Describing the Uncertainties in Experimental Results

Abstract It is no longer acceptable, in most circles, to present experimental results without describing the uncertainties involved. Besides its obvious role in publishing, uncertainty analysis provides the experimenter a rational way of evaluating the significance of the scatter on repeated trials. This can be a powerful tool in locating the source of trouble in a misbehaving experiment. To the user of the data, a statement (by the experimenter) of the range within which the results of the present experiment might have fallen by chance alone is of great help in deciding whether the present data agree with past results or differ from them. These benefits can be realized only if both the experimenter and the reader understand what an uncertainty analysis is, what it can do (and cannot do), and how to interpret its results. This paper begins with a general description of the sources of errors in engineering measurements and the relationship between error and uncertainty. Then the path of an uncertainty analysis is traced from its first step, identifying the intended true value of a measurement, through the quantitative estimation of the individual errors, to the end objective—the interpretation and reporting of the results. The basic mathematics of both single-sample and multiple-sample analysis are presented, as well as a technique for numerically executing uncertainty analyses when computerized data interpretation is involved. The material presented in this paper covers the method of describing the uncertainties in an engineering experiment and the necessary background material.