Chapter 8

1. Chapter 8 Producing Data: Sampling Chapter 8 Sampling 1

2. Objectives (BPS chapter 8) Producing Data: Sampling Observation versus experiment Population versus sample Sampling methods How to sample badly Simple random samples Other sampling designs Caution about sample surveys Learning about populations from samples (inference)

3. Experiments vs. Observational Studies Experiment Deliberately imposes some treatment on individuals in order to observe their responses. Studies whether the treatment causes change in the response. experimenter determines which units receive which treatments (ideally using some form of random allocation) Observational study compare units that happen to have received each of the treatments often useful for identifying possible causes of effects, but cannot reliably establish causation Only properly designed and executed experiments can reliably demonstrate causation. Chapter 8 Sampling 3

4. Population The complete collection of all subjects or objects (scores, people, measurements, and so on) that are being studied. The collection is complete in the sense that it includes all subjects to be studied. Chapter 8 Sampling 4

5. Census:The collection of data from every individual in a population. Sample :A subset of elements drawn from a population from which we collect data. The sample must be a good representative of the entire population. A sampling design describes exactly how to choose a sample from the population. Chapter 8 Sampling 5

6. Population individuals Chapter 8 Sampling 6

7. Sampling Frame List of individuals that could possibly be selected for the sample (not necessarily the same as the population) Chapter 8 Sampling 7

8. Census  3 4 5  6 2  1 7 10  11 8 12  9  13 15  17 14 16    3 4 5 6  2  1 7 10 11 8  12  9 13 15  17 16 14   List of Individuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Census Chapter 8 Sampling 8

9. Sampling Frame 3 4 5  6 2 1 7 10 11 8 12 9   13 15 17 14 16  Sample  List of Individuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Chapter 8 Sampling 9

10. Example Suppose we are interested in the average ageof all Malaspina students. The relevant population is all Malaspina students (including students in all campuses). Possible Sampling Frame: List of Malaspina students at the Nanaimo campus. Chapter 8 Sampling 10

11. Example Cont. A sample can be students in this Math 161 class, or, 50 randomly selected Malaspina students at the Nanaimo campus. If we use the ages of all Malaspina students, then we have a census. Chapter 8 Sampling 11

12. Thought Question Popular magazines often contain surveys that ask their readers to answer questions about hot topics in the news. Do you think the responses the magazines receive are representative of public opinion? Explain why or why not. Chapter 2 12

13. Thought Question Suppose you access an online listing of all courses at your institution, alphabetized by department, to determine what proportion of all courses have a statistics course as a prerequisite. If you decide to sample 50 courses in order to get a representative sample of courses, how would you select them? Would it be appropriate to simply select the first 50 courses listed? Chapter 2 13

14. Bad Sampling Plans Convenience sampling selecting individuals who are easiest to reach Problem: Sample might not be representative of the target population. Chapter 2 14

15. Convenience Sampling Sampling mice from a large cage to study how a drug affects physical activity lab assistant reaches into the cage to select the mice one at a time until 10 are chosen Which mice will likely be chosen? could this sample yield biased results? Chapter 2 15

16. Bad Sampling Plans Voluntary response sampling allowing individuals to choose to be in the sample Problem: People with strong opinions (or feelings) about the issue tend to respond. Example: RateMyProfessor.com Chapter 2 16

17. Voluntary Response To prepare for her book Women and Love, Shere Hite sent questionnaires to 100,000 women asking about love, sex, and relationships. 4.5% responded Hite used those responses to write her book Moore (Statistics: Concepts and Controversies, 1997) noted: respondents “were fed up with men and eager to fight them…” “the anger became the theme of the book…” “but angry women are more likely” to respond Chapter 2 17

18. CNN on-line surveys: Bias: People have to care enough about an issue to bother replying. This sample is probably a combination of people who hate “wasting the taxpayers’ money” and “animal lovers.”

19. Bias The design of a statistical study is biased if it systematically favours certain outcomes. Convenience Sampling and Voluntary Response Sampling often produce biasedsamples. Chapter 2 19

20. Polls and Surveys Data carelessly collected (even if the sample size is large), is subject to a high degree of bias. To avoid biases, samples must be randomly chosen. Chapter 2 20

21. Avoiding Bias We select a sample in order to get information about some population. How can we choose a sample that fairly represents the population? Probability Sample: A sample chosen by chance. We must know what samples are possible and what chance (probability), each possible sample has. Chapter 2 21

22. Simple Random Sampling Each individual in the population has the same chance of being chosen for the sample Each group of individuals in the population of the required size (n) has the same chance of being the sample actually selected Chapter 2 22

23. Simple Random Sample (SRS) A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being selected. Chapter 2 23

24. How to choose an SRS Label each individual in the population with a unique number “drawing names (numbers) out of a hat” random number table (see Table B on pg. 686 of text) computer software (www.randomizer.org) or see textbook website (http://bcs.whfreeman.com/bps4e) Statistical Applets – Simple Random Sample Chapter 2 24

25. Choosing a simple random sample We need to select a random sample of 5 from a class of 20 students. • List and number all members of the population, which is the class of 20. • The number 20 is two digits long. • Parse the list of random digits into numbers that are two digits long. Here we chose to start with line 103, for no particular reason. 45 46 71 17 09 77 55 80 00 95 32 86 32 94 85 82 22 69 00 56

26. The first individual selected is Ramon, number 17. Then Henry (9 or “09”). That’s all we can get from line 103. We then move on to line 104. The next three to be selected are Moe, George, and Amy (13, 7, and 2). 45 46 71 17 09 77 55 80 00 95 32 86 32 94 85 82 22 69 00 56 52 71 13 88 89 93 07 46 02 … 01 Alan 02 Amber 03 Andrew 04 Ashley 05 Candice 06 Chase 07 Dana 08 Elisha 09 Gwen 10 James 11 Adrienne 12 Arron 13 Beverly 14 Bryce 15 Caleigh 16 Carl 17 Carly 18 Chanel 19 Christina 20 Christine • Choose a random sample of size 5 by reading through the list of two-digit random numbers, starting with line 103 and on. • The first five random numbers matching numbers assigned to people make the SRS. • Remember that 1 is 01, 2 is 02, etc. • Under sampling without replacement, if you were to hit 17 again before getting five people, don’t sample Ramon twice—you just keep going.

27. Simple Random Sampling Suppose there are 800 courses at an institution, alphabetized by department (and numbered 001-800), and you decide to randomly select 50 of them to determine what proportion of all the courses have a statistics course as a prerequisite. Use a random number table to select which 50 courses to sample. Example: Courses with Statistics Prerequisite Page 686 of textbook: Pick a line and column at random: suppose we get line 111, column 3 Random numbers: 605 130 929 700 412 712 … TRY: Use line 126, column 1: Random numbers: … 969 271 993 136 809 741 Chapter 2 27

28. Systematic Sample randomly select a member of the sampling frame for the sample using a set procedure or rule, select the rest of the individuals for the sample for example, Suppose we must choose 4 addresses out of 100, because 100/4 =25, we randomly select an individual from the sampling frame (01-25), and then select every 25th member of the sampling frame to be in the sample Example:Page 210, # 8.44 Chapter 4 28

29. Stratified Random Sample first divide the population into groups of similar individuals, called strata second, choose a separate simple random sample in each stratum third, combine these simple random samples to form the full sample if only certain strata are (randomly) chosen to be used, and all subjects in these strata make up the sample, then we have a cluster sample. the population is often divided according to geographic regions (called clusters). Chapter 4 29

30. Multistage Sample divide the population of interest into groups randomly select some of those groups divide the resulting collection of individuals into smaller groups randomly select some of those groups continue dividing the resulting collection of individuals into groups and randomly selecting some of those groups until you can simply list all of the resulting individuals and randomly select n of them for your sample Chapter 4 30

31. Probability Sampling Plans Simple random sampling (SRS) Systematic sampling Stratified random sampling Cluster sampling Multistage sampling Chapter 4 31

32. Steps for Designing a Study Identify your objective Develop a plan: Experiment or Observational study Use a random procedure to collect data Analyze the data and form conclusions Chapter 4 32

33. _________________ Sampling -use results that are readily available Hey! Do you believe in the death penalty? Chapter 2 33

34. __________________ - selection so that each has an equalchance of being selected Chapter 4 34

35. _____________ Sampling - Select some starting point and then select every Kth element in the population Chapter 4 35

36. _______________ Sampling - subdivide the population into subgroups (strata) that share the same characteristic, then draw a sample from each stratum Chapter 4 36

37. __________________ Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters Chapter 4 37

38. Thought Question When surveying students on their opinions on their professor’s teaching methods, do you think it matters who conducts the interviews? Explain your answer with an example. Chapter 4 38

39. Sources of Error in Surveys Random sampling reduces bias in choosing a sample and allows control of variability. Sampling in the real world is more complex and less reliable than we might hope for. Confidence statements do not reflect all sources of error that are present in sampling. Chapter 4 39

40. Sampling Errors –Errors that are caused by the act of taking a sample. Random Sampling Error: the difference between a sample result and the true population result; such an error results from chance (sample fluctuations). - Measured by the margin or error. Nonsampling Errors – Errors that are not related to the act of taking a sample. Example: Sample data that are incorrectly collected, recorded, or analyzed (such as using a defective instrument, or copying the data incorrectly). Nonsampling errors can be much larger than the sampling errors. Chapter 4 40

41. Sampling Errors • Using the wrong sampling frame. Undercoverage: Excluding some units in the population. Chapter 4 41

42. Sampling Errors Disasters Using voluntary response (self selection) Using a convenience or haphazard sample cannot extend results to the population of interest(need a broad cross-section of the population) Chapter 4 42

43. Difficulties Processing errors (data entry, calculations) Wording of questions / Response error Disasters Nonresponse (cannot contact subjects or they do not respond) Nonsampling Errors Chapter 4 43

44. Sources of Nonsampling Errors Non-response bias: Cannot contact subjects or they do not respond. - Nonrespondents often behave or think differently from respondents. low response rates can lead to huge biases. Processing Errors: Data that are incorrectly collected, recorded, calculated etc. Chapter 4 44

45. Nonsampling errors cont. Survey format effects:Factors such as question order, questionnaire layout, self -administered questionnaire or interviewer, can affect the results. Interviewer effects:Different interviewers asking the same questions can tend to obtain different answers. Response bias:Fancy term for lying when you think you should not tell the truth. Like if your family doctor asks: “How much do you drink?” Or a survey of female students asking: “How many men do you date per week?” People also simply forget and often give erroneous answers to questions about the past. Chapter 4 45

46. Concerns when Asking Survey Questions Deliberate bias Unintentional bias Desire to please Asking the uninformed Unnecessary complexity Ordering of questions Confidentiality and anonymity Chapter 4 46

47. Confidentiality and Anonymity Confidential answer respondent is known, but the information is a secret facilitates follow-up studies Anonymous answer the respondent is not known, or cannot be linked to his/her response usually yields more truthful answers Chapter 4 47

48. Dealing with errors Statistical methods are available for estimating the likely size of sampling errors. -margin of error gives the sampling error. All we can do with nonsampling errors is to try to minimize them at the study-design stage. Pilot Survey:One tests a survey on a relatively small group of people to try to identify any problems with the survey design before conducting the survey proper. Chapter 4 48

49. Learning about Populations from Samples The techniques of inferential statistics allow us to draw inferences or conclusions about a population from a sample. Your estimate of the population is only as good as your sampling design  Be sure to eliminate possible biases . Your sample is only an estimate—and if you randomly sampled again, you would probably get a somewhat different result. The bigger the sample the better. We’ll get back to it in later chapters. Chapter 4 49

50. Quiz For each study, identify: the population, the sample, the sampling method and any possible biases. 1) To assess the opinions of students at VIU regarding campus safety, a reporter interviews 15 students he meets walking on the campus late at night who are willing to give their opinions. 2) An SRS of 1200 adult Americans is selected and asked: “In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?” Thirty-nine percent of those responding answered yes. Chapter 4 50