HS 67BPS Chapter 81 Chapter 8 Producing Data: Sampling

HS 67BPS Chapter 82 From Exploration to Inference Exploratory Data AnalysisStatistical Inference Purpose: identify and describe patterns in data Purpose: answer specific question Conclusions apply to data and specific circumstance Conclusions apply beyond data and to broad circumstance Conclusion are informalConclusions are formal

HS 67BPS Chapter 83 Types of Studies Observational studies → individuals are studied without an experimental intervention (e.g., most surveys) Experimental studies → individuals receive an experimental intervention to determine its effect (e.g., a study of a drug effectiveness)

HS 67BPS Chapter 84 Example of an Observational Study (Weight Gain & CHD) Purpose: understand relationship between weight gain and coronary heart disease (CHD) 115,818 women, 30 to 55 years of age, recruited in 1976 Measure weight and height at age 18 and at recruitment, record weight gain Followed individuals for 14 years Record fatal and nonfatal CHD outcomes (1292 cases) Adjusted results for lurking variables such as smoking and family history of CHD Source: JAMA 1995;273(6):461-5

HS 67BPS Chapter 85 Illustrative Example: Results Compared to subjects who gained less than 11 pounds: Subjects who gains 11 to 17 lbs: 25% more likely to develop CHD 17 to 24 lbs gained: 64% more likely 24 to 44 lbs gained: 92% more likely 44+ lbs gained: 165% more likely

HS 67BPS Chapter 86 Illustrative Example (Questions) What is the population in this study? What is the sample? What makes this study observational? Can we say that weight gain caused CHD? Can we say weight gain is associated with CHD?

HS 67BPS Chapter 87 Poor quality samples favor a certain outcome  misleading results  sampling bias Examples –Voluntary response sampling: Allows individuals to choose to be in the study, e.g., call-in polls (pp. 178–9 in text) –Convenience sampling: individuals that are easiest to reach are selected, e.g., Interviewing at the mall (p. 179) Sample Quality

HS 67BPS Chapter 88 Voluntary Response Bias To prepare for her book Women and Love, Shere Hite sent questionnaires to 100,000 women asking about love and sexual relationships Only 4.5% responded Respondents “were fed up with men and eager to fight them…” Selection bias: “angry women [were] more likely” to respond  sampling bias

HS 67BPS Chapter 89 Convenience Sample A lab study was conducted to see if a drug affected physical activity in lab animals The lab assistant reached into the cage to select the mice for study The less active mice were chosen  made it seem like the drug decreased physical activity  sampling bias

HS 67BPS Chapter 810 Simple Random Sample (SRS) To avoid sampling biases, use chance (random) mechanisms to select subjects The most basic random sampling mechanism  Simple Random Sample (SRS) SRSs  every conceivable subset has the same chance to be studied

HS 67BPS Chapter 811 Selecting a SRS Methods: we can “pick them from a hat”, use a random number generator, or use a table of random digits (Table B) to derive our sample We will use Table B –Each digit 0 to 9 is equally likely –Entries are independent (knowledge of one entry gives no information about any other entries)

HS 67BPS Chapter 812 Choosing a Simple Random Sample (SRS) STEP 1: Label each individual in the population with a identification number STEP 2: Use Table B to select numbers at random (enter table at a different location each time it is used)

HS 67BPS Chapter 813 Selecting a SRS (Illustration) Population of N = 30 individuals Labeled the individuals 01 – 30 Select a row in table at random Enter table at different random location each time (e.g., to illustrate, enter at row 106) Row 106 with lines to indicate pairs 68|41|7 3|50|13| 15|52|9 First two individuals relevant entries are 13 and 15

HS 67BPS Chapter 814 Remainder of Chapter Not responsible for the sampling designs discussed on pp. 200–201 Are responsible for the cautions (pp. 201–202) –Undercoverage: some population groups left out of sampling process  sampling bias –Nonresponse bias: some individuals do not respond or refuse to participate  sampling bias –Even good quality samples may not be a perfect reflection of the population due to random sampling error  unavoidable & dealt with in future chapters