The Symmetric-Range Accuracy under a One-Way Random Model with Balanced or Unbalanced Data

Abstract

The symmetric-range accuracy A of a sampler is defined as the fractional range, symmetric about the true concentration, that includes a specified proportion of sampler measurements. In this article, we give an explicit expression for A assuming that the sampler measurements follow a one-way random model so as to capture different components of variability, for example, variabilities among and within different laboratories or variabilities among and within exposed workers. We derive an upper confidence limit for A based on the concept of a 'generalized confidence interval'. A convenient approximation is also provided for computing the upper confidence limit. Both balanced and unbalanced data situations are investigated. Monte Carlo evaluation indicates that the proposed upper confidence limit is satisfactory even for small samples. The statistical procedures are illustrated using an example.