Statistical Methods Of Stratified Cluster Sampling On Sensitive Questions Survey And Its Application

Objective: This paper is one part of the study sampling design on sensitive questions survey which is supported by National Natural Science Foundation of China. Before the study, the multichotomous and quantitative sensitive question randomized response technique (RRT) researches were developed and studied with the restriction that the sample was selected through simple random sampling. In the applications of RRT, the respondents were restricted to a small population coming from simple random sampling or the formulas 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. the sum model and the multiplication model, to explore the 10 methods to investigate sensitive issues with the sample selected by cluster sampling and stratified cluster sampling. In this way, we can provide scientific and effective methods and formulas on sensitive questions under the condition of stratified clustered sampling from large population.Method: The theory of five RRT models, cluster sampling and stratified cluster sampling techniques, Cochran's classic sampling theory, probability, variance characteristics and evaluative reliability and validity were employed.Result: The formulas have been derived for the estimator of the population proportion and its variance when the five RRT models are applied to investigate sensitive questions with the sample selected by cluster sampling and stratified clustered sampling. Investigations on the grade and number of academic dishonesty have been conducted and the college students in the Dushu Lake campus of Soochow University were interviewed from September 2007 till October 2007. We adopted the stratified cluster sampling and select 20 clusters of undergraduates and 18 clusters of postgraduates and the number of subjects was 1,734. The multiple-grade sensitive question model and the other three RRT models (the sum model, the multiplication model and the non-related question model) were applied to obtain the data of academic dishonesty, respectively. With help of the formulas we derived, the estimator of the population proportion and its variance are calculated. The estimated populated proportions of those who have no times, 1~2 times and greater than 2 times of academic dishonesty are 69.06%, 19.59% and 11.28%. The mean number of academic dishonesty captured by the other three quantitative sensitive question RRT models is 1.1639, 1.1190, and 1.0573, respectively.Conclusion: Analyzing the correlationship between results of same subjects and the same target (mean number of academic dishonesty) captured by the three quantitative sensitive questions RRT models, we get that the r value is greater than 0.88 and the P value is less than 0.001, which provide high congruence reliability. 30 experts all over the country evaluated the survey methods and research contents and the eligible rate was 100%. So we can draw the conclusion that the results of the methods and formulas are scientific, valid and reliable. The randomized response technique has an extensive application in sensitive issue investigation on a large scale.