Mean Testing: II. Comparison of Several Alternative Procedures

Abstract

The purpose of this article is to compare six procedures for comparing the estimated mean of data drawn from a lognormal distribution to a long-term average occupational exposure limit (LTA OEL): the standard t-test, the American Industrial Hygiene Association's (AIHA's) mean test, the modified Cox mean test, Rappaport and Selvin's mean test, Lyles and Kupper's mean test, and Land's mean test (a procedure based on Land's exact confidence intervals). In principle, all of these procedures, with one exception, can be used as either an employer's test or an inspector's test. Computer simulation was used to determine (1) the actual confidence level for each procedure for the situation where exposures are lognormally distributed and the true mean equals an LTA OEL, and (2) the power of each procedure when the true mean is different from the LTA OEL. Land's mean test consistently provided confidence levels near the nominal confidence level for all sample sizes and geometric standard deviations (GSDs) evaluated. Furthermore, at any given true long-term average above the LTA OEL the alternative procedures were, in general, more likely to result in the false conclusion that the work environment was acceptable. For the employer's test, Lyles and Kupper's test closely approximated Land's test. Regarding the inspector's test, Rappaport and Selvin's mean test and the AIHA mean test came closest to Land's test. The author recommends Land's mean test because it delivers the advertised confidence level regardless of sample size and underlying GSD, and for most situations it is the more powerful test for detecting true mean exposures greater than the LTA OEL.