1. BPS - 3rd Ed. Chapter 71 Producing Data: Sampling

2. BPS - 3rd Ed. Chapter 72 u Researchers often want to answer questions about some large group of individuals (this group is called the population) u Often the researchers cannot measure (or survey) all individuals in the population, so they measure a subset of individuals that is chosen to represent the entire population (this subset is called a sample) u The researchers then use statistical techniques to make conclusions about the population based on the sample Population and Sample

3. BPS - 3rd Ed. Chapter 73 How Data are Obtained u Observational Study –Observes individuals and measures variables of interest but does not attempt to influence the responses –Describes some group or situation –Sample surveys are observational studies u Experiment –Deliberately imposes some treatment on individuals in order to observe their responses –Studies whether the treatment causes change in the response.

4. BPS - 3rd Ed. Chapter 74 Experiment versus Observational Study Both typically have the goal of detecting a relationship between the explanatory and response variables. u Experiment –create differences in the explanatory variable and examine any resulting changes in the response variable (cause-and-effect conclusion) u Observational Study –observe differences in the explanatory variable and notice any related differences in the response variable (association between variables)

5. BPS - 3rd Ed. Chapter 75 Why Not Always Use an Experiment? u Sometimes it is unethical or impossible to assign people to receive a specific treatment. u Certain explanatory variables, such as handedness or gender, are inherent traits and cannot be randomly assigned.

6. BPS - 3rd Ed. Chapter 76 Confounding u The problem: –in addition to the explanatory variable of interest, there may be other variables (explanatory or lurking) that make the groups being studied different from each other –the impact of these variables cannot be separated from the impact of the explanatory variable on the response

7. BPS - 3rd Ed. Chapter 77 Confounding u The solution: –Experiment: randomize experimental units to receive different treatments (possible confounding variables should “even out” across groups) –Observational Study: measure potential confounding variables and determine if they have an impact on the response (may then adjust for these variables in the statistical analysis)

8. BPS - 3rd Ed. Chapter 78 Question A recent newspaper article concluded that smoking marijuana at least three times a week resulted in lower grades in college. How do you think the researchers came to this conclusion? Do you believe it? Is there a more reasonable conclusion?

9. BPS - 3rd Ed. Chapter 79 Case Study The Effect of Hypnosis on the Immune System reported in Science News, Sept. 4, 1993, p. 153

10. BPS - 3rd Ed. Chapter 710 Case Study The Effect of Hypnosis on the Immune System Objective: To determine if hypnosis strengthens the disease-fighting capacity of immune cells.

11. BPS - 3rd Ed. Chapter 711 Case Study u 65 college students. –33 easily hypnotized –32 not easily hypnotized u white blood cell counts measured u all students viewed a brief video about the immune system.

12. BPS - 3rd Ed. Chapter 712 Case Study u Students randomly assigned to one of three conditions –subjects hypnotized, given mental exercise –subjects relaxed in sensory deprivation tank –control group (no treatment)

13. BPS - 3rd Ed. Chapter 713 Case Study u white blood cell counts re-measured after one week u the two white blood cell counts are compared for each group u results –hypnotized group showed larger jump in white blood cells –“easily hypnotized” group showed largest immune enhancement

14. BPS - 3rd Ed. Chapter 714 Case Study The Effect of Hypnosis on the Immune System What is the population? What is the sample?

15. BPS - 3rd Ed. Chapter 715 Case Study The Effect of Hypnosis on the Immune System Is this an experiment or an observational study?

16. BPS - 3rd Ed. Chapter 716 Case Study The Effect of Hypnosis on the Immune System Does hypnosis and mental exercise affect the immune system?

17. BPS - 3rd Ed. Chapter 717 Case Study Weight Gain Spells Heart Risk for Women “Weight, weight change, and coronary heart disease in women.” W.C. Willett, et. al., vol. 273(6), Journal of the American Medical Association, Feb. 8, 1995. (Reported in Science News, Feb. 4, 1995, p. 108)

18. BPS - 3rd Ed. Chapter 718 Case Study Objective: To recommend a range of body mass index (a function of weight and height) in terms of coronary heart disease (CHD) risk in women. Weight Gain Spells Heart Risk for Women

19. BPS - 3rd Ed. Chapter 719 Case Study u Study started in 1976 with 115,818 women aged 30 to 55 years and without a history of previous CHD. u Each woman’s weight (body mass) was determined u Each woman was asked her weight at age 18.

20. BPS - 3rd Ed. Chapter 720 Case Study u The cohort of women were followed for 14 years. u The number of CHD (fatal and nonfatal) cases were counted (1292 cases). u Results were adjusted for other variables (smoking, family history, menopausal status, post-menopausal hormone use).

21. BPS - 3rd Ed. Chapter 721 Case Study u Results: compare those who gained less than 11 pounds (from age 18 to current age) to the others. –11 to 17 lbs: 25% more likely to develop heart disease –17 to 24 lbs: 64% more likely –24 to 44 lbs: 92% more likely –more than 44 lbs: 165% more likely

22. BPS - 3rd Ed. Chapter 722 Case Study What is the population? What is the sample? Weight Gain Spells Heart Risk for Women

23. BPS - 3rd Ed. Chapter 723 Case Study Is this an experiment or an observational study? Weight Gain Spells Heart Risk for Women

24. BPS - 3rd Ed. Chapter 724 Case Study Does weight gain in women increase their risk for CHD? Weight Gain Spells Heart Risk for Women

25. BPS - 3rd Ed. Chapter 725 Bad Sampling Designs u Voluntary response sampling –allowing individuals to choose to be in the sample u Convenience sampling –selecting individuals that are easiest to reach v Both of these techniques are biased –systematically favor certain outcomes

26. BPS - 3rd Ed. Chapter 726 Voluntary Response u 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 u 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

27. BPS - 3rd Ed. Chapter 727 Convenience Sampling u 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 u Which mice will likely be chosen? –could this sample yield biased results?

28. BPS - 3rd Ed. Chapter 728 Simple Random Sampling u Each individual in the population has the same chance of being chosen for the sample u Each group of individuals (in the population) of the required size (n) has the same chance of being the sample actually selected u Random selection: –“drawing names out of a hat” –table of random digits –computer software

29. BPS - 3rd Ed. Chapter 729 Table of Random Digits u Table B on pg. 654 of text –each entry is equally likely to be any of the 10 digits 0 through 9 –entries are independent of each other (knowledge of one entry gives no information about any other entries) –each pair of entries is equally likely to be any of the 100 pairs 00, 01,…, 99 –each triple of entries is equally likely to be any of the 1000 values 000, 001, …, 999

30. BPS - 3rd Ed. Chapter 730 Choosing a Simple Random Sample (SRS) STEP 1: Label each individual in the population STEP 2: Use Table B to select labels at random

31. BPS - 3rd Ed. Chapter 731 Probability Sample u a sample chosen by chance u must know what samples are possible and what chance, or probability, each possible sample has of being selected u a SRS gives each member of the population an equal chance to be selected

32. BPS - 3rd Ed. Chapter 732 Stratified Random Sample u first divide the population into groups of similar individuals, called strata u second, choose a separate SRS in each stratum u third, combine these SRSs to form the full sample

33. BPS - 3rd Ed. Chapter 733 Stratified Random Sample Example Suppose a university has the following student demographics: Undergraduate Graduate First Professional Special 55% 20% 5% 20% A stratified random sample of 100 students could be chosen as follows: select a SRS of 55 undergraduates, a SRS of 20 graduates, a SRS of 5 first professional students, and a SRS of 20 special students; combine these 100 students.

34. BPS - 3rd Ed. Chapter 734 Multistage Sample u several stages of sampling are carried out u useful for large-scale sample surveys u samples at each stage may be SRSs, but are often stratified u stages may involve other random sampling techniques as well (cluster, systematic, random digit dialing, …)

35. BPS - 3rd Ed. Chapter 735 Cautions about Sample Surveys u Undercoverage –some individuals or groups in the population are left out of the process of choosing the sample u Nonresponse –individuals chosen for the sample cannot be contacted or refuse to cooperate/respond u Response bias –behavior of respondent or interviewer may lead to inaccurate answers or measurements u Wording of questions –confusing or leading (biased) questions; words with different meanings

36. BPS - 3rd Ed. Chapter 736 Nonresponse u 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 –angry women are more likely to respond

37. BPS - 3rd Ed. Chapter 737 Response Bias u A door-to-door survey is being conducted to determine drug use (past or present) of members of the community. Respondents may give socially acceptable answers (maybe not the truth!) u For this survey on drug use, would it matter if a police officer is conducting the interview? (bias from interviewer)

38. BPS - 3rd Ed. Chapter 738 Asking the Uninformed Washington Post National Weekly Edition (April 10-16, 1995, p. 36) u A 1978 poll done in Cincinnati asked people whether they “favored or opposed repealing the 1975 Public Affairs Act.” –There was no such act! –About one third of those asked expressed an opinion about it. Response Bias

39. BPS - 3rd Ed. Chapter 739 Wording of Questions A newsletter distributed by a politician to his constituents gave the results of a “nationwide survey on Americans’ attitudes about a variety of educational issues.” One of the questions asked was, “Should your legislature adopt a policy to assist children in failing schools to opt out of that school and attend an alternative school--public, private, or parochial--of the parents’ choosing?” From the wording of this question, can you speculate on what answer was desired? Explain.

40. BPS - 3rd Ed. Chapter 740 Wording: Deliberate Bias u “If you found a wallet with $20 in it, would you return the money?” u “If you found a wallet with $20 in it, would you do the right thing and return the money?”

41. BPS - 3rd Ed. Chapter 741 Wording: Unintentional Bias u “I have taught several students over the past few years.” –How many students do you think I have taught? –How many years am I referring to? u “Over the past few days, how many servings of fruit have you eaten?” –How many days are you considering? –What constitutes a serving?

42. BPS - 3rd Ed. Chapter 742 Wording: Unnecessary Complexity u “Do you sometimes find that you have arguments with your family members and co-workers?” –Arguments with family members –Arguments with co-workers

43. BPS - 3rd Ed. Chapter 743 Wording: Ordering of Questions u “How often do you normally go out on a date? about ___ times a month.” u “How happy are you with life in general.” –Strong association between these questions. –If the ordering is reversed, then there would be no strong association between these questions

44. BPS - 3rd Ed. Chapter 744 Inferences about the Population u Values calculated from samples are used to make conclusions (inferences) about unknown values in the population u Variability –different samples from the same population may yield different results for a particular value of interest –estimates from random samples will be closer to the true values in the population if the samples are larger –how close the estimates will likely be to the true values can be calculated -- this is called the margin of error