Abstract #300972

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JSM 2003 Abstract #300972
Activity Number: 342
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 9:00 AM to 10:50 AM
Sponsor: Section on Health Policy Statistics
Abstract - #300972
Title: On a Number of Flawed Sample Size Formulas in the California Hazardous Materials Laboratory User's Manual
Author(s): Chamont Wei-Hong Wang*+ and Wendy Woodring
Companies: College of New Jersey and The College of New Jersey
Address: Dept. of Mathematics and Statistics, Trenton, NJ, 08628-0718,
Keywords: sample size ; simulation ; noncentral chi-square distribution ; noncentral F distribution ; marginal probability density
Abstract:

The Hazardous Materials Laboratory, located in Berkeley, California, has published a User's Manual as instructional documentation for its employees. This lab is responsible for testing ground, water, and air for high concentrations of contaminants, and the employees use this manual to assist them in the testing process. However, some formulas used in the current manual are flawed. The formulas are designed to calculate the sample size needed to make an accurate measure of contamination. Yet, a problem occurs in the lab's formulas because they use denominators containing random variables, which inevitably take on different values and hence produce erratic results for sample sizes. Such erratic results are depicted in computer simulations and graphs produced by SAS. In addition, we use SAS to compare the behaviors of a standard sample size formula and a formula used in the California Hazardous Materials Laboratory. To go beyond computer simulations, the probability density functions involved in both the lab's formula and the proven one were analyzed mathematically, showing the profound difference between the flawed equation and the standard one.

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