1. 16-1 COMPLETE BUSINESS STATISTICS by AMIR D. ACZEL & JAYAVEL SOUNDERPANDIAN 6 th edition (SIE)

2. 16-2 Chapter 16 Sampling Methods

3. 16-3 Using Statistics Nonprobability Sampling and Bias Stratified Random Sampling Cluster Sampling Systematic Sampling Nonresponse Sampling Methods 16

4. 16-4 Apply nonprobability sampling methods Decide when to conduct a stratified sampling method Compute estimates from stratified sample results Decide when to conduct a cluster sampling method LEARNING OUTCOMES 16 After studying this chapter you should be able to:

5. 16-5 Compute estimates from cluster sampling results Decide when to conduct a systematic sampling method Compute estimates from systematic sample results Avoid nonresponse biases in estimates LEARNING OUTCOMES (2) 16 After studying this chapter you should be able to:

6. 16-6 nonprobability sampling methods Sampling methods that do not use samples with known probabilities of selection are know as nonprobability sampling methods. In nonprobability sampling methods, there is no objective way of evaluating how far away from the population parameter the estimate may be. Frame Frame - a list of people or things of interest from which a random sample can be chosen. 16-2 Nonprobability Sampling and Bias

7. 16-7 stratified random sampling In stratified random sampling, we assume that the population of N units may be divided into m groups with N i units in each group i=1,2,...,m. The m strata are nonoverlapping and together they make up the total population: N 1 + N 2 +...+ N m =N. 16-3 Stratified Random Sampling The m strata are non-overlapping. Population

8. 16-8 stratified random sampling In stratified random sampling, we assume that the population of N units may be divided into m groups with N i units in each group i=1,2,...,m. The m strata are nonoverlapping and together they make up the total population: N 1 + N 2 +...+ N m =N. 7654321 Group NiNi NiNi Population Distribution 7654321 Group nini nini Sample Distribution proportional allocation In proportional allocation, the relative frequencies in the sample (n i /n) are the same as those in the population (N i /N). 16-3 Stratified Random Sampling (Continued)

9. 16-9 Relationship Between the Population and a Stratified Random Sample

10. 16-10 Properties of the Stratified Estimator of the Sample Mean

11. 16-11 Properties of the Stratified Estimator of the Sample Mean (continued)

12. 16-12 When the Population Variance is Unknown

13. 16-13 Confidence Interval for the Population Mean in Stratified Sampling

14. 16-14 Population TrueSampling NumberWeightsSampleFraction Groupof Firms (W i ) Sizes(f i ) 1. Diversified service companies1000.20200.20 2. Commercial banking companies1000.20200.20 3. Financial service companies1500.30300.30 4. Retailing companies 500.10100.10 5. Transportation companies 500.10100.10 6. Utilities 500.10100.10 N = 500n = 100 Population TrueSampling NumberWeightsSampleFraction Groupof Firms (W i ) Sizes(f i ) 1. Diversified service companies1000.20200.20 2. Commercial banking companies1000.20200.20 3. Financial service companies1500.30300.30 4. Retailing companies 500.10100.10 5. Transportation companies 500.10100.10 6. Utilities 500.10100.10 N = 500n = 100 StratumMeanVariancen i W i W i x i 152.797650200.210.54156.240 2112.664300200.222.52102.880 385.676990300.325.68184.776 412.618320100.11.2614.656 58.99037100.10.897.230 652.383500100.15.2366.800 Estimated Mean:66.12532.582 Estimated standard error of mean:23.08 Example 16-2

15. 16-15 Example 16-2 Using the template Observe that the computer gives a slightly more precise interval than the hand computation on the previous slide.

16. 16-16 Stratified Sampling for the Population Proportion

17. 16-17 Number GroupW i n i f i Interested Metropolitan0.651300.65280.140.0005756 Nonmetropolitan0.35700.35180.090.0003099 Estimated proportion:0.230.0008855 Estimated standard error: 0.0297574 90% confidence interval:[0.181,0.279] Stratified Sampling for the Population Proportion: Example 16-1 (Continued)

18. 16-18 Stratified Sampling for the Population Proportion:Example 16-1 (Continued) using the Template

19. 16-19 AgeFrequency (f i ) 20-2511 26-301645 31-352555 36-4042 41-45935 Rules for Constructing Strata

20. 16-20 Optimum Allocation

21. 16-21 Optimum Allocation: An Example

22. 16-22 Optimum Allocation: An Example using the Template

23. 16-23 7654321 Group Population Distribution In stratified sampling a random sample (n i ) is chosen from each segment of the population (N i ). Sample Distribution In cluster sampling observations are drawn from m out of M areas or clusters of the population. 16-4 Cluster Sampling

24. 16-24 Cluster Sampling: Estimating the Population Mean

25. 16-25 Cluster Sampling: Estimating the Population Proportion

26. 16-26 x i n i n i x i x i -x cl (x i -x cl ) 2 218168-0.83330.6940.00118 2281760.16670.0280.00005 11999-10.8333117.3610.25269 341034012.1667148.0280.39348 2871966.166738.0280.04953 2582003.166710.0280.01706 1810180-3.833314.6940.03906 24122882.16674.6940.01797 1911209-2.83338.0280.02582 206120-1.83333.3610.00322 3082408.166766.6940.11346 2692344.166717.3610.03738 129108-9.833396.6940.20819 178136-4.833323.3610.03974 1310130-8.833378.0280.20741 2982327.166751.3610.08738 2481922.16674.6940.00799 26102604.166717.3610.04615 1810180-3.833314.6940.03906 22112420.16670.0280.00009 3930s 2 (X cl )=1.58691 x cl =21.83 Cluster Sampling: Example 16-3

27. 16-27 Cluster Sampling: Example 16-3 Using the Template

28. 16-28 Cluster Sampling: Using the Template to Estimate Population Proportion

29. 16-29 Randomly select an element out of the first k elements in the population, and then select every kth unit afterwards until we have a sample of n elements. 16-5 Systematic Sampling

30. 16-30 Systematic Sampling: Example 16-4

31. 16-31 bias Systematic nonresponse can bias estimates Callbacks of nonrespondents Offers of monetary rewards for nonrespondents Random-response mechanism bias Systematic nonresponse can bias estimates Callbacks of nonrespondents Offers of monetary rewards for nonrespondents Random-response mechanism 16-6 Nonresponse