TY - JOUR
T1 - Improved procedures and computer programs for equivalence assessment of correlation coefficients
AU - Shieh, Gwowen
N1 - Publisher Copyright:
© 2021 Gwowen Shieh. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85106962862&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0252323
DO - 10.1371/journal.pone.0252323
M3 - Article
C2 - 34048464
AN - SCOPUS:85106962862
SN - 1932-6203
VL - 16
JO - PLoS ONE
JF - PLoS ONE
IS - 5 May 2021
M1 - e0252323
ER -