Indexes of individual repeatability and product discrimination in TDS and TCATA and their statistical inference

Abstract

There is a lack of tools for monitoring repeatability and product discrimination at an individual level in Temporal Dominance of Sensations (TDS) and Temporal Check-All-That-Apply (TCATA). To fill in this gap, the paper proposes a unified approach applicable with both methods. The basic idea is to replace the continuous time used in both TDS and TCATA by k consecutive periods of equal durations. The data for each period is the union of all attributes elicited during the period. For measuring similarity between two TDS or TCATA sequences, the Jaccard index is computed by period and then averaged over the periods. The Jaccard index can vary between 0 (full dissimilarity) to 1 (full similarity). Statistical inference based on permutations of sequences was established. This index can be computed between replicates to investigate panelist repeatability or between products to investigate product similarity. This can be done by panelist or at the panel level by averaging over panelists. Further, a discrimination ratio can be computed at both individual and panel levels as the ratio between indexes of product dissimilarity and panelist unrepeatability. If the discrimination ratio is lower or equal to one, then this panelist or this panel is inconsistent. If not, again permutations can be used for testing significance of the discrimination ratio. The computation is done for a number of periods from 1 to k (k = 5 as a default value). It aims to estimate the maximal number of periods (temporal resolution) for which the panelist or the panel is repeatable and/or discriminative. Individual and panel indexes of repeatability and discrimination are respectively presented in two tables having panelists as rows and number of periods as columns. Values in the cells are indexes, with color codes indicating significance (p < 0.05), weak significance (0.05 ≤ p ≤ 0.15) or non-significance (p > 0.15) for repeatability and discrimination and eventually inconsistency in discrimination.