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The Two‐Out‐of‐Five method is one of the basic sensory discrimination methods. It is a special case of the 'M+N' method with M = 3 and N = 2. Three variants of the method are discussed in the paper: specified, unspecified, and unspecified with forgiveness. Analytical and simulation‐derived psychometric functions for all three variants of the Two‐Out‐of‐Five method are derived and produced. The performance of the method in both difference and similarity/equivalence tests are explored. It is shown that both difference and similarity/equivalence testing powers for the specified Two‐Out‐of‐Five are larger than those for the 2‐AFC and 3‐AFC. Both difference and similarity/equivalence testing powers for the unspecified Two‐Out‐of‐Five are larger than those for the Triangle and Duo‐trio. Both difference and similarity/equivalence testing powers for the unspecified with forgiveness Two‐Out‐of‐Five are larger than those for the conventional unspecified Two‐Out‐of‐Five and unspecified Tetrads. Tables and R codes are presented and provided for estimations of the probability of correct response, Pc, Thurstonian discriminal distance δ or d', and the B value for estimating the variance of d' for the three variants of the Two‐Out‐of‐Five method. Practical Applications: The Two‐Out‐of‐Five method is a powerful sensory discrimination method. However, this method has not been used widely in sensory and consumer research, partly since the method has not been explored adequately in the literature. This paper explores the Two‐Out‐of‐Five method and shows that the method has potential for wide application. The Two‐Out‐of‐Five method involves a larger number of samples (5) and sensory fatigue may be of concern. Hence, the method may not be suitable for taste and smell tests with strong stimuli. The method is particularly suitable for manual and visual inspection testing where sensory fatigue is of a lesser concern. [ABSTRACT FROM AUTHOR]

The unspecified tetrad is a powerful non‐attribute‐specified sensory discrimination method widely used for sensory analysis and consumer research. A paired version of the method is proposed and explored in this article. It is the paired unspecified tetrad with different order (AB and BA) pairs. An analytical and a simulation‐derived psychometric function of the new method are produced. The paired unspecified tetrad with AB and BA pairs is more powerful than the conventional unspecified tetrad and the paired versions of the triangle and duo‐trio methods. A weakness of the paired version of the unspecified tetrad versus the conventional unspecified tetrad is that the new method involves in more adaption, fatigue, or memory factors. Practical Applications: The paired unspecified tetrad with different order (AB and BA) pairs has wide potential applications, especially for visual or manual inspection of food or nonfood products to detect before–after treatment effects, but may not be suitable for food tasting considering the adaption, fatigue, or memory factors. [ABSTRACT FROM AUTHOR]

There are two main objectives of this paper. One is to review the current Thurstonian models for the conventional and modified triangle and duo‐trio methods. Another objective is to develop Thurstonian models for, and assess the performances of the paired triangle and paired duo‐trio methods with AB and BA pairs. Bradley's models based on the noncentral F distribution for the triangle and duo‐trio methods are revisited and are used to derive the psychometric functions for the paired versions of the triangle and duo‐trio methods. The simulation‐derived psychometric functions for the new methods are also produced. The performances of the new methods in both difference and similarity/equivalence tests are explored and show that the new methods are more powerful than most of the conventional unspecified forced‐choice methods and are similar to the unspecified tetrad. Practical applications: The triangle and the duo‐trio methods are popular sensory discrimination methods used widely in sensory and consumer research. One weakness of the methods is relatively lower testing power. The paired triangle and paired duo‐trio methods proposed and explored in this paper overcome this weakness of the conventional methods. The paired versions of the methods are more powerful than most of the conventional unspecified discrimination methods in difference and similarity tests for products. The new methods are particularly suitable for assessment of before–after treatment effects of products. The methods have wide potential application for visual and manual inspection testing of food or non‐food products where less sensory fatigue is of concern. R codes were developed and provided in the paper for the Thurstonian models of both the conventional versions and the paired versions of the triangle and the duo‐trio methods. [ABSTRACT FROM AUTHOR]