## Thursday, January 31, 2013

### Accuracy Definition, What is Accuracy

In general, refers to precision and/or exactness, but to dig into this term...

In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeat-ability  the degree to which further measurements or calculations will show the same or similar results.

The results of calculations or a measurement can be accurate but not precise; precise but not accurate; neither; or both. A result is called valid if it is both accurate and precise.

The related terms in surveying are error (random variability in research) and bias (non-random or directed effects caused by a factor or factors unrelated by the independent variable).

Accuracy vs Precision - The Target Analogy

Accuracy is the degree of veracity while precision is the degree of reproducibility. The analogy used here to explain the difference between accuracy and precision is the target comparison.

In this analogy, repeated measurements are compared to arrows that are fired at a target. Accuracy describes the closeness of arrows to the bulls-eye at the target center. Arrows that strike closer to the bulls-eye are considered more accurate. The closer a system's measurements 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 repeated 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 near the bullseye. The measurements are precise, though not necessarily accurate.

However, it is not possible to reliably achieve accuracy in individual measurements without precision — if the arrows are not grouped close to one another, they cannot all be close to the bulls-eye  (Their average position might be an accurate estimation of the bulls-eye, but the individual arrows are inaccurate.)

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 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. 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

Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the known 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 and maintained by national standards organizations such as the National Institute of Standards and Technology.

Precision is usually characterized in terms of the standard deviation of the measurements, sometimes called the measurement process's standard error. The interval defined by the standard deviation is the 68.3% ("one sigma") confidence interval of the measurements. If enough measurements have been made to accurately estimate the standard deviation of the process, and if the measurement process produces normally distributed errors, then it is likely that 68.3% of the time, the true value of the measured 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 measured value.

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:

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

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 near the "true value" (accurate) and near 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 make it or you do not; there are not different levels of points that can be scored.