Systematic deviation

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Under bias (or even systematic error ) to that understands deviation of a measured value of a measured quantity of their true value , the unidirectional and is due detectable in principle causes. It can not be recognized when measurements are repeated under the same conditions . Deviations that occur between the individual measured values ​​during such repetitions are called random deviations .

Systematic deviations therefore cause a shift to one side; they tend to always mean too high or always too low measured values. A typical example of this are deviations caused by incorrectly adjusted measuring devices . However, the systematic deviation of a measuring device does not need to be constant over the entire measuring range (for example, with an incorrectly adjusted thermometer , which shows high temperatures too high and low temperatures too low.)

A systematic deviation can only be avoided if the cause is known. The causes of the measurement can consist of an incorrectly set measuring device, an incorrect reading over and over again, the change in the original reality caused by the measuring device, the influence of the environment, the use of an unsuitable evaluation or measuring method and much more .

Outside of measurement technology, for example in connection with IEC 61508 (functional safety of safety-related systems), systematic errors are also regarded as "built-in" errors - damage that is present in every product. In this sense, for example, the Pentium FDIV bug was one of the systematic errors because the correct processing of an incorrectly implemented function led to exactly the same, reproducible calculation errors in every copy of the Pentium processor. - In social research, systematic deviations are known as Response tendency .

About the nomenclature

The systematic measurement deviation can be made up of a known and an unknown deviation.

When obtained under the same conditions measured values, the systematic error is a constant measurement error, it is offset (zero) offset , shelf called or similar. A slowly increasing / decreasing measurement deviation (e.g. in the case of a change in the display that becomes recognizable over time) is of a systematic nature; it is referred to as a trend (also known as bias ) or drift . Trends and drifts are relatively easy to detect by repeated measurements. They often go back to undetected temperature influences . Even aging is the cause in question.

In accordance with English, the word bias is also used for a systematic shift , but in electronics this can also be understood as an unavoidable or deliberate one-sided pre-loading .

Causes of systematic measurement errors

The causes of systematic measurement errors are diverse. In particular, there are:

  • Imperfection of the measuring devices ( measuring device deviation , e.g. inadequate adjustment , failure to observe a calibration ),
  • Influences such as heating, wear and tear, aging (e.g. loose parts on the measuring device, thermal expansion, directional deviation or out-of- roundness of axes ),
  • Deviations of the actual values ​​of the influencing variables from the assumed values ​​(influencing effects e.g. self-heating, refraction , asymmetrical effects of temperature or wind, vibration in the subsurface),
  • Deviations of the actually present measurement object from the assumed,
  • Feedback when the measured variable is recorded by the measuring device (e.g. feedback deviation due to internal consumption in electrical measuring devices),
  • deviations caused by the observer (e.g. one-sided aiming error , parallax error );
  • Use of a relationship between quantities leading to the measurement result that does not correspond to the actual link between these quantities

Falsifications due to errors or inattentiveness on the part of the observer (e.g. incorrect numerical value when reading ), unforeseeable events (e.g. impacts) or the occurrence of gross errors , which can always be avoided, cannot be classified here. In an adjustment, however, they can usually be recognized when their residual exceeds 2–3 times the standard deviation.


Even the simple measurement with a ruler contains possibilities for systematic measurement deviations.

  1. Instrumental (incorrect scaling): If a ruler or tape measure is in the sun, it warms up and expands. If the measurement is carried out with it, the measurement is always a little too short. However, if one knows the temperature of the ruler and its thermal coefficient of linear expansion , this influence can be eliminated mathematically. The systematic deviation is now taken into account in the measurement model and thus rendered harmless - within the framework of the knowledge of the physical relationships and the required data. Without this model, operating the measuring device helps with the reference conditions for which it is designed. If the scale holder changes due to aging (especially with plastic), a new adjustment is not possible in this simple example. At most, a calibration can be used to determine a factor by which the value read is to be corrected.
  2. Incorrect handling: On the other hand, if you place the ruler at an angle on the workpiece while measuring, the reading is systematically falsified. But if you know the angle at which the ruler was placed incorrectly (or looked at it askew), you can take this into account by calculating the angle.
  3. Unfavorable circumstances: This could include an uneven or sliding surface, an annoying shadow cast by the scale and the like. Here one can mathematically not correct a lot, but the measurement should repeated in different environmental conditions.

Inner and outer accuracy

In the term “ external accuracy ”, systematic deviations are generally understood as included, while the “internal accuracy”, also known as precision , usually corresponds to the spread when the measurement is simply repeated. Both are usually given in the form of the standard deviation . The difference between the two can become apparent when changing the measuring device (see 1.), the observer  (2.) or the external circumstances (3.), such as the weather situation .

An astronomical latitude determination with stars and a passage instrument or a digital astrolabe has an internal accuracy of 0.1 ", but can vary by 0.5" from one night to the next. The reason for such "evening errors" lies in anomalies in the atmospheric layers ( astronomical refraction , dome or hall refraction ) or in small temperature effects , for example when the telescope is bent .

Dealing with the systematic measurement error

The determination of systematic deviations of a measurement is (quotation from)

  1. Detective work, in which you have to uncover sources of error,
  2. physical-philosophical consideration, whether the ignorance lies within or outside the theoretical framework,
  3. Professional data analysis, in which the errors are prioritized in their importance and, if necessary, suitable correctors are introduced.

A systematic deviation that is constant over time cannot be determined or influenced by repetition; you have to make the known deviation

An unknown systematic measurement deviation can only be estimated with sufficient experience and limited by means of intervals.

Examples of time constant unknown systematic deviations

  • the mechanical adjustment of a measuring device to a correct value , which can only be achieved with finite accuracy ,
  • Heat dissipation through a thermometer protection tube at a point where the temperature is to be measured.

For the unknown and the observable in principle, but not determined in detail measuring error is added a margin of error (or a deviation threshold amount) of such that is. It is unsigned by definition.

In the case of a drifting measuring device, the measurement deviations are subject to a trend - unlike in the case of random deviations that scatter in a disorderly manner. In order to detect this, in contrast to time-constant systematic deviations, repeated measurements as a time series are required.

In another context, statistics have developed their own, completely different procedures for the treatment of time series , for example stock exchange prices.

See also

Individual evidence

  1. The term measurement error does not correspond to the current standard DIN1319-1, but is still to be found occasionally.
  2. a b c d DIN 1319-1, Basics of measurement technology - Part 1: Basic terms . 1995.
  3. a b Lothar Papula: Mathematics for Engineers and Natural Scientists Volume 2 . Vieweg + Teubner, 6th edition 2011, p. 651.
  4. a b Georg Streck: Introduction to statistics for geoecologists and other natural scientists . Books on Demand 2004, p. 159.
  5. Martin Erdmann, Thomas Hebbeker: Experimentalphysik 5: Modern methods of data analysis . Springer 2013, p. 139.