1. Slide 1 Shakeel Nouman M.Phil Statistics Sampling Methods Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

2. Slide 2 Using Statistics Nonprobability Sampling and Bias Stratified Random Sampling Cluster Sampling Systematic Sampling Nonresponse Summary and Review of Terms Sampling Methods  Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

3. Slide 3 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

4. Slide 4 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. PopulationPopulation Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

5. Slide 5 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. 7 7 6 6 5 5 4 4 3 3 2 2 1 1 Group NiNi NiNi Population Distribution 7 7 6 6 5 5 4 4 3 3 2 2 1 1 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) Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

6. Slide 6 Relationship Between the Population and a Stratified Random Sample Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

7. Slide 7 Properties of the Stratified Estimator of the Sample Mean Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

8. Slide 8 Properties of the Stratified Estimator of the Sample Mean (continued) Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

9. Slide 9 When the Population Variance is Unknown Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

10. Slide 10 Confidence Interval for the Population Mean in Stratified Sampling Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

11. Slide 11 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 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

12. Slide 12 Example 16-2 Using the template Observe that the computer gives a slightly more precise interval than the hand computation on the previous slide. Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

13. Slide 13 Stratified Sampling for the Population Proportion Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

14. Slide 14 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] 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) Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

15. Slide 15 Stratified Sampling for the Population Proportion:Example 16-1 (Continued) using the Template Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

16. Slide 16 Age Frequency (f i ) 20-2511 26-301645 31-352555 36-4042 41-45935 Age Frequency (f i ) 20-2511 26-301645 31-352555 36-4042 41-45935 Rules for Constructing Strata Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

17. Slide 17 Optimum Allocation Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

18. Slide 18 Optimum Allocation: An Example Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

19. Slide 19 Optimum Allocation: An Example using the Template Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

20. Slide 20 7 7 6 6 5 5 4 4 3 3 2 2 1 1 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

21. Slide 21 Cluster Sampling: Estimating the Population Mean Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

22. Slide 22 Cluster Sampling: Estimating the Population Proportion Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

23. Slide 23 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 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

24. Slide 24 Cluster Sampling: Example 16-3 Using the Template Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

25. Slide 25 Cluster Sampling: Using the Template to Estimate Population Proportion Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

26. Slide 26 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

27. Slide 27 Systematic Sampling: Example 16-4 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

28. Slide 28 bias l Systematic nonresponse can bias estimates Callbacks of nonrespondents Offers of monetary rewards for nonrespondents Random-response mechanism bias l Systematic nonresponse can bias estimates Callbacks of nonrespondents Offers of monetary rewards for nonrespondents Random-response mechanism 16-6 Nonresponse Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

29. Slide 29 M.Phil (Statistics) GC University,. (Degree awarded by GC University) M.Sc (Statistics) GC University,. (Degree awarded by GC University) Statitical Officer (BS-17) (Economics & Marketing Division) Livestock Production Research Institute Bahadurnagar (Okara), Livestock & Dairy Development Department, Govt. of Punjab Name Shakeel Nouman Religion Christian Domicile Punjab (Lahore) Contact # 0332-4462527. 0321-9898767 E.Mail sn_gcu@yahoo.comsn_gcu@yahoo.com sn_gcu@hotmail.com Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer