Subitization is the rapid, accurate enumeration of low-numerosity displays, distinguished from counting by a sharp non-linearity in the plot of response times. Below is a representative plot, from Watson, D. G., Maylor, E. A., & Bruce, L. A. M. (2007). Notice that mean enumeration times for displays 1-3 increases roughly linearly, but mean enumeration time for 4 does not follow the linear trend. Some research suggests that the subitization 'limit' is dependent on task conditions and participant working memory.
I'm looking for a way to test where the elbow is, with the ultimate goal of identifying what a participant's subitization limit is. Currently, my best idea is to do something like repeated polynomial contrasts. Basically, I would test for a quadratic trend in numerosities 1-3, then in numerosities 1-4, etc. I would want to say that I have passed the subitization limit when the quadratic trend becomes significant (adjusting for repeated tests).
That's about the limits of my statistical savvy, though, so I can't evaluate this idea too well. Thoughts?
Thanks in advance.