A Method for Evaluating Exposure to Nitrous Oxides by Application of Lognormal Distribution
A Method for Evaluating Exposure to Nitrous Oxides by Application of Lognormal Distribution: S.S. Borjanovic, et al. Department of Work Physiology, Institute of Occupational Health “Dr Dragomir Karajovic”—A lognormal distribution adequately describes exposure to nitrous oxides in a work environment. The aim of this paper was to assign to the measured data a certain degree of variability which defines the interval in which real concentrations can be found with a given probability. Exposures may be evaluated by using estimates of the geometric mean (GM) and the geometric standard deviation (GSD), i.e. central value and dispersion index, to calculate the confidence interval (Cl) around the mean exposure and compare this interval to the occupational exposure limit. The concentration of nitrous oxides (114 random temporal measurements covering all three shifts, during 6 consecutive days) on coated electrode welding in a car manufacturing plant, was determined with colourimetric direct reading method. Statistical analysis (chi‐square and Kolmogorov‐Smirnov goodness of fit tests, lognormal and Gaussian distribution fitting and Q‐G plots) was performed. The distribution of the nitrous oxides concentration in the work environment studied closely resembled that of lognormal distribution. The geometric mean was 4.098 mg/m3, median 4.00 mg/m3, geometric standard deviation 1.829 and 95% confidence interval 3.66‐4.58 mg/m3. It is possible to apply the computed GSD for evaluation of exposure limits to nitrous oxides in any other work environment, even with only a few measurements.
Generalized P-Values and Confidence Intervals: A Novel Approach for Analyzing Lognormally Distributed Exposure Data
The problem of assessing occupational exposure using the mean of a lognormal distribution is addressed. The novel concepts of generalized p-values and generalized confidence intervals are applied for testing hypotheses and computing confidence intervals for a lognormal mean. The proposed methods perform well, they are applicable to small sample sizes, and they are easy to implement. Power studies and sample size calculation are also discussed. Computational details and a source for the computer program are given. The procedures are also extended to compare two lognormal means and to make inference about a lognormal variance. In fact, our approach based on generalized p-values and generalized confidence intervals is easily adapted to deal with any parametric function involving one or two lognormal distributions. Several examples involving industrial exposure data are used to illustrate the methods. An added advantage of the generalized variables approach is the ease of computation and implementation. In fact, the procedures can be easily coded in a programming language for implementation. Furthermore, extensive numerical computations by the authors show that the results based on the generalized p-value approach are essentially equivalent to those based on the Land's method. We want to draw the attention of the industrial hygiene community to this accurate and unified methodology to deal with any parameter associated with the lognormal distribution.
Environmental versus analytical variability in exposure measurements.
Measurements of 8-hr time-weighted average (TWA) exposures are subject to environmental variability and collection and analytical error. Environmental variability can be represented by the geometric standard deviation (GSD) of the lognormally distributed 8-hr TWAs; analytical variability can be represented by the coefficient of variation (CV) of the normally distributed collection and analytical errors. A mathematical expression is derived for the variance of the measured 8-hr TWAs as a function of the GSD of the true daily average exposures and the total CV of the industrial hygiene method used in monitoring. For typical values of the GSD and CV, environmental variability is far more important than analytical variability in determining the variance of the measured 8-hr TWAs. A resulting policy implication is that the Occupational Safety and Health Administration inappropriately focuses on analytical variability when determining compliance with its permissible exposure limits.