The distribution of Student's t-statistic for small samples from lognormal exposure distributions

To assess compliance with industrial hygiene exposure criteria (e.g., TLVs), it may be necessary to perform statistical tests of hypotheses based on relatively small samples. For pollutants with long biological half-lives, the parameter most relevant for determining the risk faced by workers is the long-term arithmetic average concentration of the pollutant. In industrial environments it is common for pollutant concentrations to be approximately lognormal. Unfortunately, when based on small samples from lognormal distributions, the ordinary Student's t-statistic has some undesirable characteristics which are not recognized widely by practicing industrial hygienists. The difficulties in using the ordinary Student's t-statistic to evaluate the average exposure have been demonstrated. The properties of alternative test statistics have been explored. Some general observations on the implications of these findings have been made.