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Chapter 11

Chapter 11. Basic Sampling Issues. What is sampling. Sampling: a way of studying a subset of the population but still ensuring “generalizability” (vs. census – study of entire population) – does the study have external validity?. Definitions of Important Terms.

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Chapter 11

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  1. Chapter 11 Basic Sampling Issues

  2. What is sampling • Sampling: a way of studying a subset of the population but still ensuring “generalizability” (vs. census – study of entire population) – does the study have external validity?

  3. Definitions of Important Terms • Population or Universe – entire set of elements to be studied • Census – all elements that completely make up the population. • Sample – a subset

  4. Steps in Developing a Sample Plan Step 2: Choose a Data collection Method Step 3: Choosing a Sampling Frame Step 1: Define the Population of Interest Step 4: Selecting a Sampling Method Step 5: Sample Size Boundaries Operational Implementability

  5. Sampling Method • Probability samples: Samples in which every element of the population has a known, nonzero probability of selection. • Generalizable • Sampling error • Expensive; More time and effort needed • Non-probability samples: Samples that include elements from the population selected in a nonrandom manner. • Hidden agendas • Biased towards well known members of the population; Biased against unusual population members

  6. Sampling and Nonsampling Errors • Parameter vs. Statistic (Estimate) • Sample statistic: statistic (e.g. mean) computed from sample data • - Population parameter: true value for statistic (e.g. mean) for population (we don’t know this) • - Sampling error: population parameter – sample statistic (we don’t know this) • - Confidence interval: interval in which we can be confident that true value lies, based on sample statistic and its standard error

  7. Advantages Of Probability Samples • Information from a representative cross-section • Sampling error can be computed • Results are projectable to the total population. • Disadvantages Of Probability Samples • More expansive than nonprobabiity samples • Take more time to design and execute.

  8. Disadvantages of Nonprobability Samples • Sampling error cannot be computed • Representativeness of the sample is not known • Results cannot be projected to the population. • Advantages of Nonprobability Samples • Cost less than probability • Can be conducted more quickly • Produces samples that are reasonably representative

  9. Classification of Sampling Methods Sampling Methods Quota Probability Samples Non- probability Cluster Systematic Stratified Convenience Snowball Simple Random Judgment

  10. ns X =  s X = sample mean  = true population mean + + - - s ns = sampling error = nonsampling error Sampling And Nonsampling Errors Remember? Sampling Error The error that results when the same sample is not perfectly representative of the population.

  11. Sampling And Nonsampling Errors • Sampling Error • The error that results when the same sample is not perfectly representative of the population. • Administrative error: problems in the execution of the sample (can be reduced) • Random error: due to chance and cannot be avoided; but can be contolled by random sampling and…..estimated! • Measurement or Nonsampling Error • Includes everything other than sampling error that can cause inaccuracy and bias (data entry, biased q’s, bad analysis etc).

  12. Probability Sampling Methods • Simple Random Sampling • A probability sample is a sample in which every element of the population has a known and equal probability of being selected into the sample- EPSEM. Sample Size Probability of Selection = Population Size

  13. Probability Sampling Methods • Systematic Sampling • Probability sampling in which the entire population is numbered, and elements are drawn using a skip interval. Population Size Skip Interval = Sample Size

  14. Probability Sampling Methods • Stratified Samples • Probability samples that select elements from relevant population subsets to be more representative. • Cluster Samples • Probability sample of geographic areas

  15. Stratified Samples • Probability samples that select elements from relevant population subsets to be more representative. • Three steps: In implementing a properly stratified sample: • 1. Identify salient demographic or classification factors correlated with the behavior of interest. • 2. Determine what proportions of the population fall into various sub subgroups under each stratum. • proportional allocation • disproportional or optimal allocation • 3. Select separate simple random samples from each stratum

  16. Cluster Samples • Sampling units are selected in groups. • 1. The population of interest is divided into mutually exclusive and exhaustive subsets. • A random sample of the subsets is selected. • One-stage cluster—all elements in subset selected • Two-stage cluster—elements selected in some probabilistic manner from the selected subsets

  17. Handout 1 – Baseball Example • 1. Ramon Aviles 0.277 • 2. Larry Bowa 0.267 • 3. Pete Rose 0.282 • 4. Mike Schmidt 0.286 • 5. Manny Trillo 0.292 • 6. John Yukovich 0.161 • Mean = 1.565 / 6 = 0.261

  18. SRS of sample size = 2 • Mean Error • Aviles, Bowa 0.272 +0.011 • Aviles, Rose 0.280 +0.019 • Aviles, Schmidt 0.282 +0.021 • Aviles, Trillo 0.285 +0.024 • Aviles, Yukovich 0.219 -0.042 • Bowa, Rose 0.275 +0.014 • Bowa, Schmidt 0.277 +0.016

  19. SRS of sample size = 2 • Bowa, Trillo 0.280 +0.019 • Bowa, Yukovich 0.214 -0.047 • Rose, Schmidt 0.284 +0.023 • Rose, Trillo 0.287 +0.026 • Rose, Yukovich 0.222 -0.039 • Schmidt, Trillo 0.289 +0.028 • Schmidt, Yukovich 0.224 -0.037 • Trillo, Yukovich 0.227 -0.034

  20. Stratification • Let’s divide the sample into two strata • One with Yukovich and another with all others • Stratum 1: Yukovich • Stratum 2: Aviles, Bowa, Rose, Trillo, Schmidt

  21. Stratified Sampling • 1. Yukovich, Aviles • 2. Yukovich, Bowa • 3. Yukovich, Rose • 4. Yukovich, Schmidt • 5. Yukovich, Trillo • Weight the sample. Why? • For anyone from Stratum 2, multiply their value by 5

  22. Example – Mean computation • Yukovich, Schmidt • Yukovich = 0.161 • Schmidt = 0.286 • Therefore, Schmidt’s value is (0.286 * 5) which is 1.43 • Yukovich + Schmidt = 0.161 + 1.43 = • Mean (Yukovich + Schmidt) = 1.591 / 6 = 0.265

  23. Stratified Sampling • 1. Yukovich Aviles 0.258 -0.003 • 2. Yukovich, Bowa 0.249 -0.012 • 3. Yukovich, Rose 0.262 +0.001 • 4. Yukovich, Schmidt 0.265 +0.004 • 5. Yukovich, Trillo 0.270 +0.009 • What’s happening to errors of estimate?

  24. Nonprobability Sampling Methods • Convenience Samples • Nonprobability samples used primarily because they are easy to collect ; Theory testing • Judgment Samples • Nonprobability samples in which the selection criteria are based on personal judgment that the element is representative of the population under study

  25. Nonprobability Sampling Methods • Snowball Samples • Nonprobability samples in which selection of additional respondents is based on referrals from the initial respondents. • Quota Samples • Nonprobability samples in which a population subgroup is classified on the basis of researcher judgment • Different from Stratified

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