分类敏感问题分层二阶段抽样调查的统计方法及应用
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摘要
目的:本文是国家自然科学基金项目《敏感性问题的抽样调查设计》(编号30571620)研究结果的一部分。本项目研究前,国内外对二分类敏感问题和多分类敏感问题抽样调查的统计方法研究,仅仅局限于简单随机抽样,实际应用也主要局限于小范围特殊人群小样本的简单随机抽样调查,或将分层简单随机抽样、(分层)整群抽样、(分层)多阶段抽样调查资料误用简单随机抽样调查有关公式来统计分析。本文选定了二分类敏感问题Warner随机应答模型、Simmons随机应答模型和改进的随机应答模型以及多分类敏感问题单一样本随机应答模型、间接随机应答模型五种RRT(Randomized Response Technique, RRT)模型,对五种RRT模型与二阶段抽样、分层二阶段抽样组合的10种调查方法及其统计公式进行探讨,并对所研究的调查方法及其统计公式进行了信度评价与效度评价,为二分类敏感问题和多分类敏感问题较大规模的抽样调查提供了科学的调查方法及有效、可靠的统计公式。
方法:在本文研究中,五种RRT模型,二阶段抽样、分层二阶段抽样方法,Cochran的经典抽样理论、全概率公式、方差的性质等概率论与数理统计学理论方法及信度评价、效度评价的方法被采用。
结果:本文分别在二分类敏感问题Warner模型、Simmons模型和改进的RRT模型以及多分类敏感问题单一样本RRT模型、间接RRT模型五种RRT模型与二阶段抽样、分层二阶段抽样两种抽样方法组合的10种调查方法下,推导出敏感问题总体比例的估计量及其方差、估计方差的计算公式。于2007年10月至2007年12月,采用分层二阶段抽样(各层内即为二阶段抽样)的方法,在苏州大学新校区本科生层和研究生层中各随机抽取5个学院,从被抽中学院内随机抽取部分学生作为调查对象(共计1552名学生),分别运用二分类敏感问题Warner模型、Simmons模型及改进的RRT模型调查学生婚前性行为发生比例,运用多分类敏感问题单一样本RRT模型调查上两个学期(2006-2007学年)考试作弊程度。运用本文推导的分层二阶段抽样条件下有关统计量的计算公式,在三种模型下估计出苏州大学新校区学生婚前性行为发生比例分别为18.52%、18.99%和17.71%;上两个学期考试作弊次数为0、1-2次、>2次的学生比例分别为61.25%、22.31%和16.44%。
结论:对同一批调查对象的同一调查指标(是否发生婚前性行为),三种二分类敏感问题RRT模型的分层二阶段抽样调查方法的调查计算结果基本一致,重测信度与和谐信度均较高(各相关系数大于0.80,P <0.01);经全国范围内30名相关学科专家对各调查方法进行的表面效度与内容效度评价,优良一致率达100%;将三种二分类敏感问题RRT模型分层二阶段抽样调查结果p分别与效度准则指标p0作假设检验,p与p0的差异均无统计学意义(P>0.05),准则效度较好;表明本文研究的调查方法及其统计计算公式科学、可靠、有效,具有广泛的应用前景。
Objective: This paper is a part of the study sampling design on sensitive questions survey which is supported by National Natural Science Foundation of China. Before the study, researches of randomized response technique (RRT) for dichotomous and multichotomous sensitive questions were developed and studied with the restriction that the sample was selected through simple random sampling. In the applications of RRT, respondents were restricted to a small population coming from simple random sampling or the formulae for simple random sampling were abused when the sample was selected by stratified sampling, cluster sampling or other relatively complicated sampling methods. In this regard, we select five RRT models, e.g. Warner model ,Simmons model and the improved RRT model, to explore the 10 methods to investigate sensitive issues with the sample selected by two-stage sampling and stratified two-stage sampling. In this way, we can provide scientific and effective methods and formulae on dichotomous and multichotomous sensitive questions survey under the situation of relatively complicated sampling such as two-stage sampling and stratified two-stage sampling from a large population.
Method: Two-stage sampling and stratified two-stage sampling techniques, Cochran’s classic sampling theories, total probability formulae, properties of the variance were applied to five RRT models.In addition, reliability and validity were used to evaluate the statistical methods.
Result: Formulae were deduced for the estimator of the population proportion and its estimated variance for Warner model, Simmons model and the improved RRT model used for dichotomous sensitive questions survey in two-stage sampling and stratified two-stage sampling. With the help of those formulae, the estimator of the population proportion and its estimated variance of those who have had premarital sex in Dushu Lake campus of Soochow University were calculated.The results got by the three RRT models were 18.52%, 18.99% and17.71%,respectively.
Formulae were also deduced for the estimator of the population proportion and its estimated variance for two RRT models which are used for multichotomous sensitive questions survey in two-stage sampling and stratified two-stage sampling. With the help of those formulae,the estimator of the population proportion and its estimated variance of the grade of academic dishonesty among students in Dushu Lake campus of Soochow University in recent two semesters were calculated. The estimated populated proportions of those who had no times, 1~2 times and greater than 2 times of academic dishonesty were 61.25%, 22.31% and 16.44%, respectively.
Conclusion: Results of the same item (proportion of premarital sex) of the same subjects got by the three dichotomous sensitive questions RRT models are almost consistent, with high test-retest reliability and congruence relaiability (correlation coefficient r > 0.80 , P < 0.01). 30 experts all over the country evaluated the face validity and content validity of the survey methods , the rate of“excellent”and“good”was 100%. Comparing the results p got by the three dichotomous sensitive questions RRT models with the valid criterion p0, there are no statistically significant difference between p and p0. So we can draw the conclusion that our survey methods and corresponding formulae are scientific, reliable and valid. The randomized response technique has an extensive application in sensitive questions survey on a large scale.
方法:在本文研究中,五种RRT模型,二阶段抽样、分层二阶段抽样方法,Cochran的经典抽样理论、全概率公式、方差的性质等概率论与数理统计学理论方法及信度评价、效度评价的方法被采用。
结果:本文分别在二分类敏感问题Warner模型、Simmons模型和改进的RRT模型以及多分类敏感问题单一样本RRT模型、间接RRT模型五种RRT模型与二阶段抽样、分层二阶段抽样两种抽样方法组合的10种调查方法下,推导出敏感问题总体比例的估计量及其方差、估计方差的计算公式。于2007年10月至2007年12月,采用分层二阶段抽样(各层内即为二阶段抽样)的方法,在苏州大学新校区本科生层和研究生层中各随机抽取5个学院,从被抽中学院内随机抽取部分学生作为调查对象(共计1552名学生),分别运用二分类敏感问题Warner模型、Simmons模型及改进的RRT模型调查学生婚前性行为发生比例,运用多分类敏感问题单一样本RRT模型调查上两个学期(2006-2007学年)考试作弊程度。运用本文推导的分层二阶段抽样条件下有关统计量的计算公式,在三种模型下估计出苏州大学新校区学生婚前性行为发生比例分别为18.52%、18.99%和17.71%;上两个学期考试作弊次数为0、1-2次、>2次的学生比例分别为61.25%、22.31%和16.44%。
结论:对同一批调查对象的同一调查指标(是否发生婚前性行为),三种二分类敏感问题RRT模型的分层二阶段抽样调查方法的调查计算结果基本一致,重测信度与和谐信度均较高(各相关系数大于0.80,P <0.01);经全国范围内30名相关学科专家对各调查方法进行的表面效度与内容效度评价,优良一致率达100%;将三种二分类敏感问题RRT模型分层二阶段抽样调查结果p分别与效度准则指标p0作假设检验,p与p0的差异均无统计学意义(P>0.05),准则效度较好;表明本文研究的调查方法及其统计计算公式科学、可靠、有效,具有广泛的应用前景。
Objective: This paper is a part of the study sampling design on sensitive questions survey which is supported by National Natural Science Foundation of China. Before the study, researches of randomized response technique (RRT) for dichotomous and multichotomous sensitive questions were developed and studied with the restriction that the sample was selected through simple random sampling. In the applications of RRT, respondents were restricted to a small population coming from simple random sampling or the formulae for simple random sampling were abused when the sample was selected by stratified sampling, cluster sampling or other relatively complicated sampling methods. In this regard, we select five RRT models, e.g. Warner model ,Simmons model and the improved RRT model, to explore the 10 methods to investigate sensitive issues with the sample selected by two-stage sampling and stratified two-stage sampling. In this way, we can provide scientific and effective methods and formulae on dichotomous and multichotomous sensitive questions survey under the situation of relatively complicated sampling such as two-stage sampling and stratified two-stage sampling from a large population.
Method: Two-stage sampling and stratified two-stage sampling techniques, Cochran’s classic sampling theories, total probability formulae, properties of the variance were applied to five RRT models.In addition, reliability and validity were used to evaluate the statistical methods.
Result: Formulae were deduced for the estimator of the population proportion and its estimated variance for Warner model, Simmons model and the improved RRT model used for dichotomous sensitive questions survey in two-stage sampling and stratified two-stage sampling. With the help of those formulae, the estimator of the population proportion and its estimated variance of those who have had premarital sex in Dushu Lake campus of Soochow University were calculated.The results got by the three RRT models were 18.52%, 18.99% and17.71%,respectively.
Formulae were also deduced for the estimator of the population proportion and its estimated variance for two RRT models which are used for multichotomous sensitive questions survey in two-stage sampling and stratified two-stage sampling. With the help of those formulae,the estimator of the population proportion and its estimated variance of the grade of academic dishonesty among students in Dushu Lake campus of Soochow University in recent two semesters were calculated. The estimated populated proportions of those who had no times, 1~2 times and greater than 2 times of academic dishonesty were 61.25%, 22.31% and 16.44%, respectively.
Conclusion: Results of the same item (proportion of premarital sex) of the same subjects got by the three dichotomous sensitive questions RRT models are almost consistent, with high test-retest reliability and congruence relaiability (correlation coefficient r > 0.80 , P < 0.01). 30 experts all over the country evaluated the face validity and content validity of the survey methods , the rate of“excellent”and“good”was 100%. Comparing the results p got by the three dichotomous sensitive questions RRT models with the valid criterion p0, there are no statistically significant difference between p and p0. So we can draw the conclusion that our survey methods and corresponding formulae are scientific, reliable and valid. The randomized response technique has an extensive application in sensitive questions survey on a large scale.
引文
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