Simple Procedures for Calculating Confidence Intervals around the Sample Mean and Exceedance Fraction Derived from Lognormally Distributed Data

Abstract

The determination that a work environment is acceptable or unacceptable is often based upon the calculation of the mean exposure and/or exceedance fraction [i.e., the fraction of measurements expected to exceed an occupational exposure limit (OEL)] for an employee or exposure group. The purpose of this article is to introduce simplified procedures for calculating accurate estimates of the 95 percent lower confidence limit (LCL) and 95 percent upper confidence limit (UCL) for (1) the sample arithmetic mean and (2) the sample exceedance fraction for lognormally distributed exposure data. The procedure for the arithmetic mean is adapted from Land's procedure for calculating exact confidence intervals around the mean of lognormally distributed data. The procedure for the exceedance fraction is based on the Odeh and Owen confidence limits for a proportion in one tail of the normal distribution. Both procedures are graphically based and require no hard-to-find references. The two 95 percent confidence limits can be used to form a 90 percent confidence interval (5% is in each tail). The 90 percent confidence intervals indicate the degree of uncertainty in the point estimates of the mean and exceedance fraction. (This uncertainty is a function of both the inherent environmental variability in exposures and the sample size.) The resulting confidence limits can also be used for hypothesis tests by simply comparing the UCL or LCL to target values such as a long-term average OEL or an acceptable exceedance fraction. These procedures are simple, accurate, and can be used in lieu of (1) the means test procedures of the American Industrial Hygiene Association (AIHA 1991 monograph on exposure assessment) and Rappaport and Selvin (Am. Ind. Hyg. Assoc. J. 48:374-379, 1987) and (2) the exceedance fraction tests described by Tuggle (Am. Ind. Hyg. Assoc. J. 43:338-346, 1982) and Leidel and Busch (Patty's, Vol. 3A, 1994).