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Observational error is the difference between a measured value of quantity and its true value. There are no perfect instruments in the real world. Every scientist knows this, but as long as he can manage the observational error, research can continue.

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 (see dynamic models).

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