Sample Surveys

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Chapter 12

• Sample Surveys

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Idea 1 Take a Sample

• Examine a part of the whole.

Population
Sample
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Idea 1 Take a Sample

• Population
• Group of people we want information from
• Examples
• Registered voters in US
• ISU undergraduates
• Generally large
• Impractical or too expensive to talk to everyone

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Idea 1 Take a Sample

• Sample
• Smaller group of people from population
• Examples
• 200 registered voters
• 100 ISU undergrads
• Group we get information from

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Properties of a Sample

• Would like the sample to be representative of the
  population.
• This may not be possible, but at least we would
  like a sample that is not biased.

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Idea 2 Select the Sample Randomly

• Controls for factors that you know in the data
• Examples Gender, Race, Religion, etc.
• Controls for factors you dont know in data
• Allows you to make inferences about Population
• The point of Statistics
• Without random selection, your sample does not
  tell you anything about population
• Selecting items for the sample should be done at
  random so as to reduce the chance of getting a
  biased sample.

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Idea 3 Sample Size Matters

• Size of sample matters
• Fraction of the population sampled is not
  important!
• Want sample to be fairly large
• Why not do a census?
• Impractical
• Expensive
• Difficult to do
• Populations are often dynamic
• Can be more complex

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Terminology

• Information (what do we want to know?)
• Examples
• Percent of Registered Voters that would vote for
  a candidate.
• Mean age of ISU undergraduates
• Population
• Parameter
• Percent of all registered voters that will vote
  for a candidate
• Mean age of all ISU undergrads
• Sample
• Statistic
• Percent of the sample that will vote for a
  candidate
• Mean age of sample

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Terminology

• Population All students at ISU.
• Question Are the hours the Parks Library is
  open convenient?
• Population parameter Proportion of all ISU
  students who would answer yes.
• Sample 400 ISU students.
• Sample statistic the proportion of the 400
  students in the sample who say yes.

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Parameters and Statistics

• Most common parameters and statistics

Name Statistic Parameter
Mean   m
Std. Dev. s s
Proportion   p
Correlation r r
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How do we select the 400?

• Put an ad in the ISU Daily with the question and
  ask students to drop off their answers.
• Stand in front of the library and ask the first
  400 students who come by.

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Simple Random Sample

• Want a representative sample but will settle for
  one that is not biased.
• SRS Each combination of 400 ISU students has
  the same chance of being the sample selected.

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Simple Random Sample

• Sampling Frame
• A list of all students at ISU (the Registrar has
  such a list)
• Use random numbers to select 400 students at
  random from this list.

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Simple Random Sample

• If one were to do this more than once
• Different random numbers will give different
  samples of 400 students.
• We have introduced variability by sampling!

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Stratified Random Sample

• Large population will be made up of smaller
  homogenous groups
• Make sure each group is included in sample
• Usually in proportion of population
• Divide population into groups
• Take SRS from each group
• Combine SRSs Stratified Random Sample

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Example Stratified Sample

• Population 200 employees at a company 120 are
  men and 80 are women
• Opinions on policy of arrival of children
• Sample 20 people
• Stratify into men and women
• Sample 12 men and 8 women

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Cluster Sampling

• Difficult to get sampling frame for large
  population
• Sample group or cluster first
• Then take SRS from each cluster
• Combined SRSs Cluster Sample

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Example Cluster Sample

• Opinion of Catholics church goers in Boston
• Cluster Catholic churches
• Take SRS of churches
• Take SRS of members of selected churches

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Systematic Sampling

• Use a system to select the sample
• Every 10th person on an alphabetical list of
  students
• OK if the order of the list is not going to be
  associated with the responses
• Must start a systematic sample randomly (randomly
  choose where to start on the list)

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Sampling Variability

• Take several samples from a population and
  compute a statistic (i.e. mean)
• These means will not be the same
• This is the natural tendency of randomly drawn
  samples to vary from trial to trial
• Sometimes called sampling error, but it is not an
  error just a natural tendency

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What Can Go Wrong?

• Bias any systematic failure of a sample to
  represent its population
• Biased Samples
• Voluntary Response Sampling
• A large group of people are invited to respond,
  and those who do respond are counted
• Problem Not representative of pop - those with
  very strong opinions on subject are most likely
  to respond.
• This is called voluntary response bias

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What Can Go Wrong?

• More Biased Samples
• Convenience Sampling
• This approach simply includes those at hand, or
  easily available
• Problem Not representative of population

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Cautions about Samples

• Undercoverage Missing part of the population
• Household Surveys
• Phone Surveys
• Avoid undercoverage by having an accurate and
  complete sampling frame
• Non-response bias People elect not to
  participate in survey.

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Cautions about Samples

• Response bias People will lie
• Illegal or unpopular behavior
• Leading questions from interviewer
• Faulty memory
• Wording of questions
• Confusing wording, i.e., use of double negatives
• Leading questions

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Inference about Population

• Biased samples tell us nothing about the
  population
• Good samples have sampling variability
• Statistics will be different for each sample
• Statistics will be different for population
  paramters
• These differences obey certain laws of
  probability, but only for random samples
• Larger samples give more accurate results