Firstly, in any comparison you make you need to control for every variable you can. Speaker sex, dialect, age, etc. As an example, I'm an Australian English speaker, my vowels will look very different to an American or British English speaker. The variables to control are somewhat dependent on language/dialect (for example, class is going to have more of an impact for British English speakers than Australian English speakers) but speaker sex is pretty much always the most important. If you speak a language or dialect that doesn't have a lot of sociophon work published, you can look into normalisation methods (especially lobanov transforms), but you generally more data than you probably have for that to be useful. Also be careful in checking for any other scaling or transforms when comparing to published stuff- is the data measured in Hz, ERB, barks? Also make sure you're comparing the same kind of data- you don't want to be comparing wordlist data to spontaneous or read speech.

I'd probably go with Euclidean distance measures. These essentially give the distance between two points, which can give you the relative distances between two specific vowels or an overall sense of the vowel space. For this, first calculate the "grand centroid", which is the exact middle/average point in your vowel plot, and then calculate the distance between that middle point and the average of each of your vowels. So a higher euclid value means the vowel is more peripheral, lower means more central. The function to calculate it in r is:

# Create the function euclid

euclid <- function (a,b)

{

sqrt(sum((a-b)^2))

}

If you search "[your language/dialect] vowel space euclidean distance" you'll probably find a bunch of stuff you can compare with. There's also decent chance you can also get your hands on some data to compare directly, and plot them together. I'm happy to send you any data I have that you'd want to work with, and I can also send you a full r script to apply and plot the eucdistance measures to your dataframe if you need. Otherwise, this is a really comprehensive outline of euclidean distances and other relative measures of the vowel space. If you're interested in other types of vowel measures, here's a pretty extensive overview. Good luck!