Aggregation rules valid at the data level are invalid at the semantic level.

Evidence

A key thing to note is that the mean is the dominant and most obvious structural principal at the data–indicator level. Conversely, it usually does not make much sense at the secondary, semantic level. Principles of completeness and nonredundancy make the mean an inappropriate choice. This makes the levels very important in the analysis and construction of concepts, because they often embody different principles of concept construction. Failure to recognize the levels in concepts can easily lead to problematic conceptualization and measurement. — Gary Goertz, Social Science Concepts and Measurement, 284

Categorization

• SEED: Angle: ‘Why the average is the wrong instinct’ — how importing statistical aggregation into conceptual definition silently corrupts measurement.