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# Sampling

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• In drawing a sample with simple random sampling, each population element has an equal chance of being selected into the samples. The sample is drawn using a random number table or generator. This slide shows the advantages and disadvantages of using this method. The probability of selection is equal to the sample size divided by the population size. Exhibit 14-6 covers how to choose a random sample. The steps are as follows: Assign each element within the sampling frame a unique number. Identify a random start from the random number table. Determine how the digits in the random number table will be assigned to the sampling frame. Select the sample elements from the sampling frame.
• In drawing a sample with systematic sampling, an element of the population is selected at the beginning with a random start and then every K th element is selected until the appropriate size is selected. The kth element is the skip interval, the interval between sample elements drawn from a sample frame in systematic sampling. It is determined by dividing the population size by the sample size. To draw a systematic sample, the steps are as follows: Identify, list, and number the elements in the population Identify the skip interval Identify the random start Draw a sample by choosing every kth entry. To protect against subtle biases, the research can Randomize the population before sampling, Change the random start several times in the process, and Replicate a selection of different samples.
• In drawing a sample with stratified sampling, the population is divided into subpopulations or strata and uses simple random on each strata. Results may be weighted or combined. The cost is high. Stratified sampling may be proportion or disproportionate. In proportionate stratified sampling, each stratum’s size is proportionate to the stratum’s share of the population. Any stratification that departs from the proportionate relationship is disproportionate.
• In drawing a sample with cluster sampling, the population is divided into internally heterogeneous subgroups. Some are randomly selected for further study. Two conditions foster the use of cluster sampling: the need for more economic efficiency than can be provided by simple random sampling, and 2) the frequent unavailability of a practical sampling frame for individual elements. Exhibit 14-7 provides a comparison of stratified and cluster sampling and is highlighted on the next slide. Several questions must be answered when designing cluster samples. How homogeneous are the resulting clusters? Shall we seek equal-sized or unequal-sized clusters? How large a cluster shall we take? Shall we use a single-stage or multistage cluster? How large a sample is needed?
• ### Sampling

1. 1. Research Methodology Chapter 6:Sample Designs and Sampling Procedures
2. 2. Sampling Terminology• Sample• Population or universe• Population element• Census
3. 3. Sample• Subset of a larger population
4. 4. Population• A population is the total collection of elements about which we wish to make some inferences.• Any complete group– People– Sales territories– Stores
5. 5. Census• Investigation of all individual elements that make up a populationA census is a count ofall the elements in a population.
6. 6. Sampling• The process of using a small number of items or parts of larger population to make a conclusions about the whole population
7. 7. Selecting samples Population, sample and individual cases Source: Saunders et al. (2009)Figure 7.1 Population, sample and individual cases
8. 8. The need to sampleSampling- a valid alternative to a census when• A survey of the entire population is impracticable• Budget constraints restrict data collection• Time constraints restrict data collection• Results from data collection are needed quickly
9. 9. Overview of sampling techniques Sampling techniques Source: Saunders et al. (2009)Figure 7.2 Sampling techniques
10. 10. Stages in the Define the target populationSelectionof a Sample Select a sampling frame Determine if a probability or nonprobability sampling method will be chosen Plan procedure for selecting sampling units Determine sample size Select actual sampling units Conduct fieldwork
11. 11. Target Population• The specific , complete group to research project
12. 12. Sampling Frame• A sample frame is the listing of all population elements from which the sample will be drawn.
13. 13. Sampling Units• Group selected for the sample• Primary Sampling Units (PSU)• Secondary Sampling Units• Tertiary Sampling Units
14. 14. Random Sampling Error• The difference between the sample results and the result of a census conducted using identical procedures• Statistical fluctuation due to chance variations
15. 15. Systematic Errors• Nonsampling errors• Unrepresentative sample results• Not due to chance• Due to study design or imperfections in execution
16. 16. Errors Associated with Sampling• Sampling frame error• Random sampling error• Nonresponse error
17. 17. Two Major Categories of Sampling• Probability sampling • Known, nonzero probability for every element• Nonprobability sampling • Probability of selecting any particular member is unknown
18. 18. Nonprobability Sampling• Convenience• Judgment• Quota• Snowball
19. 19. Probability Sampling• Simple random sample• Systematic sample• Stratified sample• Cluster sample• Multistage area sample
20. 20. Convenience Sampling• Convenience samples are nonprobability samples where the element selection is based on ease of accessibility. They are the least reliable but cheapest and easiest to conduct.• Examples include informal pools of friends and neighbors, people responding to an advertised invitation, and “on the street” interviews.
21. 21. Judgment Sampling• Also called purposive sampling• An experienced individual selects the sample based on his or her judgment about some appropriate characteristics required of the sample member
22. 22. Quota Sampling• Ensures that the various subgroups in a population are represented on pertinent sample characteristics• To the exact extent that the investigators desire• It should not be confused with stratified sampling.
23. 23. Snowball Sampling• A variety of procedures• Initial respondents are selected by probability methods• Additional respondents are obtained from information provided by the initial respondents
24. 24. Simple Random Sampling• A sampling procedure that ensures that each element in the population will have an equal chance of being included in the sample
25. 25. Simple RandomAdvantages Disadvantages•Easy to implement with •Requires list ofrandom dialing population elements •Time consuming •Larger sample needed •Produces larger errors •High cost 14-25
26. 26. Systematic Sampling• A simple process• Every nth name from the list will be drawn
27. 27. SystematicAdvantages Disadvantages•Simple to design •Periodicity within•Easier than simple population may skewrandom sample and results•Easy to determine •Trends in list may biassampling distribution of resultsmean or proportion •Moderate cost 14-27
28. 28. Stratified Sampling• Probability sample• Subsamples are drawn within different strata• Each stratum is more or less equal on some characteristic• Do not confuse with quota sample
29. 29. StratifiedAdvantages Disadvantages•Control of sample size in •Increased error if subgroupsstrata are selected at different rates•Increased statistical efficiency •Especially expensive if strata•Provides data to represent and on population must be createdanalyze subgroups •High cost•Enables use of differentmethods in strata 14-29
30. 30. Cluster Sampling• The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample.• The primary sampling unit is no longer the individual element in the population• The primary sampling unit is a larger cluster of elements located in proximity to one another
31. 31. ClusterAdvantages Disadvantages•Provides an unbiased estimate •Often lower statisticalof population parameters if efficiency due to subgroupsproperly done being homogeneous rather than•Economically more efficient heterogeneousthan simple random •Moderate cost•Lowest cost per sample•Easy to do without list 14-31
32. 32. Examples of ClustersPopulation Element Possible Clusters in the United StatesU.S. adult population States Counties Metropolitan Statistical Area Census tracts Blocks Households
33. 33. Examples of ClustersPopulation Element Possible Clusters in the United StatesCollege seniors CollegesManufacturing firms Counties Metropolitan Statistical Areas Localities Plants
34. 34. Examples of ClustersPopulation Element Possible Clusters in the United StatesAirline travelers Airports PlanesSports fans Football stadiums Basketball arenas Baseball parks
35. 35. What is the Appropriate Sample Design?• Degree of accuracy• Resources• Time• Advanced knowledge of the population• National versus local• Need for statistical analysis
36. 36. Internet Sampling is Unique• Internet surveys allow researchers to rapidly reach a large sample.• Speed is both an advantage and a disadvantage.• Sample size requirements can be met overnight or almost instantaneously.• Survey should be kept open long enough so all sample units can participate.
37. 37. Internet Sampling• Major disadvantage – lack of computer ownership and Internet access among certain segments of the population• Yet Internet samples may be representative of a target populations. – target population - visitors to a particular Web site.• Hard to reach subjects may participate
38. 38. Web Site Visitors• Unrestricted samples are clearly convenience samples• Randomly selecting visitors• Questionnaire request randomly "pops up"• Over- representing the more frequent visitors
39. 39. Panel Samples• Typically yield a high response rate – Members may be compensated for their time with a sweepstake or a small, cash incentive.• Database on members – Demographic and other information from previous questionnaires• Select quota samples based on product ownership, lifestyle, or other characteristics.• Probability Samples from Large Panels
40. 40. Internet Samples• Recruited Ad Hoc Samples• Opt-in Lists
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