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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]

Highlights • The 4I2AFC is a paired 2-AFC with AB and BA pairs. • The 4I2AFC can be used to detect small changes of stimuli. • The 4I2AFC can be used to identify direction of stimuli changes. • The 4I2AFC is more powerful than the tetrads in both difference and similarity testing. • The 4I2AFC is particularly suitable for visual or manual evaluations with less sensory fatigue. Abstract The four-interval, two-alternative forced-choice (4I2AFC) is a paired version of the 2-AFC with AB and BA pairs as two alternatives, where A is a signal or a stronger stimulus and B is a noise or a weaker stimulus. The task of the subject in 4I2AFC is to select the pair (AB) with decreasing stimuli change. The 4I2AFC is a powerful sensory discrimination forced-choice method to detect small, directional changes of stimuli particularly suitable for visual or manual evaluations with less sensory fatigue. This paper explores the 4I2AFC method and includes an applied illustrative case study for measuring facial skin smoothness visually using the method. An analytical psychometric function is derived. The performances of the 4I2AFC in both difference testing and similarity/equivalence testing are compared with those of the conventional sensory discrimination forced-choice methods. The 4I2AFC is theoretically more powerful than any of the published conventional methods including the tetrads. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of sensory discrimination methods, i.e., paired versions of various sensory discrimination forced-choice methods, which can be regarded as modified versions of the same-different method. The new type of methods possesses the advantage of the same-different test for measuring overall sensory difference, but overcomes its weaknesses of large variations of response bias and lower testing power. An important finding is that this type of methods is closely related to the same-different area theorem and its extension. The same-different area theorem establishes an equivalence between the area under the receiver operating characteristic (ROC) curve of the same-different method and the proportion of correct responses ( P c ) in the dual-pair method. This paper re-demonstrates and extends the same-different area theorem. An analytical expression of a general psychometric function for the new type of methods is derived. Performances of the new type of methods are evaluated with testing power and sample size in both difference and similarity/equivalence tests. R codes are provided for the new type of methods for P c , Thurstonian discriminal distance δ, and variance of d′ , where d′ is an estimator of δ. [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]