Calculation and Allocation of Sample Size of Post-Enumeration Survey for Population Census
This paper aims to establish a new system for calculating and allocating the sample size of post-enumeration surveys,in order to solve the problem that some governmental statistical departments in some countries do not strictly follow the sam-pling theory to calculate and allocate the sample size of post-enumeration surveys.To achieve the goal,mathematical models and parameter estimation methods are used to calculate the design effects of the 2020 sampling plan(Q)and the sample size of the 2030 simple sampling plan(S),and the two are multiplied to obtain the sample size of the 2030 sampling plan(Q).The theoretical and empirical results show that the design effect of the complex sampling plan(Q)in 2020 is 0.91,indicating that this sampling plan is better than that of the simple sampling plan(S);the single-system estimator of the simple sampling plan(S)need not be built in the homogeneous population stratum,while the combined three-system estimator of the sampling plan(Q)must be built in the homogeneous population stratum;the stratified jack-knife method is suitable for approximately calculating the sampling variance of the com-bined three-system estimator;the proportional distribution method is more suitable for the sample size allocation of the post-enumeration survey than the optimal allo-cation method.The innovation lies in proposing a design effect formula for sampling variance estimators based on combined three-system estimator and single-system es-timator,and providing the mathematical logic for calculating sample size indirectly by design effect.This thesis is expected to serve as an important reference for the National Statistical Bureau to formulate the sample size calculation and allocation plan for the post-enumeration survey in 2030,or be adopted and applied.
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