Estimation of Thurstonian Models for Various Forced-Choice Sensory Discrimination Methods as a Form of the "M+N" Test

Psychometric functions for discrimination tests, which connect probabilities of correct response, p_c, with Thurstonian discriminal distances, d′, are of theoretical and practical significance. This paper uses a computer-intensive approach to produce simulation-derived psychometric functions for the "M+N" test, which is a generalization and can be considered as a framework of many forced-choice methods. The paper demonstrates and describes chance probabilities in different situations for the "M+N" test. The paper compares the performances of the specified and unspecified "M+N" test with the M=N test. The paper provides novel tables for p_c and d′ for four specific versions of the "M+N" test: the specified "two-out-of-five" test (i.e., the "M+N" test with M=3 and N=2); the unspecified "one-out-of-four" test (i.e., the "M+N" test with M=3 and N=1); the specified and unspecified octad tests (i.e., the "M+N" test with M=N=4). The corresponding B values, for calculation of the variances of d' for the tests, are also provided. The concept and practice of pseudo-correct response, i.e., forgiveness introduced by Ennis, are discussed and generalized.