2014 SAS Paper

Application of Survey Sampling for Quality Control

Transcript

1. SAS® Global Forum 2014 March 23-26 Washington, DC
2. Application of Survey Sampling for Quality Control Yi Du Freddie Mac
3. 3 Goals  Stratified sampling method with “many” strata  Use SAS procedures to implement the proposed sampling method  A SAS macro you can use TODAY
5. 5 Problems and Inspiration
6. 6 Reasons to Use Sampling  Information-intensive society encourages us to manage more information with limited time and resources  Sampling becomes one of the solutions to satisfy people’s needs to more information  Different sampling methods would be applied under different study scenarios
7. 7 Stratified Sampling  This paper’s focus: stratified sampling  What is stratified sampling?  Separate the whole population into different strata such that the population within the same stratum is as homogeneous as possible while the population between strata is as heterogeneous as possible  The whole sample is selected from each stratum
8. 8 Benefit vs. Limitation  Benefit – Increase efficiency and decrease error  Limitation – Benefit is usually offset while the number of stratum is too many  Solution – Group the stratum with small population into one group and sample as a whole
9. 9 Statistical Approach
10. 10 Idea  The stratum itself constitutes the distribution of sample population by size  The size in each stratum could differ  The strata which become outliers would be grouped as a whole and sampled together whereas non-outlier strata will be sampled as is Note: the outliers are defined based on box-and-whisker plot
11. 11 Illustration  Before: 10 9 8 8 7 7 7 6 6 2 1 0 1 2 3 4 5 6 7 8 9 10 Stratum 1 Stratum 2 Stratum 3 Stratum 4 Stratum 5 Stratum 6 Stratum 7 Stratum 8 Stratum 9 Stratum 10 Stratum 11 Size Q1 = 6 Q3 = 8 IQR = 2 Outliers in (2, 1)
12. 12  After: 10 9 8 8 7 7 7 6 6 0 1 2 3 4 5 6 7 8 9 10 Stratum 1 Stratum 2 Stratum 3 Stratum 4 Stratum 5 Stratum 6 Stratum 7 Stratum 8 Stratum 9 Stratum 10 (New) Size New stratum constructed by outliers 3
13. 13 Sample Allocation  Once the sample population is re-stratified, the total sample size would be allocated among strata with optimal allocation method  Two more key pieces of information need to be defined:  Variance  Cost
14. 14 Sample Allocation Cont.  The variance by strata is well defined by characteristics or the sample interest  The characteristics could be calculated directly  When the sample interest is used to estimate the variance, the proxy variable is used to signal the variance of strata
15. 15 Sample Allocation Cont.  The cost of sample varies based on the specific research scenario  It could be derived empirically, such as the time or labor in quality control using past information as reference  Or it could be derived based on the efforts to get the sample, such as the survey channels
16. 16 SAS Macro
17. 17 SAS Procedures Involved Proc Univariate: Use Q1, Q3 and IQR to identify outliers Proc Univariate Data = {sasdataset}; Var count; Output Out = {output} Q1 = q1 Q3 = q3 Qrange = IQR; Run;
18. 18 Proc Surveyselect: Used for sample selection Note 1: alloc could be optimal, Neyman, or proportional Note 2: var and cost define the parameters used for optimal allocation method Proc Surveyselect Data = {sasdataset} Seed = Method = Out = {outputdata} Sampsize = ; Stratum / alloc = var = cost = allocmin = ; Run;
19. 19 Discussions
20. 20 Application  Proposed stratified sampling method is used to solve the problem when stratified sampling is applied with too many strata  It could be applied in different areas, for example:  Estimate the income by majors for recently graduated students  Measure the popularity of TV shows by channels
21. 21 Limitation and Improvement  Limitation:  The stratified sampling method is to improve the efficiency of sample but the increase in number of strata would undermine the accuracy by using it  The proposed method is to use box-and-whisker outliers to re- stratify the total population but applying it, the detection of outliers is a necessary prerequisite. Failing to identify outliers will fail to apply this method
22. 22  Improvement:  Box-and-whisker outliers is only one of many ways to identify outliers based on the assumption of normal distribution  Some other methods could also be applied, such as kernel density estimation, clustering, etc…
23. 23 Recap