# Thurstonian Scaling for Sensory Discrimination Methods
## 1 Introduction  
Contamination may lead to changes of food sensory properties and consumers' sensory perceptions. Sensory discrimination methods can be used to detect the sensory difference/similarity of samples.  
Sensory discrimination methods are an important methodology of Sensory and Consumer Science. For more about sensory discrimination methods, see, e.g., [PERSON] et al. [1], [PERSON] and [PERSON] [2], [PERSON] et al. [3], [PERSON] [4], [PERSON] et al. [5], and various ASTM and ISO Standards about sensory discrimination methods (see ASTM [6, 7, 8, 9, 10, 11, 12] and ISO [13, 14, 15, 16, 17]).  
Thurstonian scaling, i.e., Thurstonian discriminant distance \(\delta\) or \(d^{\prime}\), which can be regarded as an estimator of \(\delta\), provides a unified framework for the sensory discrimination methods. Thurstonian discriminant distance \(d^{\prime}\) can be estimated from a Thurstonian model, i.e., a psychometric function for any one of the sensory discrimination methods, and can be used as a unique sensory measurement index. An advantage of \(d^{\prime}\) is that it is theoretically independent of the methods or scales used for its estimation. \"As such, \(\delta\) provides a common scale of measure for comparing samples measured under a variety of test conditions.\" (ASTM-E2262-03 [7]).  
For more details about Thurstonian models of sensory discrimination methods, see, e.g., [PERSON] [18], [PERSON] [19], [PERSON] and [PERSON] [20], [PERSON] [21], [PERSON] [22, 23], [PERSON] et al. [24], [PERSON] [25, 26], [PERSON] and [PERSON] [27], [PERSON] et al. [28], [PERSON] [29, 30, 31], [PERSON] and [PERSON] [32], [PERSON] and [PERSON] [33, 34], [PERSON] et al. [35, 36, 37], [PERSON] and [PERSON] [38],[PERSON] [39], [PERSON] and [PERSON] [40], [PERSON] et al. [41], [PERSON] and [PERSON] [42], and [PERSON] and [PERSON] [43]. Signal Detection Theory (SDT) is also an important theoretical source of Thurstonian models of sensory discrimination methods. For SDT, see, e.g., [PERSON] and [PERSON] [44], [PERSON] and [PERSON] [45], and [PERSON] et al. [46]. The R package'sensR' ([PERSON] et al. [47]) provides R programs for calculations of \(d^{\prime}\) values from some basic sensory discrimination methods. Additionally, novel uses of Thurstonian modeling may be found, including applicability scoring by [PERSON] and [PERSON] [48] and scaling of ratings data by [PERSON] et al. [49].  
The main objectives of this paper include the following: (1). to estimate \(d^{\prime}\) and its variance from some basic sensory discrimination methods; (2). to conduct statistical testing including difference testing and equivalence/similarity testing for individual \(d^{\prime}\) for a test sample and a control sample in a sensory discrimination method; (3). to conduct statistical testing including difference testing, equivalence/similarity testing, and multiple comparisons for multiple \(d^{\prime}\) values for multiple test samples; (4). to discuss generally the application and significance of Thurstonian scaling for sensory discrimination methods; (5). to develop and provide corresponding R codes using R programs (R Core Team [50]) in the Supplementary Materials in the online version of this paper.