Section 5.1 Designing Samples

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Section 5.1Designing Samples

• AP Statistics
• www.toddfadoir.com/apstats

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Observational vs. Experiment

• An observational study observes individuals and
  measures variable of interest but does not
  attempt to influence the responses.
• An experiment, on the other hand, deliberately
  imposes some treatment on individuals in order to
  observe their responses.

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Population and Sample

• The entire group of individuals that we want
  information about is called the population.
• A sample is a part of the population that we
  actually examine in order to gather information.

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Sampling vs. a Census

• Sampling involves studying a part in order to
  gain information about the whole.
• A census attempts to contact every individual in
  the entire population.

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How to capture a Sample

• Getting a portion of the population is not
  difficult.
• Getting a good sample is difficult.
• Creating a plan to do this is called sample
  design.

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How not to sample

• Voluntary response sample (example Call in
  opinion polls).
• The problem with call in opinion polls is that
  the people who answer the polls tend to have
  strong opinions, especially strong negative
  opinions.
• This sample is biased this sample is not
  representative of the population.

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How not to sample

• Convenience sample (example Mall intercept
  interviews)
• Convenience sampling may not get you access to
  all the people in the population.
• Interviewers often avoid people who may make them
  feel uncomfortable.
• This sample is biased this sample is not
  representative of the population.

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Bias

• The design of a study is biased if it
  systematically favors certain outcomes.

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How to sample

• The best way to sample is to use a simple random
  sample
• A simple random sample (SRS) of size n consists
  of n individuals from the population chosen in
  such a way that every set of n individuals has an
  equal chance to be the sample actually selected.

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How to create a SRS

• Choose an SRS in two steps
• Step 1 Label. Assign a numerical label to every
  individual in the population.
• Step 2 Random Assignment.
• Random number table (Table B)
• Random number generator (RandInt in the TI-83)

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Stratified Random Sample

• To select a stratified random sample, first
  divide the population into groups of similar
  individuals, called strata. Then choose a
  separate SRS in each stratum and combine these
  SRSs to form the full sample.

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Multistage Sampling Design

• Randomly choose stage 1 strata (for example,
  states)
• Randomly choose stage 2 strata (for example,
  cities within states)
• and so on until you get down to the sample size.

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Random is the key

• Good sampling technique uses random selection to
  reduce the possibility of bias.

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Cautions about sample surveys

• Undercoverage occurs when some groups in the
  population are left out of the process of
  choosing the sample.
• Nonresponse occurs when an individual chosen for
  the sample cant be contacted or does not
  cooperate.

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Cautions about sample surveys

• Response bias. Respondents may lie if they feel
  uncomfortable telling the truth.

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Cautions about sample surveys

• Wording of questions. It is estimated that
  disposable diapers account for less than 2 of
  the trash in todays landfills. In contrast,
  beverage containers, third-class mail and yard
  wastes are estimated to account for about 21 of
  the trash in landfills. Given this, in your
  opinion, would it be fair to ban disposable
  diapers?

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Why Sample?

• We want to make inferences about the population
  as a whole.
• We cant afford to talk to everyone.
• Even though two samples, following the same
  design most probably will give us different
  results, those results are reasonable estimates
  of the population as a whole

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How to get the best estimates?

• Large random sample give more precise results
  than smaller sample.

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Assignment

• Exercises 5.1-9 all, 11-15 odd