Sampling

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Sampling

• Research Process and Design
• Spring 2006
• Class 9 (Week 10)

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Todays objectives

• To answer any questions you have
• To describe various sampling approaches
• To introduce sampling theory and the central
  limit theorem
• To discuss concept of standard error and
  confidence intervals

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Quality perspective (Groves, et al., p. 48)
Measurement
Representation
_ Y
Target Population
m1
Construct
Coverage Error
Validity
_ yc
Measurement
Sampling Frame
Yi
Sampling Error
Measurement Error
_ ys
Sample
Response
yi
Nonresponse Error
Processing Error
_ yr
Respondents
Edited Response
Adjustment Error
yip
Postsurvey Adjustments
_ yrw
_ yprw
Survey Statistic
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Representation definitions

• Target population - a group of elements or cases
  that conform to specific criteria and we intend
  to generalize the results of the research
• Sample frame- a subset of the population list
  from which a sample is drawn
• Sample - subjects selected from a larger group of
  people
• Respondents Those successfully measured

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Discussion questions (from Light, Singer, and
Willett)

• Why do we sample? Why not study the entire
  population?
• What is the ultimate goal of sampling?
• What factors should we consider when determining
  who to sample?

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Nonobservational error

• Coverage error
• Gap between the target population and the
  sampling frame
• The result of not allowing all members of the
  survey population to have an equal or nonzero
  chance of being sampled for participation
• People that can never be sampled (telephone
  survey/no telephone)
• Exists before the sample is drawn
• Sampling error
• Gap between the sampling frame and the sample
• The result of surveying only some, and not all,
  elements of the survey population

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Nonobservational error (continued)

• Nonresponse error
• Gap between the sample and the respondent pool
• People who respond are different than sampled
  individuals who do not respond in a way relevant
  to the study
• Adjustment error
• Statistical adjustments may introduce error in
  the form of bias or variance

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Two sampling approaches

• Probability sample
• Each element in the sampling frame has a known
  and nonzero probability of being selected
• Probabilities do not need to be equal
• E.g., simple random sample, cluster sample
• Non-probability sample
• The probability of being selected is unknown

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Non-probability samples

• Common terms
• Convenience
• Purposeful
• Snowball
• Always to be avoided!
• there is no direct theoretical support for
  using them to describe the characteristics of the
  larger frame population. Groves et al. p. 95

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Probability samples

• Simple random
• Finite population correction
• Cluster
• Design effect
• Stratified random
• Proportionate allocation
• Disproportionate allocation
• What are the strengths and weaknesess of each?

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Group research proposals

• What is your population?
• How will you sample?
• Who will you study?
• How will you get access to these people?

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Commonly asked questions?

• What do researchers mean when they say plt.05?
• What is a margin of error of 3?
• What is a standard error?
• How do I determine how large my sample should be?
• Answers to these questions and more will be
  covered this week and next!!!

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Probability samples and standard errors

• Random selection
• Human influence is removed from the selection
  process
• E.g., dice, random number generator
• Probability samples use random selection to draw
  a subset of the sampling frame
• Sampling error arises because of this
• Standard errors allow us to quantify this error

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Laws of Sampling Theory

• Whenever a random sample is taken from a
  population there will be sampling error.
• If sample is truly random, then characteristics
  of sample will be an unbiased estimate of
  population characteristics.
• As sample size increases, the range (the size) of
  sampling error decreases.

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Central Limit Theorem

• The sampling distribution, or the distribution of
  the sampling error for any sample drawn from a
  given population, approximates a normal curve.
• Standard error - standard deviation of the sample
  estimates of means that would be formed if an
  infinite number of samples.

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Standard error

• Relies on the concept of repeated samples from a
  population
• Due to chance, the means of these samples will
  vary around the population mean
• We can measure this variance and determine how
  much the typical sample will deviate from the
  population mean (i.e., the standard deviation or
  SD)
• This SD is the standard error (SE)
• http//www.ruf.rice.edu/lane/stat_sim/sampling_di
  st/index.html

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Standard errors

• Standard error of the mean
• s is the SD from our sample n is sample size
• We can see that as n increases, SE decreases
• Different formulas for different statistics
  (proportions, comparing two means, etc.), but
  they have a similar form

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Confidence Intervals

• The range within which the parameter in question
  could be expected to be included a specified
  percentage of the time if procedure were to be
  repeated.
• C Z statistic associated with the confidence
  level 1.96 corresponds to the .95,
• 2.33 corresponds to the 98 level,
• and 2.58 corresponds to the 99 confidence level

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Standard errors

• Confidence intervals (CI) use SE and tell us the
  precision of our estimates
• 95 CI for a mean
• Very specific definition if we calculated
  similar CIs on 100 similar samples, 95 of them
  would bracket the population parameter
• Does not mean there is a 95 probability that
  population parameter falls in your CI either it
  does or it doesnt
• http//www.ruf.rice.edu/lane/stat_sim/conf_interv
  al/

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Standard errors

• Margin of error in polls is a confidence
  interval, usually a 95 CI

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How large a sample?

• Usually depends on resources
• When doing surveys, dont forget to take into
  account nonresponse
• Sample size calculator (courtesy of Mike Valiga,
  ACT)
• Can be found at http//www.uiowa.edu/c07b209/Sam
  pleSize_CI_calc.xls
• Countless websites (e.g., http//www.surveysystem.
  com/sscalc.htm)

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For next week

• Hypothesis testing and inferential statistics
• Readings for next week
• Jaeger Chapters 7-10
• Assignment due One page description of method.
  Bring 3 copies to class.