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

Abstract

G*Power (Erdfelder, Faul, & Buchner, 1996) was designed as a general stand-alone power analysis program for statistical tests commonly used in social and behavioral research. G*Power 3 is a major extension of, and improvement over, the previous versions. It runs on widely used computer platforms (i.e., Windows XP, Windows Vista, and Mac OS X 10.4) and covers many different statistical tests of thet, F, and χ2 test families. In addition, it includes power analyses forz tests and some exact tests. 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. Like its predecessors, G*Power 3 is free.

References

  • Akkad, D. A., Jagiello, P., Szyld, P., Goedde, R., Wieczorek, S., Gross, W. L., &Epplen, J. T. (2006). Promoter polymorphism rs3087456 in the MHC class II transactivator gene is not associated with susceptibility for selected autoimmune diseases in German patient groups.International Journal of Immunogenetics,33, 59–61.

    Article  PubMed  Google Scholar 

  • Back, M. D., Schmukle, S. C., &Egloff, B. (2005). Measuring taskswitching ability in the Implicit Association Test.Experimental Psychology,52, 167–179.

    PubMed  Google Scholar 

  • Baeza, J. A., &Stotz, W. (2003). Host-use and selection of differently colored sea anemones by the symbiotic crabAllopetrolisthes spinifrons.Journal of Experimental Marine Biology & Ecology,284, 25–39.

    Article  Google Scholar 

  • Barabesi, L., &Greco, L. (2002). A note on the exact computation of the Student t, Snedecor F, and sample correlation coefficient distribution functions.Journal of the Royal Statistical Society,51D, 105–110.

    Article  Google Scholar 

  • Berti, S., Münzer, S., Schröger, E., &Pechmann, T. (2006). Different interference effects in musicians and a control group.Experimental Psychology,53, 111–116.

    PubMed  Google Scholar 

  • Bradley, D. R., Russell, R. L., &Reeve, C. P. (1998). The accuracy of four approximations to noncentralF. Behavior Research Methods, Instruments, & Computers,30, 478–500.

    Article  Google Scholar 

  • Bredenkamp, J. (1969). Über die Anwendung von Signifikanztests bei Theorie-testenden Experimenten [The application of significance tests in theory-testing experiments].Psychologische Beiträge,11, 275–285.

    Google Scholar 

  • Bredenkamp, J., &Erdfelder, E. (1985). Multivariate Varianzanalyse nach dem V-Kriterium [Multivariate analysis of variance based on the V-criterion].Psychologische Beiträge,27, 127–154.

    Google Scholar 

  • Buchner, A., Erdfelder, E., &Faul, F. (1996). Teststärkeanalysen [Power analyses]. In E. Erdfelder, R. Mausfeld, T. Meiser, & G. Rudinger (Eds.),Handbuch Quantitative Methoden [Handbook of quantitative methods] (pp. 123–136). Weinheim, Germany: Psychologie Verlags Union.

    Google Scholar 

  • Buchner, A., Erdfelder, E., & Faul, F. (1997). How to use G*Power [Computer manual]. Available at www.psycho.uni-duesseldorf.de/aap/projects/gpower/how_to_use_gpower.html.

  • Busbey, A. B. I. (1999). Macintosh shareware/freeware earthscience software.Computers & Geosciences,25, 335–340.

    Article  Google Scholar 

  • Cohen, J. (1988).Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • D’Agostino, R. B., Chase, W., &Belanger, A. (1988). The appropriateness of some common procedures for testing the equality of two independent binomial populations.American Statistician,42, 198–202.

    Article  Google Scholar 

  • Erdfelder, E. (1984). Zur Bedeutung und Kontrolle desb-Fehlers bei der inferenzstatistischen Prüfung log-linearer Modelle [Significance and control of theb error in statistical tests of log-linear models].Zeitschrift für Sozialpsychologie,15, 18–32.

    Google Scholar 

  • Erdfelder, E., Buchner, A., Faul, F., &Brandt, M. (2004). GPOWER: Teststärkeanalysen leicht gemacht [Power analyses made easy]. In E. Erdfelder & J. Funke (Eds.),Allgemeine Psychologie und deduktivistische Methodologie [Experimental psychology and deductive methodology] (pp. 148–166). Göttingen: Vandenhoeck & Ruprecht.

    Google Scholar 

  • Erdfelder, E., Faul, F., &Buchner, A. (1996). GPOWER: A general power analysis program.Behavior Research Methods, Instruments, & Computers,28, 1–11.

    Article  Google Scholar 

  • Erdfelder, E., Faul, F., &Buchner, A. (2005). Power analysis for categorical methods. In B. S. Everitt & D. C. Howell (Eds.),Encyclopedia of statistics in behavioral science (pp. 1565–1570). Chichester, U.K.: Wiley.

    Google Scholar 

  • Farrington, C. P., &Manning, G. (1990). Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unity relative risk.Statistics in Medicine,9, 1447–1454.

    Article  PubMed  Google Scholar 

  • Field, A. P. (2005).Discovering statistics with SPSS (2nd ed.). London: Sage.

    Google Scholar 

  • Fleiss, J. L. (1981).Statistical methods for rates and proportions (2nd ed.). New York: Wiley.

    Google Scholar 

  • Frings, C., &Wentura, D. (2005). Negative priming with masked distractor-only prime trials: Awareness moderates negative priming.Experimental Psychology,52, 131–139.

    PubMed  Google Scholar 

  • Gart, J. J., &Nam, J. (1988). Approximate interval estimation of the ratio in binomial parameters: A review and correction for skewness.Biometrics,44, 323–338.

    Article  PubMed  Google Scholar 

  • Gart, J. J., &Nam, J. (1990). Approximate interval estimation of the difference in binomial parameters: Correction for skewness and extension to multiple tables.Biometrics,46, 637–643.

    Article  PubMed  Google Scholar 

  • Geisser, S., &Greenhouse, S. W. (1958). An extension of Box’s results on the use of theF distribution in multivariate analysis.Annals of Mathematical Statistics,29, 885–891.

    Article  Google Scholar 

  • Gerard, P. D., Smith, D. R., &Weerakkody, G. (1998). Limits of retrospective power analysis.Journal of Wildlife Management,62, 801–807.

    Article  Google Scholar 

  • Gigerenzer, G., Krauss, S., &Vitouch, O. (2004). The null ritual: What you always wanted to know about significance testing but were afraid to ask. In D. Kaplan (Ed.),The SAGE handbook of quantitative methodology for the social sciences (pp. 391–408). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Gleissner, U., Clusmann, H., Sassen, R., Elger, C. E., &Helmstaedter, C. (2006). Postsurgical outcome in pediatric patients with epilepsy: A comparison of patients with intellectual disabilities, subaverage intelligence, and average-range intelligence.Epilepsia,47, 406–414.

    Article  PubMed  Google Scholar 

  • Goldstein, R. (1989). Power and sample size via MS/PC-DOS computers.American Statistician,43, 253–262.

    Article  Google Scholar 

  • Hager, W. (2006). Die Fallibilität empirischer Daten und die Notwendigkeit der Kontrolle von falschen Entscheidungen [The fallibility of empirical data and the need for controlling for false decisions].Zeitschrift für Psychologie,214, 10–23.

    Article  Google Scholar 

  • Haseman, J. K. (1978). Exact sample sizes for use with the Fisher—Irwin test for 2 × 2 tables.Biometrics,34, 106–109.

    Article  Google Scholar 

  • Hoenig, J. N., &Heisey, D. M. (2001). The abuse of power: The pervasive fallacy of power calculations for data analysis.American Statistician,55, 19–24.

    Article  Google Scholar 

  • Hoffmann, J., &Sebald, A. (2005). Local contextual cuing in visual search.Experimental Psychology,52, 31–38.

    PubMed  Google Scholar 

  • Huynh, H., &Feldt, L. S. (1970). Conditions under which mean square ratios in repeated measurements designs have exactF-distribution.Journal of the American Statistical Association,65, 1582–1589.

    Article  Google Scholar 

  • Keppel, G., &Wickens, T. D. (2004).Design and analysis. A researcher’s handbook (4th ed.). Upper Saddle River, NJ: Pearson Education International.

    Google Scholar 

  • Kornbrot, D. E. (1997). Review of statistical shareware G*Power.British Journal of Mathematical & Statistical Psychology,50, 369–370.

    Google Scholar 

  • Kromrey, J., &Hogarty, K. Y. (2000). Problems with probabilistic hindsight: A comparison of methods for retrospective statistical power analysis.Multiple Linear Regression Viewpoints,26, 7–14.

    Google Scholar 

  • Lenth, R. V. (2001). Some practical guidelines for effective sample size determination.American Statistician,55, 187–193.

    Article  Google Scholar 

  • Levin, J. R. (1997). Overcoming feelings of powerlessness in “aging” researches: A primer on statistical power in analysis of variance designs.Psychology & Aging,12, 84–106.

    Article  Google Scholar 

  • McKeon, J. J. (1974).F approximations to the distribution of Hotelling’sT02.Biometrika,61, 381–383.

    Google Scholar 

  • Mellina, E., Hinch, S. G., Donaldson, E. M., &Pearson, G. (2005). Stream habitat and rainbow trout (Oncorhynchus mykiss) physiological stress responses to streamside clear-cut logging in British Columbia.Canadian Journal of Forest Research,35, 541–556.

    Article  Google Scholar 

  • Miettinen, O., &Nurminen, M. (1985). Comparative analysis of two rates.Statistics in Medicine,4, 213–226.

    Article  PubMed  Google Scholar 

  • Müller, J., Manz, R., &Hoyer, J. (2002). Was tun, wenn die Teststärke zu gering ist? Eine praktikable Strategie für Prä-Post-Designs [What to do if statistical power is low? A practical strategy for prepost-designs].Psychotherapie, Psychosomatik, Medizinische Psychologie,52, 408–416.

    Article  PubMed  Google Scholar 

  • Muller, K. E., &Barton, C. N. (1989). Approximate power for repeatedmeasures ANOVA lacking sphericity.Journal of the American Statistical Association,84, 549–555.

    Article  Google Scholar 

  • Muller, K. E., LaVange, L. M., Landesman-Ramey, S., &Ramey, C. T. (1992). Power calculations for general linear multivariate models including repeated measures applications.Journal of the American Statistical Association,87, 1209–1226.

    Article  Google Scholar 

  • Muller, K. E., &Peterson, B. L. (1984). Practical methods for computing power in testing the multivariate general linear hypothesis.Computational Statistics & Data Analysis,2, 143–158.

    Article  Google Scholar 

  • Myers, J. L., &Well, A. D. (2003).Research design and statistical analysis (2nd ed.). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • O’Brien, R. G., &Kaiser, M. K. (1985). MANOVA method for analyzing repeated measures designs: An extensive primer.Psychological Bulletin,97, 316–333.

    Article  PubMed  Google Scholar 

  • O’Brien, R. G., &Muller, K. E. (1993). Unified power analysis fort-tests through multivariate hypotheses. In L. K. Edwards (Ed.),Applied analysis of variance in behavioral science (pp. 297–344). New York: Dekker.

    Google Scholar 

  • O’Brien, R. G., & Shieh, G. (1999).Pragmatic, unifying algorithm gives power probabilities for common F tests of the multivariate general linear hypothesis. Available at www.bio.ri.ccf.org/UnifyPow.

  • Ortseifen, C., Bruckner, T., Burke, M., &Kieser, M. (1997). An overview of software tools for sample size determination.Informatik, Biometrie & Epidemiologie in Medizin & Biologie,28, 91–118.

    Google Scholar 

  • Ostle, B., &Malone, L. C. (1988).Statistics in research: Basic concepts and techniques for research workers (4th ed.). Ames: Iowa State Press.

    Google Scholar 

  • Pillai, K. C. S., &Mijares, T. A. (1959). On the moments of the trace of a matrix and approximations to its distribution.Annals of Mathematical Statistics,30, 1135–1140.

    Article  Google Scholar 

  • Pillai, K. C. S., &Samson, P., Jr. (1959). On Hotelling’s generalization ofT2.Biometrika,46, 160–168.

    Google Scholar 

  • Quednow, B. B., Kühn, K.-U., Stelzenmueller, R., Hoenig, K., Maier, W., &Wagner, M. (2004). Effects of serotonergic and noradrenergic antidepressants on auditory startle response in patients with major depression.Psychopharmacology,175, 399–406.

    PubMed  Google Scholar 

  • Rao, C. R. (1951). An asymptotic expansion of the distribution of Wilks’s criterion.Bulletin of the International Statistical Institute,33, 177–180.

    Google Scholar 

  • Rasch, B., Friese, M., Hofmann, W. J., &Naumann, E. (2006a).Quantitative Methoden 1: Einführung in die Statistik (2. Auflage) [Quantitative methods 1: Introduction to statistics (2nd ed.)]. Heidelberg, Germany: Springer.

    Google Scholar 

  • Rasch, B., Friese, M., Hofmann, W. J., &Naumann, E. (2006b).Quantitative Methoden 2: Einführung in die Statistik (2. Auflage) [Quantitative methods 2: Introduction to statistics (2nd ed.)]. Heidelberg, Germany: Springer.

    Google Scholar 

  • Rencher, A. C. (1998).Multivariate statistical inference and applications. New York: Wiley.

    Google Scholar 

  • Richardson, J. T. E. (1996). Measures of effect size.Behavior Research Methods, Instruments, & Computers,28, 12–22.

    Article  Google Scholar 

  • Scheffé, H. (1959).The analysis of variance. New York: Wiley.

    Google Scholar 

  • Schwarz, W., &Müller, D. (2006). Spatial associations in numberrelated tasks: A comparison of manual and pedal responses.Experimental Psychology,53, 4–15.

    PubMed  Google Scholar 

  • Sheppard, C. (1999). How large should my sample be? Some quick guides to sample size and the power of tests.Marine Pollution Bulletin,38, 439–447.

    Article  Google Scholar 

  • Shieh, G. (2003). A comparative study of power and sample size calculations for multivariate general linear models.Multivariate Behavioral Research,38, 285–307.

    Article  Google Scholar 

  • Smith, R. E., &Bayen, U. J. (2005). The effects of working memory resource availability on prospective memory: A formal modeling approach.Experimental Psychology,52, 243–256.

    PubMed  Google Scholar 

  • Steidl, R. J., Hayes, J. P., &Schauber, E. (1997). Statistical power analysis in wildlife research.Journal of Wildlife Management,61, 270–279.

    Article  Google Scholar 

  • Suissa, S., &Shuster, J. J. (1985). Exact unconditional sample sizes for 2 × 2 binomial trial.Journal of the Royal Statistical Society A,148, 317–327.

    Article  Google Scholar 

  • Thomas, L., &Krebs, C. J. (1997). A review of statistical power analysis software.Bulletin of the Ecological Society of America,78, 126–139.

    Google Scholar 

  • Upton, G. J. G. (1982). A comparison of alternative tests for the 2 3 2 comparative trial.Journal of the Royal Statistical Society A,145, 86–105.

    Article  Google Scholar 

  • Westermann, R., &Hager, W. (1986). Error probabilities in educational and psychological research.Journal of Educational Statistics,11, 117–146.

    Article  Google Scholar 

  • Zumbo, B. D., &Hubley, A. M. (1998). A note on misconceptions concerning prospective and retrospective power.The Statistician,47, 385–388.

    Google Scholar 

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Correspondence to Franz Faul or Edgar Erdfelder.

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Manuscript preparation was supported by Grant SFB 504 (Project A12) from the Deutsche Forschungsgemeinschaft and a grant from the state of Baden-Württemberg, Germany (Landesforschungsprogramm „Evidenzbasierte Stressprävention”).

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Faul, F., Erdfelder, E., Lang, AG. et al. G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods 39, 175–191 (2007). https://doi.org/10.3758/BF03193146

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  • DOI: https://doi.org/10.3758/BF03193146

Keywords

  • Power Analysis
  • Negative Priming
  • Implicit Association Test
  • Main Window
  • Noncentrality Parameter