Summary
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement uncertainty. When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are "errors" in the sense in which that term is used in statistics; see errors and residuals in statistics. Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results. The common statistical model used is that the error has two additive parts: Systematic error which always occurs, with the same value, when we use the instrument in the same way and in the same case. Random error which may vary from observation to another. Systematic error is sometimes called statistical bias. It may often be reduced with standardized procedures. Part of the learning process in the various sciences is learning how to use standard instruments and protocols so as to minimize systematic error. Random error (or random variation) is due to factors that cannot or will not be controlled. One possible reason to forgo controlling for these random errors is that it may be too expensive to control them each time the experiment is conducted or the measurements are made.
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