The Research Of Successive Sampling For Quantitative Sensitive Questions Survey And Its Application

ObjectiveThe Sensitive Questions Survey: If the variable or individual is the sensitive questions related to personal privacy, or not recognized by society, the method of direct investigation causes partly out of self-preservation survey psychology and a certain degree of non-cooperation or even refused to answer, and survey results can not reflect the true characteristics of the overall in the sample survey. Due to the special nature of the sensitive questions, we should not study by using the conventional methods of investigation; this requires that investigators continue to make special, new scientific and feasible ways to reduce errors and improve the response rate of respondent, to make the results more realistic and reliable. In order to improve the correct response rate of the sensitive questions, by introducing randomization means, Warner achieved in the ratio occurs without exposing the privacy of the response obtained for a population of sensitive issues, and developed the RRT(Randomized Response Technique,RRT).The Sample Survey is an important statistical method of economic sociology, health and medical research, and is the basic content of statistics. With the continuous development and socio-economic changes, the overall number of respondents also continues to develop and change. On the one hand, our survey system is the establishment of the survey mainly with regular continuous survey, which the causes is the level of the overall investigation and the change in different times, the cumulative or average, especially a lot of important investigations, etc., need a continuous survey(at regular intervals repeated surveys of the same overall). On the other hand, several surveys for the fixed sample exits two serious problems: the representative sample loss and fatigue; there are also several other serious problems in a different survey re-extracted sample new and different: Preliminary data of the existing fixed samples cannot be used to made of high precision current estimate of the overall portfolio return, compared with the fixed sample, investigation costs higher, more difficult and longer and etc. In order to weigh the two issues, domestic and international statisticians have already developed the Sample Rotation Method(In the sample size the same premise, at regular intervals to replace part of the sample units).Study abroad for one-time sampling survey has more mature theory and methods,however, there are less continuous survey research, theory and method is very immature. Prior to our research team, research on continuous sample survey at home and abroad mainly confined to the study of sample rotation problem that is related to the simple random sampling survey, but little confined to the study of sample rotation problem that is related to the continuous survey under the complex sampling methods. In particular, research on the sensitive issue of continuous sample survey is empty so far. Continuous sample survey research of sensitive issue is the development trend of domestic and international health and medical statistics and statistical sampling in the study, and is the home to statistics and statistical theory and methodology of an important research topic. Based on this, the first part of this article, additive constant RRT model for quantitative sensitive questions and multiplicative RRT model for quantitative sensitive questions are combined with the research of successive sampling under simple random sampling, the research of successive sampling under simple random stratified sampling, the research of successive sampling under the cluster sampling, the research of successive sampling under stratified cluster sampling, the research of successive sampling under two-stage sampling, the research of successive sampling under stratified two-stage sampling, which produce 12 kinds of survey method. Provide an overall estimate of the mean, optimal sample rotation rate, and the regression formula for calculating the number of combinations of the estimated optimal weight. The second part of this article, we use the survey methods and statistical formulas in the first part of the study. We made the continuous sampling survey analysis to the MSM in Beijing AIDS high-risk groups, and provided accurate and reliable data for the prevention and control of AIDS. The third part of this article, to 12 kinds of survey methods for sensitive issues continuous sample and statistical formulas, respectively using computer simulation sampling large number of samples analyzed, reliability and validity were evaluated.MethodFirst, In the derivation of the design and statistical formulas to prove the method of investigation: Statistical sampling theory, the theory of regression estimation method, the Abstract The Research of Successive Sampling for Quantitative Sensitive Questions Survey and Its Application ratio estimation theory, theory of continuous survey sample rotation theoretical approaches and the basic theory of probability and statistics were applied. Six kinds of sampling methods-simple random sampling, stratified random sampling, cluster sampling, stratified cluster sampling, two-stage sampling, stratified two-stage sampling have been adopted. Additive constant RRT model for quantitative sensitive questions and multiplicative RRT model for quantitative sensitive questions are used.Second, for seven survey method—the research of successive sampling under simple random stratified sampling, the research of successive sampling under the cluster sampling, the research of successive sampling under stratified cluster sampling, the research of successive sampling under two-stage sampling, the research of successive sampling under stratified two-stage sampling, the research of successive sampling under two-stage cluster sampling the research of successive sampling under stratified two-stage cluster sampling, this paper deduced the overall average estimator and the calculating formula of variance, making the preschool discuss the methodology for this article.Third, sample rotation is an important means to improve the efficiency of the investigation, to reduce and control the sampling error. For sample rotation, it retains some of the original units and adds some new sample units, so it assembled the advantages of both the fixed sample and completely new sample, striking the balance between sampling cost and sampling precision, and has been used in domestic large-scale survey of continuous sampling. We use the survey methods and statistical formulas, making the continuous sampling survey analysis to the MSM in Beijing AIDS high-risk groups, which the data management and computing done through Excel 2003 and MATLAB software.Fourth, to 12 kinds of survey methods for sensitive issues continuous sample and statistical formulas, respectively using computer simulation sampling large number of samples analyzed, evaluating the reliability and validity. Through the evaluation of the reliability and validity, the use of the evaluation method, simulation platform, data analysis, computer programming design-related procedures and results analysis are implemented by MATLAB software.Results:First, statistical formulas are derived under 12 kinds of research of successive sampling for Sensitive Questions:1. In this paper, additive quantitative RRT model for the research of successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.2. In this paper, multiplications RRT model for the research of successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.3. In this paper, additive quantitative RRT model for the research of stratified successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.4. In this paper, multiplications RRT model for the research of stratified successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.5. In this paper, additive quantitative RRT model for the research of cluster successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.6. In this paper, additive quantitative RRT model for the research of stratified cluster successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.7. In this paper, multiplications RRT model for the research of cluster successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.8. In this paper, multiplications RRT model for the research of stratified cluster successive sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.9. In this paper, additive quantitative RRT model for the research of stratified two-stage random sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.10. In this paper, additive quantitative RRT model for the research of two-stage random sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.11. In this paper, multiplications RRT model for the research of stratified two-stage random sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.12. In this paper, multiplications RRT model for the research of two-stage random sampling for quantitative sensitive questions survey, the design of the survey methodology to derive an overall estimate of the amount of a sensitive issue and its variance and the mean number of optimal weight and optimal sample rotation rate calculation formula.Second, Beijing MSM population sample rotation under cluster sampling and stratifiedCluster sampling of continuous survey.In this paper, the characteristics of the additive model number of sensitive issues,respectively in 2010, 2012 two consecutive surveys of men aged 15-49 in Beijing for the first time behavior of the age, MSM different number of sexual partners per month, the monthly per capita number of male behavior(See Appendix 1: RRT sensitive issues of MSM survey program).Number of sensitive feature addition RRT model under the sample rotation of cluster sampling and stratified cluster sampling in continuous surveys.1 The number of sensitive issue features addition RRT model samples under rotation of cluster sampling continuous the findings(1) The first survey of MSM, the first occurrence of MSM average age of the estimated value of 20.36 years old, calculation of the estimated 2012 population for the first time in Beijing, MSM average age is 23.14 years old, Thus available in 2012 for the first time in Beijing occurred among MSM, MSM overall mean age of the 95% confidence interval is 22.22~24.02(years old).(2)The first survey estimates calculated MSM different male partners in the value of the monthly average number of 3.48 people, calculation of the 2012 different male partners of MSM in Beijing average monthly estimated number is 3.20, calculation of its variance is 0.0448. Among MSM population in Beijing last month in 2012 different number of male sexual partners overall mean 95% confidence internal is 2.79~3.61(people).To calculate the first survey MSM male behavior happened last month estimates of the average number was 5.56 times of month, Calculated in 2012 male behavior among MSM population in Beijing last month what had happened the average number of estimate is 4.30 times, Calculation of its variance is 0.1338, Available monthly occurrence frequency of the behavior of the overall MSM mean 95% confidence interval is 3.58~5.02(time) on the MSM population in Beijing in 2012.2. For additive quantitative RRT model for the research of stratified cluster successive sampling for quantitative sensitive questions survey, its results as follows:(1) The first survey in 2010, the first layer of MSM first known occurrence of MSM estimate average age is 19.664 years old, the first survey of second layers of MSM first known occurrence of MSM estimate average age is 21.10 years old; In 2012 second survey of the population of MSM 15-29 years old in Beijing city for the first time in MSM average age estimate is 21.97 years old, in 2012 second survey of the population of MSM 30-49 years old in Beijing city for the first time in MSM average age estimate is 27.11 years old, in 2012 second survey estimates of MSM population in Beijing city for the first time male behavior, the average age of the value is 24.01 years old, MSM population in Beijing city in 2012 for the first time the MSM age population mean 95% confidence interval is 23.491~24.525(years old).(2) The first survey in 2010, the first layer of gay men and male behavior of different sexual partners per capita monthly estimate of the number of 3.38 people, the calculation of the first survey of second layers of male behavior of different sexual partners per capita monthly estimate of the number of 3.50 people, the calculation of the second time survey in 2012 of MSM among 15-29 years old in Beijing city of men and male sex partners per capita monthly estimates for 2.96 people, the calculation in 2012 second survey of MSM population in Beijing city male behavior of different sexual partners per capita monthly estimate of the number of 2.30 people, MSM population in Beijing city in 2012 last month male behavior with different number of population mean 95% confidence interval is1.7987~2.81 persons).(3) The calculation of the first survey of the first layer of gay men and male behavior of monthly average estimate value is 5.12 times, the calculation of the first survey of second layers of MSM monthly average estimate value is 5.66 times, the calculation of 2012 second survey populations of MSM 15-29 years old in Beijing city for the first time in MSM monthly average estimate value is 4.61 times, the calculation of second time the crowd MSM 30-49 years old in Beijing city for the first time the MSM month average number of survey in 2012 estimates is 2.91 times, the calculation in 2012 second survey of MSM population in Beijing City MSM month average number of different sex with an estimated 3.90 times, MSM population in Beijing city in 2012 for the first time the number of MSM population mean 95% confidence interval is 3.69~4.12(times).Third, the Research of Successive Sampling for Sensitive Questions Survey,Reliability and Validity of a computer-based simulation1. Additive quantitative RRT model for the research of successive sampling under simple random sampling.The relative standard error RSE is 0.000012168, far less than the 0.01; relative absolute error RAE is 0.00036479, far less than the 0.01. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.2. Multiplications quantitative RRT model for the research of successive sampling under simple random sampling.The relative standard error RSE is 0.0007541, far less than the 0.01; relative absolute error RAE is 0.0003870 far less than the 0.01. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.3. Additive quantitative RRT model for the research of successive sampling under simple random stratified sampling.The relative standard error RSE is 0.000011415, far less than the 0.01; relative absolute error RAE is 0.00016318, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.4. Multiplications quantitative RRT model for the research of successive sampling under simple random stratified sampling.The relative standard error RSE is 0.0184, far less than the 0.01; relative absolute error RAE is 0.0021, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.5. Additive quantitative RRT model for the research of successive sampling under cluster sampling.The relative standard error RSE is 0.00082199, far less than the 0.01; relative absolute error RAE is 0.000099452, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.6. Additive quantitative RRT model for the research of successive sampling under stratified cluster sampling.The relative standard error RSE is 0.0071451, far less than the 0.01; relative absolute error RAE is 0.00037591, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.7. Multiplications quantitative RRT model for the research of successive sampling under cluster sampling.The relative standard error RSE is 0.0011, far less than the 0.01; relative absolute error RAE is 0.00022685, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.8. Multiplications quantitative RRT model for the research of successive sampling under stratified cluster sampling.The relative standard error RSE is 0.0069, far less than the 0.01; relative absolute error RAE is 0.00089859, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.9. Additive quantitative RRT model for the research of successive sampling under two-stage sampling.The relative standard error RSE is 0.00077796, far less than the 0.01; relative absolute error RAE is 0.000099244, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.10. Additive quantitative RRT model for the research of successive sampling under stratified two-stage sampling.The relative standard error RSE is 0.00056284, far less than the 0.01; relative absolute error RAE is 0.00089019, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%) include analog overall mean.11. Multiplications quantitative RRT model for the research of successive sampling under two-stage sampling.The relative standard error RSE is 0.00059809, far less than the 0.01; relative absolute error RAE is 0.00029276, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for 100 samples, all(100%) include analog overall mean.12. Multiplications quantitative RRT model for the research of successive sampling under stratified two-stage sampling.The relative standard error RSE is 0.00091709, far less than the 0.01; relative absolute The Research of Successive Sampling for Quantitative Sensitive Questions Survey and Its Application Abstract error RAE is 0.00023691, far less than the 0.01, close to the overall mean. For the analog sampled 100 samples, calculate the estimator and the variance about 100 samples, and obtained overall mean 95% confidence interval for100 samples, all(100%)include analog overall mean.Conclusion:1. Two RRT models for sensitive questions are combined with six continuous sampling methods, which produce 12 kinds of survey methods. Provide an overall estimate of the mean, optimal sample rotation rate, and the regression formula for calculating the number of combinations of the estimated optimal weight. Continuous sampling method fills in the blank of research on statistical sampling method.2. Investigation method and statistical formula is adopted in this study, and the deduced formulae were successfully applied in a Beijing CDC project to investigate sensitive features of men who have sex with men(MSM), who are the high risk group of AIDS. We achieved good effect in practical application: the research of successive sampling under stratified cluster sampling has less sampling error than the research of successive sampling under the cluster sampling, and its confidence interval has higher accuracy. The result that is calculated based on our formulas provide scientific basis for health authority to make regional policies and decisions for effectively control HIV/AIDS among MSM.3. Reliability and validity of the evaluation results based on computer simulation for the research of successive sampling for quantitative sensitive questions survey explain: 12 kinds of survey methods for sensitive issues continuous sample and statistical formulas has very high reliability and validity.