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. 2020 Jan 18:7:100790.
doi: 10.1016/j.mex.2020.100790. eCollection 2020.

A method for comparing perceptual distances and areas with multidimensional scaling

Phil J Howson  1   2 , Philip J Monahan  3   4
Affiliations

A method for comparing perceptual distances and areas with multidimensional scaling

Phil J Howson et al. MethodsX. .

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.

Keywords: Distance and area comparison with multidimensional scaling; Linguistics; Principle Coordinate Analysis; Speech perception.

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Figures

None
Graphical abstract
Fig. 1
Fig. 1
MDS solution involving our method of using the average coordinates of every participants MDS solution (left) versus the MDS solution involving the standard method of using the coordinates from the grand mean of the input dissimilarity matrix (right).
Fig. 2
Fig. 2
An example of the perceptual space we want to compare. Lines visualize the distances we are comparing between /r/ and /ɻ/ and /r/ and /ʀ/.
Fig. 3
Fig. 3
Violin plot for the distance between /r/ and /ɻ/ (left) and /ʀ/ and /ɻ/ (right).
Fig. 4
Fig. 4
Plot of the rhotic and fricative groups we are comparing within the perceptual space (left); and a scatterplot with ellipses to show the variance in the groups (right).
Fig. 5
Fig. 5
Violin plot of the area for the two groups, rhotics and fricatives.
Fig. 6
Fig. 6
MDS solution for participants 1–4 in our perceptual experiment.
See this image and copyright information in PMC

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