Observational error (or measurement 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.
Science and experiments
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:
- systematic error which always occurs, with the same value, when we use the instrument in the same way and in the same case, and
- random error which may vary from observation to observation.
Systematic error is sometimes called statistical bias. It may often be reduced 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.
The term observational error is also sometimes used to refer to response errors and some other types of non-sampling error. In survey-type situations, these errors can be mistakes in the collection of data, including both the incorrect recording of a response and the correct recording of a respondent's inaccurate response.
- Errors and residuals in statistics
- Replication (statistics)
- Statistical theory
- Regression dilution
- Test method
- Propagation of uncertainty
- Instrument error
- Measurement uncertainty
- Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
Errors of Measurement in Statistics, W. G. Cochran, Technometrics, Vol. 10, No. 4 (Nov., 1968), pp. 637-666: http://www.jstor.org/stable/1267450