Commentary: Understanding practical lot quality assurance sampling.

Lot Quality Assurance Sampling (LQAS) is a statistical method emanating from the brilliant work of Dodge and Romig, which, together with that of Shewhart, developed into what is known today as Statistical Quality Control. Since the 1980s, LQAS has transitioned into the health sciences and has gained considerable appeal in a wide range of applications. We disagree with the statement in the obloquy by Rhoda and colleagues that LQAS has devolved into two methods; it remains a single methodology. LQAS does consist of two stages: the first stage obtains random samples from, say, districts within a region in order to classify each as belonging to one of two classes that is often labeled either ‘acceptable’ or ‘unacceptable’; and the second stage deals with estimation. It sells LQAS short to say that it ‘is supposed to provide a rapid and inexpensive estimate of the prevalence . . .’. This quote reveals an academic bias in Rhoda and colleagues’ view that overlooks a primary consequence of LQAS; namely, classifications carried out at the local level. The first stage is the focus taken by Rhoda et al. and the one that is often the most important to practitioners in the field, although, ironically, the second stage is where prevalence estimation occurs. Rhoda et al. cast LQAS into a hypothesis testing framework, and, as with any analogy, it should not be extended. The Dodge–Romig work preceded the Neyman–Pearson developments and the attempt by Rhoda et al. to straitjacket LQAS, does not do it justice. This is evident in Concern 1, e.g. where they admit that the manuals they assail do not state a null hypothesis. Yet, not wishing to acknowledge that it is unnecessary to have a null hypothesis, they invent one—and then attack it! This straw man serves no purpose other than to advance a polemic. Some think that the hypothetico-deductive method, including statistical hypothesis testing, has served us well in advancing empiricism, but the first step of LQAS simply deals with classification. To say that one of these classifications is the ‘null hypothesis’ appends unnecessary labelling baggage. For example, one ‘accepts the null’, which then leads to an addlepated admonition that ‘accepting a null hypothesis is always a statistical error’. This, of course, belies the fact that in hypothesis testing a Type II error is sometimes called the ‘acceptance’ error, as we teach our beginning students—(e.g. p. 240). Perhaps the authors mean to direct their admonition toward ‘proving’ the null as opposed to accepting it, but such an assumption is kind speculation on our part. One must accept classification into one of the two established classes, which may explain why this methodology is also called acceptance sampling. In an early published application of LQAS to the health sciences they recognized that the local sample sizes were too small to provide ‘meaningful confidence intervals’ in the first stage. In the binomial setting we have here, there is a complete duality between confidence intervals and hypothesis testing. Thus this warning should also be taken by hypothesis testers to mean that the samples are too small for meaningful hypothesis testing—LQAS is different: at the first stage, it classifies. The complete probabilistic characterization of the first step in LQAS is the operating characteristic (OC) curve, such as Figure 1. This particular design was chosen by Valadez because the value of the OC curve at 80% is 90% and its value at 50% is 10%. These two thresholds, 50 and 80%, play a pivotal role in LQAS as opposed to the single threshold in hypothesis testing. Note that there is also a certain symmetry in the probabilities of the potential errors at these thresholds, and this is noteworthy for those who feel secure in hypothesis testing, since this equivalence equalizes the ‘value’ of the ‘null’ Published by Oxford University Press on behalf of the International Epidemiological Association