Comparison of survey estimates of the finite population variance

The Environmental Monitoring and Assessment Program (EMAP) of the U.S. Environmental Protection Agency has conducted several probability surveys of aquatic resources. Such surveys usually have unequal probability of including population elements in the sample. The Northeast lakes survey, which motivated this study of variance estimation, was such a survey. We examine ten estimators for the finite population variance using a Monte Carlo factorial experiment that considers three population characteristics. The results show that the correlation between the inclusion probabilities and the response is the most important factor that differentiates the estimators. Under conditions of low correlation (approximately < 0.4), a common feature in environmental surveys, the sample variance is best, elsewhere, two ratio estimators, one based on consistency and the Horvitz-Thompson Theorem (HT) and the other based on the Yates-Grundy form, behave similarly and best.