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TESTING FOR DIFFERENCES BETWEEN CUMULATIVE DISTRIBUTION FUNCTIONS FROM COMPLEX ENVIRONMENTAL SAMPLING SURVEYS
Citation:
Kincaid, T. M. TESTING FOR DIFFERENCES BETWEEN CUMULATIVE DISTRIBUTION FUNCTIONS FROM COMPLEX ENVIRONMENTAL SAMPLING SURVEYS. Presented at Joint Statistical Meetings, Indianapolis, IN, August 13-17, 2000.
Description:
The U.S. Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP) employs the cumulative distribution function (cdf) to measure the status of quantitative variables for resources of interest. The ability to compare cdf's for a resource from, say, two different subregions is an inferential situation that occurs frequently for EMAP data. Although extensive methodology exists for inference about cdf's in the context of simple random sampling, there is relatively little literature that addresses inference about cdf's for complex sampling designs such as those used by EMAP. Inferential procedures that incorporate features from a complex sampling design are presented. Specifically, the Wald statistic and two Chi-squared statistics suggested by Rao and Scott (1981) are developed for testing differences between cdf's. A simulation study to investigate power of the inferential procedures is presented. For comparison, the study includes the Kolmogorov-Smirnov, Cramer-von Mises, and Pearson Chi-squared test statistics. The study shows that, under a wide range of circumstances, the Wald statistic and the Chi-squared statistics suggested by Rao and Scott provide superior power to detect differences between cdf's in comparison to the procedures that assume simple random sampling.