Observational error

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 a 'mistake'. Variability is an inherent part of the results of measurements and of the measurement process. 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 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 error and systematic error. 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 an inaccuracy (involving either the observation or measurement process) 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. 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 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 which cannot or will not be controlled. Some possible reason to forgo controlling for these random errors is because it may be too expensive to control them each time the experiment is conducted or the measurements are made. Other reasons may be that whatever we are trying to measure is changing in time (see dynamic models), or is fundamentally probabilistic (as is the case in quantum mechanics — see Measurement in quantum mechanics). Random error often occurs when instruments are pushed to the extremes of their operating limits. For example, it is common for digital balances to exhibit random error in their least significant digit. Three measurements of a single object might read something like 0.9111g, 0.9110g, and 0.9112g. Measurement errors can be divided into two components: random error and systematic error. Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading. Random errors show up as different results for ostensibly the same repeated measurement. They can be estimated by comparing multiple measurements, and reduced by averaging multiple measurements.