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Sample size formulae for estimating the true arithmetic or geometric mean of lognormal exposure distributions.

Am Ind Hyg Assoc J 1995 Mar; 56(3):219-225
Simple formulas were developed to calculate the approximate size of sample needed to estimate either the true arithmetic or true geometric mean of a lognormal distribution to within a specified accuracy with a specified level of confidence. Such formulas could be used in prospective and cross sectional occupational health studies, and for developing an exposure database for studies on the effects of exposure on worker health. Computer simulation was used to validate the formulas. Results indicated that large sample sizes may be required if existing parameter estimates are derived from a limited number of prior measurements, or if the true exposure distribution has a large geometric standard deviation. The author suggests that reasonably accurate exposure data should be collected during the pilot study phase of a prospective study, as the accurate estimation of the true arithmetic mean or geometric mean of a single exposure group can require a sizable commitment in sampling resources. When the required accuracy is reduced, the size of the samples is also significantly lessened. To obtain an accuracy on the order of many medical measurements the sample sizes needed can be quite large. By performing a pilot study in which reasonably precise initial estimates of the distribution parameters for each exposure group are obtained, by grouping workers into exposure groups where the group geometric standard deviation is 2 or less, and by keeping the desired accuracy at a reasonable level, the total sample burden can be reduced.
NIOSH-Author; Epidemiology; Exposure-levels; Sampling-methods; Mathematical-models; Occupational-exposure; Industrial-hygiene
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American Industrial Hygiene Association Journal