The uncertainty of measurements of carbon and oxygen stable-isotope ratios of carbonate materials is commonly assumed to be the analytical uncertainty determined from replicate analyses of single samples, but this ignores the possibility that heterogeneity of the material studied is greater than the analytical uncertainty. To test this question, we took eight samples from each of 13 layers or specimens of various non-marine (“continental”) carbonates and found ranges of δ13C and δ18O of 0.3 to 5.1‰, all exceeding the range of the typical lab-reported analytical uncertainty, ± 0.1‰, placed around single samples. These results are similar to previous replicate sampling of marine limestone layers, which revealed ranges of 0.2 to 2.8‰. Both sets of results, and other published data, demonstrate that analytical uncertainty derived from replicate analysis of a single sample is not a valid estimate of the uncertainty of δ13C or δ18O values characterizing a layer or specimen, and they remind us that we should not place great credence in anomalies or events defined by single samples of layers or specimens, regardless of the replication of analysis of that single sample. Our results indicate that the required layer-level or specimen-level uncertainty can be derived only from replicate sampling at different locations in layers or specimens, and that the layer-level or specimen-level uncertainty is inevitably greater than typical lab-reported analytical uncertainty. Credibility of anomalies or events in time series would be increased by replicate sampling of a random or dispersed subset of layers to estimate the variability of all layers and/or by replicate sampling of layers at and around a potential but unconfirmed event. The significance of the variability discussed above is evident in use of δ18O data to estimate paleotemperatures, where a difference of 1‰ in δ18O implies a difference of 4°C in temperature. Use of a single sample resulting in mischaracterization of the δ18O of an ancient material by 1.5‰ relative to the true mean for that material (which our results suggest is quite possible) would lead to a corresponding misestimation of temperature of 6°C, a significant difference in paleoenvironmental studies.