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# Abdm4064 week 09 10 sampling

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Research design, Sampling

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• This &quot;Deco&quot; border was drawn on the Slide master using PowerPoint&apos;s Rectangle and Line tools. A smaller version was placed on the Notes Master by selecting all of the elements (using Select All from the Edit menu), deselecting the unwanted elements such as the Title (holding down the Shift key and clicking on the unwanted elements), and then using Paste as Picture from the Edit menu to place the border on the Notes Master. After pasting as a picture, we used the resize handles (with Shift to maintain the proportions) to reduce it to the size you see. Be sure to delete this word processing box before using this template for your own presentation.
• Exhibit 6-1 illustrates design in the research process and highlights the topics covered by the term research design. Subsequent chapters will provide more detailed coverage of the research design topics.
• Exhibit 14-1 represents the several decisions the researcher makes when designing a sample. The sampling decisions flow from two decisions made in the formation of the management-research question hierarchy: the nature of the management question and the specific investigative questions that evolve from the research question.
• The basic idea of sampling is that by selecting some of the elements in a population, we may draw conclusions about the entire population. A population element is the individual participant or object on which the measurement is taken. It is the unit of study. It may be a person but it could also be any object of interest. A population is the total collection of elements about which we wish to make some inferences. A census is a count of all the elements in a population. A sample frame is the listing of all population elements from which the sample will be drawn.
• This slide lists the reasons researchers use a sample rather than a census.
• The advantages of sampling over census studies are less compelling when the population is small and the variability within the population is high. Two conditions are appropriate for a census study. A census is feasible when the population is small and necessary when the elements are quite different from each other.
• The ultimate test of a sample design is how well it represents the characteristics of the population it purports to represent. In measurement terms, the sample must be valid. Validity of a sample depends on two considerations: accuracy and precision. Here a sample is being taken of water, using a can suspended on a fishing line. Accuracy is the degree to which bias is absent from the sample. When the sample is drawn properly, the measure of behavior, attitudes, or knowledge of some sample elements will be less than the measure of those same variables drawn from the population. The measure of other sample elements will be more than the population values. Variations in these sample values offset each other, resulting in a sample value that is close to the population value. For these offsetting effects to occur, there must be enough elements in the sample and they must be drawn in a way that favors neither overestimation nor underestimation. Increasing the sample size can reduce systematic variance as a cause of error. Systematic variance is a variation that causes measurements to skew in one direction or another. Precision of estimate is the second criterion of a good sample design. The numerical descriptors that describe samples may be expected to differ from those that describe populations because of random fluctuations inherent in the sampling process. This is called sampling error and reflects the influence of chance in drawing the sample members. Sampling error is what is left after all known sources of systematic variance have been accounted for. Precision is measured by the standard error of estimate, a type of standard deviation measurement. The smaller the standard error of the estimate, the higher is the precision of the sample.
• Exhibit 14-2 The members of a sample are selected using probability or nonprobability procedures. Nonprobability sampling is an arbitrary and subjective sampling procedure where each population element does not have a known, nonzero chance of being included. Probability sampling is a controlled, randomized procedure that assures that each population element is given a known, nonzero chance of selection.
• This slide addresses the steps in sampling design.
• The greater the dispersion or variance within the population, the larger the sample must be to provide estimation precision. The greater the desired precision of the estimate, the larger the sample must be. The narrower or smaller the error range, the larger the sample must be. The higher the confidence level in the estimate, the larger the sample must be. The greater the number of subgroups of interest within a sample, the greater the sample size must be, as each subgroup must meet minimum sample size requirements. Cost considerations influence decisions about the size and type of sample and the data collection methods. A cheese factory is pictured here. Ask students if taking a sample would require a large or small sample of the output and what would influence their answer.
• With a subjective approach like nonprobability sampling, the probability of selecting population elements is unknown. There is a greater opportunity for bias to enter the sample and distort findings. We cannot estimate any range within which to expect the population parameter. Despite these disadvantages, there are practical reasons to use nonprobability samples. When the research does not require generalization to a population parameter, then there is no need to ensure that the sample fully reflects the population. The researcher may have limited objectives such as those in exploratory research. It is less expensive to use nonprobability sampling. It also requires less time. Finally, a list may not be available.
• 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. Judgment sampling is purposive sampling where the researcher arbitrarily selects sample units to conform to some criterion. This is appropriate for the early stages of an exploratory study. Quota sampling is also a type of purposive sampling. In this type, relevant characteristics are used to stratify the sample which should improve its representativeness. The logic behind quota sampling is that certain relevant characteristics describe the dimensions of the population. In most quota samples, researchers specify more than one control dimension. Each dimension should have a distribution in the population that can be estimated and be pertinent to the topic studied. Snowball sampling means that subsequent participants are referred by the current sample elements. This is useful when respondents are difficult to identify and best located through referral networks. It is also used frequently in qualitative studies.
• 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?
• Exhibit 14-7
• Area sampling is a cluster sampling technique applied to a population with well-defined political or geographic boundaries. It is a low-cost and frequently used method.
• In drawing a sample with double (sequential or multiphase) sampling, data are collected using a previously defined technique. Based on the information found, a subsample is selected for further study.
• Exhibit 14a-1 shows the Metro U dining club study population (N = 20,000) consisting of five subgroups based on their preferred lunch times. The values 1 through 5 represent preferred lunch times, each a 30-minute interval, starting at 11:00 a.m. Next we sample 10 elements from this population without knowledge of the population’s characteristics. We draw four samples of 10 elements each. The means for each sample are provided in the slide. Each mean is a point estimate, the best predictor of the unknown population mean. None of the samples shown is a perfect duplication because no sample perfectly replicates its population. We cannot judge which estimate is the true mean of the population but we can estimate the interval in which the true mean will fall by using any of the samples. This is accomplished by using a formula that computes the standard error of the mean.
• Exhibit 14a-2 The standard error creates an interval estimate that brackets the point estimate. The interval estimate is an interval or range of values within which the true population parameter is expected to fall. In this example, mu is predicted o be 3.0 or 12:00 noon plus or minus .36. Thus we would expect to find the true population parameter to be between 11:49 a.m. and 12:11 p.m. We have 68% confidence in this estimate because one standard error encompasses plus or minus 1 Z. This is illustrated in Exhibit 14a-3 on the next slide.
• Exhibit 14a-3 The area under the curve represents the confidence estimates that one makes about the results. The combination of the interval range and the degree of confidence creates the confidence interval. With 95% confidence, the interval in which we would find the true mean increases from 11:39 a.m. to 12:21 p.m. We find this by multiplying the standard error by plus or minus 1.96 Z, which covers 95% of the area under the curve.
• Exhibit 14a-4 These are the Z scores associated with various degrees of confidence. To increase the degree of confidence that the true population parameter falls within a given range, the standard error is multiplied by the appropriate z score.
• Exhibit 14a-5, Part B According to the central limit theorem, for sufficiently large samples (n  30), the sample means will be distributed around the population mean approximately in a normal distribution. If researchers draw repeated samples, as we did in the Metro U dining club study, the means for each sample could be plotted, and will form a normal distribution.
• Exhibit 14a-6 In this example, we want to know how many visits the dining club users make to the dining club each month. Using the formula for standard error of the mean with the standard deviation of the sample (because the value for the standard deviation of the population is unknown), we find that the standard error of the mean is .51 visits. 1.96 standard errors are equal to 1 visit. The researcher can estimate with 95% confidence that the population mean of expected number of visits is within 10 (the sample mean) plus or minus 1 visit or between 9 and 11 visits per month. The confidence level is a percentage that reflects the probability that the results will be correct. We might want a higher degree of confidence than the 95% level used. The table illustrates the interval ranges at various levels of confidence. If we want an estimate that will hold for a much smaller range, for example, 10.0 plus or minus .2 visits, we must either accept a lower level of confidence or take a sample large enough to provide this smaller interval with the highest desired confidence level.
• To compute the desired sample size for questions involving means, we need certain information. The precision and how to quantify it: The confidence level we want with our estimate. The size of the interval estimate. The expected dispersion in the population for the investigative question used. Whether a finite population adjustment is needed. When the size of the calculated sample exceeds 5% of the population, the finite limits of the population constrain the sample size needed. A correction factor formula is available in that event. In most sample calculations, population size does not have a major effect on sample size.
• Exhibit 14a-7 In this example, the researcher wants to know what size sample is necessary to estimate the number of meals per month consumed by dining club members. The questions mentioned on the previous slide must be addressed. The desired confidence level is 95% which means we will use a Z score of 1.96. The interval estimate that the researcher is willing to accept is plus or minus .5 meals per month. These two items represent the desired precision. The sample mean is 10 and the standard deviation is 4.1. These figures were derived from a pretest. If a pretest had not provided the standard deviation, then the population dispersion could have been used to get a standard deviation. This is discussed further on the following slide. To calculate the standard error of the mean, the interval estimate is divided by the z score. This figure is then used in the sample size calculation. The standard deviation squared divided by the standard error of the mean squared is equal to the calculated sample size. Note that the more precise the desired results, the larger the sample size must be.
• Exhibit 14a-7 In this example, the researcher wants to know what size sample is necessary to estimate what percentage of the population says it would join the dining club, based on the projected rates and services. A pretest told us that 30% of those in the pretest sample were interested in joining. In this case, dispersion is measured in terms of p * q (in which q is the proportion of the population not having the attribute and q = (1-p). The measure of dispersion of the sample statistic also changes from the standard error of the mean to the standard error of the proportion. Like before, the desired confidence level is 95% which means we will use a Z score of 1.96. The interval estimate that the researcher is willing to accept is plus or minus .10 or 10% (this is a subjective decision). These two items represent the desired precision. To calculate the standard error of the proportion, the interval estimate is divided by the z score. This figure is then used in the sample size calculation. The dispersion divided by the standard error of the proportion squared is equal to the calculated sample size. In this case, the sample size is smaller than the one in the previous example. If both questions were relevant to the research, the larger sample size would be used.
• Exhibit 14a Random Samples of Preferred Lunch Times.
• Exhibit 14a-3 Confidence Levels and the Normal Curve
• Exhibit 14a-5 Metro U Dining Club Study
• ### Abdm4064 week 09 10 sampling

1. 1. Research Design :Research Design :Sampling &Sampling &Data CollectionData CollectionResearch Design :Research Design :Sampling &Sampling &Data CollectionData CollectionABDM4064 BUSINESS RESEARCHABDM4064 BUSINESS RESEARCHbyStephen OngPrincipal Lecturer (Specialist)Visiting Professor, Shenzhen
3. 3. 14-3Sampling DesignSampling Designwithin the Research Processwithin the Research Process
4. 4. Sampling DesignSampling Design
5. 5. LEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMES1. Explain reasons for taking a sample rather than acomplete census2. Describe the process of identifying a targetpopulation and selecting a sampling frame3. Compare random sampling and systematic(nonsampling) errors4. Identify the types of nonprobability sampling,including their advantages and disadvantagesAfter studying this chapter, you should be able to
6. 6. LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)5. Summarize the advantages and disadvantages ofthe various types of probability samples6. Discuss how to choose an appropriate sampledesign, as well as challenges for Internet sampling7. Understand basic statistical terminology8. Interpret frequency distributions, proportions, andmeasures of central tendency and dispersion9. Distinguish among population, sample, andsampling distributions10. Summarize the use of confidence intervalestimatesAfter studying this chapter, you should
7. 7. 14-7Small Samples Can EnlightenSmall Samples Can Enlighten““The proof of the pudding is in theThe proof of the pudding is in theeating.eating.ByBy a small samplea small sample we may judge of thewe may judge of thewhole piece.”whole piece.”Miguel de Cervantes SaavedraMiguel de Cervantes Saavedraauthorauthor
8. 8. 14-8The Nature of SamplingThe Nature of SamplingPopulationPopulationPopulation ElementPopulation ElementCensusCensusSampleSampleSampling frameSampling frame
9. 9. Sampling TerminologySampling Terminology Sample A subset, or some part, of a largerpopulation. Population (universe) Any complete group of entities that sharesome common set of characteristics. Population Element An individual member of a population. Census An investigation of all the individualelements that make up a population.
10. 10. 14-10Why Sample?Why Sample?GreaterGreateraccuracyaccuracyAvailabilityAvailabilityof elementsof elementsAvailabilityAvailabilityof elementsof elementsGreaterGreaterspeedspeedGreaterGreaterspeedspeedSamplingSamplingprovidesprovidesSamplingSamplingprovidesprovidesLowerLowercostcostLowerLowercostcost
11. 11. 14-11What Is a SufficientlyWhat Is a SufficientlyLarge Sample?Large Sample?““In recent Gallup ‘Poll on polls,’ . . . When askedIn recent Gallup ‘Poll on polls,’ . . . When askedabout the scientific sampling foundation on whichabout the scientific sampling foundation on whichpolls are based . . . most said that a survey ofpolls are based . . . most said that a survey of1,500 – 2,000 respondents—a larger than average1,500 – 2,000 respondents—a larger than averagesample size for national polls—cannot representsample size for national polls—cannot representthe views of all Americans.”the views of all Americans.”Frank NewportFrank NewportThe Gallup Poll editor in chiefThe Gallup Poll editor in chiefThe Gallup OrganizationThe Gallup Organization
12. 12. 14-12When Is a CensusWhen Is a CensusAppropriate?Appropriate?NecessaryNecessaryFeasibleFeasible
13. 13. 14-13What Is a Valid Sample?What Is a Valid Sample?AccurateAccurate PrecisePrecise
14. 14. Why Sample?Why Sample? Pragmatic Reasons Budget and time constraints. Limited access to total population. Accurate and Reliable Results Samples can yield reasonably accurateinformation.information. Strong similaritiesStrong similarities in population elements makesin population elements makessampling possible.sampling possible. Sampling may beSampling may be more accuratemore accurate than a census.than a census. Destruction of Test UnitsDestruction of Test Units SamplingSampling reduces the costsreduces the costs of research in finiteof research in finitepopulations.populations.
15. 15. A Photographic Example of How Sampling WorksA Photographic Example of How Sampling Works
16. 16. 16–16Stages inStages inthetheSelectionSelectionof aof aSampleSample
17. 17. 14-17Types of Sampling DesignsTypes of Sampling DesignsElementSelectionProbability Nonprobability•UnrestrictedUnrestricted • Simple randomSimple random • ConvenienceConvenience•RestrictedRestricted • Complex randomComplex random • PurposivePurposive• SystematicSystematic • JudgmentJudgment•ClusterCluster •QuotaQuota•StratifiedStratified •SnowballSnowball•DoubleDouble
18. 18. 14-18Steps in Sampling DesignSteps in Sampling DesignWhat is the target population?What is the target population?What is the target population?What is the target population?What are the parameters ofWhat are the parameters ofinterest?interest?What are the parameters ofWhat are the parameters ofinterest?interest?What is the sampling frame?What is the sampling frame?What is the sampling frame?What is the sampling frame?What is the appropriateWhat is the appropriatesampling method?sampling method?What is the appropriateWhat is the appropriatesampling method?sampling method?What size sample is needed?What size sample is needed?What size sample is needed?What size sample is needed?
19. 19. 14-19When to Use Larger Sample?When to Use Larger Sample?DesiredDesiredprecisionprecisionDesiredDesiredprecisionprecisionNumber ofNumber ofsubgroupssubgroupsNumber ofNumber ofsubgroupssubgroupsConfidenceConfidencelevellevelConfidenceConfidencelevellevelPopulationPopulationvariancevarianceSmall errorSmall errorrangerange
20. 20. Practical Sampling ConceptsPractical Sampling Concepts Defining the Target Population Once the decision to sample has been made,the first question concerns identifying thetarget population. What is the relevant population? In many casesthis is easy to answer, but in other cases, thedecision may be difficult. At the outset of the sampling process it isvitally important to carefully define the targetpopulation so that the proper source fromwhich the data are to be collected can beidentified. To implement the sample in the field, tangiblecharacteristics (e.g. age, gender etc) should beused to define the population.
21. 21. Practical Sampling ConceptsPractical Sampling Concepts(cont’d)(cont’d) The Sampling Frame In practice, the sample will be drawn from alist of population elements that often differssomewhat from the defined target population. A sampling frame is a list of elements fromwhich the sample may be drawn. The sampling frame is also called the workingpopulation, because these units willeventually provide units involved in theanalysis. The discrepancy between the definition of thepopulation and a sampling frame is the firstpotential source of error associated withsample selection.
22. 22. ExampleExample Target population: Students inMalaysia between 18 years old and 22years old. Sampling frame: students from ahigher education institution.
23. 23. Practical Sampling ConceptsPractical Sampling Concepts(cont’d)(cont’d) The Sampling Frame A sampling frame error occurs whencertain sample elements are excluded orwhen the entire population is notaccurately represented in the samplingframe. Population elements can be either under-or overrepresented in a sampling frame.
24. 24. Sampling UnitsSampling Units Sampling Unit A single element or group of elementssubject to selection in the sample. Primary Sampling Unit (PSU) A unit selected in the first stage of sampling. Secondary Sampling Unit A unit selected in the second stage ofsampling. Tertiary Sampling Unit A unit selected in the third stage of sampling.
25. 25. EXAMPLETarget population: Students in Malaysiabetween 18 years old and 22 years old.Sample frame: students from a highereducation institution.Sampling units: Advanced Diploma students only (primarysampling unit) School of Business Studies only (secondarysampling unit) ABU only (tertiary sampling unit)16–25
26. 26. Random Sampling andRandom Sampling andNonsampling ErrorsNonsampling Errors If a difference exists between the valueof a sample statistic of interest and thevalue of the corresponding populationparameter, a statistical error hasoccurred. Two basic causes of differencesbetween statistics and parameters:random sampling errorssystematic (nonsampling) errors
27. 27. Random Sampling and Nonsampling Errors (cont’d)Random Sampling and Nonsampling Errors (cont’d) Random Sampling Error Random sampling error is the difference between thesample result and the result of a census conducted usingidentical procedures. Random sampling error occurs because of chancevariation in the scientific selection of sampling units. Because random sampling errors follow chance variations,they tend to cancel one another out when averaged. This means that properly selected samples are generallygood approximations of the population. Random sampling error is a function of sample size. As sample size increases, random sampling errordecreases It is possible to estimate the random sampling error thatmay be expected with various sample sizes.
28. 28. Random Sampling andRandom Sampling andNonsampling Errors (cont’d)Nonsampling Errors (cont’d) Systematic Sampling Error Systematic (nonsampling) errors resultfrom nonsampling factors, primarily thenature of a study’s design and thecorrectness of execution. These errors are not due to chancefluctuations. Sample biases account for a large portionof errors in research.
29. 29. Random Sampling andRandom Sampling andNonsampling Errors (cont’d)Nonsampling Errors (cont’d) Less than Perfectly RepresentativeSamples Random sampling errors and systematicerrors associated with the sampling processmay combine to yield a sample that is lessthan perfectly representative of thepopulation. Additional errors will occur if individualsrefuse to be interviewed or cannot becontacted. Such nonresponse error may also cause thesample to be less than perfectlyrepresentative.
30. 30. EXHIBIT 16.EXHIBIT 16.44 Errors Associated with SamplingErrors Associated with Sampling
31. 31. Probability versusProbability versusNonprobability SamplingNonprobability Sampling Several alternative ways to takeSeveral alternative ways to takea sample are available.a sample are available. The main alternative samplingThe main alternative samplingplans may be grouped into twoplans may be grouped into twocategories:categories: 1. probability techniques1. probability techniques 2. nonprobability techniques.2. nonprobability techniques.
32. 32. Probability versus Nonprobability SamplingProbability versus Nonprobability Sampling(cont’d)(cont’d) Probability Sampling In probability sampling, every element inthe population has a known, nonzeroprobability of selection. The simple random sample, in which eachmember of the population has an equalprobability of being selected, is the best-known probability sample.
33. 33. Probability versus NonprobabilityProbability versus NonprobabilitySampling (cont’d)Sampling (cont’d) Nonprobability sampling In nonprobability sampling, the probability of anyparticular member of the population being chosenis unknown. The selection of sampling units in nonprobabilitysampling is quite arbitrary, as researchers relyheavily on personal judgment. Technically, no appropriate statistical techniquesexist for measuring random sampling error from anonprobability sample. Therefore, projecting the data beyond the sample istechnically speaking, statistically inappropriate. Nevertheless, nonprobability samples arepragmatic and are used in business research.
34. 34. 14-34Nonprobability SamplesNonprobability SamplesCostCostFeasibilityFeasibilityFeasibilityFeasibilityTimeTimeTimeTimeNo need toNo need togeneralizegeneralizeLimitedLimitedobjectivesobjectivesLimitedLimitedobjectivesobjectives
35. 35. 14-35NonprobabilityNonprobabilitySampling MethodsSampling MethodsConvenienceConvenienceConvenienceConvenienceJudgmentJudgmentJudgmentJudgmentQuotaQuotaQuotaQuotaSnowballSnowballSnowballSnowball
36. 36. Nonprobability SamplingNonprobability SamplingMethodsMethods Convenience Sampling Obtaining those people or units that are mostconveniently available. Mall interception survey is applying thismethod. Judgment (Purposive) Sampling An experienced individual selects the samplebased on personal judgment about someappropriate characteristic of the samplemember. E.g. Consumer Price Index (CPI)
37. 37. Nonprobability Sampling (cont’d)Nonprobability Sampling (cont’d) Quota Sampling Ensures that various subgroups of a population will berepresented on pertinent characteristics to the exact extent thatthe investigator desires. E.g. SOT – 20, SBS - 30 Possible Sources Of Bias Respondents chosen because they were: Similar to interviewer Easily found Willing to be interviewed Middle-class Advantages of Quota Sampling Speed of data collection Lower costs Convenience
38. 38. Nonprobability SamplingNonprobability Sampling(cont’d)(cont’d) Snowball Sampling A sampling procedure in which initialrespondents are selected by probabilitymethods and additional respondents areobtained from information provided by theinitial respondents. E.g. 1 respondent (selected throughprobability method) recommended another5 respondents; then the 5 additionalrespondents recommended another 25respondents.
39. 39. Probability SamplingProbability Sampling Simple Random Sampling Simple random sampling is a sampling procedurethat assures that each element in the populationwill have an equal chance of being included in thesample. Drawing names from a hat is a typical example ofsimple random sampling; each person has anequal chance of being selected. To use this method, we must have a list of allmembers in a population, then we draw lots. Systematic Sampling A starting point is selected by a random processand then every nth number on the list is selected. E.g. for the list of all members in a population,every 10thname will be selected.
40. 40. 14-40Simple RandomSimple RandomAdvantagesAdvantages•Easy to implementEasy to implementwith random dialingwith random dialingDisadvantagesDisadvantages•Requires list ofRequires list ofpopulation elementspopulation elements•Time consumingTime consuming•Larger sampleLarger sampleneededneeded•Produces largerProduces largererrorserrors•High costHigh cost
41. 41. 14-41SystematicSystematicAdvantagesAdvantages•Simple to designSimple to design•Easier than simpleEasier than simplerandomrandom•Easy to determineEasy to determinesampling distributionsampling distributionof mean or proportionof mean or proportionDisadvantagesDisadvantages•Periodicity withinPeriodicity withinpopulation may skewpopulation may skewsample and resultssample and results•Trends in list mayTrends in list maybias resultsbias results•Moderate costModerate cost
42. 42. Proportional versus DisproportionalProportional versus DisproportionalSamplingSampling Stratified Sampling Simple random subsamples that are more or less equal onsome characteristic are drawn from within each stratum(subgroup) of the population. E.g. based on the same characteristics, we divide studentsinto 3 subgroups (e.g. students with straight-pass,students with re-sit units, students with repeat units), thenwe use simple random sampling method to draw asubsample. Proportional Stratified Sample The number of sampling units drawn from each stratumis in proportion to the population size of that stratum. Disproportional Stratified Sample The sample size for each stratum is allocated accordingto analytical considerations.
43. 43. EXHIBIT 16.EXHIBIT 16.55 Disproportional Sampling: Hypothetical ExampleDisproportional Sampling: Hypothetical Example
44. 44. 14-44StratifiedStratifiedAdvantagesAdvantages•Control of sample size inControl of sample size instratastrata•Increased statisticalIncreased statisticalefficiencyefficiency•Provides data toProvides data torepresent and analyzerepresent and analyzesubgroupssubgroups•Enables use of differentEnables use of differentmethods in stratamethods in strataDisadvantagesDisadvantages•Increased error ifIncreased error ifsubgroups are selected atsubgroups are selected atdifferent ratesdifferent rates•Especially expensive ifEspecially expensive ifstrata on population muststrata on population mustbe createdbe created•High costHigh cost
45. 45. Cluster SamplingCluster Sampling The purpose of cluster sampling is to sampleeconomically while retaining the characteristics of aprobability sample. In a cluster sample, the primary sampling unit is nolonger the individual element in the population (e.g.,grocery stores) but a larger cluster of elementslocated in proximity to one another (e.g., cities). Cluster sampling is classified as a probabilitysampling technique because of either the randomselection of clusters or the random selection ofelements within each cluster. Cluster samples frequently are used when lists of thesample population are not available.
46. 46. EXHIBIT 16.EXHIBIT 16.66 Examples of ClustersExamples of Clusters
47. 47. 14-47ClusterClusterAdvantagesAdvantages•Provides an unbiasedProvides an unbiasedestimate of populationestimate of populationparameters if properlyparameters if properlydonedone•Economically moreEconomically moreefficient than simpleefficient than simplerandomrandom•Lowest cost per sampleLowest cost per sample•Easy to do without listEasy to do without listDisadvantagesDisadvantages•Often lower statisticalOften lower statisticalefficiency due toefficiency due tosubgroups beingsubgroups beinghomogeneous rather thanhomogeneous rather thanheterogeneousheterogeneous•Moderate costModerate cost
48. 48. Multistage Area SamplingMultistage Area Sampling Multistage Area Sampling Involves using a combination of two ormore probability sampling techniques. Typically, geographic areas are randomlyselected in progressively smaller (lower-population) units. Researchers may take as many steps asnecessary to achieve a representative sample. Progressively smaller geographic areas arechosen until a single housing unit is selectedfor interviewing.
49. 49. EXHIBIT 16.EXHIBIT 16.88 Geographic Hierarchy Inside Urbanized AreasGeographic Hierarchy Inside Urbanized Areas
50. 50. 14-50Stratified and Cluster SamplingStratified and Cluster SamplingStratifiedStratified•Population divided intoPopulation divided intofew subgroupsfew subgroups•Homogeneity withinHomogeneity withinsubgroupssubgroups•Heterogeneity betweenHeterogeneity betweensubgroupssubgroups•Choice of elementsChoice of elementsfrom within eachfrom within eachsubgroupsubgroupClusterCluster•Population divided intoPopulation divided intomany subgroupsmany subgroups•Heterogeneity withinHeterogeneity withinsubgroupssubgroups•Homogeneity betweenHomogeneity betweensubgroupssubgroups•Random choice ofRandom choice ofsubgroupssubgroups
51. 51. 14-51Area SamplingArea Sampling
52. 52. 14-52Double SamplingDouble SamplingAdvantagesAdvantages•May reduce costs ifMay reduce costs iffirst stage results infirst stage results inenough data to stratifyenough data to stratifyor cluster theor cluster thepopulationpopulationDisadvantagesDisadvantages•Increased costs ifIncreased costs ifdiscriminately useddiscriminately used
53. 53. What Is the AppropriateWhat Is the AppropriateSample Design? (cont’d)Sample Design? (cont’d) Resources The cost associated with the differentsampling techniques varies tremendously. If the researcher’s financial and humanresources are restricted, certain options willhave to be eliminated. Managers concerned with the cost of theresearch versus the value of the informationoften will opt for cost savings from a certainnonprobability sample design rather thanmake the decision to conduct no research atall.
54. 54. What Is the Appropriate SampleWhat Is the Appropriate SampleDesign? (cont’d)Design? (cont’d) Time Researchers who need to meet a deadline orcomplete a project quickly will be more likely toselect simple, less time-consuming sampledesigns. Advance Knowledge of the Population In many cases, a list of population elementswill not be available to the researcher. A lack of adequate listslack of adequate lists may automatically ruleout systematic sampling, stratified sampling,or other sampling designs, or it may dictatethat a preliminary study, such as a shorttelephone survey using random digit dialing,be conducted to generate information to builda sampling frame for the primary study.
55. 55. What Is the AppropriateWhat Is the AppropriateSample Design? (cont’d)Sample Design? (cont’d) National versus Local Project Geographic proximity of populationelements will influence sample design. When population elements are unequallydistributed geographically, a clustersample may become much more attractive.
56. 56. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.16–56EXHIBIT 16.EXHIBIT 16.99 Comparison of Sampling Techniques: Nonprobability SamplesComparison of Sampling Techniques: Nonprobability Samples
57. 57. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.16–57EXHIBIT 16.EXHIBIT 16.1010 Comparison of Sampling Techniques: Probability SamplesComparison of Sampling Techniques: Probability Samples
58. 58. Determination of sample sizeDetermination of sample size Descriptive and Inferential StatisticsThere are two applications ofstatistics:(1) to describe characteristics ofthe population or sample(descriptive statistics) and(2) to generalize from the sample tothe population (inferentialstatistics).
59. 59. Sample Statistics and PopulationSample Statistics and PopulationParametersParameters The primary purpose of inferential statistics is to make ajudgment about the population, or the collection of allelements about which one seeks information. The sample is a subset or relatively small fraction of thetotal number of elements in the population. Sample statistics are variables in the sample ormeasures computed from the sample data. Population parameters are variables or measuredcharacteristics of the population. We will generally use Greek lowercase letters to denotepopulation parameters (e.g., μ or σ) and English lettersto denote sample statistics (e.g., X or S).
60. 60. Making Data UsableMaking Data Usable To make data usable, this informationmust be organized and summarized. Methods for doing this include:frequency distributionsproportionsmeasures of central tendencyand dispersion
61. 61. Making Data Usable (cont’d)Making Data Usable (cont’d) Frequency Distributions Constructing a frequency table or frequencydistribution is one of the most common means ofsummarizing a set of data. The frequency of a value is the number of timesa particular value of a variable occurs. Exhibit 17.1 represents a frequency distributionof respondents’ answers to a question askinghow much customers had deposited in thesavings and loan. It is also quite simple to construct a distributionof relative frequency, or a percentagedistribution, which is developed by dividing thefrequency of each
62. 62. EXHIBIT 17.EXHIBIT 17.11 Frequency Distribution of DepositsFrequency Distribution of Deposits
63. 63. EXHIBIT 17.EXHIBIT 17.22 Percentage Distribution of DepositsPercentage Distribution of Deposits
64. 64. EXHIBIT 17.EXHIBIT 17.33 Probability Distribution of DepositsProbability Distribution of Deposits
65. 65. Population MeanMaking Data Usable (cont’d)Making Data Usable (cont’d) Proportion The percentage of elements that meetsome criterion Measures of Central Tendency Mean: the arithmetic average. Median: the midpoint; the value belowwhich half the values in a distribution fall. Mode: the value that occurs most often.Sample Mean
66. 66. EXHIBIT 17.EXHIBIT 17.44 Number of Sales Calls per Day by SalespersonNumber of Sales Calls per Day by Salesperson
67. 67. EXHIBIT 17.EXHIBIT 17.55 Sales Levels for Two Products with Identical Average SalesSales Levels for Two Products with Identical Average Sales
68. 68. Measures of DispersionMeasures of DispersionThe RangeThe distance between thesmallest and the largestvalues of a frequencydistribution.
69. 69. EXHIBIT 17.EXHIBIT 17.66 Low Dispersion versus High DispersionLow Dispersion versus High Dispersion
70. 70. Measures of Dispersion (cont’d)Measures of Dispersion (cont’d) Why Use the Standard Deviation? Variance A measure of variability or dispersion. Its square root is the standard deviation. Standard deviation A quantitative index of a distribution’s spread, orvariability; the square root of the variance for adistribution. The average of the amount of variance for adistribution. Used to calculate the likelihood (probability) of anevent occurring.
71. 71. Calculating DeviationCalculating DeviationStandard Deviation =
72. 72. EXHIBIT 17.EXHIBIT 17.77 Calculating a Standard Deviation: Number of Sales Calls per Day for EightCalculating a Standard Deviation: Number of Sales Calls per Day for EightSalespeopleSalespeople
73. 73. The Normal DistributionThe Normal Distribution Normal Distribution A symmetrical, bell-shaped distribution(normal curve) that describes the expectedprobability distribution of many chanceoccurrences. 99% of its values are within ± 3 standarddeviations from its mean. Example: IQ scores Standardized Normal Distribution A purely theoretical probability distributionthat reflects a specific normal curve for thestandardized value, z.
74. 74. EXHIBIT 17.EXHIBIT 17.88 Normal Distribution: Distribution of Intelligence Quotient (IQ) ScoresNormal Distribution: Distribution of Intelligence Quotient (IQ) Scores
75. 75. The Normal Distribution (cont’d)The Normal Distribution (cont’d) Characteristics of a Standardized NormalDistribution1. It is symmetrical about its mean; the tails onboth sides are equal.2. The mean identifies the normal curve’s highestpoint (the mode) and the vertical line aboutwhich this normal curve is symmetrical.3. The normal curve has an infinite number ofcases (it is a continuous distribution), and thearea under the curve has a probability densityequal to 1.0.4. The standardized normal distribution has amean of 0 and a standard deviation of 1.
76. 76. EXHIBIT 17.EXHIBIT 17.99 Standardized Normal DistributionStandardized Normal Distribution
77. 77. The Normal Distribution (cont’d)The Normal Distribution (cont’d) Standardized Values, Z Used to compare an individual value to thepopulation mean in units of the standarddeviation The standardized normal distribution can beused to translate/transform any normal variable,X, into the standardized value, Z. Researchers can evaluate the probability of theoccurrence of many events without anydifficulty.
78. 78. EXHIBIT 17.EXHIBIT 17.1010 Standardized Normal Table: Area under Half of the Normal CurveStandardized Normal Table: Area under Half of the Normal Curveaa
79. 79. EXHIBIT 17.EXHIBIT 17.1111 StandardizedStandardizedValues can beValues can beComputed fromComputed fromFlat or PeakedFlat or PeakedDistributionsDistributionsResulting in aResulting in aStandardizedStandardizedNormal CurveNormal Curve
80. 80. EXHIBIT 17.12EXHIBIT 17.12 Standardized Distribution CurveStandardized Distribution Curve
81. 81. 17–81Population Distribution, SamplePopulation Distribution, SampleDistribution, and SamplingDistribution, and SamplingDistributionDistribution Population Distribution A frequency distribution of the elements of apopulation. Sample Distribution A frequency distribution of a sample. Sampling Distribution A theoretical probability distribution of samplemeans for all possible samples of a certain sizedrawn from a particular population. Standard Error of the Mean The standard deviation of the samplingdistribution.
82. 82. Three Important DistributionsThree Important Distributions
83. 83. EXHIBIT 17.EXHIBIT 17.1313FundamentalFundamentalTypes ofTypes ofDistributionsDistributions
84. 84. Central-limit TheoremCentral-limit Theorem Central-limit Theorem The theory that, as sample size increases,the distribution of sample means of size n,randomly selected, approaches a normaldistribution.
85. 85. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.17–85EXHIBIT 17.14EXHIBIT 17.14The MeanThe MeanDistribution ofDistribution ofAnyAnyDistributionDistributionApproachesApproachesNormal asNormal as nnIncreasesIncreases
86. 86. EXHIBIT 17.15EXHIBIT 17.15 Population Distribution: Hypothetical Product DefectPopulation Distribution: Hypothetical Product Defect
87. 87. EXHIBIT 17.16EXHIBIT 17.16 Calculation of Population MeanCalculation of Population Mean
88. 88. EXHIBIT 17.17EXHIBIT 17.17 ArithmeticArithmeticMeans ofMeans ofSamples andSamples andFrequencyFrequencyDistributionDistributionof Sampleof SampleMeansMeans
89. 89. Estimation of Parameters and ConfidenceEstimation of Parameters and ConfidenceIntervals (for inference statistics)Intervals (for inference statistics) Point Estimates An estimate of the population mean in the formof a single value, usually the sample mean. Gives no information about the possible magnitudeof random sampling error. Confidence Interval Estimate A specified range of numbers within which apopulation mean is expected to lie. An estimate of the population mean based onthe knowledge that it will be equal to the samplemean plus or minus a small sampling error. i.e. μ = X + a small sampling error.
90. 90.  The information can be used toestimate market demand. E.g. with 95 percent confidence, theaverage number of unit used per week isbetween 2.3 and 2.9.
91. 91. Confidence IntervalsConfidence Intervals Confidence Level A percentage or decimal value that tellshow confident a researcher can be aboutbeing correct. It states the long-run percentage ofconfidence intervals that will include thetrue population mean. The crux of the problem for a researcher isto determine how much random samplingerror to tolerate. Traditionally, researchers have used the95% confidence level (a 5% tolerance forerror).
92. 92. Calculating a ConfidenceCalculating a ConfidenceIntervalIntervalEstimation of the sampling errorApproximate location (value) of the populationmean
93. 93. Calculating a Confidence IntervalCalculating a Confidence Interval(cont’d)(cont’d)
94. 94. Sample SizeSample Size Random Error and Sample Size Random sampling error varies with samplesof different sizes. Increases in sample size reduce samplingerror at a decreasing rate. Diminishing returns - random sampling error isinversely proportional to the square root of n.
95. 95. EXHIBIT 17.18EXHIBIT 17.18 Relationship between Sample Size and ErrorRelationship between Sample Size and Error
96. 96. EXHIBIT 17.19EXHIBIT 17.19 Statistical Information Needed to Determine Sample Size forStatistical Information Needed to Determine Sample Size forQuestions Involving MeansQuestions Involving Means
97. 97. Factors of Concern in ChoosingFactors of Concern in ChoosingSample SizeSample Size Variance (or Heterogeneity) A heterogeneous population has morevariance (a larger standard deviation) whichwill require a larger sample. A homogeneous population has lessvariance (a smaller standard deviation) whichpermits a smaller sample. Magnitude of Error (Confidence Interval) How precise must the estimate be? Confidence Level How much error will be tolerated? Forbusiness research, 95 percent confidence95 percent confidencelevel is used.
98. 98. Estimating Sample Size forEstimating Sample Size forQuestions Involving MeansQuestions Involving Means Sequential Sampling Conducting a pilot study to estimate thepopulation parameters so that another, largersample of the appropriate sample size may bedrawn. Estimating sample size:
99. 99. Sample Size ExampleSample Size Example Suppose a survey researcher, studying expenditureson lipstick, wishes to have a 95 percent confidencelevel (Z) and a range of error (E) of less than \$2.00.The estimate of the standard deviation is \$29.00.What is the calculated sample size?
100. 100. Sample Size ExampleSample Size Example Suppose, in the same example as the one before,the range of error (E) is acceptable at \$4.00. Samplesize is reduced.
101. 101. Calculating Sample Size at theCalculating Sample Size at the99 Percent Confidence Level99 Percent Confidence Level
102. 102. Determining Sample Size for ProportionsDetermining Sample Size for Proportions
103. 103. Determining Sample Size for ProportionsDetermining Sample Size for Proportions(cont’d)(cont’d)
104. 104. 753=001225.922.=001225)24)(.8416.3(=)035( .)4)(.6(.)961.(n4.q6.p22===Calculating Example SampleCalculating Example SampleSize at the 95 PercentSize at the 95 PercentConfidence LevelConfidence Level
105. 105. EXHIBIT 17.20EXHIBIT 17.20 Selected Tables for Determining Sample Size When the Characteristic ofSelected Tables for Determining Sample Size When the Characteristic ofInterest Is a ProportionInterest Is a Proportion
106. 106. EXHIBIT 17.21EXHIBIT 17.21 Allowance for Random Sampling Error (Plus and Minus PercentageAllowance for Random Sampling Error (Plus and Minus PercentagePoints) at 95 Percent Confidence LevelPoints) at 95 Percent Confidence Level
107. 107. The Nature of FieldworkThe Nature of Fieldwork Fieldworker An individual who is responsible forgathering data in the field. Typical fieldwork activities: Administering a questionnaire door to door Telephone interview calling from a centrallocation Counting pedestrians in a shopping mall Supervising the collection of data
108. 108. Making Initial ContactMaking Initial Contact Personal Interviews Making opening remarks that will convince therespondent that his or her cooperation is important. Telephone Interviews Giving the interviewer’s name personalizes the call. Providing the name of the research agency is usedto imply that the caller is trustworthy. Providing an accurate estimate of the time helpsgain cooperation. Internet Surveys Respondent may receive an e-mail requestingassistance.
109. 109. Gaining ParticipationGaining Participation Foot-in-the-Door Compliance Technique Compliance with large or difficult task isinduced by first obtaining the respondent’scompliance with a smaller request. Door-in-the-Face Compliance Technique A two-step process for securing a highresponse rate. Step 1: An initial request, so large that nearlyeveryone refuses it, is made. Step 2: A second request is made for a smallerfavour; respondents are expected to comply withthis more reasonable request.
110. 110. Asking the QuestionsAsking the Questions Major Rules for Asking Questions:1. Ask questions exactly as they are worded inthe questionnaire.2. Read each question very carefully andclearly.3. Ask the questions in the specified order.4. Ask every question specified in thequestionnaire.5. Repeat questions that are misunderstood ormisinterpreted.
111. 111. Probing When No Response IsProbing When No Response IsGivenGiven Probing Verbal attempts made by a field-worker whenthe respondent must be motivated tocommunicate his or her answers more fully. Probing Tactics that Enlarge and Clarify: Repeating the question Using a silent probe Repeating the respondent’s reply Asking a neutral question
112. 112. EXHIBIT 18.EXHIBIT 18.11 Commonly Used Probes and Their AbbreviationsCommonly Used Probes and Their Abbreviations
113. 113. Recording the ResponsesRecording the Responses Rules for recording responses to fixed-alternativequestions vary with the specific questionnaire. Rules for recording open-ended answers include: Record responses during the interview. Use the respondent’s own words. Do not summarize or paraphrase the respondent’s answer. Include everything that pertains to the question objectives. Include all of your probes. How answers are recorded can affect researchers’interpretation of the respondent’s answers.
114. 114. 18–114EXHIBIT 18.EXHIBIT 18.22 A Completed Portion of a Response Form with NotesA Completed Portion of a Response Form with Notes
115. 115. Terminating the InterviewTerminating the Interview How to close the interview is important: Fieldworkers should wait to close theinterview until they have secured all pertinentinformation including spontaneous commentsof the respondent. Fieldworkers should answer any respondentquestions concerning the nature and purposeof the study to the best of his or her ability. Avoiding hasty departures is a matter ofcourtesy. It is important to thank the respondent for hisor her time and cooperation as reinterviewingmay be required.
116. 116. Principles of Good InterviewingPrinciples of Good Interviewing The Basics:1. Have integrity, and be honest.2. Have patience and tact.3. Pay attention to accuracy and detail.4. Exhibit a real interest in the inquiry at hand,but keep your own opinions to yourself.5. Be a good listener.6. Keep the inquiry and respondents’ responsesconfidential.7. Respect others’ rights.
117. 117. Principles of GoodPrinciples of GoodInterviewing (cont’d)Interviewing (cont’d) Required Practices1. Complete the number of interviews according to thesampling plan assigned to you.2. Follow the directions provided.3. Make every effort to keep schedules.4. Keep control of each interview you do.5. Complete the questionnaires meticulously.6. Check over each questionnaire you have completed.7. Compare your sample execution and assigned quota withthe total number of questionnaires you have completed.8. Clear up any questions with the research agency.
118. 118. Further ReadingFurther Reading COOPER, D.R. AND SCHINDLER, P.S. (2011)BUSINESS RESEARCH METHODS, 11THEDN,MCGRAW HILL ZIKMUND, W.G., BABIN, B.J., CARR, J.C. ANDGRIFFIN, M. (2010) BUSINESS RESEARCHMETHODS, 8THEDN, SOUTH-WESTERN SAUNDERS, M., LEWIS, P. AND THORNHILL, A.(2012) RESEARCH METHODS FOR BUSINESSSTUDENTS, 6THEDN, PRENTICE HALL. SAUNDERS, M. AND LEWIS, P. (2012) DOINGRESEARCH IN BUSINESS & MANAGEMENT, FTPRENTICE HALL.
119. 119. DETERMINING SAMPLE SIZEDETERMINING SAMPLE SIZEAPPENDIXAPPENDIX
120. 120. 14-120Random SamplesRandom Samples
121. 121. 14-121Increasing PrecisionIncreasing Precision
122. 122. 14-122Confidence Levels & theConfidence Levels & theNormal CurveNormal Curve
123. 123. 14-123Standard ErrorsStandard ErrorsStandard Error(Z score)% of Area ApproximateDegree ofConfidence1.00 68.27 68%1.65 90.10 90%1.96 95.00 95%3.00 99.73 99%
124. 124. 14-124Central Limit TheoremCentral Limit Theorem
125. 125. 14-125Estimates of Dining VisitsEstimates of Dining VisitsConfidence Zscore% ofAreaInterval Range(visits permonth)68% 1.00 68.27 9.48-10.5290% 1.65 90.10 9.14-10.8695% 1.96 95.00 8.98-11.0299% 3.00 99.73 8.44-11.56
126. 126. 14-126Calculating Sample Size forCalculating Sample Size forQuestions involving MeansQuestions involving MeansPrecisionPrecisionConfidence levelConfidence levelSize of interval estimateSize of interval estimatePopulation DispersionPopulation DispersionNeed for FPANeed for FPA
127. 127. 14-127Metro U Sample Size for MeansMetro U Sample Size for MeansSteps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)Size of the interval estimate ±± .5 meals per month.5 meals per monthExpected range inpopulation0 to 30 meals0 to 30 mealsSample mean 1010Standard deviation 4.14.1Need for finite populationadjustmentNoNoStandard error of the mean .5/1.96 = .255.5/1.96 = .255Sample size (4.1)(4.1)22/ (.255)/ (.255)22= 259= 259
128. 128. 14-128Proxies of theProxies of thePopulation DispersionPopulation Dispersion Previous research on thePrevious research on thetopictopic Pilot test or pretestPilot test or pretest Rule-of-thumb calculationRule-of-thumb calculation 1/6 of the range1/6 of the range
129. 129. 14-129Metro U Sample Size forMetro U Sample Size forProportionsProportionsSteps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)Size of the interval estimate ±± .10 (10%).10 (10%)Expected range in population 0 to 100%0 to 100%Sample proportion with givenattribute30%30%Sample dispersion Pq = .30(1-.30) = .21Pq = .30(1-.30) = .21Finite population adjustment NoNoStandard error of theproportion.10/1.96 = .051.10/1.96 = .051Sample size .21/ (.051).21/ (.051)22= 81= 81
130. 130. 14-130Random SamplesRandom Samples
131. 131. 14-131Confidence LevelsConfidence Levels
132. 132. 14-132Metro U. Dining Club StudyMetro U. Dining Club Study