The Logic of Sampling

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Chapter 7

• The Logic of Sampling

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Political Polls and Survey Sampling

• One of the most visible uses of survey sampling
  is political polling that is then tested by
  election results.
• In the 2000 Presidential election, pollsters came
  within a couple of percentage points of
  estimating the votes of 100 million people.
• To gather this information, they interviewed
  fewer than 2,000 people.

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Election Eve Polls - Voting for U.S.Presidential
Candidates, 2000
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Sampling

• The process of selecting observations is sampling
  (contrast with getting them all)
• Polls and other forms of social research, rest on
  observations
• Probability sampling that uses random selection
  allows us to generalize to the larger aggregate
  (sampling frame)
• When probability sampling isnt possible or
  feasible, we use nonprobability sampling

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Historical Methods of Sampling

• 1936 Literary Digest Poll
• Used a sampling frame of telephone subscribers
  and automobile owners
• Completely missed the Roosevelt reelection.
  Problem?
• 1936 George Gallup used quota sampling and
  predicted correctly
• Sample more accurately reflected the population
• Gallup failed in 1948 with the same process
• Based on old data

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Nonprobability Sampling

• How else could you sample college students?
• There are four methods of nonprobability
  sampling
• Reliance on available subjects (convenience
  sampling)
• Only justified if less risky sampling methods are
  not possible
• Researchers must exercise great caution in
  generalizing from their data
• No control over samples representativeness

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Nonprobability Sampling

• 2. Purposive or judgmental sampling
• Selecting a sample on the basis of knowledge of
  a population, its elements, and the purpose of
  the study
• Often used when field researchers are interested
  in studying cases that dont fit into regular
  patterns of attitudes and behaviors

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Nonprobability Sampling

• 3. Snowball sampling
• Appropriate when members of a population are
  difficult to locate (homeless, migrant workers,
  undocumented immigrants).
• Researcher collects data on members she can
  locate, then asks those individuals to help
  locate other members of that population.

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Nonprobability Sampling

• 4. Quota sampling
• Begins with a matrix of the target population
• Data is collected from people with the
  characteristics of a given cell
• Each group is assigned a weight appropriate to
  their portion of the total population
• When the elements are properly weighted, the data
  should provide a representation of the total
  population

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Qualitative Research and Sampling

• Often uses informants
• A member of a group that can act as a source of
  information about the group
• The informant should be representative of the
  group
• Can cause obvious problems
• Gender, status, viewpoint etc.
• Dont confuse informant with respondent

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Probability Sampling

• When researchers want precise, statistical
  descriptions of large populations
• Should (will, if done right) contain the same
  variations that exist in the population
• Representativeness when the relevant
  characteristics of the sampling frame match those
  of the aggregate
• All members should have an equal chance of
  selection
• Probability sampling permits us to estimate the
  representativeness of a sample
• Sampling bias when those selected are not
  representative of the aggregate
• Isnt always, or even usually, intentional

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Important Concepts

• Element same as Unit of analysis
• The unit about which information is collected
• Basis of statistical analysis
• Population
• Aggregation of elements you wish to generalize
  about
• Study population
• Aggregation of elements from which the sample is
  actually selected
• Also Sampling frame

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Important Concepts

• Random selection
• Each element has an equal chance of selection
  independent of other elements
• Important because
• Controls for bias
• Allows us to use statistical methods that depend
  on it
• Statistic vs. parameter
• One describes a variable of a sample, the other a
  variable of a population

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Sample Size

• The greater the number of randomly-selected
  samples, the more representative the statistic
• And the more reliable the data
• See example pages 202-205
• The greater the number of samples, the greater
  the chance that well be measuring the actual
  mean
• Each sample will yield a different statistic
• But close
• The taking of many independent random samples
  selected from a population will cluster around
  the population parameter in a regular pattern

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Sampling

• Probability theory also allows us to calculate
  the sampling error very precisely
• A function of the sample size
• Answers the question how likely is my
  statistical finding due to chance? Leads to
• Confidence level and confidence interval
  percentage of confidence that our statistic is
  within a certain percentage of the population
  parameter. Well use a single measurement p
• Sampling frame the total group of elements from
  which we draw our sample
• Samples can only describe sampling frames

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Types of Sampling Designs

• Simple random sampling (SRS)
• Not always possible
• Systematic sampling
• Selecting every k th element (sampling interval)
  of the total list, starting randomly
• Can cause problems, but is sometimes more
  accurate
• Stratified sampling
• Technique that can be applied in addition to
  either of the above methods
• First stratify your sampling frame along
  population parameters, than sample each

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Stratified sampling
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Multistage Cluster Sampling

• Used when it's impossible or impractical to
  compile an exhaustive list of the elements
  composing the target population.
• Involves repetition of two basic steps listing
  and sampling. Can also use stratification
• Highly efficient but less accurate.
• Sometimes the only way
• Best way is to favor more clusters than samples
  within each cluster
• 400 clusters with 5 samples each is better than 5
  clusters with 400 samples each

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Cluster Sampling