Meta-analysis aims to combine results from multiple experiments. For example, a neutron reaction rate or cross section is typically measured in multiple experiments, and a single estimate and its uncertainty are provided for users of the estimated reaction rate. It is often difficult to combine estimates from multiple laboratories because there can be important differences in experimental protocols among laboratories and because laboratories do not always provide all the information needed to assess the estimate's uncertainty, particularly if total uncertainty (random and systematic) is required. The paper illustrates that explicit measurement error models are essential for understanding measurement processes and for guiding how to combine multiple measurements, whether the measurements are consistent or not. We emphasize that both the consensus estimate and its estimated uncertainty depend on the assumed measurement error model, and we investigate measurement error model selection options for two examples.