Accuracy and precision
From Wikipedia, the free encyclopedia Jump to: navigation, search "Accuracy" redirects here. For the song by The Cure, see Three Imaginary Boys. In the fields of science, engineering, industry and statistics, the accuracy[1] of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual (true) value. The precision[1] of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.[2] Although the two words reproducibility and repeatability can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.
Accuracy indicates proximity of measurement results to the true value, precision to the repeatability or reproducibility of the measurement 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 end 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 designated 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 measurementsthat 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 the case of full reproducibility, such as when rounding a number to a representable floating point number, the word precision has a meaning not related to reproducibility. For example, in
the IEEE 754-2008 standard it means the number of bits in the significand, so it is used as a measure for the relative accuracy with which an arbitrary number can be represented.
Accuracy versus precision: the target analogy
High accuracy, but low precision
High precision, but low accuracy
Accuracy is the degree of veracity while in some contexts precision may mean the degree of reproducibility.[citation needed] 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 shot 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 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 shot, precision would be the size of the arrow cluster. (When only one arrow is shot, 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, even 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 precisionif 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.
