Randomization of Systematic Errors and Its Consequences for the Evaluation of Measurements

Abstract

The evaluation of measurements represents an essential and often time consuming part in gaining a final experimental result for the value of the physical quantity under consideration. This result may be described as a conclusion, based on a finite set of observations, on the true value of the quantity. The finite number of measurements leads to an uncertainty in this conclusion, which usually is called “measurement uncertainty”, but for several reasons is not an optimal wording. Moreover, it is rather common to call the standard deviation or the standard deviation of the mean, as measures for the precision of the experiment, the “uncertainty” of the measurement. The precision, of course, is an important component in characterizing the true value of the quantity, but standing for itself it does not suffice for this purpose¹. Beside others, one of the reasons for this is the frequent occurance of systematic errors in the experiment. This kind of error may be described by an (unknown) deviation of the measured value from the true value, this deviation behaving in a non statistical way during the time a sequence of measurements is taken. In most cases it can be assumed that it does not influence the precision of the measurements, but obviously has some implications on the conclusion on the true value of the quantity of interest.