This chapter is inspired by work in comparative sociolinguistics and quantitative dialectometry. We use a corpus-based method (Variation-Based Distance and Similarity Modeling – VADIS for short) to quantify the similarity between, and coherence across, the varieties of English under study as a function of the correspondence of the ways in which language users choose between different ways of saying the same thing. Key findings include the result that probabilistic grammars are remarkably stable across varieties but that coherence across alternations is not perfect.

This chapter sets out by discussing the way in which multidimensional techniques and visualizations have been used to analyse linguistic data. While, for instance, multidimensional scaling and unrooted phenograms (or NeighborNets) have primarily been designed for exploratory purposes, the author argues that they are in fact regularly used to put linguistic assumptions or hypotheses to the test. Cluster goodness (in terms of internal coherence and external distance from other clusters) in such approaches are typically evaluated based on a two-dimensional visualization. The author compares the affordances and limitations of visual inspection with a quantitative set of metrics that directly relates to visual displays but adds a degree of precision not attained by the human eye. The empirical part of the paper applies both approaches to a study of concessive constructions in six varieties of English, based on spoken and written material from the International Corpus of English. The author suggests that the new metrics can be usefully applied to a variety of multidimensional techniques to endow them with a measure of objectivity.