SP 225
Lecture 2
Writing with Statistics
Sampling Methods
Agenda
 Survey Sampling
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Sampling basics
United States Census
 Census Issue Essay
Designing Studies
 Selection Method
 Questionnaire Design
 United States Census
Population vs. Sample
 Population: All subjects in a study
population
 Sample: Subset of subjects included in
the study
Parameter vs. Statistic
Sample: 3 Randomly Selected
People
Population: All People
Parameter: 5 of 15 or 33% wear glasses
Statistic: 0 of 3 or 0% wear
glasses
Random Sampling
 Random sample: each individual
member of a population has an equal
chance of being selected
 EPSEM
 Important Questions:
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Is every member of a population equally
likely to be chosen?
Is every combination of members equally
likely to be chosen?
Convenience Sampling
uses results that are easy to get
Systematic Sampling
Select some starting point and then
select every k th element in the population
Stratified Sampling
subdivide the population into at
least two different subgroups that share the same characteristics,
then draw a sample from each subgroup (or stratum)
Cluster Sampling
divide the population into sections
(or clusters); randomly select some of those clusters; choose all
members from selected clusters
Sampling Error
 Sample Error: Difference between
sample result and true population result
 Non-Sample Error: Difference caused by
data that has been incorrectly collected,
recorded or analyzed
Common Study Problems
 Loaded questions
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Would you vote for Mr. President if you knew
he had gone to prison? (push-polling)
 Order of questions
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Would you say traffic contributes more to air
pollution than industry? (45% traffic, 27% ind.)
Would you say industry contributes more to
pollution than traffic? (24% traffic, 57% ind.)
The United States Census
 Every 10 Years the Census Bureau attempts to
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count and survey all citizens of the United States
Number of US Representatives in each state are
determined by the census
The amount of Federal funds each state receives
depends on the Census (over $185 billion each year)
Approximately 310 million residents
Requires 860,000 employees to conduct the census
All households receive a short-form questionnaire
and 1 in 6 receive a long-form questionnaire that
takes about 40 minutes to complete
Census Methodology
 The census is used to calculate
population parameters
 Is the census successful?
Differential Undercount
 Some groups counted at different rates
 The General Accounting Office estimates some
states were entitled to and additional $208
million while some states were overpaid $368
million
 In 1980 a House district was taken from Indiana
and given to Florida after count correction
 Legal challenges against imputation and to
require the use of sampling to correct counts
http://www.gao.gov/new.items/d09832t.pdf
http://www.census.gov/srd/papers/pdf/rrs2005-01.pdf
Census Correction
 http://2010.census.gov/2010census/
 Count Question Resolution petition for
local governments
Statistical Methods for
Correction
 1850 counts for California counties lost at sea
 1940 sampling was used to determine personal
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characteristics so less households were
required to use the long form
Imputation used alone or with sampling
1970 used to correct count when the post office
had only partial updated address listings
 Sampling estimates number missed
 Imputation determines characteristics
1980 Census tries synthetic estimation
1990 sampling used for those on probation with
help of probation officers
Sampling in the 2000 Census
 Sampling for non response
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Sample non responders in each census
tract (1700 households) to test rate of
vacancy
 Capture-recapture for large geographic
areas
 Multiplicity estimation for homeless
combines count with usage
Census Discussion
 What groups of people are more likely to be
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missed by the census?What does the term
differential undercount mean?
How are census results confirmed?
How has sampling historically been used in the
census?
What arguments are there in favor of sampling
in the census?
What arguments are there against sampling in
the census?
Census Essay
 Write a position paper arguing either the
Democratic or Republican position on the use of
sampling methods considered during the 2000
Census to arrive at an adjusted count in the 2010
Census
 In your essay:
 Clearly state and justify the position
 Explain usage, operation and scope of
sampling methods under consideration
 Enumerate the consequences of your position
 Address the counter position
Reading
 Chapter 1 of Essentials of Social
Research