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10/12/2004 9:20 am Geog 237a 1
SamplingSampling(Babbie, Chapter 7)
• Why sample• Probability and Non-Probability
Sampling• Probability Theory
Geography 237Geography 237Geographic Research: Methods and Issues
10/12/2004 9:20 am Geog 237a 2
Why Sample?Why Sample?
What is a sample?
Why do we sample in social research?
10/12/2004 9:20 am Geog 237a 3
Two Classes of SamplingTwo 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
10/12/2004 9:20 am Geog 237a 4
Non-Probability SamplingNon-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
10/12/2004 9:20 am Geog 237a 5
Non-Probability SamplingNon-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
10/12/2004 9:20 am Geog 237a 6
Non-Probability SamplingNon-Probability Sampling
Snowball Sample• new respondents selected based on
recommendation of existing respondents
• difficult populations• rapport important• e.g., homeless, members of activist
group
10/12/2004 9:20 am Geog 237a 7
Non-Probability SamplingNon-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%
10/12/2004 9:20 am Geog 237a 8
Non-Probability SamplingNon-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
10/12/2004 9:20 am Geog 237a 9
Probability SamplingProbability SamplingPrinciples/TerminologyPrinciples/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 SamplingProbability SamplingProblems with These?Problems with These?
Source: www.globeandmail.com
10/12/2004 9:20 am Geog 237a 11
Probability SamplingProbability SamplingPrinciples/TerminologyPrinciples/Terminology
Population• group about whom you want to
draw inferences• more theoretical than quantifiable• e.g., Ontarians, smokers
10/12/2004 9:20 am Geog 237a 12
Probability SamplingProbability SamplingPrinciples/TerminologyPrinciples/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
10/12/2004 9:20 am Geog 237a 13
Probability SamplingProbability SamplingPrinciples/TerminologyPrinciples/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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sample
sample frame
study population
population
Probability SamplingProbability SamplingRelationship Between TermsRelationship Between Terms
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Probability SamplingProbability SamplingSampling DistributionSampling 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 SamplingProbability SamplingSampling DistributionSampling 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 SamplingProbability SamplingSampling DistributionSampling 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
10/12/2004 9:20 am Geog 237a 19
Probability SamplingProbability SamplingSampling DistributionSampling Distribution
10/12/2004 9:20 am Geog 237a 20
Probability SamplingProbability SamplingSampling DistributionSampling Distribution
Properties of Sampling Error• as sample size increases standard
error decreases ˆsampling error decreases
• the greater the split in the parameter the greater the standard error ˆgreater the sampling error– i.e. more homogeneous populations
have lower sampling error
10/12/2004 9:20 am Geog 237a 21
Probability SamplingProbability SamplingTypesTypes
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 SamplingProbability SamplingSimple Random SampleSimple Random Sample
10/12/2004 9:20 am Geog 237a 23
Probability SamplingProbability SamplingSimple Random SampleSimple Random Sample
10/12/2004 9:20 am Geog 237a 24
Probability SamplingProbability SamplingTypesTypes
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!)
10/12/2004 9:20 am Geog 237a 25
Probability SamplingProbability SamplingSystematic SampleSystematic Sample
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Probability SamplingProbability SamplingTypesTypes
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
10/12/2004 9:20 am Geog 237a 27
Probability SamplingProbability SamplingTypesTypes
(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