Statistical analysis of local atomic distortions in crystalline materials is a powerful tool for understanding coupled electronic and structural phase transitions in transition metal compounds. The analyses of such complex materials, however, often require significant domain knowledge to recognize limitations in the available data, whether it be experimentally reported crystal structures, property measurements, or computed quantities, and to understand when additional experiments or simulations may be necessary. Here we show how additional descriptive statistics and computational experiments can help researchers explicitly recognize these limitations and fill in missing gaps by constructing amplitude ( a) and normalized-amplitude ( n) distortion-mode property correlation-coefficient heat maps, aCCHMs and nCCHMs, respectively. We demonstrate this utility within the rare-earth nickelate perovskites RNiO3 (R = rare earth ≠ La), which exhibit antiferromagnetic and metal-insulator transitions with crystallographic symmetry breaking, and analyze the CCHMs obtained from experimental and first-principles derived symmetry modes. In contrast with the crystallographic trends gleaned from the reported experimental structures, the equilibrium structures obtained from density functional theory indicate that the Jahn-Teller distortion mode plays a negligible role in affecting the Néel temperature. We explain this discrepancy and discuss how different researchers might draw disparate conclusions from the same evidence, in particular from aCCHMs and nCCHMs. Last, we propose a general method for utilizing CCHMs for screening large databases of structures.