Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles

Stan Lipovetsky,Michael Conklin

doi:10.3390/stats1010012

Abstract

A description of Likert scales can be given using the multipoles technique known in quantum physics and applied to behavioral sciences data. This paper considers decomposition of Likert scales by the multipoles for the application of decreasing the respondents’ heterogeneity. Due to cultural and language differences, different respondents habitually use the lower end, the mid-scale, or the upper end of the Likert scales which can lead to distortion and inconsistency in data across respondents. A big impact of different kinds of respondent is well known, for instance, in international studies, and it is called the problem of high and low raters. Application of a multipoles technique to the row-data smoothing via prediction of individual rates by the histogram of the Likert scale tiers produces better results than standard row-centering in data. A numerical example by marketing research data shows that the results are encouraging: while a standard row-centering produces a poor outcome, the dipole-adjustment noticeably improves the obtained segmentation results.

Highlights

A Likert scale is an ordinal limited rating scale of 5, 7, 10, or another finite number of levels.For example, a 7-point Likert scale in customer satisfaction studies can have the layers from the worst 1 to the best 7 values corresponding to: completely dissatisfied, very dissatisfied, somewhat dissatisfied, neither dissatisfied nor satisfied, somewhat satisfied, very satisfied, completely satisfied
This paper describes the multipoles approach and develops it for data smoothing via prediction of individual rates by the histogram of the Likert scale levels
For the dipole adjustment in a row, we find how many times each box of the Likert scale is found in this row, build a pair regression of the box number by the box counts, and take the predicted value of each box as the adjustment made due to the distribution by the boxes, or by the shape of their histogram

Summary

Introduction

A Likert scale is an ordinal limited rating scale of 5, 7, 10, or another finite number of levels. A 7-point Likert scale in customer satisfaction studies can have the layers from the worst 1 to the best 7 values corresponding to: completely dissatisfied, very dissatisfied, somewhat dissatisfied, neither dissatisfied nor satisfied, somewhat satisfied, very satisfied, completely satisfied This scale had been originated in works [1,2], and widely studied and used for statistical evaluations in applied psychological and sociological measurements, political and marketing research, and other fields [3,4,5,6,7,8,9]. The respondents can be divided into four segments by the positive or negative dipole (direction of the trend across the scale boxes) and quadrupole (convex or concave curvature) parameters These types of multipole values can be related to the respondents of various demographics, to the countries with different cultures and traditions revealing in evaluations by Likert scales.

Reducing Respondents’ Heterogeneity

Summary

Findings

A Likert scale with n points corresponds to the momentum: