A Simplified Form of the Psychometric Function for the m‐Alternative Forced Choice (mAFC) Method. Issue 4 (11th July 2016) - Bi, Jian; Kuesten, Carla
Abstract: The m ‐Alternative Forced Choice ( m AFC), including the 2AFC, 3AFC, and m AFC where m > 3, are a type of widely used sensory discrimination method. This article offers an interesting finding for the psychometric function for the m AFC. The conventional general psychometric function for the m AFC, 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 m AFC, but also an intuitive geometric interpretation for Pc in the m AFC. Moreover, the simplified form of the psychometric function for the m AFC may provide some insight for the decision strategies used in the m AFC. Practical Applications: The simplified form of the psychometric function for the m AFC derived originally in this paper can be expressed in a built‐in S‐Plus program " pmvnorm " (for 3AFC) and R program " pmvnorm " (for m AFC 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 m AFC easily. A table for Pc values in the m AFC 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 m AFC 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 m AFC is also produced.