Sampling Methods

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Name                                       Shakeel Nouman Religion                                  Christian Domicile                            Punjab (Lahore) Contact #                            0332-4462527. 0321-9898767 E.Mail                                sn_gcu@yahoo.com sn_gcu@hotmail.com

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Sampling Methods:

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

PowerPoint Presentation:

Using Statistics Nonprobability Sampling and Bias Stratified Random Sampling Cluster Sampling Systematic Sampling Nonresponse Summary and Review of Terms Sampling Methods 16 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

16-2 Nonprobability Sampling and Bias:

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 - 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

16-3 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 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

16-3 Stratified Random Sampling (Continued):

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 6 5 4 3 2 1 Group N i Population Distribution 7 6 5 4 3 2 1 Group n i Sample Distribution 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

Relationship Between the Population and a Stratified Random Sample:

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

Properties of the Stratified Estimator of the Sample Mean:

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

Properties of the Stratified Estimator of the Sample Mean (continued):

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

When the Population Variance is Unknown:

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

Confidence Interval for the Population Mean in Stratified Sampling:

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

Example 16-2:

Population True Sampling Number Weights Sample Fraction Group of Firms (W i ) Sizes (f i ) 1. Diversified service companies 100 0.20 20 0.20 2. Commercial banking companies 100 0.20 20 0.20 3. Financial service companies 150 0.30 30 0.30 4. Retailing companies 50 0.10 10 0.10 5. Transportation companies 50 0.10 10 0.10 6. Utilities 50 0.10 10 0.10 N = 500 n = 100 Stratum Mean Variance n i W i W i x i 1 52.7 97650 20 0.2 10.54 156.240 2 112.6 64300 20 0.2 22.52 102.880 3 85.6 76990 30 0.3 25.68 184.776 4 12.6 18320 10 0.1 1.26 14.656 5 8.9 9037 10 0.1 0.89 7.230 6 52.3 83500 10 0.1 5.23 66.800 Estimated Mean: 66.12 532.582 Estimated standard error of mean: 23.08 Example 16-2 Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

Example 16-2 Using the template:

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

Stratified Sampling for the Population Proportion:

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

Stratified Sampling for the Population Proportion: Example 16-1 (Continued):

Number Group W i n i f i Interested Metropolitan 0.65 130 0.65 28 0.14 0.0005756 Nonmetropolitan 0.35 70 0.35 18 0.09 0.0003099 Estimated proportion: 0.23 0.0008855 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

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

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

Rules for Constructing Strata:

Age Frequency (f i ) 20-25 1 1 26-30 16 4 5 31-35 25 5 5 36-40 4 2 41-45 9 3 5 Rules for Constructing Strata Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

Optimum Allocation:

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

Optimum Allocation: An Example:

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

Optimum Allocation: An Example using the Template:

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

16-4 Cluster Sampling:

7 6 5 4 3 2 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

Cluster Sampling: Estimating the Population Mean:

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

Cluster Sampling: Estimating the Population Proportion:

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

Cluster Sampling: Example 16-3:

x i n i n i x i x i -x cl (x i -x cl ) 2 21 8 168 -0.8333 0.694 0.00118 22 8 176 0.1667 0.028 0.00005 11 9 99 -10.8333 117.361 0.25269 34 10 340 12.1667 148.028 0.39348 28 7 196 6.1667 38.028 0.04953 25 8 200 3.1667 10.028 0.01706 18 10 180 -3.8333 14.694 0.03906 24 12 288 2.1667 4.694 0.01797 19 11 209 -2.8333 8.028 0.02582 20 6 120 -1.8333 3.361 0.00322 30 8 240 8.1667 66.694 0.11346 26 9 234 4.1667 17.361 0.03738 12 9 108 -9.8333 96.694 0.20819 17 8 136 -4.8333 23.361 0.03974 13 10 130 -8.8333 78.028 0.20741 29 8 232 7.1667 51.361 0.08738 24 8 192 2.1667 4.694 0.00799 26 10 260 4.1667 17.361 0.04615 18 10 180 -3.8333 14.694 0.03906 22 11 242 0.1667 0.028 0.00009 3930 s 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

Cluster Sampling: Example 16-3 Using the Template:

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

Cluster Sampling: Using the Template to Estimate Population Proportion:

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

16-5 Systematic Sampling:

Randomly select an element out of the first k elements in the population, and then select every k th 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

Systematic Sampling: Example 16-4:

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

16-6 Nonresponse:

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

PowerPoint Presentation:

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.com sn_gcu@hotmail.com Sampling Methods By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer