American Physical Society Four Corner Section Meeting
An important question often encountered in experimental physics is, are two observables related or not? Quantile-quantile (q-q) analysis compares the cumulative distributions of two observations (or one set of observations and a theoretical curve) in a way that is both visually apparent and statistically quantifiable. If the two observables follow the same distribution, the q-q plot will be linear; if they are identical the plot will have unity slope. Deviations from a linear q-q plot indicate that the two observables do not follow the same distribution. We show that the q-q analysis method is applicable to a wide range of scenarios in experimental physics. As an example, we present a case study of a series of voltage step-up to dielectric breakdown tests with two observables—non-shorting pre-arcs and critical electrostatic discharge (ESD) breakdowns. In each test many pre-arcs are observed, but only one ESD. Initially it was unclear whether or not the field distributions of these two observations were related. Q-q analysis found an extremely significant correlation between pre-arcs and ESD events. Establishing the more copious pre-arcs as an indication of ESD behavior has the potential to greatly accelerate material characterization test times and facilitate selection from numerous candidate materials for applications. This work was supported by a NASA Space Technology Research Fellowship.
Andersen, Allen and Dennison, JR, "Comparing Experimental Apples and Oranges with Quantile-Quantile Plots" (2015). American Physical Society Four Corner Section Meeting. Presentations. Paper 119.