Measurement

Measurement is an observation that reduces an uncertainty expressed as a quantity. As a verb, measurement is making such observations. It includes the estimation of a physical quantity such as distance, energy, temperature, or time. It could also include such things as assessment of attitudes, values and perception in surveys or the testing of aptitudes of individuals.

In the physical sciences, measurement is most commonly thought of as the ratio of some physical quantity to a standard quantity of the same type, thus a measurement of length is the ratio of a physical length to some standard length, such as a standard meter. Measurements are usually given in terms of a real number times a unit of measurement, for example 2.53 meters, but sometimes measurements use complex numbers, as in measurements of electrical impedance. Measurements always involve some error, and so in science measurements are often accompanied by error bounds, as in 2.53 meters plus or minus .01 meters. The study of this narrower type of measurement is called metrology.

This narrower definition of measurement was broadened by Stanely S. Stevens. He defined types of measurements to include nominal, ordinal, interval and ratio.

The field called Measurement Theory treats measurement as a type of mapping between sets of values and states of nature. The mapping concept is broad enough to include all of Stevens categories.

The concept of measurement is often confused with counting, which implies an exact mapping of integers to clearly separate objects. Counting, strictly speaking, is a subset of measurement but since measurement allows for error and it allows for mappings other than those with only integers, there are many measurements that are not merely counting.

The concept of measurement is also often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement. One may assign a value to a person's height, but unless it was based on some observation, it was not a measurement. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement since it is not based on an observation.