Paired versions of various sensory discrimination forced-choice methods and the same-different area theorem

This paper proposes a new type of sensory discrimination methods, i.e., paired versions of various sensory discrimination forced-choice methods, which can be regarded as modified versions of the same-different method. The new type of methods possesses the advantage of the same-different test for measuring overall sensory difference, but overcomes its weaknesses of large variations of response bias and lower testing power. An important finding is that this type of methods is closely related to the same-different area theorem and its extension. The same-different area theorem establishes an equivalence between the area under the receiver operating characteristic (ROC) curve of the same-different method and the proportion of correct responses (Pc) in the dual-pair method. This paper re-demonstrates and extends the same-different area theorem. An analytical expression of a general psychometric function for the new type of methods is derived. Performances of the new type of methods are evaluated with testing power and sample size in both difference and similarity/equivalence tests. R codes are provided for the new type of methods for Pc, Thurstonian discriminal distance δ, and variance of d′, where d′ is an estimator of δ.