I'm looking at this blog to try to understand the Wilson Score interval. I understand it somewhat, but I'm confused by the part under the title "Excerpt". In particular, I don't understand what he's calling the "Interval equality principal" and how he arrived at the below graph:
Could someone elaborate on it, or really just explain how/why the Wilson Score Interval is arrived at from the basic Wald Interval (normal approximation)? Basically, what I'm trying to understand is why the Wilson Score Interval is more accurate than the Wald test / normal approximation interval?