Statistical Methods For Qualitative Sensitive Questions Survey In Stratified Two-stage Sampling And Its Application

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.