On the number of perceivers in a triangle test with replications

In discrimination tests, two different questions usually arise: First of all, we are interested in deciding whether or not there are product differences at all that might be perceived by the assessors. However, often this is not our most important concern, since the main question is whether or not the consumers (in contradiction to e. g. a trained panel) might perceive the difference and, if so, how many of them are supposed to do so. While the first question has been addressed frequently in recent times, the known models for estimating the proportion of perceivers use strong conditions, e. g. that the assessors taste the difference always or never. We propose a more general model that allows the assessors to perceive differences once in a while and derive a method that takes this assumption into account. Several examples show that the estimates for the proportion of interest are quite reasonable.