The Precision Associated with the Sampling Frequency of Log-Normally Distributed Air Pollutant Measurements

Abstract

The frequency of air monitoring necessary to characterize an air pollutant for a given time period and area is an important problem. This paper deals with the precision of measuring an air pollutant concentration. Past research has shown that the distribution of many air pollutants can be described as log-normal. Using this result equations have been developed that predict the precision of the sample mean of the air pollutant as a function of: the frequency of sampling, the standard deviation of the logarithms of the air pollution measurements, and the level of confidence. An illustration is given to demonstrate their use. The equations are used to compare sampling plans. Tables are presented showing the precision associated with five sampling plans, for three geometric standard deviations, for three levels of confidence, and five periods of time over which the sampling plan is employed.

In an Appendix a mathematical development is presented showing the theoretical derivation of the equations. With these equations the precision of a sampling plan can be determined for any level of confidence or period of time. All that is needed is an estimate of the geometric standard deviation for the air pollution measurements.

Finally, the theoretical model is applied to air monitoring data that were collected at Roselawn School in Cincinnati, Ohio, between January 3, 1968, and April 1, 1968. The 90-day period was divided into three 30-day periods. All possible samples of size three were taken from each of the 30-day periods and their means and confidence intervals were calculated. The number of times the confidence intervals contained the true means was determined. The actual number of samples accepted as having contained the true mean, for the 80, 90, 95, and 9 9% level of confidence compared favorably with the theoretical. It is concluded that the model adequately described the behavior of air pollutants.