A Fuzzy Coding Approach to Data Processing Using the Bar

Abstract

The bar is an alternative to Likert-type scale as a response format option used in closed-form questionnaires. An important advantage of using the bar is that it provides a variety of data post-processing options (i.e., ways of partitioning the values of a continuous variable into discrete groups). In this context, continuous variables are usually divided into equal-length or equalarea intervals according to a user-specified distribution (e.g. the Gaussian). However, this transition from continuous into discrete can lead to a significant loss of information. In this work, we present a fuzzy coding of the original variables which exploits linear and invertible triangular membership functions. The proposed coding scheme retains all of the information in the data and can be naturally combined with an exploratory data analysis tech nique, Correspondence Analysis, in order to visually investigate both linear and non-linear variable associations. The proposed approach is illustrated with a real-world application to a student course evaluation dataset.

Keywords

• Likert scale
• Bar
• Correspondence Analysis
• fuzzy coding
• triangular membership functions