6 Measurement Error and Meta-Analysis

Most quantities used in statistical models arise from measurements. Most of these measurements are taken with some error. When the measurement error is small relative to the quantity being measured, its effect on a model is usually small. When measurement error is large relative to the quantity being measured, or when precise relations can be estimated being measured quantities, it is useful to introduce an explicit model of measurement error. One kind of measurement error is rounding.

Meta-analysis plays out statistically much like measurement error models, where the inferences drawn from multiple data sets are combined to do inference over all of them. Inferences for each data set are treated as providing a kind of measurement error with respect to true parameter values.