Measurement

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Various meters

The process of measurement involves estimating the ratio of the magnitude of a quantity to the magnitude of a unit of the same type (length, time, mass, etc.). A measurement is the result of such a process, expressed as the product of a real number and a unit, where the real number is the estimated ratio. An example is 9 metres, which is an estimate of an object's length relative to a unit of length, the metre. Unlike a count, or integer quantity of items that is known exactly, every measurement is an estimate that has some uncertainty.

:A measurement is a comparison to a standard. -- William Shockley

:By number we understand not so much a multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same kind, which we take for Unity. -- Sir Isaac Newton (1728)

Contents

1 Overview
2 Units and systems of measurement
3 Metrology
4 History
5 Probabilistic measurement
6 Difficulties in measurement
7 Other uses of the term
8 Miscellaneous
9 See also
10 References
11 External links

Overview

In the natural sciences, the act of measuring an object normally involves comparing the magnitude of a quantity possessed by an object with a standard unit by using an instrument under controlled conditions. Examples of measuring instruments include the thermometer, speedometer, weighing scale and voltmeter. In order to measure accurately, measuring instruments must be carefully constructed and calibrated. However, all measurements have some degree of uncertainty associated with them, which is usually expressed as a standard error of measurement. This means that while a measurement is usually given as a number followed by a unit, every measurement has three components; the estimate, an error bound, and a probability that the actual magnitude lies within the error bound of the estimate. For example, a measurement of a plank might result in a measurement of 9 meters plus or minus 0.01 meters, with a probability of 0.95.

A measurement is usually distinguished from a count. A measurement is a real number, and is never exact. A count is a natural number and may be exact. For example, we can determine that there are exactly 12 eggs in a carton by counting them. However some groups are not so easily counted, and estimating their numbers can involve similar issues to physical measurement. For example, figures for the number of people with HIV or the number of stars in the Milky Way will have associated standard errors, and can be viewed as estimates rather than exact counts.

Measurement is fundamental to most fields of science, including physics, chemistry and biology. Measurement is also essential to a diverse range of industries and commercial applications such as in engineering, construction, manufacturing, pharmaceutical production and electronics.

Units and systems of measurement

Main articles: Units of measurement and Systems of measurement

Because measurement involves the estimation of magnitudes of quantities relative to particular quantities, called units, the specification of units is of fundamental importance to measurement. The definition or specification of precise standards of measurement involves two key features, which are evident in the International System of Units (SI). Specifically, in this system the definition of each of the base units makes reference to specific empirical conditions and, with the exception of the kilogram, also to other quantitative attributes. Each derived SI unit is defined purely in terms of a relationship involving itself and other units; for example, the unit of velocity is 1 m/s. Due to the fact that derived units make reference to base units, the specification of empirical conditions is an implied component of the definition of all units.

The measurement of a specific entity or relation results in at least two numbers for the relationship between the entity or relation under study and the referenced unit of measurement, where at least one number estimates the statistical uncertainty in the measurement, also referred to as measurement error. Measuring instruments are used to estimate ratios of magnitudes to units. Prior comparisons underlie the calibration, in terms of standard units, of commonly used instruments constructed to measure physical quantities.

Metrology

Metrology is the study of measurement. In general, a metric is a scale of measurement defined in terms of a standard: i.e. in terms of well-defined unit. The quantification of phenomena through the process of measurement relies on the existence of an explicit or implicit metric, which is the standard to which measurements are referenced. If one says I am 5, that person is indicating a measurement without supplying an applicable standard. He could mean I am 5 years old or I am 5 feet high, however the implicit metric is that he is 5 years old.

History

Laws to regulate measurement were originally developed to prevent fraud. However, units of measurement are now generally defined on a scientific basis, and are established by international treaties. In the United States, commercial measurements are regulated by the National Institute of Standards and Technology NIST, a division of the United States Department of Commerce.

The history of measurements is a topic within the history of science and technology. The metre (us: meter) was standardized as the unit for length after the French revolution, and has since been adopted throughout most of the world. The United States and the UK are in the process of converting to the SI system. This process is known as metrication.

Probabilistic measurement

Measurement is not limited to physical quantities and relations but can extend to the quantification of a magnitude of any kind. In the social sciences and other fields such as health, biology and market research, probabilistic models such as the Rasch model for measurement are applied in order to measure using instruments such as questionnaires and assessments which enable comparisons between persons. The field of psychometrics is concerned with the theory and technique of measurement of psychological and mental phenomena.

Difficulties in measurement

Measurement of many quantities is very difficult and prone to large error. Part of the difficulty is due to uncertainty, and part of it is due to the limited time available in which to make the measurement.

Examples of things that are very difficult to measure in some respects and for some purposes include social related items such as:

A person's knowledge (as in testing, see also assessment)
A person's feelings, emotions, or beliefs
A person's senses (qualia)

Even for physical quantities gaining accurate measurement can be difficult. It is not possible to be exact, instead, repeated measurements will vary due to various factors affecting the quantity such as temperature, time, electromagnetic fields, and especially measurement method. As an example in the measurement of the speed of light, the quantity is now known to a high degree of precision due to modern methods, but even with those methods there is some variability in the measurement. Statistical techniques are applied to the measurement samples to estimate the speed. In earlier sets of measurements, the variability was greater, and comparing the results shows that the variability and bias in the measurement methods was not properly taken into account. Proof of this is that when various group's measurements are plotted with the estimated speed and error bars showing the expected variability of the estimated speed from the actual number, the error bars from each of the experiments did not all overlap. This means a number of groups incorrectly accounted for the true sources of error and overestimated the accuracy of their methods.

Other uses of the term

In addition to the definition of measurement given above, the term is also often used in a looser fashion to refer to any process which numbers are assigned to entities to represent increasing amount or degree in some sense. For example, counts of raw scores on tests are someties referred to as measurements. Other examples include consumer confidence and the rate of increase in the price of a good or service.

Miscellaneous

Measuring the ratios between physical quantities is an important sub-field of physics.

Some important physical quantities include:

References

Newton, I. (1728/1967). Universal Arithmetic: Or, a Treatise of Arithmetical Composition and Resolution. In D.T. Whiteside (Ed.), The mathematical Works of Isaac Newton, Vol. 2 (pp. 3-134). New York: Johnson Reprint Corp.

External links

[[zh-yue:量度]]

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