An analytical psychometric function for the dual reference duo-trio (DRDT) method

The dual reference duo-trio (DRDT) is an improved balanced-reference duo-trio method, in which two same references are presented in a test but the reference is changed across the tests. The performance of the DRDT has been investigated theoretically based on a simulation-derived psychometric function in a previous paper published in this journal. The DRDT method is more powerful than the conventional duo-trio and the triangle methods. This paper derives an analytical psychometric function for the DRDT. Another form of the psychometric function for the DRDT is also derived based on the Torgerson's method of triads. Tables and R codes are provided for presentations and calculations of P_c, δ (or d^'), and variance of d^' (B-value) based on the analytical psychometric function for the method.