Exercise in Quality Assurance: A Laboratory Exercise

In recent years there has been additional focus on quality assurance in analytical chemistry, and the effort must be supported by teaching and presentation of some of the novel tools of statistics (1–6). It has been long recognized that linear calibration is not as simple as anticipated when uncertainties are taken into consideration (2–4). Frequently, the familiar coefficient of correlation is associated with quality of analytical results but it does not provide much information on the uncertainty of an unknown. Thus, to estimate uncertainties on measurements, more delicate tools of statistics are required (7–9). It is imperative that the predicted uncertainties of calibrations correspond exactly to the uncertainties obtained by repetitive measurements of unknowns. However, as shown by the present analysis, the uncertainties of calibrations by the law of propagation of errors (LPE) correspond well to the uncertainty obtained by repetitive determinations of unknowns. If these two uncertainties did not correspond, it would become difficult to convince the student about the reliability of the method. The uncertainty of calibrations may be estimated by including in the LPE the term of covariance (10, 11). However, as shown by Salter and de Levie (5), covariance may be omitted in the expression of calibration uncertainty when regression parameters are truly independent, which may be accomplished in practice by applying to calculations the Microsoft Excel Solver in favor of least-squares linear regression, thus simplifying considerably the estimation of uncertainties. To the broad majority of students, the mathematical procedures are cumbersome but we present a laboratory exercise that seemed to arouse an interest among students and promoted enthusiasm and understanding. There are several schools of quality assurance (3–7, 10–13) and each has its own advantages and drawbacks. It is the aim of this article to simplify and suggest a general approach to the problem of estimating uncertainty, which also promotes understanding of statistics. Initially, a number of straightforward procedures ought to be followed if the investigation of quality is going to be successful. First, the number of measurements must be high, preferably close to one hundred, according to the central-limit theorem of statistics (4). Second, the concept of uncertainty should be recognized as the true measure of quality; coefficients of correlation are unimportant (14). It should also be recognized that quality to the analytical chemist means that the true uncertainty (3, 4) should be attached to the measurement; that is, quality of measurement was obtained when the predicted uncertainty corresponded to the observed uncertainty. The uncertainty of measurement is represented by standard deviation that approaches an inherently true value that is specific for the detector, given that a high number of repetitions were performed. Thus, a low uncertainty is not necessarily a token of quality.