Sampling

1
Sampling
2
Observational vs. Experiment

• Observational observe and measure but do not
  influence
• Experimental impose treatments and measure
  responses

3
Other ways to produce data

• Simulation when logistically difficult or
  ethically questionable to obtain a sample or run
  an experiment
• http//www.whatifsports.com/beyondtheboxscore/defa
  ult.asp?article2009WorldSeriesGT139002

4
Pollsters

• www.gallup.com
• http//blog.nielsen.com/nielsenwire/
• www.bls.gov/cps/
• www.norc.org/projects/gensoc.asp

5
Statistical Inference

• Ability to answer specific questions based on
  data with a known degree of confidence.
• Careful design of data production is the most
  important prerequisite for valid inference

6
Population vs. Sample

• Population the entire group of individuals that
  we want information about
• Sample a part of the population that we study
  in order to gather information about the whole

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Parameter vs. Statistic

• Parameter a measure from the entire population
• Statistic a measure calculated from a sample or
  experiment

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Sampling vs. Census

• Sampling study a part
• Census attempts to study every individual in
  the population

9
Bias

• Systematic favoring of certain outcomes

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Sources of Bias

• Voluntary Response respondents who choose
  themselves those with strong opinions,
  particularly negative, are most likely to respond

11
Sources of Bias

• Convenience Sampling individuals who are
  easiest to reach are the only ones included in a
  sample

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Probability Sample

• A sample chosen by chance
• The use of chance to select the sample is the
  essential principle of statistical sampling

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Simple Random Sample

• A sample of size n individuals chosen so that
  every possible set of n individuals has an equal
  chance of being selected

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Stratified Random Sample

• Divides the population into groups of similar
  individuals then chooses a separate SRS from each
  group

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Stratified Random Sampling

• Divide the population into homogeneous groups
  called strata.

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Stratified Random Sampling

• Then choose a separate SRS in each stratum and
  combine these SRS to form the full sample.

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Stratified Random Sampling Example

• Radio stations owe royalties to composers when
  they play their music.

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Stratified Random Sampling Example

• ASCAP collects royalties for its members
  according to licensing agreements with the
  stations.

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Stratified Random Sampling Example

• How does ASCAP distribute the 435 million a year
  it collects to the composers of the 4 millions
  songs in its library?

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Stratified Random Sampling Example

• Radio stations are stratified by type of
  community, geographic location, and the size of
  the license fee paid to ASCAP.
• In all there are 432 strata.

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Stratified Random Sampling Example

• Tapes are made at random hours for randomly
  selected stations in each stratum.

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Stratified Random Sampling Example

• The tapes are reviewed by experts who can
  identify almost every piece of music ever written
  and the composers are paid according to their
  popularity.

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Stratified Random Sampling Example

• ASCAP samples 60,000 hours out of the 53 million
  hours of radio programs each year.

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Cautions about sample surveys

• Undercoverage some groups in the population are
  left out
• Nonresponse an individual chosen for the sample
  cant or wont cooperate

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More Sources of Bias

• Response Bias
• Respondents may lie
• Respondents may not remember accurately
• Interviewer may favor certain responses
• Race or sex of interviewer may affect response
• Wording of questions confusing or leading

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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 21 of the trash in landfills. Given
  this, in your opinion, would it be fair to ban
  disposable diapers?

27
Grade Inflation Article

• Students self-reported GPA
• Overstated or Understated?

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Sampling Error

• Larger random samples give more accurate results
  than smaller samples

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Cluster Sampling

• Divides the population into groups, or clusters.
  Some of these clusters are randomly selected.
  

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Cluster Sampling Example

• What do AP Statistics students think?

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Cluster Sampling Example

• Enough time on free-response section?

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Cluster Sampling Example

• List of all schools offering AP Stat.

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Cluster Sampling Example

• A number of schools are randomly selected and
  EVERY student in that school is asked if they
  felt they had enough time on the free-response
  questions on the AP Stat test.

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Multistage Sampling Design

• Random sample chosen in stages
• Common for U. S. household surveys
• See TB p. 340, Example 5.7 What Do AP Students
  Think? for more details

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Sampling Frame

• The list of individuals from which a sample is
  actually selected
• Ideally every individual in the population

36
Choosing SRS Using Random Digits

• TB p. 336 Example 5.5 Joans Accounting Firm

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Closing

• Describe the relationship between a sample and a
  population.
• Describe the relationship between a statistic and
  a parameter