Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses

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.

References

  1. Armitage, P., Berry, G., & Matthews, J. N. S. (2002). Statistical methods in medical research (4th ed.). Oxford: Blackwell.

    Google Scholar 

  2. Benton, D., & Krishnamoorthy, K. (2003). Computing discrete mixtures of continuous distributions: Noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient. Computational Statistics & Data Analysis, 43, 249–267.

    Google Scholar 

  3. Bonett, D. G., & Price, R. M. (2005). Inferential methods for the tetrachoric correlation coefficient. Journal of Educational & Behavioral Statistics, 30, 213–225.

    Article  Google Scholar 

  4. Bredenkamp, J. (1969). Über die Anwendung von Signifikanztests bei theorie-testenden Experimenten [On the use of significance tests in theory-testing experiments]. Psychologische Beiträge, 11, 275–285.

    Google Scholar 

  5. Brown, M. B., & Benedetti, J. K. (1977). On the mean and variance of the tetrachoric correlation coefficient. Psychometrika, 42, 347–355.

    Article  Google Scholar 

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

    Google Scholar 

  7. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Erlbaum.

    Google Scholar 

  8. Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in Medicine, 26, 3385–3397.

    PubMed  Article  Google Scholar 

  9. Demidenko, E. (2008). Sample size and optimal design for logistic regression with binary interaction. Statistics in Medicine, 27, 36–46.

    PubMed  Article  Google Scholar 

  10. Dunlap, W. P., Xin, X., & Myers, L. (2004). Computing aspects of power for multiple regression. Behavior Research Methods, Instruments, & Computers, 36, 695–701.

    Article  Google Scholar 

  11. Dunn, O. J., & Clark, V. A. (1969). Correlation coefficients measured on the same individuals. Journal of the American Statistical Association, 64, 366–377.

    Article  Google Scholar 

  12. Dupont, W. D., & Plummer, W. D. (1998). Power and sample size calculations for studies involving linear regression. Controlled Clinical Trials, 19, 589–601.

    PubMed  Article  Google Scholar 

  13. Erdfelder, E. (1984). Zur Bedeutung und Kontrolle des beta-Fehlers bei der inferenzstatistischen Prüfung log-linearer Modelle [On significance and control of the beta error in statistical tests of log-linear models]. Zeitschrift für Sozialpsychologie, 15, 18–32.

    Google Scholar 

  14. 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 

  15. Erdfelder, E., Faul, F., Buchner, A., & Cüpper, L. (in press). Effektgröße und Teststärke [Effect size and power]. In H. Holling & B. Schmitz (Eds.), Handbuch der Psychologischen Methoden und Evaluation. Göttingen: Hogrefe.

  16. Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175–191.

    PubMed  Article  Google Scholar 

  17. Friese, M., Bluemke, M., & Wänke, M. (2007). Predicting voting behavior with implicit attitude measures: The 2002 German parliamentary election. Experimental Psychology, 54, 247–255.

    PubMed  Google Scholar 

  18. Gatsonis, C., & Sampson, A. R. (1989). Multiple correlation: Exact power and sample size calculations. Psychological Bulletin, 106, 516–524.

    PubMed  Article  Google Scholar 

  19. Hays, W. L. (1972). Statistics for the social sciences (2nd ed.). New York: Holt, Rinehart & Winston.

    Google Scholar 

  20. Hsieh, F. Y., Bloch, D. A., & Larsen, M. D. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine, 17, 1623–1634.

    PubMed  Article  Google Scholar 

  21. Lee, Y.-S. (1972). Tables of upper percentage points of the multiple correlation coefficient. Biometrika, 59, 175–189.

    Google Scholar 

  22. Lyles, R. H., Lin, H.-M., & Williamson, J. M. (2007). A practical approach to computing power for generalized linear models with nominal, count, or ordinal responses. Statistics in Medicine, 26, 1632–1648.

    PubMed  Article  Google Scholar 

  23. Mendoza, J. L., & Stafford, K. L. (2001). Confidence 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. Educational & Psychological Measurement, 61, 650–667.

    Article  Google Scholar 

  24. Nosek, B. A., & Smyth, F. L. (2007). A multitrait—multimethod validation of the Implicit Association Test: Implicit and explicit attitudes are related but distinct constructs. Experimental Psychology, 54, 14–29.

    PubMed  Google Scholar 

  25. Perugini, M., O’Gorman, R., & Prestwich, A. (2007). An ontological test of the IAT: Self-activation can increase predictive validity. Experimental Psychology, 54, 134–147.

    PubMed  Google Scholar 

  26. Rindskopf, D. (1984). Linear equality restrictions in regression and loglinear models. Psychological Bulletin, 96, 597–603.

    Article  Google Scholar 

  27. Sampson, A. R. (1974). A tale of two regressions. Journal of the American Statistical Association, 69, 682–689.

    Article  Google Scholar 

  28. Shieh, G. (2001). Sample size calculations for logistic and Poisson regression models. Biometrika, 88, 1193–1199.

    Article  Google Scholar 

  29. Shieh, G., & Kung, C.-F. (2007). Methodological and computational considerations for multiple correlation analysis. Behavior Research Methods, 39, 731–734.

    PubMed  Article  Google Scholar 

  30. Signorini, D. F. (1991). Sample size for Poisson regression. Biometrika, 78, 446–450.

    Article  Google Scholar 

  31. Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87, 245–251.

    Article  Google Scholar 

  32. Steiger, J. H., & Fouladi, R. T. (1992). R2: A computer program for interval estimation, power calculations, sample size estimation, and hypothesis testing in multiple regression. Behavior Research Methods, Instruments, & Computers, 24, 581–582.

    Article  Google Scholar 

  33. Tsujimoto, S., Kuwajima, M., & Sawaguchi, T. (2007). Developmental fractionation of working memory and response inhibition during childhood. Experimental Psychology, 54, 30–37.

    PubMed  Google Scholar 

  34. Whittemore, A. S. (1981). Sample size for logistic regression with small response probabilities. Journal of the American Statistical Association, 76, 27–32.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Franz Faul or Edgar Erdfelder.

Additional information

Manuscript preparation was supported by Grant SFB 504 (Project A12) from the Deutsche Forschungsgemeinschaft. We thank two anonymous reviewers for valuable comments on a previous version of the manuscript.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Faul, F., Erdfelder, E., Buchner, A. et al. Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods 41, 1149–1160 (2009). https://doi.org/10.3758/BRM.41.4.1149

Download citation

Keywords

  • Implicit Association Test
  • Multiple Correlation Coefficient
  • Linear Multiple Regression
  • Effect Size Measure
  • Noncentrality Parameter