Editing Measurement (section)

== Definitions and theories ==

=== Classical definition ===
In the classical definition, which is standard throughout the physical sciences, ''measurement'' is the determination or estimation of ratios of quantities.<ref name="Michell, J. 1999">Michell, J. (1999). Measurement in psychology: a critical history of a methodological concept. New York: Cambridge University Press.</ref> Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to [[John Wallis]] and [[Isaac Newton]], and was foreshadowed in [[Euclid's Elements]].<ref name="Michell, J. 1999"/>

=== Representational theory ===
In the representational theory, ''measurement'' is defined as "the correlation of numbers with entities that are not numbers".<ref>Ernest Nagel: "Measurement", Erkenntnis, Volume 2, Number 1 / December 1931, pp.&nbsp;313–335, published by [[Axel Springer AG|Springer]], the Netherlands</ref> The most technically elaborated form of representational theory is also known as [[additive conjoint measurement]]. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of [[Stanley Smith Stevens]],<ref>Stevens, S.S. ''On the theory of scales and measurement'' 1946. Science. 103, 677–80.</ref> numbers need only be assigned according to a rule.

The concept of measurement is 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 in terms of the requirements of additive conjoint measurement.  One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

Three type of representational theory
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#; Empirical relation : In science, an ''empirical relationship'' is a relationship or correlation based solely on [[observation]] rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis.
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#; The rule of mapping : The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range.
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#; The representation condition of measurement :

=== Theory ===
All data are inexact and statistical in nature.  Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity."<ref>Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21</ref>  This definition is implied in what scientists actually do when they measure something and report both the [[mean]] and [[statistics]] of the measurements.  In practical terms, one begins with an initial guess as to the expected value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value.  In this view, unlike the [[positivist]] representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement.  This also implies that there is not a clear or neat distinction between [[Approximation|estimation]] and measurement.

=== Quantum mechanics ===
In [[quantum mechanics]], a measurement is an action that determines a particular property (such as position, [[momentum]], or energy) of a quantum system. Quantum measurements are always statistical samples from a [[probability distribution]]; the distribution for many quantum phenomena is discrete, not continuous.<ref name=messiah>{{Cite book|last=Messiah|first=Albert|title=Quantum Mechanics|date=1966|publisher=North Holland, John Wiley & Sons|isbn=0486409244|language=en}}</ref>{{rp|197}} Quantum measurements alter [[quantum states]] and yet repeated measurements on a quantum state are reproducible. The measurement appears to act as a filter, changing the quantum state into one with the single measured quantum value.<ref name="messiah"></ref> The unambiguous meaning of the [[measurement problem|quantum measurement]] is an unresolved fundamental problem in [[quantum mechanics]]; the most common interpretation is that when a measurement is performed, the [[wavefunction]] of the quantum system "[[wavefunction collapse|collapses]]" to a single, definite value.<ref>{{cite book | last = Penrose | first = Roger | title = The road to reality : a complete guide to the laws of the universe | publisher = Vintage Books | location = New York | year = 2007 | isbn = 978-0-679-77631-4 }} "The jumping of the quantum state to one of the eigenstates of '''Q''' is the process referred to as ''state-vector reduction'' or ''collapse of the wavefunction''.  It is one of quantum theory's most puzzling features&nbsp;..."  "[T]he way in which quantum mechanics is used in practice is to take the state indeed to jump in this curious way whenever a measurement is deemed to take place." p 528 Later Chapter 29 is entitled the Measurement paradox.</ref>

=== Biology ===
In biology, there is generally no well established theory of measurement. However, the importance of the theoretical context is emphasized.<ref>{{Cite journal|last1=Houle|first1=David|last2=Pélabon|first2=Christophe|last3=Wagner|first3=Günter P.|last4=Hansen|first4=Thomas F.|date=2011|title=Measurement and Meaning in Biology|url=https://pdfs.semanticscholar.org/dfa6/1a6ea872d2429f6ce4b9dd7dea965a3553eb.pdf|archive-url=https://web.archive.org/web/20190529222403/https://pdfs.semanticscholar.org/dfa6/1a6ea872d2429f6ce4b9dd7dea965a3553eb.pdf|url-status=dead|archive-date=2019-05-29|journal=The Quarterly Review of Biology|language=en|volume=86|issue=1|pages=3–34|doi=10.1086/658408|pmid=21495498|s2cid=570080|issn=0033-5770}}</ref> Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion.<ref>{{Cite journal|last=Montévil|first=Maël|date=2019|title=Measurement in biology is methodized by theory|url=https://www.academia.edu/38904550|journal=Biology & Philosophy|language=en|volume=34|issue=3|doi=10.1007/s10539-019-9687-x|s2cid=96447209|issn=0169-3867}}</ref>
Among the most developed fields of measurement in biology are the measurement of genetic diversity and species diversity.<ref>Magurran, A.E. & McGill, B.J. (Hg.) 2011: Biological Diversity: Frontiers in Measurement and Assessment Oxford University Press.</ref>