Statistical inference for temporal dominance of sensations data using randomization tests

Temporal dominance of sensations (TDS) is a relatively new notion to investigate the evolution of dominant sensations of a product throughout a pre-defined period like, e.g., mastication or aftertaste. It is mainly used for a description of the characteristics of each single product over time. In contrast, valid statistical inference to compare the products globally or in pairwise comparisons has not yet been developed. We close this gap by introducing a randomization test based on distances between matrices. For this purpose, TDS sequences are unfolded to data matrices with a single non-zero entry per time point (column). The sum of the Euclidean distances between these matrices is determined and serves as a test statistic for the global test. Similar statistics are employed for pairwise comparisons and for inference by attribute or time point. Re-randomizations are used to determine the null distribution and p-values, taking the original restrictions of the randomization into account. We give the details of this procedure and sketch the underlying algorithm to perform the tests. We also propose some simple graphical methods to summarize the many p-values derived from this approach (usually at least hundreds, but more often several thousands). We apply this approach to real data and show that it gives reasonable and easily interpretable results, complementing existing methods.