A long-term look at homogeneity testing: prospects for a cheaper ‘quality control’ based test

Abstract

Homogeneity testing of materials used in analytical proficiency tests is usually carried out by selecting at random a number of the distribution units (commonly 10) and analysing them in duplicate. The results are assessed by one-way analysis of variance. Because of the limited amount of information available in these data, this analysis provides an imprecise estimate of the analytical variance σ²_an, an even more imprecise estimate of the sampling variance σ²_sam, and a test of low statistical power of the hypothesis σ²_sam = 0. When a succession of similar materials are prepared for successive rounds, under conditions where statistical control of the whole process is a reasonable assumption, the greatly increased number of degrees of freedom obtained by pooling the data allows both variance components to be well estimated, even when the sampling variance is small. A new approach to homogeneity testing is proposed, in which, after an initial phase of data collection and variance estimation, a control chart is set up and the experimental design is reduced to 10 singleton measurements. This gives a considerable reduction in expenditure, with little or no loss in statistical power.