Applying Statistical Methods To The Proton Radius Puzzle

In recent nuclear physics publications, one can find many examples where chi2 and reduced chi2 are the only tools used for the selection of models even though a chi2 difference test is only meaningful for nested models. With this in mind, we reanalyze electron scattering data, being careful to clearly define our selection criteria as well as using a co-variance matrix and confidence levels as per the statistics section of the particle data book. We will show that when applying such techniques to hydrogen elastic scattering data, the nested models often require fewer parameters than typically used and that non-nested models are often rejected inappropriately.