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Original Article

Is the Pearson r2 Biased, and if So, What Is the Best Correction Formula?

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Pages 109-125 | Published online: 07 Aug 2010

References

  • American Psychological Association. (2001). Publication manual of the American Psychological Association (5th ed.). Washington, DC: Author.
  • Boring, E. G. (1919). Mathematical vs. scientific importance. Psychological Bulletin, 16, 335-338.
  • Claudy, J. G. (1978). Multiple regression and validity estimation in one sample. Applied Psychological Measurement, 2, 595-607.
  • Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426-443.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
  • Ezekiel, M. (1929). The application of the theory of error to multiple and curvilinear correlation. American Statistical Association Journal, 24, 99-104.
  • Ezekiel, M. (1930). Methods of correlational analysis. New York: Wiley.
  • Fan, X., Felsovalyi, A., Sivo, S. & Keenan, S. C. (2003). SAS(R) for Monte Carlo studies: A guide for quantitative researchers. Cary, NC: SAS Publishing.
  • Fidler, F. (2002). The fifth edition of APA publication manual: Why its statistics recommendations are so controversial. Educational and Psychological Measurement, 62, 749-770.
  • Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-531.
  • Gage, N. L. (1978). The scientific basis of the art of teaching. New York: Teachers College Press.
  • Glass, G. V (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5(10), 3-8.
  • Grissom, R., & Kim, J. J. (2005). Effect sizes for research: A broad practical approach. Mahwah, NJ: Erlbaum.
  • Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6, 107-128.
  • Hedges, L. V. (1982). Estimation of effect size from a series of independent experiments. Psychological Bulletin, 92, 490-499.
  • Huberty, C. J (1999). On some history regarding statistical testing. In B. Thompson (Ed.), Advances in social science methodology (Vol. 5, pp. 1-23). Stamford, CT: JAI Press.
  • Huberty, C. J (2002). A history of effect size indices. Educational and Psychological Measurement, 62, 227-240.
  • Kieffer, K. M., Reese, R. J., & Thompson, B. (2001). Statistical techniques employed in AERJ and JCP articles from 1988 to 1997: A methodological review. Journal of Experimental Education, 69, 280-309.
  • Knapp, T. R. (1978). Canonical correlation analysis: A general parametric significance testing system. Psychological Bulletin, 85, 410-416.
  • Kromrey, J. D., & Hines, C. V. (1996). Estimating the coefficient of cross-validity in multiple regression: A comparison of analytical and empirical methods. Journal of Experimental Education, 64, 240-266.
  • Natesan, P., & Thompson, B. (in press). Extending Improvement-over-chance I-index effect size simulation studies to cover some small-sample cases. Paper presented at the annual meeting of the American Education Reearch Association, Montreal, Canada.
  • Olkin, E., & Pratt, J. W. (1958). Unbiased estimation of certain correlation coefficients. Annals of Mathematical Statistics, 29, 201-211.
  • Raju, N. S., Bilgic, R., Edwards, J. E., & Fleer, P. F. (1999). Accuracy of population validity and cross-validity estimation: An empirical comparison of formula-based, traditional empirical, and equal weights procedures. Applied Psychological Measurement, 23, 99-115.
  • Roberts, J. K., & Henson, R. K. (2002). Correction for bias in estimating effect sizes. Educational and Psychological Measurement, 62, 241-253.
  • Rosenthal, R. (1994). Parametric measures of effect size. In H. Cooper & L. V. Hedges (Eds.), The handbook of research synthesis (pp. 231-244). New York: Russell Sage Foundation.
  • Thompson, B. (1984). Canonical correlation analysis: Uses and interpretation. Newbury Park, CA: Sage.
  • Thompson, B. (2000). Canonical correlation analysis. In L. Grimm & P. Yarnold (Eds.), Reading and understanding more multivariate statistics (pp. 285-316). Washington, DC: American Psychological Association.
  • Thompson, B. (2002). "Statistical," "practical," and "clinical": How many kinds of significance do counselors need to consider? Journal of Counseling and Development, 80, 64-71.
  • Thompson, B. (2006a). Foundations of behavioral statistics: An insight-based approach. New York: Guilford.
  • Thompson, B. (2006b). Research synthesis: Effect sizes. In J. Green, G. Camilli, & P.B. Elmore (Eds.), Handbook of complementary methods in education research (pp. 583-603). Washington, DC: American Educational Research Association.
  • Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465-471.
  • Wherry, R. J. (1931). A new formula for predicting the shrinkage of the coefficient of multiple correlation. Annals of Mathematical Statistics, 2, 440-457.
  • Yin, P., & Fan, X. (2001). Estimating R2 shrinkage in multiple regression: A comparison of different analytic methods. Journal of Experimental Education, 69, 203-224.

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