Chapter 4

1. Chapter 4 Sampling Design

2. How do we gather data? • Surveys • Opinion polls • Interviews • Studies • Observational • Retrospective (past) • Prospective (future) • Experiments

3. the entire group of individuals that we want information about Population

4. a complete count of the population Census

5. Not accurate Very expensive Perhaps impossible If using destructive sampling, you would destroy population Breaking strength of soda bottles Lifetime of flashlight batteries Safety ratings for cars Why would we not use a census all the time?

6. A part of the population that we actually examine in order to gather information Use sample to generalize to population Sample

7. refers to the method used to choose the sample from the population Sampling design

8. a list of every individual in the population Sampling frame

9. consist of n individuals from the population chosen in such a way that every individual has an equal chance of being selected every set of n individuals has an equal chance of being selected Simple Random Sample (SRS)

10. Advantages Unbiased Easy Disadvantages Large variance May not be representative Must have sampling frame (list of population) SRS

11. population is divided into homogeneous groups called strata SRS’s are pulled from each strata Stratified random sample

12. Advantages More precise unbiased estimator than SRS Less variability Cost reduced if strata already exists Disadvantages Difficult to do if you must divide stratum Formulas for SD & confidence intervals are more complicated Need sampling frame Stratified

13. select sample by following a systematic approach randomly select where to begin Systematic random sample

14. Advantages Unbiased Don’t need sampling frame Ensure that the sample is spread across population More efficient, cheaper, etc. Disadvantages Large variance Can be confounded by trend or cycle Formulas are complicated Systematic Random Sample

15. based upon location randomly pick a location & sample all there Cluster Sample

16. Advantages Unbiased Cost is reduced Sampling frame may not be available (not needed) Disadvantages Clusters may not be representative of population Formulas are complicated Cluster Samples

17. select successively smaller groups within the population in stages SRS used at each stage Multistage sample

18. Identify the sampling design 1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group. Stratified random sample

19. Identify the sampling design 2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks. Cluster sampling

20. Identify the sampling design 3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10th customer after them, to fill it out before they leave. Systematic random sampling

21. each entry is equally likely to be any of the 10 digits digits are independent of each other Random digit table The following is part of the random digit table: Row 1 4 5 1 8 5 0 3 3 7 1 2 4 2 5 5 8 0 4 5 7 0 3 8 9 9 3 4 3 5 0 6 3

22. Suppose your population consisted of these 20 people: 1) Aidan 6) Fred 11) Kathy 16) Paul 2) Bob 7) Gloria 12) Lori 17) Shawnie 3) Chico 8) Hannah 13) Matthew 18) Tracy 4) Doug 9) Israel 14) Nan 19) Uncle Sam 5) Edward 10) Jung 15) Opus 20) Vernon Use the following random digits to select a sample of five from these people. We will need to use double digit random numbers, ignoring any number greater than 20. Start with Row 1 and read across. 1) Aidan 13) Matthew 18) Tracy 15) Opus 5) Edward Ignore. Ignore. Ignore. Ignore. Stop when five people are selected. So my sample would consist of : Aidan, Edward, Matthew, Opus, and Tracy Row 1 4 5 1 8 0 5 1 3 7 1 2 0 1 5 5 8 0 1 5 7 0 3 8 9 9 3 4 3 5 0 6 3

23. A systematic error in measuring the estimate favors certain outcomes Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method! Bias

24. things that can cause bias in your sample cannot do anything with bad data Sources of Bias

25. People chose to respond Usually only people with very strong opinions respond Voluntary response

26. Ask people who are easy to ask Produces bias results Convenience sampling

27. some groups of population are left out of the sampling process Undercoverage

28. occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponse Nonresponse

29. occurs when the behavior of respondent or interviewer causes bias in the sample wrong answers Response bias

30. wording can influence the answers that are given connotation of words use of “big” words or technical words Wording of the Questions

31. Source of Bias? 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 2.8 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc.

32. 2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at SMU. You collect register receipts for students as they leave the bookstore during lunch one day.

33. 3) To find the average value of a home in Plano, one averages the price of homes that are listed for sale with a realtor.