Accuracy and precision

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Accuracy and precision are two measures of observational error :

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Accuracy and precision of observations lying on a bell curve Accuracy and precision.svg
Accuracy and precision of observations lying on a bell curve

In the language of statistics:

In the context of observations made on a ratio or interval scale, a statistical sample can be said to be accurate if its average is close to the true value of the quantity being measured and precise if its standard deviation is small.

See Terminological disambiguation below for i) other words that refer to the same concepts; and ii) the use of the words 'accuracy' and 'precision' to refer to related but different concepts.

Common technical definition

In the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. [1] The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. [1] [2] Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.

The field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.

A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision.

A measurement system is considered valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).

The terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data.

In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement.

In numerical analysis, accuracy is also the nearness of a calculation to the true value; while precision is the resolution of the representation, typically defined by the number of decimal or binary digits.

In military terms, accuracy refers primarily to the accuracy of fire (justesse de tir), the precision of fire expressed by the closeness of a grouping of shots at and around the centre of the target. [3]

Quantification

In industrial instrumentation, accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions. [4]

Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units (abbreviated SI from French: Système international d'unités) and maintained by national standards organizations such as the National Institute of Standards and Technology in the United States.

This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.

With regard to accuracy we can distinguish:

A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Where not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 843 m would imply a margin of error of 0.5 m (the last significant digits are the units).

A reading of 8,000 m, with trailing zeros and no decimal point, is ambiguous; the trailing zeros may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 103 m indicates that all three zeros are significant, giving a margin of 0.5 m. Similarly, one can use a multiple of the basic measurement unit: 8.0 km is equivalent to 8.0 × 103 m. It indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it. For example, a source reporting a number like 153,753 with precision +/- 5,000 looks like it has precision +/- 0.5. Under the convention it would have been rounded to 150,000.

Alternatively, in a scientific context, if it is desired to indicate the margin of error with more precision, one can use a notation such as 7.54398(23) × 10−10 m, meaning a range of between 7.54375 and 7.54421 × 10−10 m.

Precision includes:

In engineering, precision is often taken as three times Standard Deviation of measurements taken, representing the range that 99.73% of measurements can occur within. [5] For example, an ergonomist measuring the human body can be confident that 99.73% of their extracted measurements fall within ± 0.7 cm - if using the GRYPHON processing system - or ± 13 cm - if using unprocessed data. [6]

ISO definition (ISO 5725)

According to ISO 5725-1, accuracy consists of trueness (proximity of measurement results to the true value) and precision (repeatability or reproducibility of the measurement). Accuracy (trueness and precision).svg
According to ISO 5725-1, accuracy consists of trueness (proximity of measurement results to the true value) and precision (repeatability or reproducibility of the measurement).

A shift in the meaning of these terms appeared with the publication of the ISO 5725 series of standards in 1994, which is also reflected in the 2008 issue of the BIPM International Vocabulary of Metrology (VIM), items 2.13 and 2.14. [1]

According to ISO 5725-1, [7] the general term "accuracy" is used to describe the closeness of a measurement to the true value. When the term is applied to sets of measurements of the same measurand, it involves a component of random error and a component of systematic error. In this case trueness is the closeness of the mean of a set of measurement results to the actual (true) value, that is the systematic error, and precision is the closeness of agreement among a set of results, that is the random error.

ISO 5725-1 and VIM also avoid the use of the term "bias", previously specified in BS 5497-1, [8] because it has different connotations outside the fields of science and engineering, as in medicine and law.

Terminological disambiguation

Concern for the measurement of error is widespread across many fields and many terms have been used to deal with the same, or related, concepts.

Different names, same concepts

The three core concepts on this page, as named in different places, are listed in the same order in each subsection below.

This Wikipedia page

Validity (avoidance of observational error, the overarching concern)

· Accuracy

· Precision

ISO 5725

Accuracy

· Trueness (avoidance of systematic error; previously, avoidance of bias)

· Precision (avoidance of random error)

Statistics

Accuracy

· Bias

· Variability

Psychometrics

Measurement properties [9]

· Validity (avoidance of constant error)

· Reliability (avoidance of variable error).

Same names, different concepts

See In_classiciation below for the use of the words 'accuracy' and 'precision' to refer to related but different concepts.

In classification

In classification, observations made against a nominal scale, the concepts of accuracy and precision remain relevant. A classifier can suffer from systematic errors and from a lack of reliability. However, in binary classification the terms 'accuracy' and 'precision' are also and primarily used with a different meaning; most commonly, the words relate to formulae for quantifying the error resulting from the reporting by a classifier of, for example, false positives.

In psychometrics and psychophysics

In psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. Precision is a synonym for reliability and variable error. The validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical techniques, classically through an internal consistency test like Cronbach's alpha to ensure sets of related questions have related responses, and then comparison of those related question between reference and target population.[ citation needed ]

In logic simulation

Comparative Waveforms for Logic values, circuit voltages, and measure voltages ACCvsPrecision.jpg
Comparative Waveforms for Logic values, circuit voltages, and measure voltages

In logic simulation, a common mistake in evaluation of accurate models is to compare a logic simulation model to a transistor circuit simulation model. This is a comparison of differences in precision, not accuracy. Precision is measured with respect to detail and accuracy is measured with respect to reality. [10] [11]


In cognitive systems

In cognitive systems, accuracy and precision is used to characterize and measure results of a cognitive process performed by biological or artificial entities where a cognitive process is a transformation of data, information, knowledge, or wisdom to a higher-valued form. (DIKW Pyramid) Sometimes, a cognitive process produces exactly the intended or desired output but sometimes produces output far from the intended or desired. Furthermore, repetitions of a cognitive process do not always produce the same output. Cognitive accuracy (CA) is the propensity of a cognitive process to produce the intended or desired output. Cognitive precision (CP) is the propensity of a cognitive process to produce the same output. [12] [13] [14] To measure augmented cognition in human/cog ensembles, where one or more humans work collaboratively with one or more cognitive systems (cogs), increases in cognitive accuracy and cognitive precision assist in measuring the degree of cognitive augmentation.

See also

Related Research Articles

<span class="mw-page-title-main">Measurement</span> Process of assigning numbers to objects or events

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.

Observational error is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated, and is specified with the measurement as, for example, 32.3 ± 0.5 cm.

In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, a sound tone, or a physical artifact, such as a meter ruler.

<span class="mw-page-title-main">Uncertainty</span> Situations involving imperfect or unknown information

Uncertainty or incertitude refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

<span class="mw-page-title-main">Sampling (statistics)</span> Selection of data points in statistics.

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population and statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work. Understanding the source of statistical bias can help to assess whether the observed results are close to actuality. Issues of statistical bias has been argued to be closely linked to issues of statistical validity.

In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:

"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 and 1.00, are usually used to indicate the amount of error in the scores."

<span class="mw-page-title-main">Engineering tolerance</span> Permissible limit or limits of variation in engineering

Engineering tolerance is the permissible limit or limits of variation in:

  1. a physical dimension;
  2. a measured value or physical property of a material, manufactured object, system, or service;
  3. other measured values ;
  4. in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel ;
  5. in mechanical engineering, the space between a bolt and a nut or a hole, etc.

Repeatability or test–retest reliability is the closeness of the agreement between the results of successive measurements of the same measure, when carried out under the same conditions of measurement. In other words, the measurements are taken by a single person or instrument on the same item, under the same conditions, and in a short period of time. A less-than-perfect test–retest reliability causes test–retest variability. Such variability can be caused by, for example, intra-individual variability and inter-observer variability. A measurement may be said to be repeatable when this variation is smaller than a predetermined acceptance criterion.

<span class="mw-page-title-main">Regression dilution</span> Statistical bias in linear regressions

Regression dilution, also known as regression attenuation, is the biasing of the linear regression slope towards zero, caused by errors in the independent variable.

In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample, such as means and quartiles, generally differ from the statistics of the entire population. The difference between the sample statistic and population parameter is considered the sampling error. For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country.

Instrument error refers to the error of a measuring instrument, or the difference between the actual value and the value indicated by the instrument. There can be errors of various types, and the overall error is the sum of the individual errors.

<span class="mw-page-title-main">Deviation (statistics)</span> Difference between a variables observed value and a reference value

In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean are called errors and residuals, respectively. The sign of the deviation reports the direction of that difference: the deviation is positive when the observed value exceeds the reference value. The absolute value of the deviation indicates the size or magnitude of the difference. In a given sample, there are as many deviations as sample points. Summary statistics can be derived from a set of deviations, such as the standard deviation and the mean absolute deviation, measures of dispersion, and the mean signed deviation, a measure of bias.

<span class="mw-page-title-main">Replication (statistics)</span> Principle that variation can be better estimated with nonvarying repetition of conditions

In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions to support the original claim, which crucial to confirm the accuracy of results as well as for identifying and correcting the flaws in the original experiment. ASTM, in standard E1847, defines replication as "... the repetition of the set of all the treatment combinations to be compared in an experiment. Each of the repetitions is called a replicate."

A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a test method should be "explicit, unambiguous, and experimentally feasible.", as well as effective and reproducible.

<span class="mw-page-title-main">Custody transfer</span> Oil and gas industry term for transfer of physical substance from one operator to another

Custody Transfer in the oil and gas industry refers to the transactions involving transporting physical substance from one operator to another. This includes the transferring of raw and refined petroleum between tanks and railway tank cars; onto ships, and other transactions. Custody transfer in fluid measurement is defined as a metering point (location) where the fluid is being measured for sale from one party to another. During custody transfer, accuracy is of great importance to both the company delivering the material and the eventual recipient, when transferring a material.

The multitrait-multimethod (MTMM) matrix is an approach to examining construct validity developed by Campbell and Fiske (1959). It organizes convergent and discriminant validity evidence for comparison of how a measure relates to other measures. The conceptual approach has influenced experimental design and measurement theory in psychology, including applications in structural equation models.

Industrial process data validation and reconciliation, or more briefly, process data reconciliation (PDR), is a technology that uses process information and mathematical methods in order to automatically ensure data validation and reconciliation by correcting measurements in industrial processes. The use of PDR allows for extracting accurate and reliable information about the state of industry processes from raw measurement data and produces a single consistent set of data representing the most likely process operation.

Forensic metrology is a branch of metrology applied to forensic sciences. Metrology has evolved various techniques for assessing the margin of error or uncertainty associated with measurements. Forensic laboratories and criminalistic laboratories perform numerous measurements and tests to support criminal prosecution and civil legal actions. Examples of forensic metrology include the measurement of alcohol content in blood using breathalyzers, quantification of controlled substances, and length measurements of firearm barrels. The results of forensic measurements are used to determine if a person is charged with a crime or may be used to determine a statutory sentencing enhancement. Other examples of forensic metrology includes tests that measure if there is a presence of a substance, latent print examination, questioned documents examination, and DNA analysis.

The Joint Committee for Guides in Metrology (JCGM) is an organization in Sèvres that prepared the Guide to the Expression of Uncertainty in Measurement (GUM) and the International Vocabulary of Metrology (VIM). The JCGM assumed responsibility for these two documents from the ISO Technical Advisory Group 4 (TAG4).

References

  1. 1 2 3 JCGM 200:2008 International vocabulary of metrology — Basic and general concepts and associated terms (VIM)
  2. ↑ Taylor, John Robert (1999). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. pp. 128–129. ISBN   0-935702-75-X.
  3. ↑ North Atlantic Treaty Organization, NATO Standardization Agency AAP-6 – Glossary of terms and definitions, p 43.
  4. ↑ Creus, Antonio. Instrumentación Industrial[ citation needed ]
  5. ↑ Black, J. Temple (21 July 2020). DeGarmo's materials and processes in manufacturing. John Wiley & Sons. ISBN   978-1-119-72329-5. OCLC   1246529321.
  6. ↑ Parker, Christopher J.; Gill, Simeon; Harwood, Adrian; Hayes, Steven G.; Ahmed, Maryam (2021-05-19). "A Method for Increasing 3D Body Scanning's Precision: Gryphon and Consecutive Scanning". Ergonomics. 65 (1): 39–59. doi: 10.1080/00140139.2021.1931473 . ISSN   0014-0139. PMID   34006206.
  7. ↑ BS ISO 5725-1: "Accuracy (trueness and precision) of measurement methods and results - Part 1: General principles and definitions.", p.1 (1994)
  8. ↑ BS 5497-1: "Precision of test methods. Guide for the determination of repeatability and reproducibility for a standard test method." (1979)
  9. ↑ Souza, Ana Cláudia de; Alexandre, Neusa Maria Costa; Guirardello, Edinêis de Brito (2017). "Psychometric properties in instruments evaluation of reliability and validity". Epidemiologia E Servicos De Saude: Revista Do Sistema Unico De Saude Do Brasil. 26 (3): 649–659. doi:10.5123/S1679-49742017000300022. ISSN   2237-9622. PMID   28977189.
  10. ↑ Acken, John M. (1997). "none". Encyclopedia of Computer Science and Technology. 36: 281–306.
  11. ↑ Glasser, Mark; Mathews, Rob; Acken, John M. (June 1990). "1990 Workshop on Logic-Level Modelling for ASICS". SIGDA Newsletter. 20 (1).
  12. ↑ Fulbright, Ron (2020). Democratization of Expertise: How Cognitive Systems Will Revolutionize Your Life (1st ed.). Boca Raton, FL: CRC Press. ISBN   978-0367859459.
  13. ↑ Fulbright, Ron (2019). "Calculating Cognitive Augmentation – A Case Study". Augmented Cognition. Lecture Notes in Computer Science. Vol. 11580. Springer Cham. pp. 533–545. arXiv: 2211.06479 . doi:10.1007/978-3-030-22419-6_38. ISBN   978-3-030-22418-9. S2CID   195891648.
  14. ↑ Fulbright, Ron (2018). "On Measuring Cognition and Cognitive Augmentation". Human Interface and the Management of Information. Information in Applications and Services. Lecture Notes in Computer Science. Vol. 10905. Springer Cham. pp. 494–507. arXiv: 2211.06477 . doi:10.1007/978-3-319-92046-7_41. ISBN   978-3-319-92045-0. S2CID   51603737.
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