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Chapter 13: Collecting Statistical Data

Chapter 13: Collecting Statistical Data. Sections 13.1-13.2: Population and Sampling. Some Important Terms. Population Collection of objects/individuals to which the statistical statement refers N-value = the number of objects/individuals in the population Sample

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Chapter 13: Collecting Statistical Data

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  1. Chapter 13: Collecting Statistical Data

  2. Sections 13.1-13.2: Population and Sampling

  3. Some Important Terms • Population • Collection of objects/individuals to which the statistical statement refers • N-value = the number of objects/individuals in the population • Sample • The subgroup chosen to provide the data • Should be representative of the population

  4. Target Population/Sampling Frame • Target population = the population for which the survey applies • Sampling frame (aka accessible population) = the actual subset of the population from which the sample will be drawn

  5. Sampling • Convenience sampling • The sample is chosen based on what is easiest, cheapest and most accessible • May not be representative of the population • Quota sampling • Forces the sample to be representative of a population through the use of quotas • The sample should have so many men, women, children, blacks, whites, Hispanics, etc.

  6. The 1948 Presidential Election • Read Case Study 3 on p. 503-504 • What is the flaw in quota sampling?

  7. Section 13.3: Random Sampling Usually the best method of sampling

  8. Simple Random Sampling • We put the name of each individual in the sample in a hat, mix the names well and draw randomly until we have N individuals. (And by “hat”, I mean computer.) • Expensive and difficult to put into effect

  9. Stratified Sampling • Break the sampling frame into categories (called strata) and then randomly choose a sample from these strata. • Example: Read Case Study 4 on p. 506

  10. Section 13.4: Sampling Terminology

  11. Vocabulary • Statistic: any kind of numerical information drawn from a sample • Parameter: numerical information we would like to have • Sampling error: difference between a parameter and a statistic used to estimate that parameter

  12. Vocabulary (continued) • Chance error: the result of the basic fact that a sample can only give us approximate information about the population • Sample bias: the result of choosing a bad sample – a very serious problem!

  13. Vocabulary (continued) • Sampling proportion: tells us that the size of the sample is intended to be x% of the population • n/N where n = the size of the sample, and N = the size of the population

  14. Example 13.4.1: Telephone Poll • The city of Cleansburg has 8325 registered voters. There is an election for mayor of Cleansburg, and there are three candidates for the position: Smith, Jones and Brown. The day before the election, a telephone poll of 680 randomly selected registered voters produced the following results: 306 people surveyed indicated that they would vote for Smith, 272 indicated that they would vote for Jones, and 102 indicated that they would vote for Brown.

  15. Example 13.1.1 (Continued) • What is the population for this poll? • What is the sample? • Describe the sampling method used. • Give the sampling proportion. • Give the sample statistic estimating the percentage of the vote going to Smith. • If in the actual election Smith received 42% of the votes, Jones 43%, and Brown 15%, find the sampling errors.

  16. Section 13.5: The Capture-Recapture Method Method for estimating the N-value of a population

  17. Example 13.5.1: Small Fish in Big Pond • A large pond is stocked with catfish. As part of a research project we need to estimate the number of catfish in the pond. An actual head count is out of the question, so our best bet is the capture-recapture method.

  18. Capture-Recapture Method • Capture: Capture a sample of size n1, mark the objects and release them back into the general population. • Recapture: After a certain period of time, capture a new sample of size n2 and take an exact head count of the marked objects. Call this number k. • Estimate: The N-value of the population can be estimated to be approximately

  19. Example 13.5.2: Cancer Registry • In a study in the Netherlands, suppose that a sample of 100 people who were known to have cancer were selected. Then, a sample of 50 people from a nearby laboratory was taken and, out of that sample, 7 of them had cancer. Use the capture-recapture method for this problem. • What information does this give you about the number of people who have cancer?

  20. Capture-Recapture Method Accused of Being Misleading • Assignment due at the end of class: Research on the Internet reasons that the Capture-Recapture Method is useful and reasons that it can be misleading. Write at least 8 sentences about the usefulness of the Capture-Recapture method, and support your reasons with examples. Cite your source(s).

  21. Section 13.6: Clinical Studies Establish connections between cause and effect

  22. Examples of Clinical Study Topics • Does taking more math classes increase your chances of getting paid a higher salary? • Does repeated exposure to secondhand smoke increase your chances of getting lung cancer? • Do daily doses of aspirin reduce your chances of a heart attack?

  23. Association is not causation • Just because two things are related does not mean that one causes the other. • Students who got high grades in English also got high grades in Math. • Breast cancer was more commonly found in women who received regular breast cancer screenings. • As ice cream sales increase, so do deaths by drowning.

  24. “Statistics show that of those who contract the habit of eating, very few survive.” -Wallace Irwin

  25. Case Study 5: The Alar Scare • On pages 509-510

  26. Clinical Studies • Concerned with determining whether a single variable (usually a vaccine, drug, therapy, etc.) can cause a certain effect (a disease, symptom, cure, etc.) • Controlled study: two groups are compared • Control group: subjects not receiving treatment • Treatment (or experimental) group: subjects receiving treatment • What characteristics do you think should be considered to create an accurate controlled study?

  27. The Placebo Effect • The idea of receiving treatment (not actually receiving treatment) can produce positive results. • Placebo: a make-believe form of a treatment (like a sugar pill, an injection of saline, etc.) • Controlled placebo study: The members of the control group are given a placebo

  28. Case Study 6: The 1954 Salk Polio Vaccine Field Trials • Double-blind study: Neither the subjects nor the researchers know which subjects are in the treatment group and which are in the control group. • On pages 511-512

  29. Assignment • Due at the end of class • P. 522 #73: An article in the Providence Journal about automobile accident fatalities includes the following observation: “Forty-two percent of all fatalities occurred on Friday, Saturday and Sunday, apparently because of increased drinking on the weekends.” • Give a possible argument as to why the conclusion drawn may not be justified by the data. • Give a different possible argument as to why the conclusion drawn may be justified by the data.

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