The RRT Model For Inquiring Multichotomous Sensitive Questions Under Cluster Sampling And Assessment Of Validity And Reliability Through Computer Simulation

Objective: Respondents often refuse to answer or providing a false answer facinga sensitive question. In order to solve that problem, randomized response models wasproposed by Warner in1965(Warner model). That method presumed two yes/noquestions were provided for each respondent and a randomization device was used toprotect the privacy of answers. And then, a lot of statisticians have devoted toimprovement of Randomized Response Technique (RRT). So there are series of RRTmodels resolving different sensitive questions today.Before this paper, researches of RRT were performed with rigorous restriction thatthe sample was selected through simple random sampling. It does not apply tolarge-scale situation. What’s more, researchers often concentrate on dichotomous andquantitive sensitive questions. Meanwhile, papers about validity and reliability of RRTare rare. Considering above conditions, we studied the RRT model special formultichotomous sensitive questions combining cluster sampling method and derivedrelevant formulas. Using the method, we also successfully investigated sensitivequestions about sexually transmitted disease (including HIV) in sex worker of Xichang.According to the results of practical survey, to assess validity and reliability of ourmethod, we sampled in theoretical population repeatedly by using computer simulation.In this way, we may provide a scientific and effective method for inquiringmultichotomous sensitive questions under the condition of cluster sampling (or othersampling methods combining cluster sampling) from large population.Method: Cluster sampling techniques, Cochran’s classic sampling theories, totalprobability formulae, properties of the variance was applied to multichotomoussensitive question RRT model under cluster sampling. In addition, validity andreliability were used to assess our RRT model and relevant statistical methods.Formulae were deduced for the estimator of the population proportion and its estimated variance for the RRT model under cluster sampling. There were404female sex workerswho were selected randomly in Xichang during May2011to July2011. And it wassuccessfully applied RRT model to obtain their multichotomous sensitive characters.Additionally, we used.NET software to simulate the real situation and repeatedlysampling100times in same theoretical population. Then we obtained100samples andinvestigated everyone by using multichotomous RRT model. At the same time weinvestigated same samples through Direct Question Technique (DQT) and we took itsaverage value as criterion. Finally, to assess the validity and reliability, we compared theresults of multichotomous RRT model with criterion by using chi-square test.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 itsestimated variance for RRT model used for multichotomous sensitive question survey incluster sampling.2. The investigation method and the statistical formula of the RRT model wereapplied to obtain the results of four sensitive questions of female sex workers inXichang. The results are as follows:(a) The results of STD test were classified into five types, which were not checked,an uncertain result, checked but not know the results, negative and positive. Theproportion of five results was44.8894%,4.3131%,11.0406%,33.5066%and6.2502%respectively last year.(b) The results of HIV test were classified into five types, which were not checked,an uncertain result, checked but not know the results, negative and positive. Theproportion of five results was62.2879%,6.4127%,7.2410%,23.7035%and0.3549%respectively last year.(c) The proportion of Condom breakage, which was classified into not use ofcondom, no damage and broken. The proportion of three results was1.8858%,22.1076%and76.0066%respectively in last commerical sex service.(d) The proportion of using condoms, which was classified into never used,sometimes used and always used. The proportion of three results was2.2680%,4.0022%and93.7298%respectively last month.3. According to results of Xichang, we successfully simulated investigation of RRTmethod and DQT method using computer. Comparing100results of RRT method with criterion,99results are not statistically significant different from criterion.(Chi-squaretest, a=0.05)Conclusion:1. The method and corresponding formulas on multichotomoussensitive questions survey with the sample selected by cluster sampling were feasible.2. The results of survey indicates that the situation of using condom of female sexworkers in Xichang is optimistic, but the proportions of examination for STD and HIVstill need improve.3. According simulation results, we believe the validity and reliability of ourmethod are high. So we can draw the conclusion that our survey method andcorresponding formulae are scientific, valid and reliable.