Nonparametric Estimation of d′ and Its Variance for the A-Not A with Reminder

The A-Not A with reminder (A-Not AR) is a relatively new method in the sensory literature. This paper derives and demonstrates the function illustrating the relationship between the area under the receiver operating characteristic (ROC) curve and d′ for the A-Not AR with the differencing strategy. This function shows that the area under an ROC curve for the A-Not AR is equal to the maximum proportion of correct responses in an A-Not A. This theoretic function can be used to estimate d′ and its variance from the ratings of the A-Not AR. A simulation study shows that the nonparametric estimation based on this function is close to those obtained by using the maximum likelihood estimation. The estimation of the variance of d′ based on the delta method is close to that obtained by using the bootstrap method. R codes are provided for the estimations of d′ and its variance as well as simulations.