Behavior Research Methods

, Volume 39, Issue 4, pp 731–734 | Cite as

Methodological and computational considerations for multiple correlation analysis

  • Gwowen ShiehEmail author
  • Chien-Feng Kung


The squared multiple correlation coefficient has been widely employed to assess the goodness-of-fit of linear regression models in many applications. Although there are numerous published sources that present inferential issues and computing algorithms for multinormal correlation models, the statistical procedure for testing substantive significance by specifying the nonzero-effect null hypothesis has received little attention. This article emphasizes the importance of determining whether the squared multiple correlation coefficient is small or large in comparison with some prescribed standard and develops corresponding Excel worksheets that facilitate the implementation of various aspects of the suggested significance tests. In view of the extensive accessibility of Microsoft Excel software and the ultimate convenience of general-purpose statistical packages, the associated computer routines for interval estimation, power calculation, and sample size determination are also provided for completeness. The statistical methods and available programs of multiple correlation analysis described in this article purport to enhance pedagogical presentation in academic curricula and practical application in psychological research.


Multiple Correlation Analysis Interval Estimation Minimum Sample Size Limited Statistical Function Multiple Correlation Coefficient 
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.


  1. Alf, E. F., Jr., &Graf, R. G. (2002). A new maximum likelihood estimator for the population squared multiple correlation.Journal of Educational & Behavioral Statistics,27, 223–235.CrossRefGoogle Scholar
  2. Algina, J., &Olejnik, S. (2003). Sample size tables for correlation analysis with applications in partial correlation and multiple regression analysis.Multivariate Behavioral Research,38, 309–323.CrossRefGoogle Scholar
  3. Barnette, J. J. (2005). ScoreRel CI: An Excel program for computing confidence intervals for commonly used score reliability coefficients.Educational & Psychological Measurement,65, 980–983.CrossRefGoogle Scholar
  4. Dunlap, W. P., Xin, X., &Myers, L. (2004). Computing aspects of power for multiple regression.Behavior Research Methods, Instruments, & Computers,36, 695–701.CrossRefGoogle Scholar
  5. Fowler, R. L. (1985). Testing for substantive significance in applied research by specifying nonzero effect null hypotheses.Journal of Applied Psychology,70, 215–218.CrossRefGoogle Scholar
  6. Gatsonis, C., &Sampson, A. R. (1989). Multiple correlation: Exact power and sample size calculations.Psychological Bulletin,106, 516–524.CrossRefPubMedGoogle Scholar
  7. Johnson, N. L., Kotz, S., &Balakrishnan, N. (1995).Continuous univariate distributions (2nd ed., Vol. 2). New York: Wiley.Google Scholar
  8. Kelley, K., &Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant.Psychological Methods,8, 305–321.CrossRefPubMedGoogle Scholar
  9. Knusel, L. (2005). On the accuracy of statistical distributions in Microsoft Excel 2003.Computational Statistics & Data Analysis,48, 445–449.CrossRefGoogle Scholar
  10. Lee, Y. S. (1972). Tables of upper percentage points of the multiple correlation coefficient.Biometrika,59, 175–189.Google Scholar
  11. McCullough, B. D., &Wilson, B. (2005). On the accuracy of statistical procedures in Microsoft Excel 2003.Computational Statistics & Data Analysis,49, 1244–1252.CrossRefGoogle Scholar
  12. Mendoza, J. L., &Stafford, K. L. (2001). Confidence interval, 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.CrossRefGoogle Scholar
  13. Murphy, K. R., &Myors, B. (1999). Testing the hypothesis that treatments have negligible effects: Minimum-effect tests in the general linear model.Journal of Applied Psychology,84, 234–248.CrossRefGoogle Scholar
  14. Murphy, K. R., &Myors, B. (2004).Statistical power analysis: A simple and general model for traditional and modern hypothesis tests (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  15. Sampson, A. R. (1974). A tale of two regressions.Journal of the American Statistical Association,69, 682–689.CrossRefGoogle Scholar
  16. Shieh, G. (2006). Exact interval estimation, power calculation and sample size determination in normal correlation analysis.Psychometrika,71, 529–540.CrossRefGoogle Scholar
  17. Smithson, M. (2003). Confidence intervals.Quantitative Applications in the Social Sciences Series (No. 140). Thousand Oaks, CA: Sage.Google Scholar
  18. Steiger, J. H. (2004). Beyond theF test: Effect size confidence intervals and tests of close fit in the analysis and contrast analysis.Psychological Methods,9, 164–182.CrossRefPubMedGoogle Scholar
  19. 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.CrossRefGoogle Scholar
  20. Stuart, A., &Ord, J. K. (1994).Kendall’s advanced theory of statistics (6th ed., Vol. 1). New York: Halsted.Google Scholar
  21. Wilcox, R. R. (1980). Some exact sample sizes for comparing the squared multiple correlation coefficient to a standard.Educational & Psychological Measurement,40, 119–124.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2007

Authors and Affiliations

  1. 1.Department of Management ScienceNational Chiao Tung UniversityHsinchu, TaiwanTaiwan

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