Waters M A, Selvin S, Rappaport S M
Department of Biomedical and Environmental Health Sciences, University of California, Berkeley 94720.
Am Ind Hyg Assoc J. 1991 Nov;52(11):493-502. doi: 10.1080/15298669191365108.
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.
对数正态分布常用于职业暴露研究，但对数正态性假设却很少得到验证。在评估对数正态模型的适用性时缺乏严谨性，部分原因在于应用正式的拟合优度检验存在困难。当尝试评估模型拟合度时，职业卫生学家依赖于暴露数据的概率绘图，而非正式的统计方法。这项工作的目标是为职业卫生学家开发一种简单的定量评估方法，以补充概率绘图法。本文描述了一种基于分布均值的两个估计量之比的对数正态模型拟合优度度量方法，这两个估计量分别是均值的简单或直接估计值以及对数正态分布均值的最大似然估计值。这种新的度量方法，即比率度量，是许多职业卫生学家常规计算的简单扩展。将比率度量的结果与概率绘图法以及两种传统的拟合优度度量方法（Lilliefors检验和W检验）针对两个职业暴露数据集进行了比较。对于各种职业暴露数据，比率检验和W检验的结果具有可比性，但Lilliefors检验过于保守，无法检测出几例明显偏离对数正态性的情况。对于职业卫生学家通常遇到的数据范围，比率度量是Lilliefors检验的有效替代方法，并且比W检验更易于执行。鼓励职业卫生学家在评估对数正态假设时将比率度量与概率绘图法结合使用。
