1. Chapter 1: Basic concepts of surveys
Handbook: chapter 1, 2
Some history of data collection
Basic principles of sampling
Some sampling designs
Some estimators
Errors in surveys

2. Data collection through the ages
Even the old empires needed statistical overviews
Initially always complete enumeration. No sampling.
China and Egypt (1000 B.C.): overviews for taxation and military affairs.
Roma Empire: counts of people and their possessions.
Census in Bethlehem (Pieter Bruegel, 1566)

3. Data collection through the ages
The Domesday book
Commissioned by William the Conqueror (1086).
Compiled by royal commissioners.
Data about 13,000 places, 10,000 facts per county.
Data about landowners, slaves, free people, woodland, pasture, mills, fish ponds, estimate value.

4. Data collection through the ages
The Quipucamayoc
Statistician in the Inca Empire ( A.C.).
Quipucamayoc in each district.
Count of people, young man, houses, llama’s.
Recorded on quipu’s.
Knots in coloured ropes, decimal system.
RAPI = Rope Assisted Personal Interviewing.

5. Data collection through the ages
The first modern censuses
New France (Canada): 1666, Jean Talon, N=3215.
Sweden: 1748, Denmark: 1769.
Netherlands: 1795, new system of electoral constituencies.
Standardized questionnaire.
Legal obligation to participate.

6. The rise of sample surveys
The period until 1895
No sampling. It is not proper to replace people by computations (discrimination).
No reliable conclusions base on sample data.
The dawn of new era
Industrialisation.
Urbanisation.
Population growth.
Central government.

7. The rise of sample surveys
Developments
1895: Anders Kiaer proposes his ‘Representative Method’ Accuracy of estimates cannot be computed.
1906: Arthur Bowley shows the importance of random sampling Probability Theory can be applied.
1934: Jerzy Neyman introduces the confidence interval He also shows that purposive sampling does not work.

8. The rise of sample surveys
The fundamental principles of sampling
Samples must be selected by means of probability sampling.
Every element must have a positive probability of selection.
All selection probabilities must be known.
Consequences
It is always possible to construct an unbiased estimator.
Estimators often have a (approximately) normal distribution.
Accuracy of estimators can be computed (confidence intervals).
Warning
For other forms of sampling (e.g. quota sampling), it is not clear how reliable and accurate the outcomes are.

9. Survey
What is a survey
Making inference about a population using data on only a small part of it.
Population typically exists of people, households, farms, companies schools, etc.
Data is collected using a questionnaire.
Why a sample?
Complete enumeration (census) is time-consuming.
Complete enumeration (census) is expensive
Response burden is decreased.
More attention can be paid to quality.

10. Target population Definition Population to be investigated
Conclusions refer to this population
Practical definition
Example: Labour Force Survey
Include people working outside the country?
Include foreign workers with temporary job?
Include illegal workers?
Include employees of foreign embassies?
Notation:
Sample size: N
Population: U = {1, 2, …, N}

11. Variables Target variables The variables we want to investigate.
Values: Y1, Y2, …, YN.
Auxiliary variables
Used for differentiating survey results and improving estimates.
Values: X1, X2, …, XN.
Example: demographic variables.
Variable types:
Quantitative variable: measures amount, size, values, or duration.
Qualitative variable: divides in groups.
Indicator variable: measures presence (1) or absence (0) of a certain property.

12. Population parameters
Population parameters for a quantitative variable
Population total Y
Population mean
Adjusted population variance
Population parameter for an indicator variable
Percentage

13. Sampling Sampling design
Random selection procedure, with known probabilities.
Sampling without replacement
Sample
Series of indicators a1, a2, …, aN, with
ak = 1 if element k is selected
ak = 0 if element k is not selected
Sample size
First order inclusion probability
Second order inclusion probability

14. Estimation Estimator Recipe / algorithm to compute an estimate
Properties
Unbiased: on average, the estimates must be equal to the value of the population parameter.
Precise: variation of possible outcomes must be small
Simple: linear combination of observed values.
Horvitz-Thompson estimator (for population mean)
Estimator:
Unbiased, with variance

15. Precision of estimates
Variance of the estimator
Standard error of the estimator
Confidence interval
Contains true value with a high probability 1- α.
Confidence level = 1 – α.
Usually α = 0.05 or α = 0.01
95% confidence interval for the population mean (α = 0.05):
Standard error must be estimated using sample data:

16. Sampling designs: simple random sample
All first order inclusion probabilities are equal
πk = n / N, for all k
πkl = n(n-1) / N(N-1), for all k ≠ l
Horvitz-Thompson estimator turns into the sample mean:
Variance:
Precision:
Increases with sample size
Independent of population size

17. Sampling designs: stratified sample
Stratification
Population is divided in L strata (sub-populations).
A sample is selected in each stratum.
Unbiased stratum estimates are combined.
Estimator:
Variance (simple random samples)
Precision
Estimator is precise if strata are homogeneous.

18. Sampling designs: sampling with unequal probabilities
Reason
Variance of Horvitz-Thompson estimator is small when Yk /k is approximately constant.
Sampling
Try to find auxiliary variable X that is strongly correlated with Y.
Take inclusion probabilities k proportional to Xk.
All Xk must be positive, and known for every element.
Example:
Survey on shoplifting
Y = Value of stolen goods
X = Floor size of shop

19. Sampling designs: cluster sampling
Practical reasons
There is no sampling frame of elements, but there is a sampling frame for cluster of elements. For example: addresses.
Cost reduction in face-to-face surveys.
Sampling
Clusters can be selected with equal or unequal probabilities.
For example: select clusters proportional to size
All elements in selected clusters are included in survey.
Disadvantages
Variances can be large (cluster effect).
No control over sample size.

20. Sampling designs: two-stage sampling
Practical reasons
There is no sampling frame of elements, but there is a sampling frame for cluster of elements. For example: municipalities.
Cost reduction in face-to-face surveys..
Sampling
Sample of clusters (with equal or unequal probabilities).
Samples of elements within selected clusters (with equal or unequal probabilities)
Properties
More control over sample size
Variances can be large (cluster effect).
Example:
First stage: municipalities
Second stage: perosns

21. Estimators Improving the precision of estimates
Using auxiliary variables
They are measured in the sample.
Population distribution is available.
Use of auxiliary variables in the sampling design
Quantitative variable: Sampling with unequal probabilities
Qualitative variable: Stratified sampling
Use of auxiliary variables in the estimator
Quantitative variable: Ratio estimator
Quantitative variable: Regression estimator
Qualitative variable: Post-stratification estimator

22. Estimators: ratio estimator
Assumed model:
Consequence:
Parameter B is estimated by
Required: population mean of auxiliary variable X
Estimator
Variance

23. Estimators: regression estimator
Assumed model:
Consequence:
Parameter B is estimated by
Required: population mean of auxiliary variable X
Estimator
Variance

24. Estimators: general regression estimator
Assumed model:
Consequence:
Parameter B is estimated by
Required: population means of all auxiliary variables
Estimator
Variance

25. Estimators: post-stratification estimator
Assumed model:
Population divided in L sub-populations (strata).
Little variation of target variable Y within strata: homogeneity.
Required: Numbers of elements in strata: N1, N2, .., NL
Estimator
Variance
Special case of general regression estimator
Introduce L dummy variables
Xkh = 1 if in stratum h, otherwise Xkh = 0
Model:

26. Errors in surveys In theory
Sample-based estimates differ from true population values.
Estimators are unbiased.
Margin of error can be computed.
Every thing under control.
In practice
Many other phenomena have an impact on estimators.
They may decrease precision (increase standard error).
They may also introduce a bias.
The bias is often independent of the sample size.
Problems do not disappear by increasing the sample size.

27. Non-observation error
Errors in surveys
Total error
Sampling error
Estimation error
Specification error
Non-sampling error
Observation error
Over-coverage error
Measurement error
Processing error
Non-observation error
Under-coverage error
Nonresponse error

28. Errors in surveys Sampling errors
Estimation error: consequence of randomization.
Specification error: sampling frame.
Non-sampling error
Under-coverage: mixed-mode data collection.
Measurement error: questionnaire design, interviewer training, editing techniques, imputation techniques.
Processing error: editing techniques, imputation techniques.
Nonresponse: reduction techniques (contact strategy, interviewer training, refusal conversion), correction techniques (weighting, adjustment).

29. The nonresponse problem
The problem
Nonresponse occurs in every survey.
Nonresponse cause estimates to be biased.
Nonresponse problems seem to increase.
It is not easy to reduce nonresponse.
It is not easy to correct for nonresponse.
The solution
Attempt to reduce nonresponse in the fieldwork.
Attempt to correct for nonresponse after the fieldwork.
Vital role for auxiliary variables.
Think about auxiliary variables in the design stage of the survey.