Different or the Same? Determination of Discriminatory Power Threshold and Category Formation for Vague Linguistic Frequency Expressions

In psychological research, many questionnaires use verbal response scales with vague linguistic terms (e.g., frequency expressions). The words’ meanings can be formalized and evaluated using fuzzy membership functions (MFs), which allow constructing distinct and equidistant response scales. The discriminatory power value of MFs indicates how distinct the functions and, hence, the verbal expressions are. The present manuscript interrogates the threshold of discriminatory power necessary to indicate a sufficient difference in meaning. Using an empirical validation procedure, participants (N = 133) estimated (1) three correspondence values for verbal expressions to determine MFs, and (2) similarities of words by pairwise comparison ratings. Results show a non-linear relationship between discriminatory power and similarity, and fuzzy MFs, as well as the searched-for threshold value for discriminatory power. Implications for the selection of verbal expressions and the construction of verbal categories in questionnaire response scales are discussed.