Quality of Analytical Measurements: Statistical Methods for Internal Validation

Every day millions of analytical determinations are made in thousands of laboratories all around the world. These measurements are necessary for evaluating merchandise in the commercial interchanges, supporting health care, nourishing security, quality control of water and the environment, characterization of raw materials and manufactured products, and forensic analyses. Practically, any aspect of the contemporary social activity is somehow supported in the analytical measurements. The cost of these measurements is high, but the cost of the decisions made based on incorrect results is much greater. For example, a test that wrongly shows the presence of a forbidden substance in a food destined for human consumption can result in an expensive claim, the confirmation of the presence of an abuse drug can lead to serious judicial sentences, and doping in the sport practice may result in severe sanction. The importance of providing a correct result is evident and also of being able to demonstrate that this result is correct. Once an analytical problem is posed to a laboratory and the analytical method is selected, the next step is the in-house validation of a method. This is the process of defining the analytical requirements to respond to the problem and to confirm that the considered method has performance characteristics consistent with those required. The results of the validation experiments have to be evaluated in order to ensure that the method meets the measurement required specification. This chapter focuses on statistical evaluation of the data in the context of validation of a method to show what information can, or cannot, be extracted from the experimental results. In Section 1.02.1, the link between measurement method and a random variable is explained to show how the probability is the natural form of expressing experimental uncertainty. Section 1.02.2 describes confidence intervals to measure bias and precision under the normality hypothesis. Also, a nonparametric interval on the median and the tolerance intervals, useful in evaluating the fit for purpose of a method, are described. In Section 1.02.3, decision making on the basis of experimental data, therefore affected by uncertainty, is described. In this section, the computation of the power of a test is systematically proposed as a key element to evaluate the quality of the decision at the desired significance level. A brief incursion into tests based on intervals is also made as they solve the problem of deciding whether an interval of values is acceptable, for example, a relative error smaller than 10% in absolute value. The section ends with some tests to evaluate the compatibility of a theoretical distribution with experimental data. Section 1.02.4 is dedicated to the analysis of variance (ANOVA) for both fixed and random effects, and in Section 1.02.5 some more specific questions related to the usual parameters of the process of validation of an analysis method are analyzed. Mathematical proofs are not covered in this chapter and to be operative from a practical point of view, several examples have been included so that the reader can verify the understanding of the formulas and the line of argument for their thoughtful use. This aspect is completed with the inclusion of an Appendix where some essential aspects related to the effectiveness of the statistical models and the limits laws are described. In the Appendix, in MATLAB® code, the necessary sentences to do all the proposed calculations in the chapter, including those of the power of tests, are incorporated.