Deriving a lower bound for the proportion of perceivers in replicated difference tests by means of multiple test theory

Analyzing repeated difference tests aims in significance testing for differences as well as in estimating the mean discrimination ability of the consumers. In addition to the average success probability, the proportion of consumers that may detect the difference between two products and therefore account for any increase of this probability is of interest. While some authors address the first two goals, for the latter one only an estimator directly linked to the average probability seems to be used. However, this may lead to unreasonable results. Therefore we propose a new approach based on multiple test theory. We define a suitable set of hypotheses that is closed under intersection. From this, we derive a series of hypotheses that may be sequentially tested while the overall significance level will not be violated. By means of this procedure we may determine a minimal number of assessors that must have perceived the difference between the products at least once in a while. From this, we can find a conservative lower bound for the proportion of perceivers within the consumers. In several examples, we give some insight into the properties of this new method and show that the knowledge about this lower bound might indeed be valuable for the investigator. Finally, an adaption of this approach for similarity tests will be proposed.