The methods of Tetrads, Hexads, and Octads: A type of more powerful sensory discrimination methods

Abstract

The well-known sensory discrimination method of Tetrads is a special case of the ‘M + N’ with M = N = 2. This paper extends the method of Tetrads to a general situation, i.e., the ‘M + N’ with M = N =k≥2. The methods of Hexads and Octads are the special cases of the ‘M + N’ with M = N = k, where k = 3, and 4, respectively. The general analytical psychometric functions for the specified and unspecified ‘M + N’ with M = N = k≥2 are produced. Simulation-derived psychometric functions for the specified and unspecified methods of Hexads and Octads are also produced. The values of the simulation-derived psychometric functions are well-matched with the values of the analytical psychometric functions. The performances of the methods of Hexads and Octads in both difference and similarity/equivalence tests are explored and compared with the performances of the method of Tetrads. It is shown that both difference and similarity/equivalence testing powers for the unspecified methods of Hexads and Octads are larger than those for the unspecified method of Tetrads. It suggests that the unspecified methods of Tetrads, Hexads, and Octads are a type of more powerful unspecified sensory discrimination methods. Tables and R codes are presented and provided for estimations of probability of correct response, Pc, Thurstonian discriminal distance δ or d´, B value for estimating variance of d´ for the specified and unspecified methods of Hexads and Octads. Tables and R codes for critical values, testing powers, and sample sizes for difference and similarity/equivalence tests using the specified and unspecified methods of Hexads and Octads are also presented and provided. The methods of Hexads and Octads are appropriate for visual and manual evaluations of food or non-food products, where sensory fatigue, carryover, or adaption effects are not mainly concerned.