Nonparametric tests for the Randomized Complete Block Design with Ordered Categorical Variables

In many scientific disciplines and industrial fields, when dealing with comparisons between two or more treatments, researchers and practitioners are often faced with theoretical and practical problems within the framework of Randomized Complete Block (RCB) design with ordered categorical response variables. This situations can arise very often in the field of the evaluation of educational services or quality of products, for example in connection with the sensorial testing studies, where several useful experimental performance indicators, especially in the food and body care industry, are provided by individual sensorial evaluations by trained people (panelists) during a so-called sensory test (Meilgaard et al, 2006). Within this framework the experimental design typically handles panelists as blocks. In general, the requirement to take into consideration a RCB design occurs when the experimental units are heterogeneous, hence the notion of blocking is used to control the extraneous sources of variability. The major criteria of blocking are characteristics associated with the experimental material and the experimental setting. The purpose of blocking is to sort experimental units into blocks, so that the variation within a block is minimized while the variation among blocks is maximized. An effective blocking not only yields more precise results than an experimental design of comparable size without blocking, but also increases the range of validity of the experimental results. In this contribution we propose a general solution within the Nonparametric Combination (NPC) of Dependent Permutation Tests (Pesarin, 2001) which is particularly suitable for the RCB design, especially in case of ordered categorical response variables such that used for sensorial studies. In the next section, we present an update review of the procedures proposed in the literature for the hypothesis testing on the RCD design. In Section 3 we present the proposed permutation solution for the RCB Design. In sections 4 and 5 a comparative simulation study and a real case study are presented. Finally, we conclude, in Section 6, with some directions of current and future research.