Tetrads, triads and pairs: Experiments in self-speciﬁcation Yixun Xia a,b , Jason Zhang a , Xiaotian Zhang a , Rie Ishii a , Fang Zhong b , Michael O’Mahony a,⇑ a Department of Food Science and Technology, University of California, Davis, CA 95616, USA b Department of Food Science and Technology, Jiangnan University, Wuxi, Jiangsu, China article info Article history: Received 6 July 2014 Received in revised form 25 August 2014 Accepted 18 September 2014 Available online 28 September 2014 Keywords: Difference tests Tetrad Triangle Self-speciﬁed 2-AFC Self-speciﬁed 3-AFC Self-speciﬁcation abstract Sensory difference tests can be used to investigate how well consumers can discriminate between very similar, confusable products. For this reason, it is desirable that the products are tested in a manner as similar as possible to realistic conditions of consumption. For some of these tests, it is desirable that the experimenter does not specify the nature of the difference; the consumers have to discover this for themselves. The methods generally used for this class of tests are the triangle and duo–trio. Recently, the (unspeciﬁed) tetrad method has emerged as a candidate to replace the triangle and duo–trio tests, because it is more powerful, although not as powerful as the 2-AFC and 3-AFC. Using a model and a beverage system, it was conﬁrmed that the tetrad method was more powerful than the triangle method, despite the fact that the greater memory load of the tetrad reduced its d 0 values. To initiate an investiga- tion into more powerful tests, several self-speciﬁcation protocols were developed, which differed from those used in prior investigations. These protocols successfully converted triangle tests into self-speciﬁed 3-AFCs, with a consequent increase in power. Triangle, tetrad, self-speciﬁed 2-AFC and 3-AFC methods were then compared, with the tetrad being more powerful than the triangle and the self-speciﬁed 2-AFC and 3-AFC methods being more powerful than the tetrad. Ó 2014 Elsevier Ltd. All rights reserved. Introduction In sensory evaluation, difference tests are generally used for determining the degree of difference between food samples which are similar enough to be regarded as confusable. This can be applied to studies of the effects of ingredient change, quality assur- ance, ingredient speciﬁcation, product development, storage stud- ies, and changes in processing or packaging. Depending on the goals of the study, difference tests can be used as an analytical tool with highly trained panelists or they can be used to measure con- sumer discrimination. The former has been categorized as Sensory Evaluation I and the latter as Sensory Evaluation II (O’Mahony, 1995). In this latter case, consumers are sampled and tested in a way that is as close to the ‘real life’ consumption situation as pos- sible. A variety of statistical procedures can be applied to make inferences from the sample of consumers to the appropriate demo- graphic population or populations. Sometimes, in this situation, for reality, the nature of the difference to be detected in the test, is left unspeciﬁed so that consumers are required to discover this for themselves. It is with this class of test that the present paper is concerned. If the nature of the difference is not speciﬁed by the experi- menter, the more powerful forced-choice methods like the 2-AFC and 3-AFC are not appropriate. This leaves the triangle and duo– trio as the commonly chosen forced-choice alternatives that do not involve the experimenter’s speciﬁcation. These are consider- ably less powerful and for a given sensory difference, necessarily require much larger sample sizes to attain signiﬁcance (Ennis, 1990, 1993; Ennis & Jesionka, 2011) with a resulting increase in cost. Recently, Ennis and Jesionka (2011) examined the theoretical power of the (unspeciﬁed) tetrad method (Lockhart, 1951; O’Mahony, 2013) and reported that it was more powerful than the available unspeciﬁed difference tests. Thus, it became a prime candidate to replace the much used triangle or duo–trio methods. Tables of d 0 for the tetrad and for obtaining variances for statistical analysis are readily available (Bi & O’Mahony, 2007; Ennis, Ennis, Yip, & O’Mahony, 1998; Ennis, Rousseau, & Ennis, 2013). Yet, the tetrad requires the assessment of four products, and this would imply a heavy memory load, which has the potential to cause prob- lems due to memory loss with a subsequent reduction in d 0 and power. For example, for a given d 0 , the 3-AFC is theoretically more powerful than the 2-AFC. The greater memory load for the 3-AFC http://dx.doi.org/10.1016/j.foodqual.2014.09.005 0950-3293/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Sensory Innovation Lab, Department of Food Science and Technology, University of California, Davis, CA 95616, USA. Tel.: +1 530 756 5493. E-mail address: maomahony@ucdavis.edu (M. O’Mahony). Food Quality and Preference 40 (2015) 97–105 Contents lists available at ScienceDirect Food Quality and Preference journal homepage: www.elsevier.com/locate/foodqual