Uncertainty Analysis

Abstract

The veracious experimenter must provide the reader with some measure of the reliability of his results. Ideally, this reliability should be assured by the use of statistics applied to multiple-sample experiments. Unfortunately, estimating all the uncertainties by repetition is often not practical. So, in the case of single-sample experiments another method for the description and analysis of uncertainties has to be used. For a single observation, the “error”, which is the dif ference between the--unknown--true and the observed value, is a certain--though again unknown--number. But the “uncertainty”, the estimate of the error, may vary considerably depending upon the particular circumstances of the observation. The “result” is obtained by making corrections to or calculations with “variables”, i.e. the basic quantities observed directly. The recorded values of the variables are called “data”. The way in which uncertainties in the variables affect the uncertainties in the result is called “propagation of uncertainty”. In single-sample experiments the statements of reliability will inevitably be partly based on estimates, since by definition statistics cannot be applied to all the errors. A method for estimating andfor calculating the propagation of these uncertainties into the results has been given by KLINE (1953) and will be followed in this chapter.