Transcript Survey sampling - Carleton College

Sampling Design
• Questions, questions, questions
– Do you support U.S. role in Iraq?
http://www.gallup.com/content/?ci=11260
– What % of lettuce shipment is bad?
– How many children are obese?
– What’s the price of gas at the pump across
Minnesota?
• Practically impossible to poll entire population
• Use a part to make conclusions about the whole
• Idea #1: Use a SAMPLE to make conclusions about the
POPULATION
• But sample must be representative of population
Polling began in Pennsylvania
• Harrisburg Pennsylvanian in 1824 predicted
Andrew Jackson the victor
– He did win the popular vote
– But, like Al Gore, he didn’t win the electoral votes and
John Quincy Adams took the election
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Straw polls were convenience samples
Solicited opinions of “man on the street”
No science of sampling for 100 years
Conventional wisdom: bigger the better
1936 election and the
Literary Digest survey
• Magazine had predicted every
election since 1916
• Sent out 10 million surveys---and
2.4 million responded
• They said: Landon would win 57%
of the vote
• What happened: 62% Roosevelt
landslide
What went wrong?
• Sample not representative
• Lists came from subscriptions,
phone directories, club members
• Phones were a luxury in 1936
• Selection Bias toward the rich
• Voluntary response: Republicans
were angry and more likely to respond
• Context: Great Depression
– 9 million unemployed
– Real income down 33%
– Massive discontent, strike waves
• Economy was main issue in the election
How to do it right
• Idea #2: Randomize
• Randomization insures sample is
representative of population
• Randomization protects against bias
• Simple Random Sample (SRS): every
combination of people has equal chance
to be selected
Some examples of
non-random, biased samples
• 100 people at the Mall of America
• 100 people in front of the Metrodome after a
Twins game
• 100 friends, family and relatives
• 100 people who volunteered to answer a survey
question on your web site
• 100 people who answered their phone during
supper time
• The first 100 people you see after you wake up
in the morning
Is blind chance better than careful
planning and selection?
• Another classic fiasco
• 1948 Election:
Truman versus
Dewey
• Ever major poll
predicted Dewey
would win by 5
percentage points
Truman showing the Chicago Daily
Tribune headline the morning after the
1948 election.
What went wrong?
• Pollsters tried to design a representative sample
• Quota Sampling
• Each interviewer assigned a fixed quota of
subjects in numerous categories (race, sex, age)
• In each category, interviewers free to choose
• Left room for human choice and inevitable bias
• Republicans were wealthier, better educated,
and easier to reach
– Had telephones, permanent addresses,
“nicer” neighborhoods
• Interviewers chose too many Republicans
Quota Sampling biased
• Republican bias in Gallup Poll
Year
Prediction
Actual
of GOP vote GOP vote
Error in
favor of GOP
1936
44
38
6
1940
48
45
3
1944
48
46
2
1948
50
45
5
• Quota sampling eventually abandoned for
random sampling
• Repeated evidence points to
superiority of random sampling
How large a sample?
• Not 10 million, not even 10,000!
• Remarkably it doesn’t depend on size of
population, as long as population is at least 100
times larger than sample
• Idea #3: Validity of the sample depends on the
sample size, not population size
• Like tasting a flavor at the ice cream shop
• SRS of 100 will be as accurate on Carleton
College as in New York City!
• Most polls today rely on 1,000-2,000 people
Gallup Poll record in
presidential elections since 1948
Year
Sample
Size
Winning
candidate
Gallup
Election
prediction result
Error
1952
5,385
Eisenhower
51.0%
55.4%
4.4%
1956
8,144
Eisenhower
59.5%
57.8%
1.7%
1960
8,015
Kennedy
51.0%
50.1%
0.9%
1964
6,625
Johnson
64.0%
61.3%
2.7%
1968
4,414
Nixon
43.0%
43.5%
0.5%
1972
3,689
Nixon
62.0%
61.8%
0.2%
1976
3,439
Carter
49.5%
51.1%
1.6%
1980
3,500
Reagan
51.6%
55.3%
3.7%
1984
3,456
Reagan
59.0%
59.2%
0.2%
1988
4,089
Bush
56.0%
53.9%
2.1%
1992
2,019
Clinton
49.0%
43.2%
5.8%
1996
Clinton
52.0%
50.1%
1.9%
2000
Bush
48.0%
47.9%
0.1%
A peek ahead . . .
• A good rule of thumb is that the margin of
error in a sample is 1 , where n is the
n
sample size.
• For n = 1,600, that’s 2.5%.
• Most political polls report margins of error
between 2-3%.
• The rule of thumb margin of error doesn’t
depend on population size, only on sample
size
Other sampling schemes
Stratified sampling
• Goal: Random sample of 240 Carleton students
• To insure representation across disciplines,
divide population into strata
– Arts and Literature 20%
– Social Sciences 30%
- Humanities 15%
- Math/Natural Sciences 35%
• Choose 240 x .20 = 48 Arts and Literature
240 x .15 = 36 Humanities
240 x .30 = 72 Social Sciences
240 x .35 = 84 Math/Natural Sciences
Within strata, choose a simple random sample
Stratified sampling
• Advantages: Sample will be representative for
the strata; Can gain precision of estimate
• Disadvantages: Logistically difficult; must know
about the population; May not be possible
• Note Stratified sample is not a simple random
sample
• Every possible group of 240 students is not
equally likely to be selected
Cluster sampling – an example
• Warehouse contains 10,000 window frames
stored on pallets
• Goal: Estimate how many frames have wood rot
• Determining if a frame has wood rot is costly
• Sample 500 window frames
• Pallets numbered 1 to 400
• Each pallet contains 20 to 30 window frames
• Sample pallets, not windows.
• Pick SRS of 20 pallets from population of 400.
• Cluster sample consists of all frames on each
pallet
Cluster sampling
• Door-to-door surveys
– City blocks are the clusters
• Airlines get customer opinions
– Individual flights are the clusters
• Advantage: Much easier to implement
depending on context
• Disadvantage: Greater sampling
variability; less statistical accuracy
Who
likes
Statistics?
Most common forms of bias
 Response bias
 Anything that biases/influences responses
 Non-response bias
 When a large fraction of those sampled don’t
respond, such as
 Voluntary response bias
 Most common source of bias in polls
Sampling badly:
Convenience sampling
 Sample individuals who are at hand
 Survey students on the Quad or in
Sayles or in Stats class
 Internet polls are prime suspects
 American Family Association online poll
on gay marriage
You critique it
► Before
2000 election: What to do with large
government surplus
► (1) “Should the money be used for a tax cut, or
should it be used to fund new government
programs?”
► (2) “Should the money be used for a tax cut, or
should it be spent on programs for education, the
environment, health care, crime-fighting, and
military defense?”
► (1): 60% for tax cut; (2): 22% for tax cut
Another type of response bias
 “Some
people say that the 1975 Public
Affairs Act should be repealed. Do you
agree or disagree that it should be
repealed.”
Washington Post, Feb. 1995
Results: For repeal: 24%, Against repeal: 19%,
No opinion: 57%
 No such thing as the Public Affairs Act!
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Non-response
 Non-respondents can be very different from
respondents
 Student surveys at end of term had about 20%
response rate
 General Social Survey (www.norc.org) has 7080% response rate, with 90 minute survey!
 Huge variability in media and government
response rates
 Typically, media rates at about 25%;
government at about 50%.
 Takes large amount of money, time, and
training to insure good response.
Do you believe the poll?
What questions should you ask?
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Who carried out survey?
What is the population?
How was sample selected?
How large was the sample?
What was the response rate?
How were subjects contacted?
When was the survey conducted?
What are the exact questions asked?