Thurstonian model for the four-interval oddity task

Jian Bi, Hye Seong Lee, Michael O'Mahony

Research output: Contribution to journalArticlepeer-review


The four-interval oddity task is an extension of the Triangle method, which is the three-interval oddity task and is one of the most broadly used conventional sensory discrimination methods. It is a special case of the m-interval oddity task or the m-alternative odd-man-out task where m = 4. It is also a special situation of the unspecified ‘M + N’ with M = 3 and N = 1. Some new forms of the analytical psychometric function for the four-interval oddity task based on a normal distribution function, a bivariate normal distribution function, and a non-central F-distribution function are provided originally in this paper. The performance of the four-interval oddity task in both difference testing and similarity/equivalence testing is explored and compared with some unspecified forced-choice sensory discrimination methods including the Triangle. 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 four-interval oddity task.

Original languageEnglish
Article number104999
JournalFood Quality and Preference
StatePublished - Oct 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Ltd


  • Psychometric function
  • Sensory discrimination method
  • Thurstonian discriminal distance δ or d'
  • m-alternative odd-man-out task
  • m-interval oddity task
  • ‘M+N’ method


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