Handbook

Measurement error (Deviation) []

The word error is sometimes, mistakenly, used to refer to measurement uncertainties. However, errors, in the sense of procedural errors or mistakes, are something that should be avoided. Whereas measurement uncertainties cannot be avoided.

There is another concept that includes the word error and that is in the form of a deviation: the absolute difference between a best estimation and a reference value. To avoid confusion, the word error will only be used in the context of (fixable) mistakes.

Definition []

Error is the difference between a best estimation and a reference value: $$\text{error} = |\text{best estimation}—\text{reference value}|. \tag{4}$$ If all goes well in an experiment, the reference value should be within the uncertainty interval. The error is said to be small and within uncertainties.

However, there can be ⓘ systematic effectssystematic effects: Systematic effects can lead to a deviation in the measurement result, called the error. that lead to a shift in the measurements, the best estimation, and the uncertainty interval (but not the uncertainty itself!) with respect to a reference value. For instance, a measurement device can be falsely calibrated, the starting point of a moving object has been displaced, etc. In these cases, all measurements have the same shift in their value. When these systematic effects are identified, one can correct for this offset.

The existence of error can also be the starting point to look for causes. Is there a systematic effect, are the uncertainties underestimated in general, is the measurand defined correctly, is the reference value appropriate, etc.?

Students' ideas about error []

As discussed in Uncertainty, some students refer to measurement uncertainties as errors, which could lead them to think they have made a mistake [1–6]. In the physics classroom, it is advised to avoid using the word error in the context of measurement data in general. Instead, one could refer to measurement uncertainties to describe the variance in measurements and to a deviation to indicate a difference between the best estimation and a reference value (which could also be another measurement).

Another prevalent idea is that a small error is always better. Although a small error is an indication of good accuracy, this does not necessarily mean it is a good measurement result. Suppose two groups try to verify the resistance of a R = 100 Ω resistor. Group A measures RA = (99 ± 10) Ω and group B measures RB = (103 ± 5) Ω. The error of group A, eA = 1 Ω, is smaller than that of group B, eB = 3 Ω. However, the measurement uncertainty of group B is half that of group A, indicating a better precision. Since both measurement results are compatible with the reference value (more on the comparison of measurement results in Simple Comparison), one could argue that the result of group B is better.

Literature