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

Franziska Bocklisch

doi:10.3389/fpsyg.2019.01559

Abstract

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.

Highlights

The task of formalizing words’ meanings, such as in verbal expressions of frequency, intensity or probability, is relevant in a wide variety of research and application fields [e.g., verbal response categories and rating scales, risk and intercultural communication, medicine, forecasting, neuropsychological representation of words and numbers; cf. Teigen et al (2013) for a review as well as Beyth-Marom (1982), Wallsten et al (1986), Teigen and Brun (2003), Dhami and Wallsten (2005), and González et al (2019)]
The study was performed in accordance with relevant institutional and national guidelines and regulations (Chemnitz University of Technology, 2002; Deutsche Gesellschaft für Psychologie, 2018)
The resulting membership functions (MFs) are distributed along the numerical frequency scale in a non-equidistant manner

Summary

Introduction

The task of formalizing words’ meanings, such as in verbal expressions of frequency, intensity or probability, is relevant in a wide variety of research and application fields [e.g., verbal response categories and rating scales, risk and intercultural communication, medicine, forecasting, neuropsychological representation of words and numbers; cf. Teigen et al (2013) for a review as well as Beyth-Marom (1982), Wallsten et al (1986), Teigen and Brun (2003), Dhami and Wallsten (2005), and González et al (2019)]. Empirical estimation data, for example, numbers assigned to typical, minimum and maximum correspondence values for linguistic terms (LTs; cf Bocklisch, 2011) are modeled using fuzzy membership functions (MFs; e.g., Zadeh, 1965; Budescu et al, 2003; Bocklisch et al, 2012) to preserve the inherent vagueness of LTs’ meanings. The notion of an interval of numbers that belong to an LT

Methods

Results

Conclusion