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

16-2 Chapter 16 Sampling Methods

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

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:

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:

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 Nonprobability Sampling and Bias

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 N m =N Stratified Random Sampling The m strata are non-overlapping. Population

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 N m =N Group NiNi NiNi Population Distribution 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) Stratified Random Sampling (Continued)

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

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

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

16-12 When the Population Variance is Unknown

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

16-14 Population TrueSampling NumberWeightsSampleFraction Groupof Firms (W i ) Sizes(f i ) 1. Diversified service companies Commercial banking companies Financial service companies Retailing companies Transportation companies Utilities N = 500n = 100 Population TrueSampling NumberWeightsSampleFraction Groupof Firms (W i ) Sizes(f i ) 1. Diversified service companies Commercial banking companies Financial service companies Retailing companies Transportation companies Utilities N = 500n = 100 StratumMeanVariancen i W i W i x i Estimated Mean: Estimated standard error of mean:23.08 Example 16-2

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 Stratified Sampling for the Population Proportion

16-17 Number GroupW i n i f i Interested Metropolitan Nonmetropolitan Estimated proportion: Estimated standard error: % confidence interval:[0.181,0.279] Stratified Sampling for the Population Proportion: Example 16-1 (Continued)

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

16-19 AgeFrequency (f i ) Rules for Constructing Strata

16-20 Optimum Allocation

16-21 Optimum Allocation: An Example

16-22 Optimum Allocation: An Example using the Template

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 Cluster Sampling

16-24 Cluster Sampling: Estimating the Population Mean

16-25 Cluster Sampling: Estimating the Population Proportion

16-26 x i n i n i x i x i -x cl (x i -x cl ) s 2 (X cl )= x cl =21.83 Cluster Sampling: Example 16-3

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

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

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 Systematic Sampling

16-30 Systematic Sampling: Example 16-4

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