measures of observational error From Wikipedia, the free encyclopedia

The **accuracy and precision** of measurements have special meanings in the fields of science, engineering, industry and statistics.

- The
**accuracy**of a measurement system is how close it gets to a quantity's actual (true) value.^{[1]}

- The
**precision**of a measurement system is the degree to which repeated measurements give the same results.^{[1]}^{[2]}

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

A measurement system is 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.

The word "precision" also refers to how fine the measurement is made, as the *resolution* of the measurement, such as to the nearest meter, centimeter, or yard, foot, inch, or nanometer.

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 (number of digits in the amount), so it is used as a measure for the relative accuracy with which a number can be shown.

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