NONPARAMETRIC ESTIMATION OF d′ AND ITS VARIANCE FOR THE A–NOT A WITH REMINDER JIAN BI 1,4 , MICHAEL O’MAHONY 3 and HYE-SEONG LEE 2,5 1 Sensometrics Research and Service, Richmond, VA 23236 2 Department of Food Science and Engineering, Ewha Womans University, Seoul, South Korea 3 Department of Food Science and Technology, University of California, Davis, CA 4 Corresponding author. TEL: 804-560-1754; FAX: 804-560-1754; EMAIL: bbdjcy@aol.com 5 Corresponding author. TEL: 82-2-3277-6687; FAX: 82-2-3277-6687; EMAIL: hlee@ewha.ac.kr Accepted for Publication September 9, 2013 doi:10.1111/joss.12063 ABSTRACT 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 rela- tionship 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 propor- tion 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. PRACTICAL APPLICATIONS The A–Not AR is a variation of the conventional A–Not A method, which is used in the sensory field for discrimination testing. This method is particularly useful when it is difficult to have an adequate familiarization procedure for the test samples for panelists before a test. This approach also offers the potential for applying such a method to problems like hedonic, purchase intent, and consumer concept measures in addition to other measures in the sensory and consumer science field. This paper provides a new nonparametric method and R codes for estimating d′ and its variance from the ratings of the A–Not AR. INTRODUCTION The A–Not A with reminder (A–Not AR) is a variation of the conventional A–Not A method. For the A–Not AR, unlike the A–Not A, which is a single sample presentation, a reminder (e.g., sample A) is provided before each test sample (sample A or Not A) in order to jog the observer’s memory. The A–Not AR is not new in the psychophysics literature but is relatively new in the sensory and consumer science literature. Macmillan and Creelman (2005) discuss the reminder para- digm. Lee et al. (2007), Hautus et al. (2009), and Stocks et al. (2013) introduced the method into sensory and consumer science literature and provided an insightful description and a signal detection theory (SDT) model of the method. Hautus (2012) provides software to fit the appropriate SDT models, including A–Not AR, to the data using maximum likelihood estimation. In the A–Not AR, each test contains two intervals (meaning two sample presentations), the first of which always contains the reminder. If the reminder is S1, then the presentations are <S1, S1> and <S1, S2>, and if the reminder is S2 then the presentations are <S2, S1> and <S2, S2>. Instructions for the A–Not AR can vary, but in essence, the participant is asked to decide whether the secondly pre- sented sample is the “same” as or “different” from the reminder. Although the “same” and “different” responses are used in both the same–different and the A–Not AR methods, the two methods relate to different cognitive mechanisms. Receiver operating characteristic (ROC) analysis for the A–Not AR has not been explored adequately in sensory and consumer science literature. This paper will discuss the function of ROC curves for the A–Not AR and derive and demonstrate the relationship Journal of Sensory Studies ISSN 0887-8250 381 Journal of Sensory Studies 28 (2013) 381–386 © 2013 Wiley Periodicals, Inc.