多分类敏感问题RRT的分层抽样统计方法  

Stratified Random Sampling on the Randomized Response Technique for Multi-class Sensitive Question Survey

作　　者：李旭东[1] 高歌[1] 贺志龙[1] 于明润[1] 朱宏儒[1] 王冕[1] 

机构地区：[1]苏州大学放射医学与公共卫生学院流行病与卫生统计学教研室,江苏苏州215123

出　　处：《苏州大学学报（医学版）》2009年第4期668-670,677,共4页Suzhou University Journal of Medical Science

基　　金：国家自然科学基金资助项目(30972548)

摘　　要：目的为多分类敏感性问题提供科学的调查方法及其统计量的计算公式。方法应用多分类敏感问题随机应答技术模型,分层随机抽样方法,抽样理论,全概率公式,方差的基本性质等理论和方法。结果推导出多分类敏感问题随机应答技术模型在分层随机抽样下总体比例的估计量及其估计方差的计算公式;并成功应用该调查方法及相关公式调查估计得苏州大学新校区学生近两个学期考试作弊0次、1～2次、>2次的比例分别为68.55%、19.95%、11.50%。结论多分类敏感问题随机应答技术模型下的分层随机抽样调查方法及相应的统计计算公式科学、可行。Objective To explore scientific sampling methods and corresponding formulas for mul- ti-class sensitive questions survey on stratified random sampling. Methods Randomized response tech- nique of multi-class sensitive questions and stratified random sampling were used in this paper. More- over, sampling theories, total probability formulas and properties of variance were used. Results For- mulas for the estimator of the population proportion and its variance on randomized response model of multi-class sensitive questions in stratified random sampling were deduced. Our survey methods and for- mulas on the RRT model may have a successful application for multi-class sensitive questions survey on, what students of Soochow University cheated in exams. The severity of cheating in exams was classified into three types （never, 1-2 times, 〉2 times） and the proportion was 68.55%, 19.95% and 11.50% re- spectively. Conclusion The methods and corresponding formulas of stratified random sampling on RRT for multi-class sensitive questions survey were feasible.

关 键 词：多分类变量 敏感性问题 随机应答技术 分层随机抽样 考试作弊 

分 类 号：R195.1[医药卫生—卫生统计学]