Quantitative property
Encyclopedia
A quantitative property is one that exists in a range of magnitudes, and can therefore be measured
with a number. 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
.
. 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.
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
with a number. 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
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, and time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
. Many attributes in the social sciences, including abilities and personality traits, are also studied as quantitative properties and principles
Principles
Principles may refer to:*Value *Principles and parameters*Principles...
.
Fundamental considerations in quantitative research
Numbers obtained through an experimental procedure are considered measurements depends upon how measurement is defined. The nature of measurement depends upon the structure of a continuous quantity and the particular test methodTest method
A test method is a definitive procedure that produces a test result.A test can be considered as technical operation that consists of determination of one or more characteristics of a given product, process or service according to a specified procedure. Often a test is part of an experiment.The test...
. 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
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
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
Addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
, 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.
See also
- Levels of measurement
- MeasurementMeasurementMeasurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
- Physical quantityPhysical quantityA physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...
- Qualitative data
- Quantitative researchQuantitative researchIn the social sciences, quantitative research refers to the systematic empirical investigation of social phenomena via statistical, mathematical or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to...
- QuantityQuantityQuantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...
- Unit of measurement