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CHAPTER OVERVIEW Populations and Samples Probability Sampling Strategies Nonprobability Sampling Strategies Sampling, Sample Size, and Sampling Error

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SAMPLES AND POPULATIONS Inferential method is based on inferring from a sample to a population Sample—a representative subset of the population Population—the entire set of participants of interest Generalizability—the ability to infer population characteristics based on the sample

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CHOOSING A REPRESENTATIVE SAMPLE Probability sampling—the likelihood of any member of the population being selected is known Nonprobability sampling--the likelihood of any member of the population being selected is unknown

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PROBABILITY SAMPLING STRATEGIES Simple random sampling –Each member of the population has an equal and independent chance of being chosen –The sample should be very representative of the population

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1. Jane18. Steve35. Fred 2. Bill19. Sam36. Mike 3. Harriet20. Marvin37. Doug 4. Leni21. Ed. T.38. Ed M. 5. Micah22. Jerry39. Tom 6. Sara 23. Chitra40. Mike G. 7. Terri24. Clenna41. Nathan 8. Joan25. Misty42. Peggy 9. Jim26. Cindy43. Heather 10. Terrill27. Sy44. Debbie 11. Susie28. Phyllis45. Cheryl 12. Nona29. Jerry46. Wes 13. Doug30. Harry47. Genna 14. John S.31. Dana48. Ellie 15. Bruce A.32. Bruce M.49. Alex 16. Larry33. Daphne50. John D. 17. Bob34. Phil 1.Define the population 2.List all members of population 3.Assign numbers to each member of population 4.Use criterion to select sample CHOOSING A SIMPLE RANDOM SAMPLE

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1.Select a starting point 2.The first two digit number is 68 (not used) 3.The next number, 48, is used 4.Continue until sample is complete 23157485590183725993 05545504301053743508 14871036503240436223 38976497519405175853 97312176189975530870 11742691834433947512 43361828591101645623 93806043383826804491 49540311810842984187 36768762333794821569 USING A TABLE OF RANDOM NUMBERS

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KEYS TO SUCCESS IN SIMPLE RANDOM SAMPLING Distribution of numbers in table is random Members of population are listed randomly Selection criterion should not be related to factor of interest!!

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USING SPSS TO GENERATE RANDOM SAMPLES 1.Be sure that you’re in a data file 2.Click Data > Select Cases 3.Click Random sample of Cases 4.Click the Sample Button 5.Define Sample Size a.Click Continue b.Click OK (in next dialog box)

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1.Divide the population by the size of the desired sample: e.g., 50/10 = 5 2.Select a starting point at random: e.g., 43 = Heather 3.Select every 5 th name from the starting point SYSTEMATIC SAMPLING 1. Jane18. Steve35. Fred 2. Bill19. Sam36. Mike 3. Harriet20. Marvin37. Doug 4. Leni21. Ed. T.38. Ed M. 5. Micah22. Jerry39. Tom 6. Sara 23. Chitra40. Mike G. 7. Terri24. Clenna41. Nathan 8. Joan25. Misty42. Peggy 9. Jim26. Cindy43. Heather 10. Terrill27. Sy44. Debbie 11. Susie28. Phyllis45. Cheryl 12. Nona29. Jerry46. Wes 13. Doug30. Harry47. Genna 14. John S.31. Dana48. Ellie 15. Bruce A.32. Bruce M.49. Alex 16. Larry33. Daphne50. John D. 17. Bob34. Phil

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STRATIFIED SAMPLING The goal of sampling is to select a sample that is representative of the population But suppose— –That people in the population differ systematically along some characteristic? –And this characteristic relates to the factors being studied? Then stratified sampling is one solution

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STRATIFIED SAMPLING The characteristic(s) of interest are identified (e.g., gender) The individuals in the population are listed separately according to their classification (e.g., females and males) The proportional representation of each class is determined (e.g., 40% females & 60% males) A random sample is selected that reflects the proportions in the population, (e.g., 4 females & 6 males)

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STRATIFICATION ON MORE THAN ONE FACTOR Grade Location135Total Rural 1,200 [120] 1,200 [120] 600 [60] 3,000 [300] Urban 2,800 [280] 2,800 [280] 1,400 [140] 7,000 [700] Total 4,000 [400] 4,000 [400] 2,000 [200] 10,000 [1000]

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CLUSTER SAMPLING Instead of randomly selecting individuals –Units (groups) of individuals are identified –A random sample of units is then selected –All individuals in each unit are assigned to one of the treatment conditions Units must be homogeneous in order to avoid bias

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NONPROBABILITY SAMPLING STRATEGIES Convenience sampling –Captive or easily sampled population –Not random –Weak representativeness Quota sampling –Proportional stratified sampling is desired but not possible –Participants with the characteristic of interest are non-randomly selected until a set quota is met

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SAMPLES, SAMPLE SIZE, AND SAMPLING ERROR Sampling error = difference between sample and population characteristics Reducing sampling error is the goal of any sampling technique As sample size increases, sampling error decreases

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HOW BIG IS BIG? The goal is to select a representative sample— –Larger samples are usually more representative –But larger samples are also more expensive –And larger samples ignore the power of scientific inference

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ESTIMATING SAMPLE SIZE Generally, larger samples are needed when –Variability within each group is great –Differences between groups are smaller Because –As a group becomes more diverse, more data points are needed to represent the group –As the difference between groups becomes smaller, more participants are needed to reach “critical mass” to detect the difference

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