On the triangle test with replications

We consider the triangle test with replications. A commonly used test stati stic for this situation is the sum of all correct assessments, summed over all assessors. Several authors argue that the binomial distribution cannot be used to analyse this kind of data. Brockhoff and Schlich [Brockhoff, P.B ., & Schlich, P. (1998). Handling replications in discriminations tests. Fo od Quality and Preference, 9, 303-312.] propose an alternative model for th e triangular test with replicates, where the assessors have different proba bilities to correctly identify the odd sample even if the products are iden tical. Although we agree that assessors will have different probabilities o f correct assessment if there are true differences, we do not think that Br ockhoff and Schlich's model makes sense under the null hypothesis of equali ty of treatments. We show that all assessments are independent and have suc cess probability 1/3, if the null hypothesis is true and the experiment is properly randomized and properly carried out. This implies that the sum of all correct assessments is binomial with parameter p = 1/3. Therefore the u sual test based on this sum and the critical values of the binomial distrib ution is a level a test for the null hypothesis of equality of the products , even if there are replications. (C) 1999 Elsevier Science Ltd. All rights reserved.