Code that estimates a boundary of a slope?


I'm analyzing some data that looks at different phonetic continuums and I'm trying to determine subjects' phonetic boundaries on each of these continuums.

We calculated the proportion of responses to a list of 50 stimuli (proportion of 'b' responses out of all responses for the 'bd' continuum). We created loess scatterplots to create a curve based on these proportions.

I was wondering if anyone knows how to start or if it is possible to write a code that gives us the actual position of a "boundary" of curves made through scatterplots?

We would like to identify the position where subjects' responses cross the 50% mark (e.g. the boundary where 50% people respond b and 50% of people respond d).


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