section 5.1 continued. a simple random sample (srs) of size n contains n individuals from the...
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Designing SamplesSection 5.1 Continued
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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.
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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?
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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?
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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
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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.)
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Sample Designs
Table B in the back of your book.
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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…
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Sample Designs
Example: Using a random digit table.
Read on page 276 the example 5.4
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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.
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Sample Designs
Practice problems: 7-12 (p. 274 & 279)
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Cautions about samples
Choosing samples randomly eliminates human bias from the choice of sample, but… What problems might remain?
Brainstorm.
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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?
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Cautions about samples
Nonresponse Occurs when selected individuals cannot
be contacted or refuse to cooperate
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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.
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Response Bias
Results may be influenced by behavior of either the interviewer or the respondent
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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?”
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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?”
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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?”
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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
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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
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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)
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Inference about the population
Just know now: larger random samples give more accurate results than smaller samples.