Advertisement

Correlation and Simple Linear Regression in Applied Linguistics

  • Reza Norouzian
  • Luke Plonsky

Abstract

This chapter provides an applied description of two key methods to evaluate the association between two research variables. First, we provide a conceptual view of the notion of non-directional linear correlation. Using small datasets, we discuss the various behaviors of the correlation statistic, Pearson’s r, under different scenarios. Then, we turn our attention to a neighboring but practically different concept to evaluate the directional association between two research variables: the simple linear regression. Particularly, we shed light on one of the most useful purposes of simple linear regression and prediction. By end of the chapter, we present a conceptually overarching view that links the regression methods to all other methods that applied linguists often use to find important patterns in their data.

Keywords

Quantitative methods Statistics Correlation Regression 

References

  1. Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426–443.CrossRefGoogle Scholar
  2. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. New York, NY: Routledge.Google Scholar
  3. DeKeyser, R. (2000). The robustness of critical period effects in second language acquisition. Studies in Second Language Acquisition, 22, 499–533.Google Scholar
  4. De Winter, J. C., Gosling, S. D., & Potter, J. (2016). Comparing the Pearson and spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. Psychological methods, 21, 273–290.CrossRefGoogle Scholar
  5. Draper, N. R., & Smith, H. (1998). Applied regression analysis. New York, NY: Wiley.Google Scholar
  6. Egbert, J., & Plonsky, L. (2015). Success in the abstract: Exploring linguistic and stylistic predictors of conference abstract ratings. Corpora, 10, 291–313.CrossRefGoogle Scholar
  7. Field, A. (2013). Discovering statistics using IBM SPSS statistics. Thousand Oaks, CA: SAGE.Google Scholar
  8. Graybill, F. A., & Iyer, H. K. (1994). Regression analysis. New York, NY: Duxbury Press.Google Scholar
  9. Howell, D. C. (2013). Statistical methods for psychology. Belmont, CA: Cengage Learning.Google Scholar
  10. Johnson, J. S., & Newport, E. L. (1989). Critical period effects in second language learning: The influence of maturational state on the acquisition of English as a second language. Cognitive Psychology, 21(1), 60–99.CrossRefGoogle Scholar
  11. Kline, R. B. (2015). Principles and practice of structural equation modeling. New York, NY: Guilford.Google Scholar
  12. Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models. New York, NY: McGraw-Hill.Google Scholar
  13. Norouzian, R., & Plonsky, L. (2018). Eta- and partial eta-squared in L2 research: A cautionary review and guide to more appropriate usage. Second Language Research, 34, 257–271.CrossRefGoogle Scholar
  14. Norris, J. M. (2015). Statistical significance testing in second language research: Basic problems and suggestions for reform. Language Learning, 65(Supp. 1), 97–126.CrossRefGoogle Scholar
  15. Norris, J. M., Ross, S., & Schoonen, R. (2015). Improving second language quantitative research. Language Learning, 65(Supp. 1), 1–8.CrossRefGoogle Scholar
  16. Pearson, K. (1896). Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia. Philosophical Transactions A, 373, 253–318.CrossRefGoogle Scholar
  17. Pituch, K. A., & Stevens, J. P. (2016). Applied multivariate statistics for the social sciences: Analyses with SAS and IBM’s SPSS. New York, NY: Routledge.Google Scholar
  18. Plonsky, L. (2013). Study quality in SLA: An assessment of designs, analyses, and reporting practices in quantitative L2 research. Studies in Second Language Acquisition, 35, 655–687.CrossRefGoogle Scholar
  19. Plonsky, L. (Ed.). (2015a). Advancing quantitative methods in second language research. New York, NY: Routledge.Google Scholar
  20. Plonsky, L. (2015b). Statistical power, p values, descriptive statistics, and effect sizes: A “back-to-basics” approach to advancing quantitative methods in L2 research. In L. Plonsky (Ed.), Advancing quantitative methods in second language research (pp. 23–45). New York, NY: Routledge.CrossRefGoogle Scholar
  21. Plonsky, L., & Derrick, D. J. (2016). A Meta-Analysis of Reliability Coefficients in Second Language Research. Modern Language Journal, 100, 538–553.CrossRefGoogle Scholar
  22. Plonsky, L., & Ghanbar, H. (in press). Multiple regression in L2 research: A methodological synthesis and guide to interpreting R values. Modern Language Journal.Google Scholar
  23. Plonsky, L., & Oswald, F. L. (2014). How big is ‘big’? Interpreting effect sizes in L2 research. Language Learning, 64, 878–912.CrossRefGoogle Scholar
  24. Plonsky, L., & Oswald, F. L. (2017). Multiple regression as a flexible alternative to ANOVA in L2 research. Studies in Second Language Acquisition, 39, 579–592.CrossRefGoogle Scholar
  25. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: SAGE.Google Scholar
  26. Roever, C., & Phakiti, A. (2017). Quantitative methods for second language research: A problem-solving approach. New York, NY: Routledge.CrossRefGoogle Scholar
  27. Rosnow, R. L., & Rosenthal, R. (2008). Essentials of behavioral research: Methods and data analysis. New York, NY: McGraw-Hill.Google Scholar
  28. Schoonen, R. (2015). Structural equation modeling in L2 research. In L. Plonsky (Ed.), Advancing quantitative methods in second language research (pp. 213–242). New York, NY: Routledge.CrossRefGoogle Scholar
  29. Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  30. Thompson, B. (Ed.). (2003). Score reliability: Contemporary thinking on reliability issues. Newbury Park, CA: SAGE.Google Scholar
  31. Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.Google Scholar
  32. Wilcox, R. (2016). Understanding and applying basic statistical methods using R. New York, NY: Wiley.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Texas A&M UniversityCollege StationUSA
  2. 2.Northern Arizona UniversityFlagstaffUSA

Personalised recommendations