10/12/2004 9:20 amGeog 237a1 Sampling Sampling (Babbie, Chapter 7) Why sample Probability and Non-Probability Sampling Probability Theory Geography 237.

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

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Why Sample?Why Sample?

What is a sample?

Why do we sample in social research?

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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

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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

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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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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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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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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 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

http://www.globeandmail.com/

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Population• group about whom you want to

draw inferences• more theoretical than quantifiable• e.g., Ontarians, smokers

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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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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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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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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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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

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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

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Probability SamplingProbability SamplingSimple Random SampleSimple Random Sample

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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 SamplingProbability SamplingSystematic SampleSystematic Sample

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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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(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 SamplingProbability Sampling(Multistage) Cluster Sample

10/12/2004 9:20 amGeog 237a1 Sampling Sampling (Babbie, Chapter 7) Why sample Probability and Non-Probability Sampling Probability Theory Geography 237.

Documents

sample probability

probability sampling

simple random sample

amgeog 237a3

amgeog 237a2

london slide

random selection slide

public meeting slide