A method for comparing perceptual distances and areas with multidimensional scaling

Phil J Howson,Philip J Monahan

doi:10.1016/j.mex.2020.100790

Phil J Howson, Philip J Monahan

Open Access

https://doi.org/10.1016/j.mex.2020.100790

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Journal: MethodsX	Publication Date: Jan 1, 2020
Citations: 1	License type: cc-by

Affiliation: University of Oregon, University of Toronto

Abstract

This paper presents a method for adding additional statistical comparisons to multidimensional scaling (MDS). The object of study in our work is perceptual distances between speech sound categories. Typically, MDS solutions do not receive inferential statistical treatment and their visualizations present average results across numerous participants. This is problematic because it ignores inter-participant variation. To account for this variance, we have devised a simple technique for adding statistical power to the traditional MDS solution so that the distances between objects and the areas occupied by groups of objects can be compared more reliably than visual inspection of an MDS plot. We provide a method for comparing distances between two objects and for comparing the area of three or more objects. This method can be paired with varying statistical analysis to suit the researcher's needs.•Adds statistical power to multidimensional scaling.•Compares distances between segments.•Compares dispersion of groups of objects in multidimensional space.

Highlights

We describe how to calculate the multidimensional scaling (MDS) coordinates and compare both distances and areas of the MDS solution
The plot on the right will not accurately reflect the measurements made with our statistical method and ignores individual differences with the MDS solution
Multidimensional scaling is a powerful tool used in psychophysics and perceptual research, among other fields; since its inception, there have been issues in accounting for variance across individual participants because of the general use of averages across all participants for the dissimilarity matrix

Summary

Method Article

A method for comparing perceptual distances and areas with multidimensional scaling Phil J. Monahanc,d a University of Oregon, Department of Linguistics, United States b University of Toronto, Department of Linguistics, Canada c University of Toronto Scarborough, Centre for French & Linguistics, Canada d University of Toronto Scarborough, Department of Psychology, Canada

Background on multidimensional scaling

Findings

Summary of our method