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Mba2216 week 09 10 sampling
 

Mba2216 week 09 10 sampling

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Sampling design, Sampling methods

Sampling design, Sampling methods

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  • 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

Mba2216 week 09 10 sampling Mba2216 week 09 10 sampling Presentation Transcript

  • Research Design :Research Design : Sampling &Sampling & Data CollectionData Collection Research Design :Research Design : Sampling &Sampling & Data CollectionData Collection MBA2216 BUSINESS RESEARCH PROJECTMBA2216 BUSINESS RESEARCH PROJECT by Stephen Ong Visiting Fellow, Birmingham City University, UK
  • 6-2 Design in the Research ProcessDesign in the Research Process
  • 14-3 Sampling DesignSampling Design within the Research Processwithin the Research Process
  • Sampling DesignSampling Design
  • LEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMES 1. Explain reasons for taking a sample rather than a complete census 2. Describe the process of identifying a target population and selecting a sampling frame 3. Compare random sampling and systematic (nonsampling) errors 4. Identify the types of nonprobability sampling, including their advantages and disadvantages After this lecture, you should be able to
  • LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d) 5. Summarize the advantages and disadvantages of the various types of probability samples 6. Discuss how to choose an appropriate sample design, as well as challenges for Internet sampling 7. Understand basic statistical terminology 8. Interpret frequency distributions, proportions, and measures of central tendency and dispersion 9. Distinguish among population, sample, and sampling distributions 10. Summarize the use of confidence interval estimates
  • 14-7 Small Samples Can EnlightenSmall Samples Can Enlighten ““The proof of the pudding is in theThe proof of the pudding is in the eating.eating. ByBy a small samplea small sample we may judge of thewe may judge of the whole piece.”whole piece.” Miguel de Cervantes SaavedraMiguel de Cervantes Saavedra authorauthor
  • 14-8 The Nature of SamplingThe Nature of Sampling PopulationPopulation Population ElementPopulation Element CensusCensus SampleSample Sampling frameSampling frame
  • Sampling TerminologySampling Terminology  Sample  A subset, or some part, of a larger population.  Population (universe)  Any complete group of entities that share some common set of characteristics.  Population Element  An individual member of a population.  Census  An investigation of all the individual elements that make up a population.
  • 14-10 Why Sample?Why Sample? GreaterGreater accuracyaccuracy AvailabilityAvailability of elementsof elements AvailabilityAvailability of elementsof elements GreaterGreater speedspeed GreaterGreater speedspeed SamplingSampling providesprovides SamplingSampling providesprovides LowerLower costcost LowerLower costcost
  • 14-11 What Is a SufficientlyWhat Is a Sufficiently Large Sample?Large Sample? ““In recent Gallup ‘Poll on polls,’ . . . When askedIn recent Gallup ‘Poll on polls,’ . . . When asked about the scientific sampling foundation on whichabout the scientific sampling foundation on which polls are based . . . most said that a survey ofpolls are based . . . most said that a survey of 1,500 – 2,000 respondents—a larger than average1,500 – 2,000 respondents—a larger than average sample size for national polls—cannot representsample size for national polls—cannot represent the views of all Americans.”the views of all Americans.” Frank NewportFrank Newport The Gallup Poll editor in chiefThe Gallup Poll editor in chief The Gallup OrganizationThe Gallup Organization
  • 14-12 When Is a CensusWhen Is a Census Appropriate?Appropriate? NecessaryNecessaryFeasibleFeasible
  • 14-13 What Is a Valid Sample?What Is a Valid Sample? AccurateAccurate PrecisePrecise
  • Why Sample?Why Sample?  Pragmatic Reasons  Budget and time constraints.  Limited access to total population.  Accurate and Reliable Results  Samples can yield reasonably accurate information.information.  Strong similaritiesStrong similarities in population elements makesin population elements makes sampling 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 finite populations.populations.
  • A Photographic Example of How Sampling WorksA Photographic Example of How Sampling Works
  • 16–16 Stages inStages in thethe SelectionSelection of aof a SampleSample
  • 14-17 Types of Sampling DesignsTypes of Sampling Designs Element Selection Probability Nonprobability •UnrestrictedUnrestricted • Simple randomSimple random • ConvenienceConvenience •RestrictedRestricted • Complex randomComplex random • PurposivePurposive • SystematicSystematic • JudgmentJudgment •ClusterCluster •QuotaQuota •StratifiedStratified •SnowballSnowball •DoubleDouble
  • 14-18 Steps in Sampling DesignSteps in Sampling Design What 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 of interest?interest? What are the parameters ofWhat are the parameters of interest?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 appropriate sampling method?sampling method? What is the appropriateWhat is the appropriate sampling method?sampling method? What size sample is needed?What size sample is needed?What size sample is needed?What size sample is needed?
  • 14-19 When to Use Larger Sample?When to Use Larger Sample? DesiredDesired precisionprecision DesiredDesired precisionprecision Number ofNumber of subgroupssubgroups Number ofNumber of subgroupssubgroups ConfidenceConfidence levellevel ConfidenceConfidence levellevel PopulationPopulation variancevariance Small errorSmall error rangerange
  • Practical Sampling ConceptsPractical Sampling Concepts  Defining the Target Population  Once the decision to sample has been made, the first question concerns identifying the target population.  What is the relevant population? In many cases this is easy to answer, but in other cases, the decision may be difficult.  At the outset of the sampling process it is vitally important to carefully define the target population so that the proper source from which the data are to be collected can be identified.  To implement the sample in the field, tangible characteristics (e.g. age, gender etc) should be used to define the population.
  • Practical Sampling ConceptsPractical Sampling Concepts (cont’d)(cont’d)  The Sampling Frame  In practice, the sample will be drawn from a list of population elements that often differs somewhat from the defined target population.  A sampling frame is a list of elements from which the sample may be drawn.  The sampling frame is also called the working population, because these units will eventually provide units involved in the analysis.  The discrepancy between the definition of the population and a sampling frame is the first potential source of error associated with sample selection.
  • ExampleExample  Target population: Students in Malaysia between 18 years old and 22 years old.  Sampling frame: students from a higher education institution.
  • Practical Sampling ConceptsPractical Sampling Concepts (cont’d)(cont’d)  The Sampling Frame  A sampling frame error occurs when certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame.  Population elements can be either under- or overrepresented in a sampling frame.
  • Sampling UnitsSampling Units  Sampling Unit  A single element or group of elements subject 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 of sampling.  Tertiary Sampling Unit  A unit selected in the third stage of sampling.
  • EXAMPLE Target population: Students in Malaysia between 18 years old and 22 years old. Sample frame: students from a higher education institution. Sampling units:  Advanced Diploma students only (primary sampling unit)  School of Business Studies only (secondary sampling unit)  ABU only (tertiary sampling unit) 16–25
  • Random Sampling andRandom Sampling and Nonsampling ErrorsNonsampling Errors  If a difference exists between the value of a sample statistic of interest and the value of the corresponding population parameter, a statistical error has occurred.  Two basic causes of differences between statistics and parameters: random sampling errors systematic (nonsampling) errors
  • Random Sampling and Nonsampling Errors (cont’d)Random Sampling and Nonsampling Errors (cont’d)  Random Sampling Error  Random sampling error is the difference between the sample result and the result of a census conducted using identical procedures.  Random sampling error occurs because of chance variation 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 generally good approximations of the population.  Random sampling error is a function of sample size.  As sample size increases, random sampling error decreases  It is possible to estimate the random sampling error that may be expected with various sample sizes.
  • Random Sampling andRandom Sampling and Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)  Systematic Sampling Error  Systematic (nonsampling) errors result from nonsampling factors, primarily the nature of a study’s design and the correctness of execution.  These errors are not due to chance fluctuations.  Sample biases account for a large portion of errors in research.
  • Random Sampling andRandom Sampling and Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)  Less than Perfectly Representative Samples  Random sampling errors and systematic errors associated with the sampling process may combine to yield a sample that is less than perfectly representative of the population.  Additional errors will occur if individuals refuse to be interviewed or cannot be contacted.  Such nonresponse error may also cause the sample to be less than perfectly representative.
  • EXHIBIT 16.EXHIBIT 16.44 Errors Associated with SamplingErrors Associated with Sampling
  • Probability versusProbability versus Nonprobability SamplingNonprobability Sampling  Several alternative ways to takeSeveral alternative ways to take a sample are available.a sample are available.  The main alternative samplingThe main alternative sampling plans may be grouped into twoplans may be grouped into two categories:categories:  1. probability techniques1. probability techniques  2. nonprobability techniques.2. nonprobability techniques.
  • Probability versus Nonprobability SamplingProbability versus Nonprobability Sampling (cont’d)(cont’d)  Probability Sampling  In probability sampling, every element in the population has a known, nonzero probability of selection.  The simple random sample, in which each member of the population has an equal probability of being selected, is the best- known probability sample.
  • Probability versus NonprobabilityProbability versus Nonprobability Sampling (cont’d)Sampling (cont’d)  Nonprobability sampling  In nonprobability sampling, the probability of any particular member of the population being chosen is unknown.  The selection of sampling units in nonprobability sampling is quite arbitrary, as researchers rely heavily on personal judgment.  Technically, no appropriate statistical techniques exist for measuring random sampling error from a nonprobability sample.  Therefore, projecting the data beyond the sample is technically speaking, statistically inappropriate.  Nevertheless, nonprobability samples are pragmatic and are used in business research.
  • 14-34 Nonprobability SamplesNonprobability Samples CostCost FeasibilityFeasibilityFeasibilityFeasibility TimeTimeTimeTime No need toNo need to generalizegeneralize LimitedLimited objectivesobjectives LimitedLimited objectivesobjectives
  • 14-35 NonprobabilityNonprobability Sampling MethodsSampling Methods ConvenienceConvenienceConvenienceConvenience JudgmentJudgmentJudgmentJudgment QuotaQuotaQuotaQuota SnowballSnowballSnowballSnowball
  • Nonprobability SamplingNonprobability Sampling MethodsMethods  Convenience Sampling  Obtaining those people or units that are most conveniently available.  Mall interception survey is applying this method.  Judgment (Purposive) Sampling  An experienced individual selects the sample based on personal judgment about some appropriate characteristic of the sample member.  E.g. Consumer Price Index (CPI)
  • Nonprobability Sampling (cont’d)Nonprobability Sampling (cont’d)  Quota Sampling  Ensures that various subgroups of a population will be represented on pertinent characteristics to the exact extent that the 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
  • Nonprobability SamplingNonprobability Sampling (cont’d)(cont’d)  Snowball Sampling  A sampling procedure in which initial respondents are selected by probability methods and additional respondents are obtained from information provided by the initial respondents.  E.g. 1 respondent (selected through probability method) recommended another 5 respondents; then the 5 additional respondents recommended another 25 respondents.
  • Probability SamplingProbability Sampling Simple Random Sampling  Simple random sampling is a sampling procedure that assures that each element in the population will have an equal chance of being included in the sample.  Drawing names from a hat is a typical example of simple random sampling; each person has an equal chance of being selected.  To use this method, we must have a list of all members in a population, then we draw lots.  Systematic Sampling  A starting point is selected by a random process and then every nth number on the list is selected.  E.g. for the list of all members in a population, every 10th name will be selected.
  • 14-40 Simple RandomSimple Random AdvantagesAdvantages •Easy to implementEasy to implement with random dialingwith random dialing DisadvantagesDisadvantages •Requires list ofRequires list of population elementspopulation elements •Time consumingTime consuming •Larger sampleLarger sample neededneeded •Produces largerProduces larger errorserrors •High costHigh cost
  • 14-41 SystematicSystematic AdvantagesAdvantages •Simple to designSimple to design •Easier than simpleEasier than simple randomrandom •Easy to determineEasy to determine sampling distributionsampling distribution of mean or proportionof mean or proportion DisadvantagesDisadvantages •Periodicity withinPeriodicity within population may skewpopulation may skew sample and resultssample and results •Trends in list mayTrends in list may bias resultsbias results •Moderate costModerate cost
  • Proportional versus DisproportionalProportional versus Disproportional SamplingSampling Stratified Sampling  Simple random subsamples that are more or less equal on some characteristic are drawn from within each stratum (subgroup) of the population.  E.g. based on the same characteristics, we divide students into 3 subgroups (e.g. students with straight-pass, students with re-sit units, students with repeat units), then we use simple random sampling method to draw a subsample.  Proportional Stratified Sample  The number of sampling units drawn from each stratum is in proportion to the population size of that stratum.  Disproportional Stratified Sample  The sample size for each stratum is allocated according to analytical considerations.
  • EXHIBIT 16.EXHIBIT 16.55 Disproportional Sampling: Hypothetical ExampleDisproportional Sampling: Hypothetical Example
  • 14-44 StratifiedStratified AdvantagesAdvantages •Control of sample size inControl of sample size in stratastrata •Increased statisticalIncreased statistical efficiencyefficiency •Provides data toProvides data to represent and analyzerepresent and analyze subgroupssubgroups •Enables use of differentEnables use of different methods in stratamethods in strata DisadvantagesDisadvantages •Increased error ifIncreased error if subgroups are selected atsubgroups are selected at different ratesdifferent rates •Especially expensive ifEspecially expensive if strata on population muststrata on population must be createdbe created •High costHigh cost
  • Cluster SamplingCluster Sampling  The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample.  In a cluster sample, the primary sampling unit is no longer the individual element in the population (e.g., grocery stores) but a larger cluster of elements located in proximity to one another (e.g., cities).  Cluster sampling is classified as a probability sampling technique because of either the random selection of clusters or the random selection of elements within each cluster.  Cluster samples frequently are used when lists of the sample population are not available.
  • EXHIBIT 16.EXHIBIT 16.66 Examples of ClustersExamples of Clusters
  • 14-47 ClusterCluster AdvantagesAdvantages •Provides an unbiasedProvides an unbiased estimate of populationestimate of population parameters if properlyparameters if properly donedone •Economically moreEconomically more efficient than simpleefficient than simple randomrandom •Lowest cost per sampleLowest cost per sample •Easy to do without listEasy to do without list DisadvantagesDisadvantages •Often lower statisticalOften lower statistical efficiency due toefficiency due to subgroups beingsubgroups being homogeneous rather thanhomogeneous rather than heterogeneousheterogeneous •Moderate costModerate cost
  • Multistage Area SamplingMultistage Area Sampling  Multistage Area Sampling  Involves using a combination of two or more probability sampling techniques.  Typically, geographic areas are randomly selected in progressively smaller (lower- population) units.  Researchers may take as many steps as necessary to achieve a representative sample.  Progressively smaller geographic areas are chosen until a single housing unit is selected for interviewing.
  • EXHIBIT 16.EXHIBIT 16.88 Geographic Hierarchy Inside Urbanized AreasGeographic Hierarchy Inside Urbanized Areas
  • 14-50 Stratified and Cluster SamplingStratified and Cluster Sampling StratifiedStratified •Population divided intoPopulation divided into few subgroupsfew subgroups •Homogeneity withinHomogeneity within subgroupssubgroups •Heterogeneity betweenHeterogeneity between subgroupssubgroups •Choice of elementsChoice of elements from within eachfrom within each subgroupsubgroup ClusterCluster •Population divided intoPopulation divided into many subgroupsmany subgroups •Heterogeneity withinHeterogeneity within subgroupssubgroups •Homogeneity betweenHomogeneity between subgroupssubgroups •Random choice ofRandom choice of subgroupssubgroups
  • 14-51 Area SamplingArea Sampling
  • 14-52 Double SamplingDouble Sampling AdvantagesAdvantages •May reduce costs ifMay reduce costs if first stage results infirst stage results in enough data to stratifyenough data to stratify or cluster theor cluster the populationpopulation DisadvantagesDisadvantages •Increased costs ifIncreased costs if discriminately useddiscriminately used
  • What Is the AppropriateWhat Is the Appropriate Sample Design? (cont’d)Sample Design? (cont’d)  Resources  The cost associated with the different sampling techniques varies tremendously.  If the researcher’s financial and human resources are restricted, certain options will have to be eliminated.  Managers concerned with the cost of the research versus the value of the information often will opt for cost savings from a certain nonprobability sample design rather than make the decision to conduct no research at all.
  • What Is the Appropriate SampleWhat Is the Appropriate Sample Design? (cont’d)Design? (cont’d) Time  Researchers who need to meet a deadline or complete a project quickly will be more likely to select simple, less time-consuming sample designs.  Advance Knowledge of the Population  In many cases, a list of population elements will not be available to the researcher.  A lack of adequate listslack of adequate lists may automatically rule out systematic sampling, stratified sampling, or other sampling designs, or it may dictate that a preliminary study, such as a short telephone survey using random digit dialing, be conducted to generate information to build a sampling frame for the primary study.
  • What Is the AppropriateWhat Is the Appropriate Sample Design? (cont’d)Sample Design? (cont’d)  National versus Local Project  Geographic proximity of population elements will influence sample design.  When population elements are unequally distributed geographically, a cluster sample may become much more attractive.
  • © 2010 South-Western/Cengage Learning. All rights reserved. May not be scanned, copied or duplicated, or posted to a publically accessible website, in whole or in part. 16–56 EXHIBIT 16.EXHIBIT 16.99 Comparison of Sampling Techniques: Nonprobability SamplesComparison of Sampling Techniques: Nonprobability Samples
  • © 2010 South-Western/Cengage Learning. All rights reserved. May not be scanned, copied or duplicated, or posted to a publically accessible website, in whole or in part. 16–57 EXHIBIT 16.EXHIBIT 16.1010 Comparison of Sampling Techniques: Probability SamplesComparison of Sampling Techniques: Probability Samples
  • Determination of sample sizeDetermination of sample size  Descriptive and Inferential Statistics There are two applications of statistics: (1) to describe characteristics of the population or sample (descriptive statistics) and (2) to generalize from the sample to the population (inferential statistics).
  • Sample Statistics and PopulationSample Statistics and Population ParametersParameters  The primary purpose of inferential statistics is to make a judgment about the population, or the collection of all elements about which one seeks information.  The sample is a subset or relatively small fraction of the total number of elements in the population.  Sample statistics are variables in the sample or measures computed from the sample data.  Population parameters are variables or measured characteristics of the population.  We will generally use Greek lowercase letters to denote population parameters (e.g., μ or σ) and English letters to denote sample statistics (e.g., X or S).
  • Making Data UsableMaking Data Usable  To make data usable, this information must be organized and summarized.  Methods for doing this include: frequency distributions proportions measures of central tendency and dispersion
  • Making Data Usable (cont’d)Making Data Usable (cont’d)  Frequency Distributions  Constructing a frequency table or frequency distribution is one of the most common means of summarizing a set of data.  The frequency of a value is the number of times a particular value of a variable occurs.  Exhibit 17.1 represents a frequency distribution of respondents’ answers to a question asking how much customers had deposited in the savings and loan.  It is also quite simple to construct a distribution of relative frequency, or a percentage distribution, which is developed by dividing the frequency of each
  • EXHIBIT 17.EXHIBIT 17.11 Frequency Distribution of DepositsFrequency Distribution of Deposits
  • EXHIBIT 17.EXHIBIT 17.22 Percentage Distribution of DepositsPercentage Distribution of Deposits
  • EXHIBIT 17.EXHIBIT 17.33 Probability Distribution of DepositsProbability Distribution of Deposits
  • Population Mean Making Data Usable (cont’d)Making Data Usable (cont’d)  Proportion  The percentage of elements that meet some criterion  Measures of Central Tendency  Mean: the arithmetic average.  Median: the midpoint; the value below which half the values in a distribution fall.  Mode: the value that occurs most often. Sample Mean
  • EXHIBIT 17.EXHIBIT 17.44 Number of Sales Calls per Day by SalespersonNumber of Sales Calls per Day by Salesperson
  • EXHIBIT 17.EXHIBIT 17.55 Sales Levels for Two Products with Identical Average SalesSales Levels for Two Products with Identical Average Sales
  • Measures of DispersionMeasures of Dispersion The Range The distance between the smallest and the largest values of a frequency distribution.
  • EXHIBIT 17.EXHIBIT 17.66 Low Dispersion versus High DispersionLow Dispersion versus High Dispersion
  • 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, or variability; the square root of the variance for a distribution.  The average of the amount of variance for a distribution.  Used to calculate the likelihood (probability) of an event occurring.
  • Calculating DeviationCalculating Deviation Standard Deviation =
  • 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 Eight SalespeopleSalespeople
  • The Normal DistributionThe Normal Distribution  Normal Distribution  A symmetrical, bell-shaped distribution (normal curve) that describes the expected probability distribution of many chance occurrences.  99% of its values are within ± 3 standard deviations from its mean.  Example: IQ scores  Standardized Normal Distribution  A purely theoretical probability distribution that reflects a specific normal curve for the standardized value, z.
  • EXHIBIT 17.EXHIBIT 17.88 Normal Distribution: Distribution of Intelligence Quotient (IQ) ScoresNormal Distribution: Distribution of Intelligence Quotient (IQ) Scores
  • The Normal Distribution (cont’d)The Normal Distribution (cont’d)  Characteristics of a Standardized Normal Distribution 1. It is symmetrical about its mean; the tails on both sides are equal. 2. The mean identifies the normal curve’s highest point (the mode) and the vertical line about which this normal curve is symmetrical. 3. The normal curve has an infinite number of cases (it is a continuous distribution), and the area under the curve has a probability density equal to 1.0. 4. The standardized normal distribution has a mean of 0 and a standard deviation of 1.
  • EXHIBIT 17.EXHIBIT 17.99 Standardized Normal DistributionStandardized Normal Distribution
  • The Normal Distribution (cont’d)The Normal Distribution (cont’d)  Standardized Values, Z  Used to compare an individual value to the population mean in units of the standard deviation  The standardized normal distribution can be used to translate/transform any normal variable, X, into the standardized value, Z.  Researchers can evaluate the probability of the occurrence of many events without any difficulty.
  • EXHIBIT 17.EXHIBIT 17.1010 Standardized Normal Table: Area under Half of the Normal CurveStandardized Normal Table: Area under Half of the Normal Curveaa
  • EXHIBIT 17.EXHIBIT 17.1111 StandardizedStandardized Values can beValues can be Computed fromComputed from Flat or PeakedFlat or Peaked DistributionsDistributions Resulting in aResulting in a StandardizedStandardized Normal CurveNormal Curve
  • EXHIBIT 17.12EXHIBIT 17.12 Standardized Distribution CurveStandardized Distribution Curve
  • 17–81 Population Distribution, SamplePopulation Distribution, Sample Distribution, and SamplingDistribution, and Sampling DistributionDistribution Population Distribution  A frequency distribution of the elements of a population.  Sample Distribution  A frequency distribution of a sample.  Sampling Distribution  A theoretical probability distribution of sample means for all possible samples of a certain size drawn from a particular population.  Standard Error of the Mean  The standard deviation of the sampling distribution.
  • Three Important DistributionsThree Important Distributions
  • EXHIBIT 17.EXHIBIT 17.1313 FundamentalFundamental Types ofTypes of DistributionsDistributions
  • 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 normal distribution.
  • © 2010 South-Western/Cengage Learning. All rights reserved. May not be scanned, copied or duplicated, or posted to a publically accessible website, in whole or in part. 17–85 EXHIBIT 17.14EXHIBIT 17.14 The MeanThe Mean Distribution ofDistribution of AnyAny DistributionDistribution ApproachesApproaches Normal asNormal as nn IncreasesIncreases
  • EXHIBIT 17.15EXHIBIT 17.15 Population Distribution: Hypothetical Product DefectPopulation Distribution: Hypothetical Product Defect
  • EXHIBIT 17.16EXHIBIT 17.16 Calculation of Population MeanCalculation of Population Mean
  • EXHIBIT 17.17EXHIBIT 17.17 ArithmeticArithmetic Means ofMeans of Samples andSamples and FrequencyFrequency DistributionDistribution of Sampleof Sample MeansMeans
  • Estimation of Parameters and ConfidenceEstimation of Parameters and Confidence Intervals (for inference statistics)Intervals (for inference statistics)  Point Estimates  An estimate of the population mean in the form of a single value, usually the sample mean.  Gives no information about the possible magnitude of random sampling error.  Confidence Interval Estimate  A specified range of numbers within which a population mean is expected to lie.  An estimate of the population mean based on the knowledge that it will be equal to the sample mean plus or minus a small sampling error.  i.e. μ = X + a small sampling error.
  •  The information can be used to estimate market demand.  E.g. with 95 percent confidence, the average number of unit used per week is between 2.3 and 2.9.
  • Confidence IntervalsConfidence Intervals  Confidence Level  A percentage or decimal value that tells how confident a researcher can be about being correct.  It states the long-run percentage of confidence intervals that will include the true population mean.  The crux of the problem for a researcher is to determine how much random sampling error to tolerate.  Traditionally, researchers have used the 95% confidence level (a 5% tolerance for error).
  • Calculating a ConfidenceCalculating a Confidence IntervalInterval Estimation of the sampling error Approximate location (value) of the population mean
  • Calculating a Confidence IntervalCalculating a Confidence Interval (cont’d)(cont’d)
  • Sample SizeSample Size  Random Error and Sample Size  Random sampling error varies with samples of different sizes.  Increases in sample size reduce sampling error at a decreasing rate.  Diminishing returns - random sampling error is inversely proportional to the square root of n.
  • EXHIBIT 17.18EXHIBIT 17.18 Relationship between Sample Size and ErrorRelationship between Sample Size and Error
  • EXHIBIT 17.19EXHIBIT 17.19 Statistical Information Needed to Determine Sample Size forStatistical Information Needed to Determine Sample Size for Questions Involving MeansQuestions Involving Means
  • Factors of Concern in ChoosingFactors of Concern in Choosing Sample SizeSample Size  Variance (or Heterogeneity)  A heterogeneous population has more variance (a larger standard deviation) which will require a larger sample.  A homogeneous population has less variance (a smaller standard deviation) which permits a smaller sample.  Magnitude of Error (Confidence Interval)  How precise must the estimate be?  Confidence Level  How much error will be tolerated? For business research, 95 percent confidence95 percent confidence level is used.
  • Estimating Sample Size forEstimating Sample Size for Questions Involving MeansQuestions Involving Means  Sequential Sampling  Conducting a pilot study to estimate the population parameters so that another, larger sample of the appropriate sample size may be drawn.  Estimating sample size:
  • Sample Size ExampleSample Size Example  Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95 percent confidence level (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?
  • Sample Size ExampleSample Size Example  Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00. Sample size is reduced.
  • Calculating Sample Size at theCalculating Sample Size at the 99 Percent Confidence Level99 Percent Confidence Level
  • Determining Sample Size for ProportionsDetermining Sample Size for Proportions
  • Determining Sample Size for ProportionsDetermining Sample Size for Proportions (cont’d)(cont’d)
  • 753= 001225. 922. = 001225 )24)(.8416.3( = )035( . )4)(.6(.)961.( n 4.q 6.p 2 2 = = = Calculating Example SampleCalculating Example Sample Size at the 95 PercentSize at the 95 Percent Confidence LevelConfidence Level
  • EXHIBIT 17.20EXHIBIT 17.20 Selected Tables for Determining Sample Size When the Characteristic ofSelected Tables for Determining Sample Size When the Characteristic of Interest Is a ProportionInterest Is a Proportion
  • EXHIBIT 17.21EXHIBIT 17.21 Allowance for Random Sampling Error (Plus and Minus PercentageAllowance for Random Sampling Error (Plus and Minus Percentage Points) at 95 Percent Confidence LevelPoints) at 95 Percent Confidence Level
  • The Nature of FieldworkThe Nature of Fieldwork  Fieldworker  An individual who is responsible for gathering data in the field.  Typical fieldwork activities:  Administering a questionnaire door to door  Telephone interview calling from a central location  Counting pedestrians in a shopping mall  Supervising the collection of data
  • Making Initial ContactMaking Initial Contact  Personal Interviews  Making opening remarks that will convince the respondent 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 used to imply that the caller is trustworthy.  Providing an accurate estimate of the time helps gain cooperation.  Internet Surveys  Respondent may receive an e-mail requesting assistance.
  • Gaining ParticipationGaining Participation  Foot-in-the-Door Compliance Technique  Compliance with large or difficult task is induced by first obtaining the respondent’s compliance with a smaller request.  Door-in-the-Face Compliance Technique  A two-step process for securing a high response rate.  Step 1: An initial request, so large that nearly everyone refuses it, is made.  Step 2: A second request is made for a smaller favour; respondents are expected to comply with this more reasonable request.
  • Asking the QuestionsAsking the Questions  Major Rules for Asking Questions: 1. Ask questions exactly as they are worded in the questionnaire. 2. Read each question very carefully and clearly. 3. Ask the questions in the specified order. 4. Ask every question specified in the questionnaire. 5. Repeat questions that are misunderstood or misinterpreted.
  • Probing When No Response IsProbing When No Response Is GivenGiven  Probing  Verbal attempts made by a field-worker when the respondent must be motivated to communicate 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
  • EXHIBIT 18.EXHIBIT 18.11 Commonly Used Probes and Their AbbreviationsCommonly Used Probes and Their Abbreviations
  • Recording the ResponsesRecording the Responses  Rules for recording responses to fixed-alternative questions 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.
  • 18–114 EXHIBIT 18.EXHIBIT 18.22 A Completed Portion of a Response Form with NotesA Completed Portion of a Response Form with Notes
  • Terminating the InterviewTerminating the Interview  How to close the interview is important:  Fieldworkers should wait to close the interview until they have secured all pertinent information including spontaneous comments of the respondent.  Fieldworkers should answer any respondent questions concerning the nature and purpose of the study to the best of his or her ability.  Avoiding hasty departures is a matter of courtesy.  It is important to thank the respondent for his or her time and cooperation as reinterviewing may be required.
  • 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’ responses confidential. 7. Respect others’ rights.
  • Principles of GoodPrinciples of Good Interviewing (cont’d)Interviewing (cont’d)  Required Practices 1. Complete the number of interviews according to the sampling 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 with the total number of questionnaires you have completed. 8. Clear up any questions with the research agency.
  • Further ReadingFurther Reading  COOPER, D.R. AND SCHINDLER, P.S. (2011) BUSINESS RESEARCH METHODS, 11TH EDN, MCGRAW HILL  ZIKMUND, W.G., BABIN, B.J., CARR, J.C. AND GRIFFIN, M. (2010) BUSINESS RESEARCH METHODS, 8TH EDN, SOUTH-WESTERN  SAUNDERS, M., LEWIS, P. AND THORNHILL, A. (2012) RESEARCH METHODS FOR BUSINESS STUDENTS, 6TH EDN, PRENTICE HALL.  SAUNDERS, M. AND LEWIS, P. (2012) DOING RESEARCH IN BUSINESS & MANAGEMENT, FT PRENTICE HALL.
  • DETERMINING SAMPLE SIZEDETERMINING SAMPLE SIZE APPENDIXAPPENDIX
  • 14-120 Random SamplesRandom Samples
  • 14-121 Increasing PrecisionIncreasing Precision
  • 14-122 Confidence Levels & theConfidence Levels & the Normal CurveNormal Curve
  • 14-123 Standard ErrorsStandard Errors Standard Error (Z score) % of Area Approximate Degree of Confidence 1.00 68.27 68% 1.65 90.10 90% 1.96 95.00 95% 3.00 99.73 99%
  • 14-124 Central Limit TheoremCentral Limit Theorem
  • 14-125 Estimates of Dining VisitsEstimates of Dining Visits Confidence Z score % of Area Interval Range (visits per month) 68% 1.00 68.27 9.48-10.52 90% 1.65 90.10 9.14-10.86 95% 1.96 95.00 8.98-11.02 99% 3.00 99.73 8.44-11.56
  • 14-126 Calculating Sample Size forCalculating Sample Size for Questions involving MeansQuestions involving Means PrecisionPrecision Confidence levelConfidence level Size of interval estimateSize of interval estimate Population DispersionPopulation Dispersion Need for FPANeed for FPA
  • 14-127 Metro U Sample Size for MeansMetro U Sample Size for Means Steps InformationInformation Desired confidence level 95% (z = 1.96)95% (z = 1.96) Size of the interval estimate ±± .5 meals per month.5 meals per month Expected range in population 0 to 30 meals0 to 30 meals Sample mean 1010 Standard deviation 4.14.1 Need for finite population adjustment NoNo Standard error of the mean .5/1.96 = .255.5/1.96 = .255 Sample size (4.1)(4.1)22 / (.255)/ (.255)22 = 259= 259
  • 14-128 Proxies of theProxies of the Population DispersionPopulation Dispersion  Previous research on thePrevious research on the topictopic  Pilot test or pretestPilot test or pretest  Rule-of-thumb calculationRule-of-thumb calculation  1/6 of the range1/6 of the range
  • 14-129 Metro U Sample Size forMetro U Sample Size for ProportionsProportions Steps InformationInformation Desired 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 given attribute 30%30% Sample dispersion Pq = .30(1-.30) = .21Pq = .30(1-.30) = .21 Finite population adjustment NoNo Standard error of the proportion .10/1.96 = .051.10/1.96 = .051 Sample size .21/ (.051).21/ (.051)22 = 81= 81
  • 14-130 Random SamplesRandom Samples
  • 14-131 Confidence LevelsConfidence Levels
  • 14-132 Metro U. Dining Club StudyMetro U. Dining Club Study