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Sampling
 

Sampling

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    Sampling Sampling Presentation Transcript

    • Chapter Eleven Sampling: Design and ProceduresCopyright © 2010 Pearson Education, Inc. 11-1
    • Chapter Outline1) Overview2) Sample or Census3) The Sampling Design Process i. Define the Target Population ii. Determine the Sampling Frame iii. Select a Sampling Technique iv. Determine the Sample Size v. Execute the Sampling Process
    • Chapter Outline4) A Classification of Sampling Techniques i. Nonprobability Sampling Techniques a. Convenience Sampling b. Judgmental Sampling c. Quota Sampling d. Snowball Sampling ii. Probability Sampling Techniques a. Simple Random Sampling b. Systematic Sampling c. Stratified Sampling d. Cluster Sampling e. Other Probability Sampling Techniques
    • Chapter Outline1) Choosing Nonprobability Versus Probability Sampling2) Uses of Nonprobability Versus Probability Sampling3) Internet Sampling4) International Marketing Research5) Ethics in Marketing Research6) Summary
    • Sample Vs. CensusTable 11.1 Conditions Favoring the Use of Type of Study Sample Census 1. Budget Small Large 2. Time available Short Long 3. Population size Large Small 4. Variance in the characteristic Small Large 5. Cost of sampling errors Low High 6. Cost of nonsampling errors High Low 7. Nature of measurement Destructive Nondestructive 8. Attention to individual cases Yes No
    • The Sampling Design ProcessFig. 11.1 Define the Population Determine the Sampling Frame Select Sampling Technique(s) Determine the Sample Size Execute the Sampling Process
    • Define the Target PopulationThe target population is the collection of elements orobjects that possess the information sought by theresearcher and about which inferences are to bemade. The target population should be defined interms of elements, sampling units, extent, and time.• An element is the object about which or from which the information is desired, e.g., the respondent.• A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process.• Extent refers to the geographical boundaries.• Time is the time period under consideration.
    • Define the Target PopulationImportant qualitative factors indetermining the sample size are:• the importance of the decision• the nature of the research• the number of variables• the nature of the analysis• sample sizes used in similar studies• incidence rates• completion rates• resource constraints
    • Sample Sizes Used in Marketing Research StudiesTable 11.2 Type of Study Minimum Size Typical Range Problem identification research 500 1,000-2,500 (e.g. market potential) Problem-solving research (e.g. 200 300-500 pricing) Product tests 200 300-500 Test marketing studies 200 300-500 TV, radio, or print advertising (per 150 200-300 commercial or ad tested) Test-market audits 10 stores 10-20 stores Focus groups 2 groups 6-15 groups
    • Classification of Sampling Techniques Fig. 11.2 Sampling Techniques Nonprobability Probability Sampling Techniques Sampling TechniquesConvenience Judgmental Quota Snowball Sampling Sampling Sampling SamplingSimple Random Systematic Stratified Cluster Other Sampling Sampling Sampling Sampling Sampling Techniques
    • Convenience Sampling Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. • Use of students, and members of social organizations • Mall intercept interviews without qualifying the respondents • Department stores using charge account lists • “People on the street” interviews
    • A Graphical Illustration of ConvenienceSampling Fig. 11.3 11.3 A B C D E 1 6 11 Group D happens to 16 21 assemble at a convenient time and 2 7 12 17 22 place. So all the elements in this Group are selected. 3 8 13 18 23 The resulting sample consists of elements 16, 17, 18, 19 and 20. 4 9 14 19 24 Note, no elements are selected from group 5 10 15 20 25 A, B, C and E.
    • Judgmental Sampling Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher. • Test markets • Purchase engineers selected in industrial marketing research • Bellwether precincts selected in voting behavior research • Expert witnesses used in court
    • Graphical Illustration of JudgmentalSampling Fig. 11.3 A B C D E The researcher 1 6 11 16 21 considers groups B, C and E to be typical and convenient. Within each 2 7 12 17 22 of these groups one or two elements are selected based on 3 8 13 18 23 typicality and convenience. The resulting sample 4 9 14 19 24 consists of elements 8, 10, 11, 13, and 24. Note, no elements are selected 5 10 15 20 25 from groups A and D.
    • Quota SamplingQuota sampling may be viewed as two-stage restrictedjudgmental sampling.• The first stage consists of developing control categories, or quotas, of population elements.• In the second stage, sample elements are selected based on convenience or judgment. Control Population Sample Variable composition composition Sex Percentage Percentage Number Male 48 48 480 Female 52 52 520 ____ ____ ____ 100 100 1000
    • A Graphical Illustration of Quota Sampling Fig. 11.3 A B C D E A quota of one 1 element from each 6 11 16 21 group, A to E, is imposed. Within each 2 7 12 17 group, one element is 22 selected based on judgment or 3 8 13 18 23 convenience. The resulting sample consists of elements 4 9 14 19 24 3, 6, 13, 20 and 22. Note, one element is selected from each 5 10 15 20 25 column or group.
    • Snowball Sampling In snowball sampling, an initial group of respondents is selected, usually at random. • After being interviewed, these respondents are asked to identify others who belong to the target population of interest. • Subsequent respondents are selected based on the referrals.
    • A Graphical Illustration of Snowball Sampling Random Fig. 11.3 Selection Referrals A B C D E Elements 2 and 9 are selected randomly from 1 6 11 16 21 groups A and B. Element 2 refers 2 7 12 17 22 elements 12 and 13. Element 9 refers 3 8 element 18. The 13 18 23 resulting sample consists of elements 2, 4 9 14 19 24 9, 12, 13, and 18. Note, there are no elements 5 10 15 20 25 from group E.
    • Simple Random Sampling• Each element in the population has a known and equal probability of selection.• Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected.• This implies that every element is selected independently of every other element.
    • A Graphical Illustration ofSimple Random Sampling Fig. 11.4 A B C D E 1 6 11 16 21 Select five random numbers from 1 to 25. The 2 7 12 17 22 resulting sample consists of 3 8 13 18 23 population elements 3, 7, 9, 16, and 24. Note, 4 9 14 19 24 there is no element from 5 10 15 20 25 Group C.
    • Systematic Sampling• The sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame.• The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer.• When the ordering of the elements is related to the characteristic of interest, systematic sampling increases the representativeness of the sample.
    • Systematic Sampling• If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the representativeness of the sample. For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on.
    • A Graphical Illustration ofSystematic SamplingFig. 11.4 A B C D E Select a random 1 6 11 16 21 number between 1 and 5, say 2. The resulting sample 2 7 12 17 22 consists of population 2, 3 8 13 18 23 (2+5=) 7, (2+5x2=) 12, (2+5x3=)17, and (2+5x4=) 22. Note, all 4 9 14 19 24 the elements are selected from a 5 10 15 20 25 single row.
    • Stratified Sampling• A two-step process in which the population is partitioned into subpopulations, or strata.• The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted.• Next, elements are selected from each stratum by a random procedure, usually SRS.• A major objective of stratified sampling is to increase precision without increasing cost.
    • Stratified Sampling• The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible.• The stratification variables should also be closely related to the characteristic of interest.• Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply.
    • Stratified Sampling• In proportionate stratified sampling, the size of the sample drawn from each stratum is proportionate to the relative size of that stratum in the total population.• In disproportionate stratified sampling, the size of the sample from each stratum is proportionate to the relative size of that stratum and to the standard deviation of the distribution of the characteristic of interest among all the elements in that stratum.
    • A Graphical Illustration ofStratified SamplingFig. 11.4 A B C D E Randomly select a 1 6 11 16 21 number from 1 to 5 for each stratum, A to 2 7 12 17 22 E. The resulting sample consists of 3 8 population elements 13 18 23 4, 7, 13, 19 and 21. Note, one element 4 9 14 19 24 is selected from each column. 5 10 15 20 25
    • Cluster Sampling• The target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters.• Then a random sample of clusters is selected, based on a probability sampling technique such as SRS.• For each selected cluster, either all the elements are included in the sample (one- stage) or a sample of elements is drawn probabilistically (two-stage).
    • Cluster Sampling• Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population.• In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster.
    • A Graphical Illustration ofCluster Sampling (2-Stage)Fig. 11.4 A B C D E Randomly select 3 1 6 11 16 21 clusters, B, D and E. Within each cluster, randomly select one 2 7 12 17 22 or two elements. The resulting sample 3 8 13 18 23 consists of population elements 7, 18, 20, 21, and 23. 4 9 14 19 24 Note, no elements are selected from 5 10 15 20 25 clusters A and C.
    • Types of Cluster Sampling Fig 11.5 Cluster Sampling One-Stage Two-Stage Multistage Sampling Sampling Sampling Simple Cluster Probability Sampling Proportionate to Size Sampling
    • Strengths and Weaknesses of Basic Sampling TechniquesTable 11.4 Technique Strengths Weaknesses Nonprobability Sampling Least expensive, least Selection bias, sample not Convenience sampling time-consuming, most representative, not recommended for convenient descriptive or causal research Judgmental sampling Low cost, convenient, Does not allow generalization, not time-consuming subjective Quota sampling Sample can be controlled Selection bias, no assurance of for certain characteristics representativeness Snowball sampling Can estimate rare Time-consuming characteristics Probability sampling Easily understood, Difficult to construct sampling Simple random sampling results projectable frame, expensive, lower precision, (SRS) no assurance of representativeness Systematic sampling Can increase Can decrease representativeness representativeness, easier to implement than SRS, sampling frame not necessary Stratified sampling Include all important Difficult to select relevant subpopulations, stratification variables, not feasible to precision stratify on many variables, expensive Cluster sampling Easy to implement, cost Imprecise, difficult to compute and effective interpret results
    • A Classification of Internet SamplingFig. 11.6 Internet Sampling Online Intercept Recruited Online Other Techniques Sampling SamplingNonrandom Random Panel Nonpanel Recruited Opt-in Opt-in List Panels Panels Rentals
    • Procedures for Drawing Probability Samples Simple RandomExhibit 11.1 Sampling Simple Random Sampling 1. Select a suitable sampling frame. 2. Each element is assigned a number from 1 to N (pop. size). 3. Generate n (sample size) different random numbers between 1 and N. 4. The numbers generated denote the elements that should be included in the sample.
    • Procedures for Drawing Probability Samples Systematic SamplingExhibit 11.1, cont.1. Select a suitable sampling frame.2. Each element is assigned a number from 1 to N (pop. size).3. Determine the sampling interval i:i=N/n. If i is a fraction, round to the nearest integer.4. Select a random number, r, between 1 and i, as explained in simple random sampling.5. The elements with the following numbers will comprise the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i.
    • Procedures for Drawing Probability Samples StratifiedExhibit 11.1, cont. Sampling 1. Select a suitable frame. 2. Select the stratification variable(s) and the number of strata, H. 3. Divide the entire population into H strata. Based on the classification variable, each element of the population is assigned to one of the H strata. 4. In each stratum, number the elements from 1 to Nh (the pop. size of stratum h). 5. Determine the sample size of each stratum, nh, based on proportionate or disproportionate stratified sampling, where H nh = n h=1 6. In each stratum, select a simple random sample of size nh
    • Procedures for Drawing Probability Samples Cluster SamplingExhibit 11.1, cont.1. Assign a number from 1 to N to each element in the population.2. Divide the population into C clusters of which c will be included in the sample.3. Calculate the sampling interval i, i=N/c (round to nearest integer).4. Select a random number r between 1 and i, as explained in simple random sampling.5. Identify elements with the following numbers: r,r+i,r+2i,... r+(c-1)i.6. Select the clusters that contain the identified elements.7. Select sampling units within each selected cluster based on SRS or systematic sampling.8. Remove clusters exceeding sampling interval i. Calculate new population size N*, number of clusters to be selected c*= c-1, and new sampling interval i*.
    • Procedures for Drawing Probability SamplesExhibit 11.1, cont. Cluster Sampling Repeat the process until each of the remaining clusters has a population less than the sampling interval. If b clusters have been selected with certainty, select the remaining c-b clusters according to steps 1 through 7. The fraction of units to be sampled with certainty is the overall sampling fraction = n/N. Thus, for clusters selected with certainty, we would select ns=(n/N)(N1+N2+...+Nb) units. The units selected from clusters selected under two-stage sampling will therefore be n*=n-ns.
    • Choosing Nonprobability Vs. Probability SamplingTable 11.4 Conditions Favoring the Use of Factors Nonprobability Probability sampling sampling Nature of research Exploratory Conclusive Relative magnitude of sampling Nonsampling Sampling and nonsampling errors errors are errors are larger larger Variability in the population Homogeneous Heterogeneous (low) (high) Statistical considerations Unfavorable Favorable Operational considerations Favorable Unfavorable
    • Tennis Systematic Sampling Returns a SmashTennis magazine conducted a mail survey of its subscribers togain a better understanding of its market. Systematicsampling was employed to select a sample of 1,472subscribers from the publications domestic circulation list. Ifwe assume that the subscriber list had 1,472,000 names, thesampling interval would be 1,000 (1,472,000/1,472). Anumber from 1 to 1,000 was drawn at random. Beginningwith that number, every 1,000th subscriber was selected.A brand-new dollar bill was included with the questionnaire asan incentive to respondents. An alert postcard was mailedone week before the survey. A second, follow-up,questionnaire was sent to the whole sample ten days after theinitial questionnaire. There were 76 post office returns, so thenet effective mailing was 1,396. Six weeks after the firstmailing, 778 completed questionnaires were returned, yieldinga response rate of 56%.
    • All rights reserved. No part of this publication may bereproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall