# Introduction to measurement

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In classical physics and engineering, **measurement** generally refers to the process of estimating or determining the ratio of a magnitude of a quantitative property or relation to a unit of the same type of quantitative property or relation. A process of measurement involves the comparison of physical quantities of objects or phenomena, or the comparison of relations between objects (e.g. angles). A *particular* measurement is the result of such a process, normally expressed as the multiple of a real number and a unit, where the real number is the ratio obtained from the measurement process. For example, the measurement of the length of an object might be 5 m, which is an estimate of the object's length, a magnitude, relative to a unit of length, the meter.

Measurement is not limited to physical quantities and relations but can in principle extend to the quantification of a magnitude of any type, through application of a measurement model such as the Rasch model, and subjecting empirical data derived from comparisons to appropriate testing in order to ascertain whether specific criteria for measurement have been satisfied.

In addition, the term measurement is often used in a somewhat looser fashion than defined above, to refer to any process in which numbers are assigned to entities such that the numbers are intended to represent increasing amount, in some sense, without a process that involves the estimation of ratios of magnitudes to a unit. Such examples of measurement range from degrees of uncertainty to consumer confidence to the rate of increase in the fall in the price of a good or service. It is generally proposed that there are four different levels of measurement, and that different levels are applicable to different contexts and types of measurement process.

In scientific research, measurement is essential. It includes the process of collecting data which can be used to make claims about learning. Measurement is also used to evaluate the effectiveness of a program or product (known as an evaluand).

*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)

## 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 Système International d'Unités (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

*Main article: History of measurement*

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.

## 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.

## Miscellaneous

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

Some important physical quantities include:

- Speed of light
- Planck's constant
- Gravitational constant
- Elementary charge (electric charge of electrons, protons, etc.)
- Fine-structure constant

## See also

- Units of measurement
- Systems of measurement
- History of measurement
- Conversion of units
- Dimensional analysis
- Dimensionless number
- Levels of measurement
- Measurement in quantum mechanics
- Orders of magnitude
- Timeline of temperature and pressure measurement technology
- Timeline of time measurement technology
- Uncertainty in measurement
- Uncertainty principle
- Weights and measures
- Econometrics
- Instrumentation
- Virtual instrumentation

## 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.

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