[r] coefficient that compares ellipses

#1
I'm working on an undergraduate dissertation in Phonetics. (I am on a Linguistics programme so my knowledge of Statistics and Maths in general is rather shaky!) I am trying to demonstrate whether or not an intervention group of Spanish teenagers learn to pronounce English vowels accurately more quickly than a control group. I have been using R with the phonR package to produce plots such as the one in the attached image. The axes represent normalised resonances (formants) that characterise the vowels and are in Bark, a transformed version of Hz. Each labelled scatter point represents a realisation of the vowel. The ellipse is drawn at 1s.d. by phonR. The green data is produced by the learner, the red data by a native speaker.

What I would like to do is compute some kind of coefficient of similarity that would model the relationship between the target ellipse and the speaker's ellipse (and so give me an accuracy score that I could compare in an ANOVA). I have tried simply counting the proportion of attempts that fall within the target ellipse, but this is a rather blunt measure, and hasn't yielded very good results.

I'd be grateful for any suggestions.

Joe


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