三阶段抽样样本大小的研究及应用

The Method to Estimate the Sample Sizes for ThreeStage Sampling and its Application

目的为调查设计中常用的三阶段随机抽样方法寻求其样本大小估计公式。方法利用高等数学中的哥西不等式原理及求极小值方法。结果当采用三阶段随机抽样作参数估计时，在限定抽样误差使调查花费最小及限定调查花费使抽样误差最小两种情况下，推导出其最优样本大小的计算公式。结论本文首次推导出三阶段随机抽样样本大小的估计公式，在中国铁路职工医疗费用的抽样调查中取得了成功的应用效果。

Objective To deduce the formulate of the sample sizes for threestage sampling. Methods The minimun method and the CauchySchwarz inequality were applied. Results The authors deduced the formulate of the optimum sample sizes 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 threestage sampling. Conclusion The optimum sample sizes were deduced first for threestage sampling, the formulate were employed successfully in survey study of China Railway's staff about theatment cost.