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Designing Samples Section 5.1 Continued

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? • I want a sample of nine students form 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?

Sample Designs • Example: SRS or not? • I want a sample of nine students form 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?

Sample Designs • Better than a hat: • 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. Computers.

Sample Designs • A table of random digits is a long string of the digits 0 – 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.) TABLE B in the back of your book.

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…

Sample Designs Read example 5.4 on p. 276

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.

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

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

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

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.

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

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?”

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?”

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

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

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!)

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

Homework p. 274 & 279 # 7 – 12 You do not need your book on Friday.

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