Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data

In previous papers, it has been empirically proved that descriptive (summary measures) and inferential conclusions (in particular, tests about means p-values) with imprecise valued data are often affected by the scale considered to model such data. More concretely, conclusions from the numerical and fuzzy linguistic encodings of Likert-type data have been compared with those for fuzzy data obtained by using a totally free fuzzy assessment: the so-called fuzzy rating scale. These previous comparisons have been performed separately for each of the scales. This paper aims to perform a joint comparison in such a way that means of linked data (one associated with the fuzzy rating and the other one with the encoded Likert scale) are to be tested for equality. Two real-life examples, as well as several simulation based synthetic ones, have unequivocally shown that the fuzzy rating scale means are significantly different from those for the encoded Likert scales. (C) 2017 Elsevier Inc. All rights reserved.