Measurement procedures are not error-free. Potential users of a measurement procedure need to know the expected magnitude of the measurement error in order to justify its use, in particular in health care settings. Gold standard procedures providing exact measurements for comparisons are often lacking. Consequently, scientific investigations of the measurement error are often based on using replicates. However, a standardized terminology (and partially also methodology) for such investigations is lacking. In this paper, we explain the basic conceptual approach of such investigations with minimal reference to existing terminology and describe the link to the existing general statistical methodology. This way, some of the key measures used in such investigations can be explained in a simple manner and some light can be shed on existing terminology. We encourage clearly conceptually distinguishing between investigations of the measurement error of a single measurement procedure and the comparison between different measurement procedures or observers. We also identify an unused potential for more advanced statistical analyses in scientific investigations of the measurement error.