Choosing the Best Correction Formula for the Pearson r²Effect Size

REFERENCES

• American Educational Research Association . 2006 . Standards for reporting on empirical social science research in AERA publications . Educational Researcher , 35 ( 6 ) : 33 – 40 .
   Google Scholar
• American Psychological Association . 1994 . Publication manual of the American Psychological Association , 4th ed. , Washington , DC : Author .
   Google Scholar
• American Psychological Association . 2001 . Publication manual of the American Psychological Association , 5th ed. , Washington , DC : Author .
   Google Scholar
• Cattin , P. 1980 . Estimation of the predictive power of a regression model . Journal of Applied Psychology , 65 : 407 – 414 .
   Web of Science ®Google Scholar
• Claudy , J. G. 1978 . Multiple regression and validity estimation in one sample . Applied Psychological Measurement , 2 : 595 – 607 .
   Google Scholar
• Cumming , G. and Finch , S. 2001 . A primer on the understanding, use and calculation of confidence intervals that are based on central and noncentral distributions . Educational and Psychological Measurement , 61 : 532 – 575 .
   Web of Science ®Google Scholar
• Ezekiel , M. 1929 . The application of the theory of error to multiple and curvilinear correlation . Journal of the American Statistical Association , 24 : 99 – 104 .
   Google Scholar
• Ezekiel , M. 1930 . Methods of correlational analysis , New York , NY : Wiley .
   Google Scholar
• Fan , X. , Felsovalyi , A. , Sivo , S. A. and Keenan , S. C. 2001 . SAS for Monte Carlo studies: A guide for quantitative researchers , Cary , NC : SAS Institute .
   Google Scholar
• Fidler , F. 2005 . From statistical significance to effect estimation: Statistical reform in psychology, medicine, and ecology Victoria , , Australia Doctoral dissertation, University of MelbourneRetrieved from http://www.botany.unimelb.edu.au/envisci/fiona/fidlerphd_aug06.pdf
   Google Scholar
• Fleishman , A. I. 1978 . A method for simulating non-normal distributions . Psychometrika , 43 : 521 – 532 .
   Web of Science ®Google Scholar
• Grissom , R. J. and Kim , J. J. 2005 . Effect sizes for research: A broad practical approach , New York , NY : Psychology Press .
   Google Scholar
• Huberty , C. J. and Mourad , S. A. 1980 . Estimation in multiple correlation/prediction . Educational and Psychological Measurement , 40 : 101 – 112 .
   Web of Science ®Google Scholar
• Kieffer , K. M. , Reese , R. J. and 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 .
   Web of Science ®Google Scholar
• Kirk , R. E. 1996 . Practical significance: A concept whose time has come . Educational and Psychological Measurement , 56 : 746 – 759 .
   Web of Science ®Google Scholar
• Kromrey , J. D. and 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 .
   Web of Science ®Google Scholar
• Olkin , I. and Pratt , J. W. 1958 . Unbiased estimation of certain correlation coefficients . The Annals of Mathematical Statistics , 29 : 201 – 211 .
   Google Scholar
• Raju , N. S. , Bilgic , R. , Edwards , J. E. and Fleer , P. F. 1999 . Accuracy of population validity and cross-validity estimation: An empirical comparison of formula-based, traditional empirical, and equal weights procedure . Applied Psychological Measurement , 23 : 99 – 115 .
   Web of Science ®Google Scholar
• Shieh , G. 2008 . Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient . Organizational Research Methods , 11 : 387 – 407 .
   Web of Science ®Google Scholar
• Stuart , A. , Ord , J. K. and Arnold , S. 1994 . Kendall's advanced theory of statistics: Distribution theory , New York , NY : Halsted Press .
   Google Scholar
• Thompson , B. 2002a . “Statistical,” “practical,” and “clinical”: How many kinds of significance do counselors need to consider? . Journal of Counseling and Development , 80 : 64 – 71 .
   Web of Science ®Google Scholar
• Thompson , B. 2002b . What future quantitative social science research could look like: Confidence intervals for effect sizes . Educational Researcher , 31 ( 3 ) : 25 – 32 .
   Google Scholar
• Thompson , B. 2006a . Foundations of behavioral statistics: An insight-based approach , New York , NY : Guilford Press .
   Google Scholar
• Thompson , B. 2006b . “ Research synthesis: Effect sizes ” . In Handbook of complementary methods in education research , Edited by: Green , J. , Camilli , G. and Elmore , P. B. 583 – 603 . Washington , DC : American Educational Research Association .
   Google Scholar
• Thompson , B. 2007 . Effect sizes, confidence intervals, and confidence intervals for effect sizes . Psychology in the Schools , 44 : 423 – 432 .
   Web of Science ®Google Scholar
• Vale , C. D. and Maurelli , V. A. 1983 . Simulating multivariate nonnormal distributions . Psychometrika , 48 : 465 – 471 .
   Web of Science ®Google Scholar
• Wang , Z. and Thompson , B. 2007 . Is the Pearson r 2 biased, and if so, what is the best correction formula? . Journal of Experimental Education , 75 : 109 – 125 .
   Web of Science ®Google Scholar
• Wherry , R. J. 1931 . A new formula for predicting the shrinkage of the coefficient of multiple correlation . The Annals of Mathematical Statistics , 2 : 440 – 457 .
   Google Scholar
• Wilkinson , L. and the Task Force on Statistical Inference . 1999 . Statistical methods in psychology journals guidelines and explanations . American Psychologist , 54 : 594 – 604 .
   Web of Science ®Google Scholar
• Yin , P. and Fan , X. 2001 . Estimating R 2 shrinkage in multiple regression: A comparison of different analytical methods . Journal of Experimental Education , 69 : 203 – 224 .
   Web of Science ®Google Scholar
• Zientek , L. R. and Thompson , B. 2009 . Matrix summaries improve research reports: Secondary analyses using published literature . Educational Researcher , 38 : 343 – 352 .
   Web of Science ®Google Scholar
• Zimmerman , D. W. , Zumbo , B. D. and Williams , R. H. 2003 . Bias in estimation and hypothesis testing of correlation . Psicologica , 24 : 133 – 158 .
   Google Scholar