Review and development of Thurstonian models for the triangle and duo‐trio methods and paired versions of the methods.

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]