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Designing Samples

Section 5.1 Continued. Designing Samples. Sample Designs. A simple random sample (SRS) of size n contains n individuals from the population chosen so that every set of n individuals has an equal chance of being selected. . Sample Designs. Example: SRS or not?

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Designing Samples

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  1. Section 5.1 Continued Designing Samples

  2. Sample Designs • A simple random sample (SRS) of size n contains n individuals from the population chosen so that every set of n individuals has an equal chance of being selected.

  3. Sample Designs • Example: SRS or not? • I want a sample of nine students from the class, so I put each of your names in a hat and draw out nine of them. • Does each individual have an equal chance of being chosen? • Does each group of nine people have an equal chance of being chosen?

  4. Sample Designs • Example: SRS or not? • I want a sample of nine students from the class but I know that there are three juniors and 17 seniors in class, so I pick one junior at random and eight seniors. • Does each individual have an equal chance of being chosen? • Does each group of nine people have an equal chance of being chosen?

  5. Sample Designs • Better than a hat: computers. • Software can choose an SRS from a list of the individuals in a list. • Not quite as easy as software, but still better than a hat: a table of random digits

  6. Sample Designs • A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with two properties: • Each entry in the table is equally likely to be any of the ten digits 0 through 9. • The entries are independent of each other. (Knowing one part of the table tells you nothing about the rest of the table.)

  7. Sample Designs • Table B in the back of your book.

  8. Sample Designs • Each entry is equally likely to be 0 – 9. • Each pair of entries is equally likely to be 00 – 99. • Each triple of entries is equally likely to be 000 – 999. • And so on…

  9. Sample Designs • Example: Using a random digit table. • Read on page 276 the example 5.4

  10. Sample Designs • A stratified random sample first divides a population into groups of similar individuals called strata. Then separate SRS’s are chosen from each group (stratum) and combined to make the full sample.

  11. Sample Designs • Practice problems: • 7-12 (p. 274 & 279)

  12. Cautions about samples • Choosing samples randomly eliminates human bias from the choice of sample, but… • What problems might remain? Brainstorm.

  13. Cautions about samples • Undercoverage • Having an inaccurate list of the population • Ex: Who is excluded from a survey of “households”? • Who is excluded from a telephone survey?

  14. Cautions about samples • Nonresponse • Occurs when selected individuals cannot be contacted or refuse to cooperate

  15. Examples • Which problem (undercoverage or nonresponse) is represented? • It is impossible to keep a perfectly complete list of addresses for the U.S. Census • Homeless people do not have addresses • In 1990, 35% of people who were mailed Census forms did not return them.

  16. Response Bias • Results may be influenced by behavior of either the interviewer or the respondent

  17. Response Bias • How might response bias show up in these situations? • A survey about drug use or other illegal behavior • Questions asking people to recall events, like: “Have you visited the dentist in the last six months?”

  18. Response Bias • The wording of questions can often lead to bias • “It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail, and yard wastes are estimated to account for 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?”

  19. Response Bias • “Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?” • “Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?”

  20. Response Bias • “Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?” 22% said possible • “Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?” 1% said possible

  21. Inference about the population • Even if we can eliminate most of the bias in a sample, the results from the sample are rarely exactly the same as for the population • Each different sample pulls different individuals, so results will vary from sample to sample • Results are rarely correct for the population

  22. Inference about the population • Since we use random sampling, we can use the laws of probability (later chapters!) • We’ll be able to figure out the margin of error (also in later chapters)

  23. Inference about the population • Just know now: larger random samples give more accurate results than smaller samples.

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