgar Erdfelder +2 more
G*Power 3 provides improved effect size calculators and graphic options, supports both distribution-based and design-based input modes, and offers all types of power analyses in which users might be interested.
Psychology Press eBooksApplied Multiple Regression/Correlation Analysis for the Behavioral Sciences
20,853 Citations2014Patricia Cohen, Patricia Cohen +2 more
Psychological BulletinTests for comparing elements of a correlation matrix.
4,421 Citations1980James H. Steiger
Statistical Methods in Medical Research
1,618 Citations2002P. Armitage, George Berry +1 more
Statistics in MedicineA simple method of sample size calculation for linear and logistic regression
1,087 Citations1998F. Hsieh, D. Blöch +1 more
This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model.
Controlled Clinical TrialsPower and Sample Size Calculations for Studies Involving Linear Regression
1,028 Citations1998William D. Dupont, W. Dale Plummer
This article presents methods for sample size and power calculations for studies involving linear regression, applicable to clinical trials designed to detect a regression slope of a given magnitude or to studies that test whether the slopes or intercepts of two independent regression lines differ by a given amount.
Statistics in MedicineSample size determination for logistic regression revisited
436 Citations2006Eugene Demidenko
General Wald-based power and sample size formulas are derived and applied to minimize the total sample size in a case-control study to achieve a given power by optimizing the ratio of controls to cases.
Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie)A Multitrait-Multimethod Validation of the Implicit Association Test
405 Citations2007Brian A. Nosek, Frederick L. Smyth
It is concluded that these implicit and explicit measures assess related but distinct attitude constructs, which provides a basis for, but does not distinguish between, dual-process and dual-representation theories that account for the distinctions between constructs.
Journal of the American Statistical AssociationCorrelation Coefficients Measured on the Same Individuals
261 Citations1969Olive Jean Dunn, Virginia A. Clark
Psychological BulletinMultiple correlation: Exact power and sample size calculations.
221 Citations1989Constantine Gatsonis, Allan R. Sampson
Statistics in MedicineSample size and optimal design for logistic regression with binary interaction
191 Citations2007Eugene Demidenko
Close-form formulas are derived for interaction studies with binary exposure and covariate in logistic regression and the formula for the optimal control-case ratio is derived such that it maximizes the power function given other parameters.
Journal of the American Statistical AssociationSample Size for Logistic Regression with Small Response Probability
159 Citations1981Alice S. Whittemore
The Fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented Hessian matrix of the moment-generating function for the covariates to obtain a simple closed-form estimate of the asymptotic covariance Matrix of the maximum likelihood parameter estimates, and thus approximate sample sizes needed to test hypotheses about the parameters.
Journal of Educational and Behavioral StatisticsInferential Methods for the Tetrachoric Correlation Coefficient
124 Citations2005Douglas G. Bonett, Robert M. Price
A new and simple method of accurately approximating the tetrachoric correlation is introduced and is used to derive a simple standard error, confidence interval, and sample size planning formula, which is shown to perform far better than the confidence interval computed by SAS.
Journal of the American Statistical AssociationA Tale of Two Regressions
114 Citations1974Allan R. Sampson
Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie)Predicting Voting Behavior with Implicit Attitude Measures
94 Citations2007Malte Friese, Matthias Bluemke +1 more
This prospective study tested the hypothesis that Implicit Association Test (IAT) measures of the five major political parties in Germany would improve the prediction of voting behavior over and above explicit self-report measures in the 2002 parliamentary elections.
PsychometrikaOn the Mean and Variance of the Tetrachoric Correlation Coefficient
73 Citations1977Morton B. Brown, Jacqueline Benedetti
Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie)Developmental Fractionation of Working Memory and Response Inhibition During Childhood
62 Citations2007Satoshi Tsujimoto, Mariko Kuwajima +1 more
The results suggest that functional neural systems for visuospatial WM, auditory WM, and RI, especially those in the LPFC, become fractionated during childhood, thereby enabling more efficient processing of these critical cognitive functions.
Statistics in MedicineA practical approach to computing power for generalized linear models with nominal, count, or ordinal responses
57 Citations2006Robert H. Lyles, Hung‐Mo Lin +1 more
This work presents a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non‐continuous outcome and proves particularly flexible for handling one or more continuous covariates without any need for discretizing.
Computational Statistics & Data AnalysisComputing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient
56 Citations2003Denise Benton, K. Krishnamoorthy
The algorithms for computing the distributions of the squared sample multiple correlation coefficient, noncentral t, and noncentral chisquare so that they can be coded in any desired computer language are given.
Educational and Psychological MeasurementConfidence Intervals, Power Calculation, and Sample Size Estimation for the Squared Multiple Correlation Coefficient under the Fixed and Random Regression Models: A Computer Program and Useful Standard Tables
43 Citations2001Jorge L. Mendoza, Karen Stafford
Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie)An Ontological Test of the IAT
41 Citations2007Marco Perugini, Rick O’Gorman +1 more
Behavior Research Methods, Instruments, & ComputersComputing aspects of power for multiple regression
38 Citations2004William P. Dunlap, Xue Xin +1 more
The program offered herein is immediately downloadable at no charge, runs under Windows, is interactive, self-explanatory, flexible to fit the user’s own regression problems, and is as accurate as single precision computation ordinarily permits.
BiometrikaSample size calculations for logistic and Poisson regression models
36 Citations2001Gwowen Shieh
BiometrikaTables of upper percentage points of the multiple correlation coefficient
35 Citations1972Yoong-Sin Lee
Journal of the American Statistical AssociationSample Size for Logistic Regression with Small Response Probability
31 Citations1981Alice S. Whittemore
Journal of the American Statistical AssociationA Tale of Two Regressions
28 Citations1974Allan R. Sampson
Encyclopedia of Statistics in Behavioral SciencePower Analysis for Categorical Methods
27 Citations2005Edgar Erdfelder, Franz Faul +1 more
Behavior Research MethodsMethodological and computational considerations for multiple correlation analysis
6 Citations2007Gwowen Shieh, Chien-Feng Kung
The statistical methods and available programs of multiple correlation analysis purport to enhance pedagogical presentation in academic curricula and practical application in psychological research and develop corresponding Excel worksheets that facilitate the implementation of various aspects of the suggested significance tests.