Chap 016

Chapter 16 Sampling MethodsMcGraw-Hill/IrwinCopyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved.COMPLETE BUSINESS STATISTICSbyAMIR D. ACZEL&JAYAVEL SOUNDERPANDIAN7th edition.

Prepared by Lloyd Jaisingh, Morehead State University

Using StatisticsNonprobability Sampling and BiasStratified Random SamplingCluster SamplingSystematic SamplingNonresponseSampling Methods1616-*

Apply nonprobability sampling methodsDecide when to conduct a stratified sampling methodCompute estimates from stratified sample resultsDecide when to conduct a cluster sampling methodLEARNING OBJECTIVES16After studying this chapter you should be able to:16-*

Compute estimates from cluster sampling resultsDecide when to conduct a systematic sampling methodCompute estimates from systematic sample resultsAvoid nonresponse biases in estimatesLEARNING OBJECTIVES (2)16After studying this chapter you should be able to:16-*

16-2 Nonprobability Sampling and BiasSampling 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-*

16-3 Stratified Random SamplingIn stratified random sampling, we assume that the population of N units may be divided into m groups with Ni units in each group i=1,2,...,m. The m strata are nonoverlapping and together they make up the total population: N1 + N2 +...+ Nm =N.The m strata are non-overlapping.Population16-*

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 Ni units in each group i=1,2,...,m. The m strata are nonoverlapping and together they make up the total population: N1 + N2 +...+ Nm =N.7654321GroupNiPopulation Distribution7654321GroupniSample DistributionIn proportional allocation, the relative frequencies in the sample (ni/n) are the same as those in the population (Ni/N) .16-*

Relationship Between the Population and a Stratified Random Sample16-*

Properties of the Stratified Estimator of the Sample Mean16-*

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

When the Population Variance is Unknown16-*

Confidence Interval for the Population Mean in Stratified Sampling16-*

Example 16-2PopulationTrueSamplingNumberWeightsSampleFractionGroupof Firms (Wi) Sizes(fi) 1. Diversified service companies1000.20200.202. Commercial banking companies1000.20200.203. Financial service companies1500.30300.304. Retailing companies 500.10100.105. Transportation companies 500.10100.106. Utilities 500.10100.10N = 500n = 100StratumMeanVarianceniWiWixi 152.797650200.210.54156.240 2112.664300200.222.52102.880 385.676990300.325.68184.776 412.618320100.11.2614.656 58.99037100.10.897.230 652.383500100.15.2366.800Estimated Mean:66.12532.582Estimated standard error of mean:23.0816-*

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

Stratified Sampling for the Population Proportion16-*

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

Stratified Sampling for the Population Proportion:Example 16-1 (Continued) using the Template16-*

Rules for Constructing StrataAgeFrequency (fi) 20-251126-30164531-35255536-404241-4593516-*

Optimum Allocation16-*

Optimum Allocation: An Example16-*

Optimum Allocation: An Example using the Template16-*

16-4 Cluster Sampling16-*

Cluster Sampling: Estimating the Population Mean16-*

Cluster Sampling: Estimating the Population Proportion16-*

Cluster Sampling: Example 16-316-*

Cluster Sampling: Example 16-3 Using the Template16-*

Cluster Sampling: Using the Template to Estimate Population Proportion16-*

16-5 Systematic SamplingRandomly 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-*

Systematic Sampling: Example 16-416-*

16-6 NonresponseSystematic nonresponse can bias estimatesCallbacks of nonrespondentsOffers of monetary rewards for nonrespondentsRandom-response mechanism16-*