关键词: 设计效应, 超总体模型, 类集效应, 加权效应, 组合效应

Abstract: This paper studies the calculation of Design Effects in the sample surveys based on the super-population model. Firstly, taking the random effect model as a basis, the study clarifies the super-population models corresponding to SRS, two-stage sampling, unequal probability sampling and stratified sampling. Furthermore, through these Super-population Models, the formulas of the design effects of simple factors such as stratification, clustering and weighting，and the formulas of the combined design effects of multi-factors are derived with the corresponding estimators. The formulas show that the combined design effects of multiple factors is equal to the product of the design effect of a simple factor. Finally, the Monte Carlo simulation is conducted on the relationship between the theoretical value, the estimated value and the true value of the design effects, and their relative bias and relative mean square errors are evaluated. This research is of a guiding significance for the correct calculation and the application of the design effects in the complicated sampling.

Key words: Design Effect, Super-population Model, Clustering Effect, Weighting Effect, Combination effect.