Thurstonian model for the four-interval oddity task

The four-interval oddity task is an extension of the Triangle method, which is the three-interval oddity task and is one of the most broadly used conventional sensory discrimination methods. It is a special case of the m-interval oddity task or the m-alternative odd-man-out task where m = 4. It is also a special situation of the unspecified ‘M + N’ with M = 3 and N = 1. Some new forms of the analytical psychometric function for the four-interval oddity task based on a normal distribution function, a bivariate normal distribution function, and a non-central F-distribution function are provided originally in this paper. The performance of the four-interval oddity task in both difference testing and similarity/equivalence testing is explored and compared with some unspecified forced-choice sensory discrimination methods including the Triangle. Tables and R codes are presented and provided for estimations of the probability of correct response, P_c, Thurstonian discriminal distance δ or d´, and the B value for estimating the variance of d´ for the four-interval oddity task.