X-ray diffraction is an experimental technique that can be used to study how the component atoms of proteins fit together. In laboratories, proteins are grown into crystals and placed in an X-ray beam line, so the resulting diffraction pattern may be captured for analysis. During this crystallographic analysis, researchers conventionally choose a single best-fit atomic structure to fit the data. Even though there is heterogeneity in the crystal structure, this analysis works because most heterogeneity is the result of small, local fluctuations of the atoms around their equilibrium coordinates. A growing appreciation for the dynamic lives of proteins has motivated increased interest in modeling multiple distinct protein structures without a shared local mean. Using metrics derived from fundamental statistical principles, we develop and characterize criteria for statistically-rigorous detection of protein structural heterogeneity. We compare these information criteria to conventional crystallographic metrics. We assess their utilities, judging detection trade-offs as different models are used to fit data. We benchmark these criteria against simulated data and explore their predictions for experiment.