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This article explores the two‐interval, two‐alternative forced‐choice (2I2AFC) paradigm in signal detection theory (SDT), which can also be called the paired A‐Not A with AB and BA pairs in the sensory and consumer fields. The article describes how to estimate the parameters and their variances from the psychometric function of the method. Tables and R codes were developed and are provided for the estimations. The performance of the method is evaluated. It shows that the paired A‐Not A with AB and BA pairs is more effective and powerful than the conventional A‐Not A and the A‐Not A with reminder (A‐Not AR) tests. An extension of the method, that is, the ratings of the paired A‐Not A with AB and BA pairs is also explored. A facial shine case study applying this method is provided. Practical applications: As one of the paired versions of sensory discrimination methods, the paired A‐Not A with AB and BA pairs has wide potential applications to detect and measure sensory difference, especially to detect and measure before‐after treatment effects of products. The method can be used to detect both product effects and serving order effects. [ABSTRACT FROM AUTHOR]

The m-Alternative Forced Choice ( mAFC), including the 2AFC, 3AFC, and mAFC where m > 3, are a type of widely used sensory discrimination method. This article offers an interesting finding for the psychometric function for the mAFC. The conventional general psychometric function for the mAFC, which is based on m independent normal distributions with one signal and m−1 noise observations, can be expressed as an elegant simplified form, i.e., a single cumulative distribution function (cdf) of the standard ( m−1)-variate normal distribution. This finding provides not only an alternative approach to calculate the probability of correct responses ( Pc) and Thurstonian discriminal distance ( δ) for the mAFC, but also an intuitive geometric interpretation for Pc in the mAFC. Moreover, the simplified form of the psychometric function for the mAFC may provide some insight for the decision strategies used in the mAFC. Practical Applications The simplified form of the psychometric function for the mAFC derived originally in this paper can be expressed in a built-in S-Plus program ' pmvnorm' (for 3AFC) and R program ' pmvnorm' (for mAFC where m > 2) in the R package 'mvtnorm.' Two R codes 'mAFCp' and 'mAFCq,' which are based on the simplified form and the R package, were developed in the article. The codes can be used for calculations of Pc and δ for the mAFC easily. A table for Pc values in the mAFC is produced for m = 2 to 8, and δ from 0 to 4 with a step of 0.1. A table for δ values in the mAFC is produced for m = 2 to 8, and Pc from 0.01 to 0.99 with a step of 0.01. A table for the B values for calculation of variance of d-prime obtained from the mAFC is also produced. [ABSTRACT FROM AUTHOR]