A generalization of a hypothesis testing procedure for assessing the mean of a lognormal distribution is discussed in the context of occupational hygiene. We consider inference about the probability that the mean exposure level for an arbitrary worker in a job group exceeds the occupational exposure limit (OEL) for the toxicant under study. The approach is based on the assumption that the logged exposures (n measurements on each of k workers) conform to the one-way random effects ANOVA model. We focus on adaptations of classical large sample-based testing procedures, and we compare their performances in a variety of settings with the help of simulated data. We also discuss practical issues, including sample size approximation and alternative testing recommendations in the event of a negative between-worker variance component estimate.

Key Words
Likelihood ratio test; Lognormality; Score test; Variance components; Wald test.

Robert H. Lyles is Research Associate, Department of Epidemiology, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, MD 21205. Lawrence L. Kupper is Professor, Department of Biostatistics, and Stephen M. Rappaport is Professor, Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, CB #7400, Chapel Hill, NC 27599-7400.