Note on the Equivalence of the Significance Test of the Partial Point-Biserial Correlation and the One-Factor Analysis of Covariance for Two Treatment Groups

An identity is demonstrated between (1) the squared Student's t-statistic obtained as a transformation of the sample point-biserial correlation coefficient relating dichotomous variable, 21, to continuous variable x, with the effects of a third variable, x, partialed out; and (2) the F-statistic resulting from a one-factor, two-group (the y dichotomy) analysis of covariance on the x variable Mth the third variable, x, covaried

Analysis of covariance · Correlation · Covariance · Covariance and correlation · Discrete mathematics · Econometrics · Equivalence (formal languages) · Mathematical analysis · Partial correlation · Random variable · Statistic · Statistics · Sum of normally distributed random variables · Variable (mathematics) · Variables · Advanced Statistical Methods and Models · Mathematics