Estimation of Thurstonian Models for Various Forced‐Choice Sensory Discrimination Methods as a Form of the "M + N" Test. Issue 5 (October 2014)

• Record Type: Journal Article
• Authors: Bi, Jian; Lee, Hye‐Seong; O'Mahony, Michael
• Is Part Of: Journal of sensory studies. Volume 29:Issue 5(2014)
• Page Start: 325
• Page End: 338
• Publication Date: 2014-10
• Subjects: Sensory evaluation -- Periodicals; Food -- Sensory evaluation -- Periodicals; Food preferences -- Periodicals; 664.072
• DOI: 10.1111/joss.12114
• Languages: English
• ISSNs: 0887-8250

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <sec id="joss12114-sec-0001" sec-type="section"> <p>Psychometric functions for discrimination tests, which connect probabilities of correct response, <italic>p<sub>c</sub></italic>, with Thurstonian discriminal distances, <italic>d′</italic>, are of theoretical and practical significance. This paper uses a computer‐intensive approach to produce simulation‐derived psychometric functions for the "M + N" test, which is a generalization and can be considered as a framework of many forced‐choice methods. The paper demonstrates and describes chance probabilities in different situations for the "M + N" test. The paper compares the performances of the specified and unspecified "M + N" test with the <italic>M</italic> = <italic>N</italic> test. The paper provides novel tables for <italic>p<sub>c</sub></italic> and <italic>d′</italic> for four specific versions of the "M + N" test: the specified "two‐out‐of‐five" test (i.e., the "M + N" test with <italic>M</italic> = 3 and <italic>N</italic> = 2); the unspecified "one‐out‐of‐four" test (i.e., the "M + N" test with <italic>M</italic> = 3 and <italic>N</italic> = 1); the specified and unspecified octad tests (i.e., the "M + N" test with <italic>M</italic> = <italic>N</italic> = 4). The corresponding <italic>B</italic> values, for calculation of the variances of <italic>d'</italic> for the tests, are also provided. The concept and practice of pseudo‐correct response, i.e., forgiveness introduced by Ennis, are discussed and generalized.</p> </sec> <sec id="joss12114-sec-0002" sec-type="section"> <title>Practical Applications</title> <p>Considering the constraints imposed by the products and the circumstances of the business objective, different forms of various difference test method might be selected as the most suitable design. The proposed Thurstonian modeling approach using a simulation‐derived psychometric function makes it possible to drive psychometric functions for any one of the more than 40 different versions of the "M + N" test. This paper shows that a simulation‐derived psychometric function is compatible with an exact psychometric function. R/S‐Plus codes for the simulation‐derived psychometric functions are also developed and provided. Using this technique, various versions of commonly used sensory difference test methods, including the 2‐AFC, triangle and tetrad, can be compared with many more versions of difference test methods. In addition, using the supplied R/S‐Plus codes, the Thurstonian sensory difference measure, <italic>d′</italic>, can be computed easily and quickly for various forms of the "M + N" test.</p> </sec> </abstract>