Assessing occupational exposure via the one-way random effects model with unbalanced data

This article considers a one-way random effects model for assessing the proportion of workers whose mean exposures exceed the occupational exposure limit based on exposure measurements from a random sample of workers. Hypothesis testing and interval estimation for the relevant parameter of interest are proposed when the exposure data are unbalanced. The methods are based on the generalized p-value approach, and simplify to the ones in Krishnamoorthy and Mathews (J. Agri. Biol. Environ. Statist. 7 (2002) 440) when the data are balanced. The sizes and powers of the test are evaluated numerically. The numerical studies show that the proposed inferential procedures are satisfactory even for small samples. The results are illustrated using practical examples.