An Aggregation Metric Based on Partitioning and Consensus for Asymmetric Distributions in Likert Scale Responses

Juan Moreno-Garcia, Benito Yáñez-Araque (), Felipe Hernández-Perlines and Luis Rodriguez-Benitez
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Juan Moreno-Garcia: Department of Information Systems and Technologies, School of Industrial and Aerospace Engineering, University of Castilla-La Mancha, 45071 Toledo, Spain
Benito Yáñez-Araque: Department of Business Administration, University of Castilla-La Mancha, 45071 Toledo, Spain
Felipe Hernández-Perlines: Department of Business Administration, University of Castilla-La Mancha, 45071 Toledo, Spain
Luis Rodriguez-Benitez: Department of Information Systems and Technologies, College of Computer Science, University of Castilla-La Mancha, 13071 Ciudad Real, Spain

Mathematics, 2022, vol. 10, issue 21, 1-17

Abstract: A questionnaire is a basic tool for collecting information in survey research. Often, these questions are measured using a Likert scale. With multiple items on the same broad object, these codes could be summed or averaged to give an indication of each respondent’s overall positive or negative orientation towards that object. This is the basis for Likert scales. Aggregation methods have been widely used in different research areas. Most of them are mathematical methods, such as the arithmetic mean, the weighted arithmetic mean, or the OWA (Ordered Weighted Averaging) operator. The usual presentation of Likert scale derived data are Mean. This paper presents a new approach to compute an aggregate value that represents Likert scale responses as a histogram adequate to treat better than Mean with asymmetric distributions. This method generates a set of partitions using an approach based on successive division. After every division, each partition is evaluated using a consensus measure and the one with the best value is then selected. Once the process of division has finished, the aggregate value is computed using the resulting partitions. Promising results have been obtained. Experiments show that our method is appropriate for distributions with large asymmetry and is not far from the behavior of the arithmetic mean for symmetric distributions. Overall, the article sheds light on the need to consider other presentations of Likert scale derived data beyond Mean more suitable for asymmetric distributions.

Keywords: questionnaires; Likert scale; aggregation of information; consensus; OWA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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