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Sampling Design Sampling Terminology • Sample – A subset, or some part, of a larger population • Population or 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 A puzzle is a sample until it’s done. The sample allows one to guess at the picture. Why Sample? • Pragmatic Reasons – Budget & time constraints. – Limited access to total population. • Accurate and Reliable Results – Samples can yield reasonably accurate information. – Strong similarities in population elements makes sampling possible. – Sampling may be more accurate than a census. • Destruction of Test Units – Sampling reduces the costs of research in finite populations. Sample vs. Census CONDITIONS FAVORING THE USE OF 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 error Low High 6. Cost of nonsampling errors High Low 7. Nature of measurement Destructive Nondestructive 8. Attention to individual cases Yes No Stages in Sample Selection Identifying a Relevant Population • Defining the Target Population – What is the relevant population? – Whom do we want to talk to? • Population is operationally defined by specific & explicit tangible characteristics. • If you want to target “Women”, do you mean – All women still capable of bearing children or, – All women between the ages of 12 and 50? Identifying a Sampling Frame • A list of elements from which a sample may be drawn • Also called the working population. – Sampling Frame Error occurs when certain sample elements • are not listed, or • are not accurately represented in a sampling frame. – Sampling services (list brokers) • Provide lists or databases of the names, addresses, phone numbers, & e-mail addresses of specific populations. • Reverse directory – A directory similar to a telephone directory except that listings are by city & street address or by phone number rather than alphabetical by last name. – Online Panels • Lists of respondents who have agreed to participate in marketing research via e-mail. – International Research • Availability of sampling frames varies dramatically around the world. Sampling 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. Random Sampling & Nonsampling Errors • Random Sampling Error – The difference between the sample result & the result of a census conducted using identical procedures. – A statistical fluctuation that occurs because of chance variations in the elements selected for a sample. – Probability of such error increases as sample size decreases. • Systematic Sampling Error – Systematic (nonsampling) error results from nonsampling factors, primarily the nature of a study’s design & the correctness of execution. • It is not due to chance fluctuation. • Probability of such error increases as sample size increases. Errors Associated with Sampling Two Major Categories of Sampling • Probability sampling •Known, nonzero, & equal probability of selection for every population element • Nonprobability sampling •Probability of selecting any particular member is unknown Nonprobability Sampling • Convenience Sampling – Obtaining people or units that are most conveniently available. • Judgment (Purposive) Sampling – Experienced individual selects sample based on personal judgment about some appropriate characteristic of the sample member. • Quota Sampling – Ensures that various subgroups of a population will be represented on pertinent characteristics to the exact extent that the investigator desires. • 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. Comparing the Nonprobability Techniques Technique Strengths Weaknesses Convenience Sampling •Least expensive •Least time needed •Most convenient •Selection bias •Not representative Judgmental Sampling •Low expense •Little time needed •Convenient • Highly Subjective •Does not allow generalizations Quota Sampling •Can control sample characteristics •Greatest probability of representative sample •Selection bias •Most likely not representative Snowball Sampling •Can estimate rare characteristics •Time consuming •Most likely not representative Most Commonly-Used Probability Sampling Techniques Probability Sampling Techniques Simple Random Sampling Systematic Sampling Proportional vs. Disproportional Sampling Stratified Sampling Cluster Sampling Probability Sampling • Simple Random Sampling – Assures each element in the population of an equal chance of being included in the sample. • Systematic Sampling – A starting point is selected by a random process and then every nth number on the list is selected. • Stratified Sampling – Simple random subsamples that are more or less equal on some characteristic are drawn from within each stratum of the population. Systematically Sampling from a List Proportional vs. Disproportional Sampling • Proportional Stratified Sample – Number of sampling units drawn from each stratum is in proportion to population size of that stratum. • Disproportional Stratified Sample – Sample size for each stratum is allocated according to analytical considerations. Disproportional Sampling: Hypothetical Example Cluster Sampling • Economically efficient sampling technique in which primary sampling unit is not the individual element in the population but a large cluster of elements. • Clusters are selected randomly. Examples of Clusters What is the Appropriate Sample Design? It Depends Degree of accuracy Resources Time Advanced knowledge of the population National versus local Need for statistical analysis Internet Samples • Recruited Ad Hoc Samples – Potential subjects unaware they might be asked to participate in a study – Less expensive – Lower selection bias • Opt-in Lists – Potential subjects know they might be asked to participate in studies as they have previously agreed to receive such invitations. – More expensive – Greater chance of selection bias – “Much Better” response rates (????) Sample Size Bigger Is Better — Right? • One study indicates that 60% of consumers believe that there is too much violence in video games, but another study suggests that 75% of parents do not believe it harms children. • Another shows that 40% of Nintendo owners are highly likely to buy a new game that has been concept tested. • How good are these descriptive statistics? Consider the sample! Information Needed to Determine Sample Size • Variance (standard deviation) – 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. – Get from pilot study or rule of thumb (managerial judgment) • Magnitude of error – How precise must the estimate be? – Managerial judgment or calculation • Confidence level – How much error will be tolerated? – Managerial judgment – Most commonly used standards are a 95% confidence level (Z score = 1.96), or 99% confidence level (Z score = 2.57). Sample Size Formula for Questions Involving an Analysis of Means zs n E 2 Sample Size Formula - Example Suppose a survey researcher is studying expenditures on lipstick Wishes to have a 95 percent confident level (Z) and Range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00. Sample Size Formula - Example zs n E 2 1.9629.00 2.00 2 2 56.84 2 28 . 42 2.00 808 Sample Size Formula - Example Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00 (rather than the original $2.00), sample size is reduced. Sample Size Formula - Example zs 1.9629.00 n 4.00 E 2 2 2 56.84 2 14 . 21 4.00 202 Calculating Sample Size 99% Confidence ( 2 . 57 )( 29 ) n 2 74.53 2 2 [37.265] 1389 2 2 ( 2 . 57 )( 29 ) n 4 74 . 53 4 2 [18.6325] 347 2 2 Sample Size for an Analysis of Proportions 2 Z pq n E 2 Sample Size for a Proportion: Example • A researcher believes that a simple random sample will show that 60 percent of a population (p = .6) recognizes the name of an automobile dealership. • Note that 40% of the population would not recognize the dealership’s name (q = .4) • The researcher wants to estimate with 95% confidence (Z = 1.96) that the allowance for sampling error is not greater than 3.5 percentage points (E = 0.035) Calculating Sample Size at the 95% Confidence Level p q . 6 . 4 n ( 1. 96 (. 2 ) (. 6 )(. 4 ) 035 ( 3. 8416 )2 )(. 001225 . . 922 001225 753 24 )