Sampling (Babbie, Chapter 7)

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Sampling(Babbie, Chapter 7)
Geography 237Geographic Research Methods and
Issues

• Why sample
• Probability and Non-Probability Sampling
• Probability Theory

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Why Sample?

• What is a sample?
• Why do we sample in social research?

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Two Classes of Sampling

• Non-Probability Sampling
• not based on probability theory
• representativeness not as important
• rapport difficult populations
• qualitative research
• e.g., snowball sampling
• Probability Sampling
• based on probability theory
• representativeness imperative
• e.g., simple random sample

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Non-Probability Sampling

• Convenience Sample
• whomever is available
• pre-test a questionnaire
• e.g., students in geog237, attendees at the
  Canadian Association of Geographers annual meeting

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Non-Probability Sampling

• Purposive Sample
• units selected based on researcher judgment
• wide variety vs representative
• qualitative research
• e.g., most vocal people at a public meeting

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Non-Probability Sampling

• Snowball Sample
• new respondents selected based on recommendation
  of existing respondents
• difficult populations
• rapport important
• e.g., homeless, members of activist group

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Non-Probability Sampling

• Quota Sample
• representativeness important
• matrix theoretically important population
  components
• cells weightings same as sample
• e.g., see below sample of 1000, how many women
  in Windsor?

City Men Women 0-50K 50K
London 45 55 60 40
Windsor 49 51 57 53
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Non-Probability Sampling

• Key Informants
• insiders who know much about phenomenon of
  interest
• knowledgeable and articulate
• reconnaissance prior to contact with others
• help decide probability sampling scheme
• e.g., mayor and councilors to speak about
  residents small town

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Probability SamplingPrinciples/Terminology

• Representativeness
• sample microcosm of population
• same variation (e.g., gender, age, ethnicity)
• Avoid Bias
• selection bias those in sample not
  representative of those in population
• Equal Probability of Selection
• all members in population
• i.e., random selection

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Probability SamplingProblems with These?
Source www.globeandmail.com
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Probability SamplingPrinciples/Terminology

• Population
• group about whom you want to draw inferences
• more theoretical than quantifiable
• e.g., Ontarians, smokers

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Probability SamplingPrinciples/Terminology

• Study Population
• group from which sample is actually drawn
• subset of population
• e.g., voters registered for 2003 provincial
  election, people who buy cigarettes at stores in
  London

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Probability SamplingPrinciples/Terminology

• Sampling Frame
• the actual list from which elements are drawn
• e.g., voter registry list people observed buying
  cigarettes
• Sample
• subset of study population
• used for making statistical inferences
• e.g., 400 voters

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Probability SamplingRelationship Between Terms
sample
sample frame
study population
population
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Probability SamplingPrinciples/Terminology

• Element
• the unit that comprises the population, sample
  population and the sample
• typically the same as unit of analysis
• e.g., individuals, households

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Probability SamplingSampling Distribution

• Parameter
• a number computed from a population
• a summary description of some aspect of a
  population
• no random variation true value
• often unknown (hence, the need to sample)
• e.g., median income of Canadians

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Probability SamplingSampling Distribution

• Statistic
• a number computed from a sample
• meant to represent the corresponding population
  parameter
• random variation (sampling error)
• e.g., median income of 20 sample of Canadian
  Census

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Probability SamplingSampling Distribution

• Sampling Error
• How good are the results based on sample n?
• function of parameter, sample size, and standard
  error
• Standard Error
• average difference between a statistic and a
  parameter
• function of parameter and sample size

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Probability SamplingSampling Distribution
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Probability SamplingSampling Distribution

• Properties of Sampling Error
• as sample size increases standard error decreases
  ˆ sampling error decreases
• the greater the split in the parameter the
  greater the standard error ˆ greater the sampling
  error
• i.e. more homogeneous populations have lower
  sampling error

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Probability SamplingTypes

• Simple Random Sample
• all elements in sample frame assigned numbers
• random numbers for sample chosen and applied to
  list
• e.g., random number tables, see next.

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Probability SamplingSimple Random Sample
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Probability SamplingSimple Random Sample
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Probability SamplingTypes

• Systematic Sample
• practical alternative to simple random sampling
• every kth (sampling interval) element in a list
• typically total sample frame divided by sample
  size to determine sampling interval
• threat periodicity whereby k periodicity
• e.g., every other household (typically odd and
  even numbers on same side of street!)

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Probability SamplingSystematic Sample
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Probability SamplingTypes

• Stratified (Random) Sample
• sample frame split into mutually exclusive
  homogenous sub-groups
• random or systematic sampling within these groups
• homogeneity of sub-groups reduces sampling error
• e.g., gender age categories census tracts in
  London

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Probability SamplingTypes

• (Multistage) Cluster Sample
• impractical to compile and count elements in a
  single list (e.g., all Canadian university
  students)
• obtain lists for subgroups (i.e., all
  universities)
• randomly select some of the subgroups (e.g., 10
  universities)
• randomly select within those lists (i.e., simple
  or systematic of 200 students)
• total sample N 2000

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Probability Sampling(Multistage) Cluster Sample