A "C-sphere" specimen geometry was used to determine the failure strength distributions of a commercially-available bearing-grade silicon nitride ($Si_3N_4$) with ball diameters of 12.7 and 25.4 mm. Strengths for both diameters were determined using the combination of failure load, C-sphere geometry, and finite element analysis and fitted using two-parameter Weibull distributions. Effective areas of both diameters were estimated as a function of Weibull modulus and used to explore whether the strength distributions predictably scaled between each size. They did not. That statistical observation suggested that the same flaw type did not limit the strength of both ball diameters indicating a lack of material homogeneity between the two sizes. Optical fractography confirmed that. It showed there were two distinct strength-limiting flaw types common to both ball diameters, that one flaw type was always associated with lower strength specimens, and that a significantly higher fraction of the 25.4-mm-diameter C-sphere specimens failed from it. Predictable strength-size-scaling would therefore not result as a consequence of this because these flaw types were not homogenously distributed and sampled in both C-sphere geometries.