Measures of Interval Association

Kenneth J. Berry and Janis E. Johnston

Chapter Chapter 8 in Statistical Methods: Connections, Equivalencies, and Relationships, 2023, pp 329-377 from Springer

Abstract: Abstract Chapter 8 describes connections, equivalencies, and relationships relating to bivariate linear correlation and regression. First, Pearson’s product-moment correlation coefficient is described. Second, a permutation alternative to Pearson’s correlation coefficient is presented for bivariate data and the connection linking the two measures is described. Third, an example analysis illustrates the differences and similarities of the two measures and the asymptotic and Monte Carlo probability values are calculated and compared. Fourth, the point-biserial correlation coefficient is described, an example analysis illustrates the point-biserial correlation coefficient, and a Monte Carlo probability value for the point-biserial correlation coefficient is generated. The connection linking the point-biserial correlation coefficient and Pearson’s product-moment correlation coefficient is established. Fifth, the connection linking Spearman’s rank-order correlation coefficient and Pearson’s product-moment correlation coefficient is detailed and an example analysis illustrates the connection. Sixth, Jaspen’s multi-serial correlation coefficient for one ordinal-level variable and one interval-level variable is described and the connection linking Jaspen’s coefficient and Pearson’s product-moment correlation coefficient is established. Finally, the biserial correlation coefficient is described and the connections linking biserial correlation, point-biserial correlation, Jaspen’s multi-serial correlation, and Pearson’s product-moment correlation are delineated and illustrated.

Date: 2023
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DOI: 10.1007/978-3-031-41896-9_8

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