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Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics
Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics
Statistics for EconomistStatistics for Economist
Ch. 14 Sample SurveysCh. 14 Sample Surveys
1.1. Population and Population and SampleSample
2.2. Problems of SurveysProblems of Surveys
3.3. Sample Selection Sample Selection Methods Methods
4.4. The Gallup PollThe Gallup Poll
5.5. Telephone SurveysTelephone Surveys
6.6. Probability ErrorProbability Error
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STATISTISTATISTICSCS
INDEX
11Population and Population and SampleSample
22 Problems of SurveysProblems of Surveys
33Sample Selection Sample Selection MethodsMethods
44 The Gallup PollThe Gallup Poll
55 Telephone SurveysTelephone Surveys
66 Probability ErrorProbability Error
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STATISTISTATISTICSCS
1. Population and Sample
population
parameter
Parameter estimation :estimator
test statistic
Population estimation :estimate
test statistic
sampling
prior meaning- Random variable
posterior meaning- Realized value
inference
stiatistic stiatistic
sample
samplingsampling
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STATISTISTATISTICSCS
INDEX
1Population and Population and SampleSample
2 Problems of SurveysProblems of Surveys
3Sample Selection Sample Selection MethodsMethods
4 The Gallup PollThe Gallup Poll
5 Telephone SurveysTelephone Surveys
6 Probability ErrorProbability Error
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STATISTISTATISTICSCS
2. Problems of Surveys
SurveySurvey
Roosevelt’s percentage (%)
The election result 62
The Digest Prediction of the election result
43
Gallup’s prediction of the Digest Prediction
44
Gallup’s prediction for the election result
56
Prediction for the election of 1936The Digest vs. Gallup
Roosevelt winsRoosevelt wins
Landon winsLandon wins
Roosevelt winsRoosevelt wins
Gallup’s overwhelming victoryGallup’s overwhelming victory- Serious problems in sample selecting methods of Serious problems in sample selecting methods of the Digest.the Digest.- Gallup even predicted the wrong prediction of the Gallup even predicted the wrong prediction of the DigestDigest
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STATISTISTATISTICSCS
Problem (1)- sample selection bias
Problem (1)- sample selection bias
Sample Selecting Methodsof the Digest :-Survey using address from a tele-phone directory or club member lists-In those days, telephone or clubs were the symbols of the rich-the poor were excluded from the sample-The Digest got unfavorable results to Roosevelt who is popular to the poor
-Systematic tendency(Sample selection bias) is related to sample selection. -The sample was not selected in a fair way. -The sample does not represent the population
If there is sample selection bias, the sample doesn’t represent the population. The problem is not solved just by increasing the magnitude of the sample.
If there is sample selection bias, the sample doesn’t represent the population. The problem is not solved just by increasing the magnitude of the sample.
2. Problems of Surveys
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Problem (2)- non-response bias
Problem (2)- non-response bias
Sample Selection Procedure of The Digest
-Only 2.4 million people bothered to reply, out of the 10 million who got the questionnaire-lower-income and upper-income people tend not to respond to questionnairesso the middle class was over-represented among respondents.
Non-respondents can be very different from respondents.
(non-respondent bias).
-Respondents do not represent the sample
Non-respondents may differ from the respondents. If the percentage of the non-respondents is high, you should consider the possibility of non-respondent bias.
Non-respondents may differ from the respondents. If the percentage of the non-respondents is high, you should consider the possibility of non-respondent bias.
2. Problems of Surveys
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Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics
STATISTISTATISTICSCS
INDEX
1Population and Population and SampleSample
2 Problems of SurveysProblems of Surveys
3Sample Selection Sample Selection MethodsMethods
4 The Gallup PollThe Gallup Poll
5 Telephone SurveysTelephone Surveys
6 Probability ErrorProbability Error
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3. Sample Selection Methods
quota sampling and simple random sampling
quota sampling and simple random sampling
quota sampling
simple randomsampling
The sample is hand-picked to resemble the population
with respect to some key characteristics.
Drawing at random without replacement
-simple random sample
But, there may be unintentional bias
under part of the interviewers.
But, practically it’s difficult to do from the whole population.
- Use multistage Cluster sampling
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STATISTISTATISTICSCS multistage cluster
sampling
multistage cluster sampling
MW NEW
S1st stage : towns in North
East
2nd stage : wards
3rd stage: an electoral district
4th stage: households
Sample Selection Method of Gallup
Allocate the number of the sample according to the region.
For each stage select samples by probability methods.
Sample Selection Method of Gallup
Allocate the number of the sample according to the region.
For each stage select samples by probability methods.
3. Sample Selection Methods
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sample selecting by a probability method
sample selecting by a probability method
- Simple random sampling, Multistage cluster sampling - features The interviewers have no discretion at all as to who they interview. There is a definite procedure for selecting the sample, and it involves the planned use of probability.- With the probability method it is possible to compute the
probability that any particular individuals in the
population will get into the sample.
- For this makes the reproduced research by other people
possible, we can construct the grounds for judging the
significance of the results.
- With the probability method it is possible to compute the
probability that any particular individuals in the
population will get into the sample.
- For this makes the reproduced research by other people
possible, we can construct the grounds for judging the
significance of the results.
3. Sample Selection Methods
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STATISTISTATISTICSCS Multistage cluster sampling : deciding the
sampling probability
Multistage cluster sampling : deciding the sampling probability
It is necessary to adjust the sampling probabilities according tothe magnitude of the sampling units.
It is necessary to adjust the sampling probabilities according tothe magnitude of the sampling units.
A
Seoul
B
Pusan
The probability of selecting a zone in Selecting 3 zones from Seoul & Pusan = 3/30 = 1/10
= the probability that A zone will be selected
= the probability that B zone will be selected
For the above formula,
percentage of selecting Seoul = 2/3 percentage of selecting Pusan =1/3
The probability of selecting a zone in Selecting 3 zones from Seoul & Pusan = 3/30 = 1/10
= the probability that A zone will be selected
= the probability that B zone will be selected
For the above formula,
percentage of selecting Seoul = 2/3 percentage of selecting Pusan =1/3
It is desirable to make the probabilities of sampling each individual same.
3. Sample Selection Methods
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Multistage cluster sampling: probability adjustment of Gallup
Multistage cluster sampling: probability adjustment of Gallup
Towns Wards PrecinctsIn each stage, decide
the sampling probabilities
according the rate of the households
In each stage, decide the sampling probabilities
according the rate of the households
The probability of selecting one household is all the same regardless of the town, ward, or precincts to which the household belongs.
If we just estimate the sampling probability by the number of households, not by the number of household members, some bias is generated.
A member of more-member households is not likely to be selected rather than a member of less-members households.
household bias
3. Sample Selection Methods
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STATISTISTATISTICSCS
INDEX
1Population and Population and SampleSample
2 Problems of SurveysProblems of Surveys
3Sample Selection Sample Selection MethodsMethods
4 The Gallup PollThe Gallup Poll
5 Telephone SurveysTelephone Surveys
6 Probability ErrorProbability Error
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4. The Gallup Poll
The Gallup Poll
The Gallup Poll
The Gallup Survey predicts very accurately through a small sample using the probability methods.
To minimize bias, an impartial and objective probability methods should be used to choose the sample. But judgment and choice usually show bias, while probability is impartial.
To minimize bias, an impartial and objective probability methods should be used to choose the sample. But judgment and choice usually show bias, while probability is impartial.
Though you use probability method, you cannot exclude all the bias..-Eligible voters who does not vote-Eligible voters who didn’t make decision-Response bias & Non-response bias etc.To solve this problem Gallup made many survey questions.
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The Gallup Poll questionnaire for the 1984 election, USA
The Gallup Poll questionnaire for the 1984 election, USA
4. The Gallup Poll
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The Gallup Poll questionnaire for the 1997 election, Korea
The Gallup Poll questionnaire for the 1997 election, Korea
4. The Gallup Poll
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Non-respondents
Non-respondents
When we predict the election result, it’s good to screen out
Non-respondents fromPopulation and sample.
They tend to answer to vote, even the cases they won’t vote.
The questionnaire of Gallup:
ex. Where do you go to vote? Did you vote at previous election?
If you screen out the people not likely to vote from sample or put less weight, you can get the accurate election result more easily.
If you screen out the people not likely to vote from sample or put less weight, you can get the accurate election result more easily.
4. The Gallup Poll
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The questionnaire of Gallup
The questionnaire of Gallup
DEMOCRATIC
REPUBLICAN
MONDALE & Ferraro
REAGAN & Bush
The Gallup Poll ballot, 1984
Ex. In Politics, as of TODAY, do you consider yourself a Republican, Democrat, or Independent ?
4. The Gallup Poll
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STATISTISTATISTICSCS
Response bias & Non-response bias
Response bias & Non-response bias
response bias
Non-response bias
The answers given by respondents are influenced to some extent
by the phrasing of the questions and even the tone or attitude
of the interviewer.
Many subjects are missed. Since the interviewees tend to be different
from the subjects available but hard to get.
All interviewers use the same questionnaire, and the interview procedure is standardized as far as possible.
Give more weight to the subjects who were available but hard to get.
4. The Gallup Poll
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Checking Data & Putting Weights
Checking Data & Putting Weights
Below high school(20%) Above high school(80%)
The Gallup sample usually includes proportionately too many people with higher education.
Below high school(25%) Above high school (75%)Population
SampleLess weight is put on the responses of higher educated subjects. Lowly educated subjects (Below high school)=weight 1, highly educated subjects (Above high school)=weight 3/4
This weighting technique is an objective arithmetic technique applied to the sample after it is chosen to compensate for various small biases in the sampling procedure. But Quota sampling is a method for choosing the sample. It has large, subjective component.
This weighting technique is an objective arithmetic technique applied to the sample after it is chosen to compensate for various small biases in the sampling procedure. But Quota sampling is a method for choosing the sample. It has large, subjective component.
4. The Gallup Poll
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othersothers
Other factors that can affect political tendency are included.
Some redundancy is built into the questionnaire, so the answers can be checked for the consistency :
Gallup, USA
Gallup, Korea education, political party
, age, sex, job etc.Race and
Religion
Hometown of
grandfather
Inconsistencies suggest the interviewer may not be doing the job properly. A small percentage of the subjects are reinterviewed by administrative staff, as a further check on the quality of the work.
4. The Gallup Poll
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STATISTISTATISTICSCS
INDEX
1Population and Population and SampleSample
2 Problems of SurveysProblems of Surveys
3Sample Selection Sample Selection MethodsMethods
4 The Gallup PollThe Gallup Poll
5 Telephone SurveysTelephone Surveys
6 Probability ErrorProbability Error
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About 1/3 of residential telephones are unlisted.Rich people and poor people are more likely to have unlisted numbers,
so the telephone book tilts toward the middle class.
5. Telephone Surveys
Gallup : There are 4 time zones in the U.S. The Gallup Poll divided each zone into 3 types of areas, according to population density. That gives 12 strata. Within each stratum, the Gallup Poll just drew a simple random sample of telephone numbers, using random digit dialing.
Telephone Surveys
Telephone Surveys
Non-respondents create problems, as usual.Gallup: Most of its interviewing on evenings, and the weekends,
when people are likely to be at home.
The cost is about 1/3 as much and the predictions are fairly well on target.
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STATISTISTATISTICSCS
INDEX
1Population and Population and SampleSample
2 Problems of SurveysProblems of Surveys
3Sample Selection Sample Selection MethodsMethods
4 The Gallup PollThe Gallup Poll
5 Telephone SurveysTelephone Surveys
6 Probability ErrorProbability Error
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6. Probability Error
Probability Error
Probability Error
Thought there is no bias at all, the estimate is different from the real value. The estimate is deviates as much as the probability error.
EX) Estimating the percentage of 1’s in the box. a box with a large number of tickets,
some marked 1 and the others marked 0 Population
tickets drawn at random without replacement Sample
Thought there is no problem about response, probability error exists.
Percentage of 1’s in sample = percentage of 1’s in box + probability error
Percentage of 1’s in sample = percentage of 1’s in box + probability error