数量特征敏感问题加法模型分层二阶段抽样样本大小研究及其应用

The Method to Estimate the Sample Size for Quantitative Sensitive Questions in Stratified Two- Stage Sampling and its Application

【提要】目的为敏感问题复杂抽样调查提供科学的样本大小估计公式。方法使用哥西不等式、求条件极小值点等方法，从数学上推导出样本大小计算公式。对北京市男男性行为人群进行了预调查，为计算正式调查的样本大小估计出相关统计量的数值。结果对敏感问题加法模型分层二阶段抽样，推导出在限定抽样误差的值使调查费用达到最小和限定调查费用的值使抽样误差达到最小时所需的样本大小估计公式；在北京市男男性行为人群正式调查中，在限定抽样误差V（μ^-）的值V=0．0105使调查费用达到最小，第一层（15～29岁）需抽取的区县数n11=7（个），平均每个区县需抽取的男男性行为者人数为n21^-=115人；第二层（30～49岁）需抽取的区县数n12=7（个），平均每个区县需抽取的男男性行为者人数为n22^-=107人。结论本文提供的数量特征敏感问题加法模型分层二阶段抽样调查样本大小估计公式，具有较大的理论意义和实际应用价值。

Objective To deduce the formulas of sample size to minimize the costs of taking the samples for specified values of the sampling errors and to minimize the sampling errors for specified costs for additive model of quantitative sensitive questions in two - stage stratified sampling. Methods The minimum method and the Cauchy - Schwards inequality were ap- plied. Results The formulas of sample size for additive model of quantitative sensitive questions in stratified two - stage sam- pling were deduced and were employed successfully in survey study of the MSM in Peking about the number of the different sex- ual partners per month per person. Conclusion