Abstract
The correlation coefficient is the most commonly used measure for summarizing the magnitude and direction of linear relationship between two response variables. Considerable literature has been devoted to the inference procedures for significance tests and confidence intervals of correlations. However, the essential problem of evaluating correlation equivalence has not been adequately examined. For the purpose of expanding the usefulness of correlational techniques, this article focuses on the Pearson product-moment correlation coefficient and the Fisher's z transformation for developing equivalence procedures of correlation coefficients. Equivalence tests are proposed to assess whether a correlation coefficient is within a designated reference range for declaring equivalence decisions. The important aspects of Type I error rate, power calculation, and sample size determination are also considered. Special emphasis is given to clarify the nature and deficiency of the two one-sided tests for detecting a lack of association. The findings demonstrate the inappropriateness of existing methods for equivalence appraisal and validate the suggested techniques as reliable and primary tools in correlation analysis.
Highlights
Practical guidelines and suggestions for selecting, calculating, and interpreting effect size indices in statistical analyses have been frequently advocated in the literature
The results show that the two suggested procedures have more power than the other two two one-sided tests (TOST) counterparts
A widely recommended approach is to conduct an equivalence test to ascertain whether the observed effect size falls inside the selected equivalence boundaries
Summary
Practical guidelines and suggestions for selecting, calculating, and interpreting effect size indices in statistical analyses have been frequently advocated in the literature. According to the summary in Ferguson [6], effect size measures can fall into four general categories: (1) group difference, (2) strength of association, (3) corrected estimates, and (4) risk estimates. Pearson productmoment correlation coefficient or sample correlation coefficient r is the most commonly used strength of association measure in applied research across virtually all disciplines of social sciences. The popularity of sample correlation coefficient in the psychological literature has been documented in de Winter, Gosling and Potter [7], Hemphill [8], and Richard, Bond and Stokes-Zoota [9], among others.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
