A process by which the properties of a collection are described in terms of the sums of the properties of the units contained in that collection. The most elementary aggregative procedure is counting and a
frequency so obtained represents the properties of a set by number rather than by the list of elements it contains. Aggregation gives rise to macro theories of micro processes and yields measures and insights not demonstrable by means of the units aggregated thereby. E.g., the statement "the average family has 2.5 children" describes the property of an aggregate, not of a real family. The
correlation coefficient is also a measure that aggregates numerous observations neither is capable of demonstrating that
relation by itself. Quantum physics, economics and the social sciences are most successful in describing their objects as aggregates. Aggregation is justifiable whenever units are sufficiently
independent and similar, e.g., in expressing political opinions through voting or market preferences through individual purchases. Aggregation leads to misleading indicators and theories whenever the whole collection exhibits an
organization not expressed in a mere summation (
see system, EXTERNALITIES). In econometrics, that difference is represented in so-called interaction effects. (
krippendorff ))
