2 SamplingThe process of obtaining information from a subset (sample) of a larger group (population)The results for the sample are then used to make estimates of the larger groupFaster and cheaper than asking the entire populationTwo keysSelecting the right peopleHave to be selected scientifically so that they are representative of the populationSelecting the right number of the right peopleTo minimize sampling errors I.e. choosing the wrong people by chance
3 SAMPLINGSample -- contacting a portion of the population (e.g., 10% or 25%)best with a very large population (n)easiest with a homogeneous populationCensus -- the entire populationmost useful if the population ("n") is smallor the cost of making an error is high
4 Population Vs. SamplePopulation of InterestPopulation SampleParameter StatisticSampleWe measure the sample using statistics in order to drawinferences about the population and its parameters.
5 Characteristics of Good Samples RepresentativeAccessibleLow cost
8 Terminology Population Element (sampling unit) The entire group of people of interest from whom the researcher needs to obtain information.Element (sampling unit)one unit from a populationSamplingThe selection of a subset of the populationSampling FrameListing of population from which a sample is chosenCensusA polling of the entire populationSurveyA polling of the sample
9 Terminology Parameter Statistic Goal Critical Assumption The variable of interestStatisticThe information obtained from the sample about the parameterGoalTo be able to make inferences about the population parameter from knowledge of the relevant statistic - to draw general conclusions about the entire body of unitsCritical AssumptionThe sample chosen is representative of the population
10 Steps in Sampling Process 1. Define the population2. Identify the sampling frame3. Select a sampling design or procedure4. Determine the sample size5. Draw the sample
12 1. Define the Target Population Question: “Who, ideally, do you want to survey?”Answer: those who have the information sought.What are their characteristics.Who should be excluded?age, gender, product use, those in industryGeographic areaIt involvesdefining population unitssetting population boundariesScreening (e.g. security questions, product use )
13 1. Define the Target Population The Element individualsfamiliesseminar groupssampling Unit… individuals over 20families with 2 kidsseminar groups at ”new” universityExtent individuals who have bought “one”families who eat fast foodseminar groups doing MRTiming bought over the last seven days
14 1. Define the Target Population The target population for a toy store can be defined as all households with children living in Calgary.What’s wrong with this definition?
15 2. Determine the Sampling Frame Obtaining a “list” of population (how will you reach sample)Students who eat at McDonalds?young people at random in the street?phone bookstudents union listingUniversity mailing listProblems with listsomissionsineligiblesduplicationsProceduresE.g. individuals who have spent two or more hours on the internet in the last week
16 2. Determine the Sampling Frame Select “sample units”IndividualsHouseholdStreetsCompanies
17 3. Selecting a Sampling Design Probability sampling - equal chance of being included in the sample (random)simple random samplingsystematic samplingstratified samplingcluster samplingNon-probability sampling - - unequal chance of being included in the sample (non-random)convenience samplingjudgement samplingsnowball samplingquota sampling
18 3. Selecting a Sampling Design Probability SamplingAn objective procedure in which the probability of selection is nonzero and is known in advance for each population unit.also called random sampling.Ensures information is obtained from a representative sample of the populationSampling error can be computedSurvey results can be projected to the populationMore expensive than non-probability samples
19 Simple Random Sampling (SRS) 3. Selecting a Sampling DesignSimple Random Sampling (SRS)Population members are selected directly from the sampling frameEqual probability of selection for every member (sample size/population size)400/10,000 = .04Use random number table or random number generator
20 3. Selecting a Sampling Design Simple Random Sampling N = the number of cases in the sampling framen = the number of cases in the samplef = n/N = the sampling fractionNCn = the number of combinations (subsets) of n from NIf you have a sampling frame of the 10,000 full-time students at the U of L and you want to survey .01 percent of them, how would you do it?
21 3. Selecting a Sampling Design Objective: To select n units out of N such that each NCn has an equal chance of being selectedProcedure: Use a table of random numbers, a computer random number generator, or a mechanical device to select the sample
22 3. Selecting a Sampling Design Systematic SamplingOrder all units in the sampling frame based on some variable and number them from 1 to NChoose a random starting place from 1 to N and then sample every k units after that
23 systematic random sample number the units in the population from 1 to Ndecide on the n (sample size) that you want or needk = N/n = the interval sizerandomly select an integer between1 to kthen takeevery kth unit
24 Stratified Sampling (I) 3. Selecting a Sampling DesignStratified Sampling (I)The chosen sample contains a number of distinct categories which are organized into segments, or strataequalizing "important" variablesyear in school, geographic area, product use, etc.Steps:Population is divided into mutually exclusive and exhaustive strata based on an appropriate population characteristic. (e.g. race, age, gender etc.)Simple random samples are then drawn from each stratum.
26 Stratified Random Sampling The sample size is usually proportional to the relative size of the strata.Ensures that particular groups (e.g. males and females) within a population are adequately represented in the sampleHas a smaller sampling error than simple random sample since a source of variation is eliminated
27 Stratified Sampling (II) 3. Selecting a Sampling DesignStratified Sampling (II)Direct Proportional Stratified SamplingThe sample size in each stratum is proportional to the stratum size in the populationDisproportional Stratified SamplingThe sample size in each stratum is NOT proportional to the stratum size in the populationUsed if1) some strata are too small2) some strata are more important than others3) some strata are more diversified than others
28 3. Selecting a Sampling Design Cluster SamplingThe Population is divided into mutually exclusive and exhaustive subgroups, or clusters, usually based on geography or time periodEach cluster should be representative of the population i.e. be heterogeneous.Means between clusters should be the same (homogeneous)Then a sample of the clusters is selected.then some randomly chosen units in the selected clusters are studied.
29 cluster or area random sampling divide population into clusters (usually along geographic boundaries)randomly sample clustersmeasure units within sampled clusters
30 3. Selecting a Sampling Design When to use stratified samplingIf primary research objective is to compare groupsUsing stratified sampling may reduce sampling errorsWhen to use cluster samplingIf there are substantial fixed costs associated with each data collection locationWhen there is a list of clusters but not of individual population members
31 Non-Probability Sampling 3. Selecting a Sampling DesignNon-Probability SamplingSubjective procedure in which the probability of selection for some population units are zero or unknown before drawing the sample.information is obtained from a non-representative sample of the populationSampling error can not be computedSurvey results cannot be projected to the population
32 3. Selecting a Sampling Design Non-Probability Sampling AdvantagesCheaper and faster than probabilityReasonably representative if collected in a thorough manner
33 Types of Non-Probability Sampling (I) Convenience SamplingA researcher's convenience forms the basis for selecting a sample.people in my classesMall interceptsPeople with some specific characteristic (e.g. bald)Judgement SamplingA researcher exerts some effort in selecting a sample that seems to be most appropriate for the study.
34 Types of Non-Probability Sampling Snowball SamplingSelection of additional respondents is based on referrals from the initial respondents.friends of friendsUsed to sample from low incidence or rare populations.Quota SamplingThe population is divided into cells on the basis of relevant control characteristics.A quota of sample units is established for each cell.50 women, 50 menA convenience sample is drawn for each cell until the quota is met.(similar to stratified sampling)
35 Quota SamplingLet us assume you wanted to interview tourists coming to a community to study their activities and spending. Based on national research you know that 60% come for vacation/pleasure, 20% are VFR (visiting friends and relatives), 15% come for business and 5% for conventions and meetings. You also know that 80% come from within the province. 10% from other parts of Canada, and 10% are international. A total of 500 tourists are to be intercepted at major tourist spots (attractions, events, hotels, convention centre, etc.), as you would in a convenience sample. The number of interviews could therefore be determined based on the proportion a given characteristic represents in the population. For instance, once 300 pleasure travellers have been interviewed, this category would no longer be pursued, and only those who state that one of the other purposes was their reason for coming would be interviewed until these quotas were filled.
37 Probability Vs. Non-Probability Sampling DisadvantagesThe probability of selecting one element over another is not known and therefore the estimates cannot be projected to the population with any specified level of confidence.Quantitative generalizations about population can only be done under probability sampling.In practice, however, marketing researchers also apply statistics to study non-probability samples.
38 GeneralizationYou can only generalize to the population from which you sampledU of L students not university studentsgeographic, different majors, different jobs, etc.University students not Canadian populationyounger, poorer, etc.Canadians not people everywhereless traditional, more affluent, etc.
39 Drawing inferences from samples Population estimates% who smoke, buy your product, etc25% of samplewhat % of population?very dangerous with a non-representative sample or with low response rates
40 Errors in Survey Random Sampling Error random error- the sample selected is not representative of the population due to chancethe level of it is controlled by sample sizea larger sample size leads to a smaller sampling error.Population mean (μ) gross income = $42,300Sample 1 (400/250,000) mean (Χ) = $41,100Sample 2 (400/250,000) mean (Χ) = $43,400Sample 3 (400/250,000) mean (Χ) = $36,400
41 Non-Sampling Errors (I) systematic Errorthe level of it is NOT controlled by sample size.The basic types of non-sampling errorNon-response errorResponse or data errorA non-response error occurs when units selected as part of the sampling procedure do not respond in whole or in partIf non-respondents are not different from those that did respond, there is no non-response error
42 Non-Sampling Errors (II) A response or data error is any systematic bias that occurs during data collection, analysis or interpretationRespondent error (e.g., lying, forgetting, etc.)Interviewer biasRecording errorsPoorly designed questionnaires