Equidistance of Likert‑Type Scales and Validation of Inferential Methods Using Experiments and Simulations
Keywords:Likert-type scale; equidistance; Monte Carlo simulation; ANOVA; Kruskal-Wallis test; Brown-Forsythe test; Welch test
AbstractLikert‑type data are often assumed to be equidistant by applied researchers so that they can use parametric methods to analyse the data. Since the equidistance assumption rarely is tested, the validity of parametric analyses of Likert‑type data is often unclear. This paper consists of two parts where we deal with this validity problem in two different respects. In the first part, we use an experimental design to show that the perceived distance between scale points on a regular five‑point Likert‑type scale depends on how the verbal anchors are used. Anchors only at the end points create a relatively larger perceived distance between points near the ends of the scale than in the middle (end‑of‑scale effect), while anchors at all points create a larger perceived distance between points in the middle of the scale (middle‑of‑scale effect). Hence, Likert‑type scales are generally not perceived as equidistant by subjects. In the second part of the paper, we use Monte Carlo simulations to explore how parametric methods commonly used to compare means between severalgroups perform in terms of actual significance and power when data are assumed to be equidistant even though they are not. The results show that the preferred statistical method to analyse Likert‑type data depends on the nature of their nonequidistance as well as their skewness. Under middle‑of‑scale effect, the omnibus one‑way ANOVA works best when data are relatively symmetric. However, the Kruskal‑Wallis test works better when data are skewed except when sample sizes are unequal, in which case the Brown‑Forsythe test is better. Under end‑of‑scale effect, on the other hand, the Kruskal‑Wallis test should be preferred in most cases when data are at most moderately skewed. When data are heavily skewed, ANOVA works best unless when sample sizes are unequal, in which case the Brown‑Forsythe test should be preferred.
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