Observational error is the difference between a measured value of quantity and its true value. In statistics, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.

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 we use is that the error has two additive parts:

1. systematic error which always occurs (with the same value) when we use the instrument in the same way, and
2. random error which may vary from observation to observation.

The systematic error is sometimes called statistical bias. It is controlled by very carefully standardized procedures. Part of the education in every science is how to use the standard instruments of the discipline.

The random error (or random variation) is due to factors which we cannot (or do not) control. It may be too expensive or we may be too ignorant of these factors to control them each time we measure. It may even 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 their 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.

See also

• errors and residuals in statistics
• error in general
• Replication (statistics)
• statistical theory
• metrology
• test method

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