Quantitative

Quantitative

A quantitative attribute is one that exists in a range of magnitudes, and can therefore be measured. Measurements of any particular quantitative property are expressed as a specific quantity, referred to as a unit, multiplied by a number. Examples of physical quantities are distance, mass, and time. Many attributes in the social sciences, including abilities and personality traits, are also studied as quantitative properties and principles.

Fundamental considerations in quantitative research

Whether numbers obtained through an experimental procedure are considered measurements is, on the one hand, largely a matter of how "measurement" is defined. On the other hand, the nature of the measurement process has important implications for scientific research. Firstly, many arithmeitic operations are only justified for measurements either in the classical sense described above, or in the sense of interval and ratio-level measurements as defined by Stevens (which arguably describe the same thing). Secondly, quantitative "relationships" between different properties which feature in most natural theories and laws imply that the properties have a specific type of quantitative structure; namely, the structure of a continuous quantity. The reason for this is that such theories and laws display a multiplicative structure (for example Newton's second law).

Continuous quantities are those for which magnitudes can be represented as real numbers and for which, therefore, measurements can be expressed on a continuum. Continuous quantities may be scalar or vector quantities. For example, SI units are physical units of continuous quantitative properties, phenomena, and relations such as distance, mass, heat, force and angular separation. The classical concept of quantity described above necessarily implies the concept of continuous quantity.

Recording observations with numbers does not, in itself, imply that an attribute is quantitative. For example, judges routinely assign numbers to properties such as the perceived beauty of an exercise (e.g. 1-10) without necessarily establishing quantitative structure in any sort of rigorous fashion. A researcher might also use the number 1 to mean "Susan", 2 to mean "Michael", and so on. This, however, is not a meaningful use of numbers: the researcher can arbitrarily reassign the numbers (so that 1 means "Michael" and 2 means "Susan") without losing any information. Put another way, facts about numbers (for example, that 2 is greater than 1, that 5 is two more than 3, and that 8 is twice 4) don't mean anything about the names corresponding to those numbers. A person's name is not, therefore, a quantitative property.

Whether counts of objects or observations are considered measurements is also largely a matter of how "measurement" is defined. Again, though, an important consideration is the manner in which resulting numbers are used. Counts are not measurements of continuous quantities. If, for example, a researcher were to count the number of grains of sand in a specified volume of space on a beach, the result denumerates how many separate grains there are; i.e. the number of separate distinguishable entities of a specific type. Arithmetic operations, such as addition, have meaning only in this specific sense. For instance, combining 5 and 4 grains of sand gives 9 grains of sand. The numbers used in this case are therefore the natural numbers.

Any object is characterized by many attributes, such as colour and mass, only some of which constitute continuous quantities. For example, the "mass" of a specific grain of sand is a continuous quantity whereas the grain, as an object, is not. Thus, the "mass" of a grain of sand can be used as a unit of mass because it is possible to estimate the ratio of the mass of another object to the mass of a grain of sand, given an appropriate instrument.

In the social sciences, it is also common to count frequencies of "observations"; i.e. frequencies of observable outcomes in an experiment. Examples include the number of correct scores on an assessment of an ability, and the number of statements on a questionnaire endorsed by respondents. Provided each observable outcome is the manifestation of an underlying quantitative attribute, such frequencies will generally indicate relative magnitudes of that attribute. Strictly speaking, however, counts and frequencies do not constitute measurement in terms of a unit of continuous quantity.

References

*Michell, J. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, and Russell. "Studies in History and Philosophy of Science", Vol. 24 No. 2, 185-206.
*Nagel, E. (1932). Measurement. "Erkenntnis", 2, 313-33, reprinted in A. Danato and S. Morgenbesser (Eds.), "Philosophy of Sciences" (pp. 121-140). New York: New American Library.

ee also

*Measurement
*Quantity
*Quantitative research
*Physical quantity
*Levels of measurement
*Unit


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • quantitative — quan‧ti‧ta‧tive [ˈkwɒnttətɪv ǁ ˈkwɑːntteɪ ] adjective connected with amounts rather than with the quality or nature of something: • the introduction of new quantitative import restrictions * * * quantitative UK US /ˈkwɒntɪtətɪv/ US … …   Financial and business terms

  • Quantitative — Quan ti*ta*tive, a. [Cf. F. quantitatif.] Relating to quantity. {Quan ti*ta*tive*ly}, adv. [1913 Webster] {Quantitative analysis} (Chem.), analysis which determines the amount or quantity of each ingredient of a substance, by weight or by volume; …   The Collaborative International Dictionary of English

  • quantitative — (adj.) 1580s, from M.L. quantitativus, from L. quantitas (see QUANTITY (Cf. quantity)). Related: Quantitatively …   Etymology dictionary

  • quantitative — ► ADJECTIVE ▪ of, concerned with, or measured by quantity. DERIVATIVES quantitatively adverb …   English terms dictionary

  • quantitative — [kwänt′ə tāt΄iv] adj. [ML quantitativus] 1. having to do with quantity 2. capable of being measured 3. having to do with the quantity of a speech sound 4. having to do with a system, as in classical prosody, in which syllables are classified as… …   English World dictionary

  • quantitative — ● quantitatif, quantitative adjectif Qui concerne la quantité, en particulier par opposition à qualitatif : Produit intéressant sur le plan quantitatif. ● quantitatif, quantitative (expressions) adjectif Analyse quantitative, analyse qui… …   Encyclopédie Universelle

  • quantitative — [[t]kwɒ̱ntɪtətɪv, AM teɪt [/t]] ADJ: usu ADJ n Quantitative means relating to different sizes or amounts of things. [FORMAL] ...the advantages of quantitative and qualitative research. ...the quantitative analysis of migration. Derived words:… …   English dictionary

  • Quantitative — Analysis A*nal y*sis, n.; pl. {Analyses}. [Gr. ?, fr. ? to unloose, to dissolve, to resolve into its elements; ? up + ? to loose. See {Loose}.] 1. A resolution of anything, whether an object of the senses or of the intellect, into its constituent …   The Collaborative International Dictionary of English

  • quantitative — quan|ti|ta|tive [ˈkwɔntıtətıv US ˈkwa:ntıteı ] adj formal relating to amounts rather than to the quality or standard of something quantitative analysis/methods/data etc ▪ We need to do a proper quantitative analysis of this problem. →↑qualitative …   Dictionary of contemporary English

  • quantitative — adjective connected with amounts rather than with the quality or nature of something: quantitative estimates | quantitative chemical analysis compare qualitative quantitatively adverb …   Longman dictionary of contemporary English

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”