A measure of goodness-of-fit for the lognormal model applied to occupational exposures

Abstract

The lognormal distribution is often applied to occupational exposures, yet the assumption of lognormality is rarely verified. This lack of rigor in evaluating the appropriateness of the lognormal model has resulted, in part, from the difficulty of applying formal goodness-of-fit tests. When evaluation of model fit has been attempted, occupational hygienists have relied upon probability plotting of exposures rather than upon formal statistical methods. The goal of this work was to develop for the occupational hygienist a simple quantitative evaluation to supplement the probability plot. A measure of goodness-of-fit to the lognormal model based on the ratio of two estimators of the mean of the distribution, the simple or direct estimate of the mean and the maximum likelihood estimate of the mean of a lognormal distribution, is described. This new measure, the ratio metric, is a simple extension of calculations made routinely by many occupational hygienists. Results from using the ratio metric were compared to probability plotting and to two traditional measures of goodness-of-fit, the Lilliefors test and the W test, for two occupational exposure data sets. The results of the ratio and W tests are comparable for a variety of occupational exposure data, but the Lilliefors test is overly conservative and does not detect several cases of gross deviations from lognormality. The ratio metric is an effective alternative to the Lilliefors test and is easier to perform than the W test for the range of data usually encountered by occupational hygienists. Occupational hygienists are encouraged to use the ratio metric in conjunction with the probability plot in evaluating the lognormal assumption.