# Akurasi jeung présisi

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Dina sains, rékayasa, industri jeung statistik, akurasi nyaéta tingkatkacocogan ukuran atawa lobana itungan kana nilai sabenerna (nilai nu bener). Akurasi pakait raket jeung presisi, disebut ogé bisa dijieun deui atawa diulang deui, tingkat nu dina ukuran atawa itungan saterusna nembongkeun hasil nu sarua atawa ampir sarua. Hasil itungan atawa ukuran bisa akurat tapi teu présisi; présisi tapi teu akurat; atawa teu présisi jeung teu akurat. Hiji hasil disebut valid lamun akurat jeung presisi. Watesan nu pakait dina survey nyaéta kasalahan (variabel acak dina panalungtikan) sarta bias (teu-acak atawa akibat langsung nu disababkeun ku ayana hal nu teu pakait ku variabel mandiri).

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## Akurasi vs presisi - analogi target

Akurasi luhur, tapi presisi leutik
Presisi luhur, tapi akurasi leutik

Akurasi nyaéta tingkat kadeukeutan sedengkeun présisi nyaéta tingkat kamampuh dijieun deui. Analogi dipaké di dieu keur nerangkeun béda antara akurasi jeung présisi nyaéta babandingan target. In this analogy, repéated méasurements are compared to arrows that are fired at a target. Accuracy describes the closeness of arrows to the bullseye at the target center. Arrows that strike closer to the bullseye are considered more accurate. The closer a system's méasurements to the accepted value, the more accurate the system is considered to be.

To continue the analogy, if a large number of arrows are fired, precision would be the size of the arrow cluster. (When only one arrow is fired, precision is the size of the cluster one would expect if this were repéated many times under the same conditions.) When all arrows are grouped tightly together, the cluster is considered precise since they all struck close to the same spot, if not necessarily néar the bullseye. The méasurements are precise, though not necessarily accurate.
Further example, if a méasuring rod is supposed to be ten yards long but is only 9 yards, 35 inches méasurements can be precise but inaccurate. The méasuring rod will give consistently similar results but the results will be consistently wrong.

However, it is not possible to reliably achieve accuracy in individual méasurements without precision — if the arrows are not grouped close to one another, they cannot all be close to the bullseye. (Their average position might be an accurate estimation of the bullseye, but the individual arrows are inaccurate.) See also Circular error probable for application of precision to the science of ballistics.

## Accuracy and precision in logic level modeling and IC simulation

As described in the SIGDA Newsletter [Vol 20. Number 1, June 1990] a common mistake in evaluation of accurate modéls is to compare a logic simulation modél to a transistor circuit simulation modél. This is a comparison of differences in precision, not accuracy. Precision is méasured with respect to detail and accuracy is méasured with respect to réality. Another reference for this topic is "Logic Level Modelling", by John M. Acken, Encyclopedia of Computer Science and Technology, Vol 36, 1997, page 281-306.

## Quantifying accuracy and precision

idéally a méasurement device is both accurate and precise, with méasurements all close to and tightly clustered around the known value. The accuracy and precision of a méasurement process is usually established by repéatedly méasuring some traceable reference standard. Such standards are defined in the International System of Units and maintained by national standards organizations such as the National Institute of Standards and Technology.

Precision is usually characterised in terms of the standard deviation of the méasurements, sometimes incorrectly called the méasurement process's standard error. The interval defined by the standard deviation is the 68.3% ("one sigma") confidence interval of the méasurements. If enough méasurements have been made to accurately estimate the standard deviation of the process, and if the méasurement process produces normally distributed errors, then it is likely that 68.3% of the time, the true value of the méasured property will lie within one standard deviation, 95.4% of the time it will lie within two standard deviations, and 99.7% of the time it will lie within three standard deviations of the méasured value.

This also applies when méasurements are repéated 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 méasurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged méasurements will be closer to a normal distribution than that of individual méasurements.

With regard to accuracy we can distinguish:

• the difference between the mean of the méasurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration.
• the combined effect of that and precision.

A common convention in science and engineering is to express accuracy and/or precision implicitly by méans of significant figures. Here, when 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 8436 m would imply a margin of error of 0.5 m (the last significant digits are the units).

A réading of 8000 m, with trailing zeroes and no decimal point, is ambiguous; the trailing zeroes may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: '8.0 x 10³ m' indicates that the first zero is significant (hence a margin of 50 m) while '8.000 x 10³ m' indicates that all three zeroes are significant, giving a margin of 0.5 m. Similarly, it is possible to use a multiple of the basic méasurement unit: '8.0 km' is equivalent to '8.0 x 10³ m'. In fact, it indicates a margin of 0.05 km (50 m). However, reliance on this convention can léad to false precision errors when accepting data from sources that do not obey it.

Looking at this in another way, a value of 8 would méan that the méasurement has been made with a precision of '1' (the méasuring instrument was able to méasure only up to 1's place) wheréas a value of 8.0 (though mathematically equal to 8) would méan that the value at the first decimal place was méasured and was found to be zero. (The méasuring instrument was able to méasure the first decimal place.) The second value is more precise. Neither of the méasured values may be accurate (the actual value could be 9.5 but méasured inaccurately as 8 in both instances). Thus, accuracy can be said to be the 'correctness' of a méasurement, while precision could be identified as the ability to resolve smaller differences.

Precision is sometimes stratified into:

• Repeatability - the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repéating during a short time period; and
• Reproducibility - the variation arising using the same méasurement process among different instruments and operators, and over longer time periods.

A common way to statistically méasure precision is a Six Sigma tool called ANOVA Gage R&R. As stated before, you can be both accurate and precise. For instance, if all your arrows hit the bull's eye of the target, they are all both néar the "true value" (accurate) and néar one another (precise).

Something to think about: In the NFL, a place kicker makes 9 of 10 field goals, and another makes 6 of 10. Even if the 6 that the second kicker made were straight down the middle and the first kicker just made his in, he is still less accurate and less precise than the first kicker. This differs from the darts example because either you maké it or you do not; there are not different levels of points that can be scored.

## Accuracy in biostatistics

"Accuracy" is also used as a statistical méasure of how well a binary classification test correctly identifies or excludes a condition.

 Condition (e.g. Diséase) As determined by "Gold" standard True False Testoutcome Positive True Positive False Positive → Positive Predictive Value Negative False Negative True Negative → Negative Predictive Value ↓Sensitivity ↓Specificity Accuracy

That is, the accuracy is the proportion of true results (both true positives and true negatives) in the population. It is a paraméter of the test.

${\displaystyle {\rm {accuracy}}={\frac {{\rm {number\ of\ True\ Positives}}+{\rm {number\ of\ True\ Negatives}}}{{\rm {numbers\ of\ True\ Positives}}+{\rm {False\ Positives}}+{\rm {False\ Negatives}}+{\rm {True\ Negatives}}}}}$

An accuracy of 100% méans that the test identifies all sick and well péople correctly.

Also see Specificity (tests) and Sensitivity (tests).

Accuracy may be determined from Sensitivity and Specificity, provided Prevalence is known, using the equation:

${\displaystyle {\rm {accuracy}}=({\rm {sensitivity}})({\rm {prevalence}})+({\rm {specificity}})(1-{\rm {prevalence}})}$

## Accuracy and precision in psychometrics

In psychometrics the terms accuracy and precision are interchangéably used with validity and reliability respectively. Validity of a méasurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical technique (classically Cronbach's alpha).