© 2009 Pearson Education, Inc publishing as Prentice Hall 12-1 Sampling: Design and Procedure Sampling Size

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-2 CONDITIONS FAVORING THE USE OF SampleCensus 1. BudgetSmallLarge 2. Time availableShortLong 3. Population sizeLargeSmall 4. Variance in the characteristicSmallLarge 5. Cost of sampling errorLowHigh 6. Cost of nonsampling errorsHighLow 7. Nature of measurementDestructiveNondestructive 8. Attention to individual casesYesNo Sample vs. Census

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-3 Define the Population Determine the Sampling Frame Select Sampling Technique(s) Determine the Sample Size Execute the Sampling Process Figure Sampling Design Process

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-4 Define the Target Population The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements (eg: male or female), sampling units (eg: working telephone numbers), extent (eg: United states), and time (eg: period of time).

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-5 Figure 12.5 Sampling Frame Error Target Population: Example: Single parent households in Chicago Sampling Frame Error Sampling Frame: Example: List supplied by a commercial vendor

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-6 Figure Classification of Sampling Techniques Sampling Techniques Nonprobability Sampling Techniques Probability Sampling Techniques

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-7 Sampling Techniques Non-probability Sampling Techniques Convenience Sampling Simple Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling Probability Sampling Techniques Judgmental Sampling Quota Sampling Snowball Sampling Other Sampling Techniques Proportionate Disproportionate SAMPLING TECHNIQUES

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-8 Figure 12.7 Nonprobability Sampling Techniques Nonprobability Sampling Techniques Convenience Sampling Judgmental Sampling Quota Sampling Snowball Sampling

© 2009 Pearson Education, Inc publishing as Prentice Hall 12-9 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 –“people on the street” interviews

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 12.8 A Graphical Illustration of Non-Probability Sampling Techniques Convenience Sampling ABCDE Group D happens to assemble at a convenient time and place. So all the elements in this Group are selected. The resulting sample consists of elements 16, 17, 18, 19, and 20. Note, no elements are selected from group A, B, C, and E.

© 2009 Pearson Education, Inc publishing as Prentice Hall 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

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 12.8 A Graphical Illustration of Non-Probability Sampling Techniques Judgmental Sampling ABCDE The researcher considers groups B, C, and E to be typical and convenient. Within each of these groups one or two elements are selected based on typicality and convenience. The resulting sample consists of elements 8, 10, 13, 22, and 24. Note, no elements are selected from groups A and D.

© 2009 Pearson Education, Inc publishing as Prentice Hall Quota Sampling Quota sampling may be viewed as two-stage restricted judgmental 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. PopulationSample compositioncomposition Control CharacteristicPercentagePercentageNumber Sex Male Female ____________

© 2009 Pearson Education, Inc publishing as Prentice Hall ABCDE A quota of one element from each group, A to E, is imposed. Within each group, one element is selected based on judgment or convenience. The resulting sample consists of elements 3, 6, 13, 20, and 22. Note, one element is selected from each column or group. Figure 12.8 A Graphical Illustration of Non-Probability Sampling Techniques Quota Sampling

© 2009 Pearson Education, Inc publishing as Prentice Hall 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.

© 2009 Pearson Education, Inc publishing as Prentice Hall Random Selection Referrals ABCDE Figure 12.8 A Graphical Illustration of Non-Probability Sampling Techniques Snowball Sampling Elements 2 and 9 are selected randomly from groups A and B. Element 2 refers elements 12 and 13. Element 9 refers element 18. The resulting sample consists of elements 2, 9, 12, 13, and 18. Note, there is no element from group E.

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 12.9 Probability Sampling Techniques Probability Sampling Techniques Simple Random Sampling Cluster Sampling Stratified Sampling Systematic Sampling

© 2009 Pearson Education, Inc publishing as Prentice Hall 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.

© 2009 Pearson Education, Inc publishing as Prentice Hall ABCDE Select five random numbers from 1 to 25. The resulting sample consists of population elements 3, 7, 9, 16, and 24. Note, there is no element from Group C. Figure A Graphical Illustration of Probability Sampling Techniques Simple Random Sampling

© 2009 Pearson Education, Inc publishing as Prentice Hall 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. 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.

© 2009 Pearson Education, Inc publishing as Prentice Hall ABCDE Figure A Graphical Illustration of Probability Sampling Techniques Systematic Sampling Select a random number between 1 to 5, say 2. The resulting sample consists of population 2, (2+5=) 7, (2+5x2=) 12, (2+5x3=) 17, and (2+5x4=) 22. Note, all the elements are selected from a single row.

© 2009 Pearson Education, Inc publishing as Prentice Hall 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. The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible.

© 2009 Pearson Education, Inc publishing as Prentice Hall ABCDE Figure A Graphical Illustration of Probability Sampling Techniques Stratified Sampling Randomly select a number from 1 to 5 for each stratum, A to E. The resulting sample consists of population elements 4, 7, 13, 19, and 21. Note, one element is selected from each column.

© 2009 Pearson Education, Inc publishing as Prentice Hall 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. 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

© 2009 Pearson Education, Inc publishing as Prentice Hall ABCDE Figure A Graphical Illustration of Probability Sampling Techniques Cluster Sampling (2-Stage) Randomly select 3 clusters, B, D, and E. Within each cluster, randomly select one or two elements. The resulting sample consists of population elements 7, 18, 20, 21, and 23. Note, no elements are selected from clusters A and C.

© 2009 Pearson Education, Inc publishing as Prentice Hall Cluster SamplingStratified Sampling Only a sample of the subpopulations (clusters) is selected for sampling. All of the subpopulations (strata) are selected for sampling. Within a cluster, elements should be different (heterogeneous), whereas homogeneity of similarity is maintained between different clusters. Within a strata, elements should be homogeneous with clear differences (heterogeneity) between the strata. A sampling frame is needed only for the clusters selected for the sample. A complete sampling frame for the entire stratified subpopulations should be drawn. Table 12.3 Cluster Sampling Versus Stratified Sampling

© 2009 Pearson Education, Inc publishing as Prentice Hall TechniqueStrengthsWeaknesses Nonprobability Sampling Techniques Convenience samplingLeast expensive; least time consuming; most convenient Selection bias; sample not representative; not recommended for descriptive or causal research Judgmental samplingLow cost; convenient; not time consuming No generalization; subjective Quota samplingSample can be controlled for certain characteristics Selection bias No assurance of representativeness Table 12.4 Strengths and Weaknesses of Basic Sampling Techniques

© 2009 Pearson Education, Inc publishing as Prentice Hall Table 12.4 (Cont.) Strengths and Weaknesses of Basic Sampling Techniques TechniqueStrengthsWeaknesses Snowball samplingCan estimate rare characteristics Time consuming Probability Sampling Simple random sampling (SRS) Easily understood; results projectable Difficult to construct sampling frame; expensive; lower Precision; no assurance of representativeness Systematic samplingCan increase representativeness; easier to implement than SRS; sampling frame not needed Can decrease representativeness

© 2009 Pearson Education, Inc publishing as Prentice Hall Table 12.4 (Cont.) Strengths and Weaknesses of Basic Sampling Techniques TechniqueStrengthsWeaknesses Stratified samplingIncludes all Important Subpopulations; precision Difficult to select relevant stratification variables; not feasible to stratify on many variables; expensive Cluster samplingEasy to implement; cost effective Imprecise difficult to compute and interpret results

© 2009 Pearson Education, Inc publishing as Prentice Hall Type of StudyMinimum SizeTypical Range Problem identification research (e.g., market potential) – 2500 Problem solving research (e.g., pricing) – 500 Product tests – 500 Test marketing studies – 500 TV/radio/print advertising (per commercial or ad tested) – 300 Test-market audits10 stores10 – 20 stores Focus groups2 groups10 – 15 groups Table 12.2 Sample Sizes Used in Marketing Research Studies

© 2009 Pearson Education, Inc publishing as Prentice Hall Sampling: Final and Initial Sample-Size Determination

© 2009 Pearson Education, Inc publishing as Prentice Hall Definitions and Symbols Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population. A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken. Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter. Random sampling error: The error when the sample selected is an imperfect representation of the population of interest.

© 2009 Pearson Education, Inc publishing as Prentice Hall Definitions and Symbols Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter. Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence. Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.

© 2009 Pearson Education, Inc publishing as Prentice Hall Table 13.1 Symbols for Population and Sample VariablesTable 13.1 Symbols for Population and Sample Variables Table 13.1 Symbols for Population and Sample Variables

© 2009 Pearson Education, Inc publishing as Prentice Hall XLXL _ XUXU _ X _ Figure % Confidence Interval

© 2009 Pearson Education, Inc publishing as Prentice Hall A sample size of 400 is enough to represent China’s more than 1.3 billion people or the more than 300 million American people. The sample size is independent of the population size for large populations.