Download ppt - 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

2/26


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

3/26



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

4/26



INDEX







5/26



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

6/26



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.


7/26



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.


8/26



INDEX







9/26



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

10/26


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.


11/26



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.


12/26


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.


13/26



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


14/26



INDEX







15/26



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.

16/26



The Gallup Poll questionnaire for the 1984 election, USA

The Gallup Poll questionnaire for the 1984 election, USA

4. The Gallup Poll

17/26



The Gallup Poll questionnaire for the 1997 election, Korea

The Gallup Poll questionnaire for the 1997 election, Korea

4. The Gallup Poll

18/26



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

19/26



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

20/26



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

21/26



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

22/26



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

23/26



INDEX







24/26



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.

25/26



INDEX







26/26



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