Thurstonian Model for the Difference-from-Control Test

The difference-from-control (DFC) test is one of the sensory discrimination methods which is applicable to sensory evaluation in some areas, including process optimization and quality assessment for foods. Thurstonian models are needed for any one of the sensory discrimination methods, including the DFC. This is important because the models provide a useful sensory measure, the Thurstonian discriminal distance, $\delta$ or $d^{\prime }$, which is theoretically independent of the methods or scales used for its estimation. This paper originally derives the Thurstonian model and the estimations of the model parameters for the DFC test based on the folded normal distribution. The statistical testing, difference testing power, and sample sizes needed for the DFC test are also discussed. R codes for the estimations and tests of parameters of the model for the DFC are developed, used, and provided in the paper.