Advertisement

GPOWER: A general power analysis program

  • Edgar ErdfelderEmail author
  • Franz FaulEmail author
  • Axel BuchnerEmail author
Article

Abstract

GPOWER is a completely interactive, menu-driven program for IBM-compatible and Apple Macintosh personal computers. It performs high-precision statistical power analyses for the most common statistical tests in behavioral research, that is,t tests,F tests, andχ 2 tests. GPOWER computes (1) power values for given sample sizes, effect sizes andα levels (post hoc power analyses); (2) sample sizes for given effect sizes,α levels, and power values (a priori power analyses); and (3)α andβ values for given sample sizes, effect sizes, andβ/α ratios (compromise power analyses). The program may be used to display graphically the relation between any two of the relevant variables, and it offers the opportunity to compute the effect size measures from basic parameters defining the alternative hypothesis. This article delineates reasons for the development of GPOWER and describes the program’s capabilities and handling.

Keywords

Power Analysis Speed Mode Statistical Power Analysis Effect Size Measure Noncentrality Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bargmann, R. E., &Ghosh, S. P. (1964).Noncentral statistical distribution programs for a computer language (IBM Research Report RC-1231). Yorktown Heights, NY: IBM Watson Research Center.Google Scholar
  2. Borenstein, M., &Cohen, J. (1988).Statistical power analysis: A computer program. Hillsdale, NJ: Erlbaum.Google Scholar
  3. Borenstein, M., Cohen, J., Rothstein, H. R., Pollack, S., &Kane, J. M. (1990). Statistical power analysis for one-way analysis of variance: A computer program.Behavior Research Methods, Instruments, & Computers,22, 271–282.Google Scholar
  4. Borenstein, M., Cohen, J., Rothstein, H. R., Pollack, S., &Kane, J. M. (1992). A visual approach to statistical power analysis on the microcomputer.Behavior Research Methods, Instruments, & Computers,24, 565–572.Google Scholar
  5. Bredenkamp, J. (1972).Der Signifikanztest in der psychologischen Forschung [The test of significance in behavioral research]. Frankfurt, Germany: Akademische Verlagsgesellschaft.Google Scholar
  6. Bredenkamp, J. (1980).Theorie und Planung psychologischer Experimente [Theory and design of psychological experiments]. Darmstadt, Germany: Steinkopff.Google Scholar
  7. Bredenkamp, J., &Erdfelder, E. (1985).Multivariate Varianzanalyse nach dem V-Kriterium [Multivariate analysis of variance using the V-criterion].Psychologische Beiträge,27, 127–154.Google Scholar
  8. Buchner, A., Faul, F., &Erdfelder, E. (1992).GPOWER: A priori-, post hoc-, and compromise power analyses for the Macintosh [Computer program]. Bonn, Germany: Bonn University.Google Scholar
  9. Cohen, J. (1962). The statistical power of abnormal-social psychological research: A review.Journal of Abnormal & Social Psychology,65, 145–153.CrossRefGoogle Scholar
  10. Cohen, J. (1965). Some statistical issues in psychological research. In B. B. Wolman (Ed.),Handbook of clinical psychology (pp. 95–121). New York: McGraw-Hill.Google Scholar
  11. Cohen, J. (1969).Statistical power analysis for the behavioral sciences. New York: Academic Press.Google Scholar
  12. Cohen, J. (1977).Statistical power analysis for the behavioral sciences (rev. ed.). New York: Academic Press.Google Scholar
  13. Cohen, J. (1988).Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  14. Cohen, J. (1992). A power primer.Psychological Bulletin,112, 155–159.PubMedCrossRefGoogle Scholar
  15. Cohen, J., &Cohen, P. (1983).Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  16. Cowles, M., &Davis, C. (1982). On the origins of the.05 level of statistical significance.American Psychologist,37, 553–558.CrossRefGoogle Scholar
  17. Dixon, W. F., &Massey, F. J., Jr. (1957).Introduction to statistical analysis (2nd ed.). New York: McGraw-Hill.Google Scholar
  18. Erdfelder, E. (1984). Zur Bedeutung und Kontrolle des β-Fehlers bei der inferenzstatistischen Prüfung log-linearer Modelle [On significance and control of the β error in statistical tests of log-linear models].Zeitschrift für Sozialpsychologie,15, 18–32.Google Scholar
  19. Erdfelder, E., &Bredenkamp, J. (1994). Hypothesenprüfung [Evaluation of hypotheses]. In T. Herrmann & W. H. Tack (Eds.),Methodologische Grundlagen der Psychologie (pp. 604–648). Göttingen, Germany: Hogrefe.Google Scholar
  20. Faul, F., &Erdfelder, E. (1992).GPOWER: A priori-, post hoc-, and compromise power analyses for MS-DOS [Computer program]. Bonn, Germany: Bonn University.Google Scholar
  21. Gigerenzer, G. (1993). The superego, the ego, and the id in statistical reasoning. In G. Keren & C. Lewis (Eds.),A handbook for data analysis in the behavioral sciences: Methodological issues (pp. 311–339). Hillsdale, NJ: Erlbaum.Google Scholar
  22. Gigerenzer, G., &Murray, D. J. (1987).Cognition as intuitive statistics. Hillsdale, NJ: Erlbaum.Google Scholar
  23. Goldstein, R. (1989). Power and sample size via MS/PC-DOS computers.American Statistician,43, 253–260.CrossRefGoogle Scholar
  24. Hager, W., &Möller, H. (1986). Tables and procedures for the determination of power and sample sizes in univariate and multivariate analyses of variance and regression.Biometrical Journal,28, 647–663.CrossRefGoogle Scholar
  25. Hardison, C. D., Quade, D., &Langston, R. D. (1983). Nine functions for probability distributions. In SAS Institute, Inc. (Ed.),SUGI supplemental library user’s guide, 1983 edition (pp. 229–236). Cary, NC: SAS Institute, Inc.Google Scholar
  26. Huff, C., &Sobiloff, B. (1993). MacPsych: An electronic discussion list and archive for psychology concerning the Macintosh computer.Behavior Research Methods, Instruments, & Computers,25, 60–64.Google Scholar
  27. Johnson, N. L., &Kotz, S. (1970).Distributions in statistics: Continuous univariate distributions-2. New York: Wiley.Google Scholar
  28. Koele, P. (1982). Calculating power in analysis of variance.Psychological Bulletin,92, 513–516.CrossRefGoogle Scholar
  29. Koele, P., &Hoogstraten, J. (1980).Power and sample size calculations in analysis of variance (Révész Berichten No. 12). Amsterdam: University of Amsterdam.Google Scholar
  30. Kraemer, H. C., &Thiemann, S. (1987).How many subjects? Statistical power analysis in research. Newbury Park, CA: Sage.Google Scholar
  31. Laubscher, N. F. (1960). Normalizing the noncentralt andF distributions.Annals of Mathematical Statistics,31, 1105–1112.CrossRefGoogle Scholar
  32. Lehmann, E. L. (1975).Nonparametrics. Statistical methods based on ranks. San Francisco: Holden-Day.Google Scholar
  33. Lipsey, M. W. (1990).Design sensitivity: Statistical power for experimental research. Newbury Park, CA: Sage.Google Scholar
  34. Milligan, G. W. (1979). A computer program for calculating power of the chi-square test.Educational & Psychological Measurement,39, 681–684.CrossRefGoogle Scholar
  35. Oakes, M. (1986).Statistical inference: A commentary for the social and behavioral sciences. New York: Wiley.Google Scholar
  36. 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: Marcel Dekker.Google Scholar
  37. Onghena, P. (1994).The power of randomization tests for single-case designs. Unpublished doctoral dissertation. Leuven, Belgium: Katholieke Universiteit Leuven.Google Scholar
  38. Onghena, P., &Van Damme, G. (1994). SCRT 1.1: Single-case randomization tests.Behavior Research Methods, Instruments, & Computers,26, 369.Google Scholar
  39. Patnaik, P. B. (1949). The non-central χ2- andF-distributions and their applications.Biometrika,36, 202–232.PubMedGoogle Scholar
  40. Pollard, P., &Richardson, J. T. E. (1987). On the probability of making type I errors.Psychological Bulletin,102, 159–163.CrossRefGoogle Scholar
  41. Press, W. H., Flannery, B. P., Teukolsky, S. A., &Vetterling, W. T. (1988).Numerical recipes in C: The art of scientific computing. Cambridge: Cambridge University Press.Google Scholar
  42. Rossi, J. S. (1990). Statistical power of psychological research: What have we gained in 20 years?Journal of Consulting & Clinical Psychology,58, 646–656.CrossRefGoogle Scholar
  43. Rothstein, H., Borenstein, M., Cohen, J., &Pollack, S. (1990). Statistical power analysis for multiple regression/correlation: A computer program.Educational & Psychological Measurement,50, 819–830.CrossRefGoogle Scholar
  44. Sedlmeier, P., &Gigerenzer, G. (1989). Do studies of statistical power have an effect on the power of studies?Psychological Bulletin,105, 309–316.CrossRefGoogle Scholar
  45. Singer, B., Lovie, A. D., &Lovie, P. (1986). Sample size and power. In A. D. Lovie (Ed.),New developments in statistics for psychology and the social sciences (pp. 129–142). London: British Psychological Society and Methuen.Google Scholar
  46. Tversky, A., &Kahneman, D. (1971). Belief in the law of small numbers.Psychological Bulletin,76, 105–110.CrossRefGoogle Scholar
  47. Westermann, R., &Hager, W. (1986). Error probabilities in educational and psychological research.Journal of Educational Statistics,11, 117–146.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 1996

Authors and Affiliations

  1. 1.Psychologisches Institut der Universität BonnBonnGermany
  2. 2.Institut für Psychologie an der Universität KielKielGermany
  3. 3.FB I-PsychologieUniversität TrierTrierGermany

Personalised recommendations