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

Objective: When it comes to sensitive problem, respondents often refuse to answer or providing false answer. In order to obtain the real answers of sensitive problem and protect the privacy of respondents, randomized-response models proposed by Warner(1965) and Greenberg(1969) presumed that two yes/no questions were provided for each respondent and that a randomization device was used to determine which question would be answered.It provides a method of sensitive question survey, such as cheating in the exam, tax loophole, drugs, and so on. The randomized-response technique (RRT) can be an effective survey method to find such estimates because individual anonymity is preserved. Then it gradually formed a special investigation of sensitive problem, which was randomized response technology.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 eight RRT models, e.g. Warner model ,Simmons model, double irrelevant problem model and the improved RRT model, to explore the 8 methods to investigate sensitive issues with the sample selected by two-stage sampling. In this way, we can provide scientific and effective methods and formulas on sensitive questions under the condition of two-stage sampling from large population. Method: Two-stage sampling techniques, Cochran's classic sampling theories, total probability formulae, properties of the variance were applied to eight RRT models. In addition, reliability and validity were used to evaluate the statistical methods. Formulae were deduced for the estimator of the population proportion and its estimated variance for eight RRT model used for sensitive questions survey in two-stage sampling. There were 620 person which were drawn from a sample of MSM in Beijing in 2010. And it was successfully applied three RRT model to obtain their sensitive characters. Face validity and content validity of methods and formula of this study was evaluated by 30 selected nationwide experts in related disciplines. After seeking appropriate criterion variable, we evaluated the criteriaon validity of methods and formula about three RRT models in two-stage sampling.Result:1. Sampling technology theory was combined with the theory of RRT in this study, and formulae were deduced for the estimator of the population proportion and its estimated variance for eight RRT model used for sensitive questions survey in two-stage sampling.2. The investigation methods and the statistical formula of three RRT model were applied to obtain the results of ten sensitive questions of MSM(men who have sex with men ) in Beijing. The results of ten sensitive questions are as follows:2.1 The proportion of anal sex with condoms was 78.65%.2.2 The proportion of condoms usage in the whole anal sex, which was classified into never used, sometimes used, every time used and no anal sex, was 7.2055%, 28.8687%, 55.9630% and 7.9627% respectively last month.2.3 The proportion of average charge of commercial sex of MSM, which was classified into less than 200 RMB, 200 to 399 RMB, 400 to 599 RMB, more than 600 RMB and no commercial sex, was 3.2988%, 4.9569%, 2.6000%, 5.8566% and 87.8276% respectively last year.2.4 The proportion of results of HIV test of MSM, which were classified into positive, negative, checked but not know the results, a uncertain results and not checked, was 8.0272%, 72.4350%, 8.2792%, 5.2110% and 6.0476 respectively last year .2.5 The results of STD test were classified into five types, which were positive, negative, checked but not know the results, a uncertain results and not checked. The proportion of five results was 15.1704%,67.9019%,4.1940%,5.4319% and 7.3017% respectively last year.2.6 The proportion of way(up to ejaculation orgasm) of sexual behavior, which was anal sex, oral sex and other sexual behavior for MSM, were 64.6453%, 18.7388% and 16.6159% respectively.2.7 The proportion of Condom breakage, which was classified into broken, no damage and not use of condom for MSM, was 12.4620%, 67.7727, and 19.7653 respectively.2.8 The average age of MSM was 21.9747 years in the first time.2.9 The average number of different sexual partners of MSM was 3 person every month for per person .2.10 It was 4.8 times of the number of MSM on average monthly.3. Thirty 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 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.Conclusion:The methods and corresponding formulas on sensitive questions survey with the sample selected by two-stage sampling were feasible. The AIDS and STD high-risk behaviors of MSM in Beijing, such as no fixed sexual partners, anal sex, the low proportion of full use of condoms and high proportion of condoms breakage, should aroused the great concerns of our government and health sector.