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Measurement errors
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Measurement errors
The error of measurement is the difference between a measured value of a quantity and its true value. The term measurement uncertainty is often used as a synonym for measurement error. In metrology, the analysis of errors includes the study of uncertainties in the measurements, since no measure as far as it is carried out with care is entirely free from uncertainties.
The term error does not necessarily imply an incorrect measurement procedure by the operator, but also an uncertainty provided by the instrumentation, namely that the value presented by the measuring instrument provides a value of the measured quantity with a certain approximation. Measurement errors are caused by:
- human factors (inaccuracies in the design of the measurement chain, distractions or poor operator accuracy);
- technological factors (static and dynamic constructive and metrological qualities of the instruments);
- environmental factors (external influence quantities present in the environment in which the measurement is made).
In statistics, an error is not a “mistake”. Variability is an inherent part of the results of measurements and of the measurement process. The measurement operation is always invasive, in fact, it introduces a perturbation in the system that we want to investigate; therefore the variables involved are always altered when the measurement is performed.
The measurement error can depend on both the instrument and the observer. There are two main types of errors:
- random errors (or accidental, which may vary from observation to another);
- systematic errors (which always occurs, with the same value, when we use the instrument in the same way and in the same case).
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Random error
Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement instrument, in operating and environmental conditions or the experimenter’s interpretation of the instrumental reading.
Random errors can be analyzed statistically, as it is empirically seen that they are generally distributed according to simple laws. In particular, it is often hypothesized that the causes of these errors act in a completely random manner, thus determining deviations, with respect to the average value, both negative and positive. This allows us to expect that the effects vanish on average; substantially that the average value of the accidental errors is zero.
The smaller the random errors are, the more it is said that the measurement is precise.
Random (or accidental) errors have less impact than systematic errors because, by repeating the measurement several times and calculating the average of the values found (reliable measurement), their contribution is generally reduced for a probabilistic reason.
This observation has a fundamental consequence: if we can correct all the gross errors and the systematic ones, so we will have to deal only with accidental errors, we will just need to take repeated measures and then mediate the results: the more measures we will consider, the less the result final (average of the individual results) will be affected by accidental errors.
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Systematic error
Systematic errors are predictable and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it usually can be eliminated. An error is called systematic if the functional relationship between the magnitude of the error and the intensity of the physical quantity (that is the cause) is known. Systematic errors always occur with the same sign + or – and the same amplitude, where the measurement of a physical quantity is repeated several times with the same instrumentation and under the same operating and environmental conditions.
Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation (an error, voluntary or involuntary, committed by the observer), or interference of the environment with the measurement process, and always affect the results of an experiment in a predictable direction.
Incorrect zeroing of an instrument leading to a zero error is an example of systematic error in instrumentation.
Other types of errors are:
- gross errors;
- static errors;
- dynamic errors.