I think you could also do an interesting comparison of corporal punishment by state, versus funding for the DoE per state, versus some sort of achievement per state. My theory is that states with less money available for public schools might not stack up as well, and might have a higher rate of corporal punishment as teachers and administrators attempt to maintain control in the most basic ways.

I do feel - as a proud graduate of the Georgia public school system - that the states which rely upon corporal punisment tend to rely on really rote instruction. This reflects a general social attitude which includes politics; it's not that southerners are innately right-leaning and that comes out in our predilection for beating the bejeezus out of the kids, it's more like the tendency to be right-leaning and to hit the kids both have their roots in the idea of teaching things simply by holding only one acceptable point of view.