TEACHING THE SURVEY SAMPLING THEORY AND...

TEACHING THE SURVEY SAMPLINGTHEORY AND METHODOLOGY

IN LITHUANIA

Danute Krapavickaite and Aleksandras Plikusas

Institute of Mathematics and InformaticsVilnius Gediminas Technical University

Vilnius University

Kiev, August 23-27, 2009

Baltic-Nordic-Ukrainian SUMMER SCHOOLon Survey Statistics

Danute Krapavickaite and Aleksandras Plikusas TEACHING THE SURVEY SAMPLING THEORY AND METHODOLOGY IN LITHUANIA

Outline

1. Historical overview2. The list of courses on survey sampling in Lithuania3. Main topics of basic and advanced courses4. Self-sustaining work at Vilnius University5. Example of exam problems at Vilnius University6. Teaching at Vilnius Gediminas Technical University7. Courses at Statistics Lithuania8. Other courses


Historical overviewSample surveys started to be carried out

1989, public opinion companies1994, Statistics Lithuania

The first courses on survey sampling were given

1994, Statistics Lithuania, by Statistics Sweden1995, Vilnius University, by Aleksandras Plikusas1996, Vytautas Magnus University, by Aleksandras Plikusas1996, Klaipeda University, by Danute Krapavickaite1998, Statistics Lithuania, by A.P., D.K.

The first textbook on survey sampling for employeesSampling methods and their application, 1997, StatisticsLithuania, (in Lithuanian), by Aleksandras Plikusas


Universities having courses on survey sampling

Šiauliai University (ŠU) by Marĳus Radavičius,

Vilnius Gediminas Technical University (VGTU) by DanuteKrapavickaite,

Vytautas Magnus University (Kaunas)(VMU) by AlgimantasBikelis,

Vilnius Pedagogical University (VPU) by Dalius Pumputis,

Vilnius University (VU) by Aleksandras Plikusas.


The list of sampling courses at Lithuanian Universities (I)

Kind Course Place Timing Self-sus- ECTSof title Lec- Prac- Total taining Creditscourse tures ticals work

Basic Finite VU 32 16 48 Pract. 4Population workStatistics

Basic Sampling & VU 48 32 80 Pract. 4,5& Adv. simulation work

Basic Sampling VGTU 26 26 52 Cour. w., 4,5+1,5Methods 3 cntr. w.

Adv. Statistical VGTU 32 16 48 Cour. w., 4,5+1,5Surveys 2 cntr. w.by SamplingMethods


The list of sampling courses at Lithuanian Universities (II)

Kind Course Place Timing Self-sus- ECTSof title Lec- Prac- Total taining Creditscourse tures ticals work

Basic Sampling ŠU 32 0 32 1 cntr. w. 3methods

Basic Experiment VMU 45 15 60 1 coll. 6design

Basic Basics VPU 36 24 60 2 cntr. w. 4,5of sampletheory


Main topics included into the basic course

1. The object of survey sampling. The main concepts anddefinitions. The main parameters of estimation, accuracymeasures of estimators.

2. Simple random sampling. Sampling schemes, estimators of atotal, mean, proportion in the population and domains.Determination of the sample size.

3. Sampling with replacement, estimators of a total. Normalapproximation of the estimator distribution.

4. Unequal probability sampling with replacement.5. Estimator of the ratio of two totals and ratio estimator of a

total.6. Stratified sampling design. Allocation of the sample size and

estimators.7. One-stage and two-stage cluster sampling. Systematic sample,

analysis of variance.8. Dealing with nonresponse.9. Examples of the real surveys.


Supplements for the basic course

For the students of VU with a strong mathematical background:unequal probability sampling, Horvitz-Thompson estimator,Bernoulli, Poisson sampling,regression and calibrated estimators,resampling methods for variance estimation in complexsurveys.

For the students of VMU:Bernoulli sampling,limit theorems of Hajek (normal approximation),self-decomposable approximation of the distribution of theestimator in finite population sampling.


Main topics included into the advanced course (I)

1. The object of survey sampling. The main concepts anddefinitions. The main parameters of estimation, accuracymeasures of estimators.

2. Repetition of the basics. Sampling designs and design-basedestimators in the case of simple random sampling with andwithout replacement, unequal probability sampling withreplacement, stratified sampling.

3. Representative sampling in the direct and generalized sense.Horvitz-Thompson estimator of a total.

4. Use of auxiliary information at the estimation stage:poststratification, a separate and common ratio estimator forstratified sampling, regression estimator.

5. Estimation of variance of complex estimators byTaylor linearization,random groups,jackknife,bootstrap.


Main topics included into the advanced course (II)

6. Two-phase sampling. Its application to the ratio estimation,stratification, dealing with nonresponse.

7. Unequal probability sampling: systematic sampling withprobability proportional to size, Poisson, Pareto sampling.

8. Estimation of the median and quantile.9. Small area estimation. Synthetic and composite estimators.10. Application of sampling methods in nature surveys, methods:

detectability and sampling,line transects,capture-recapture sampling.


Main textbooks

1. Krapavickaite D., Plikusas A., Basics of samples theory,Vilnius, Technika, 2005. (in Lithuanian)

2. Cochran W.G., Sampling Techniques. John Wiley & Sons,1977.

3. Lohr, S.L. Sampling: Design and Analysis. Duxbury Press,1999.

4. Särndal C.-E., Swenson B., Wretman J., Model AssistedSurvey Sampling. Springer-Verlag, 1992.

5. Thompson S.K., Sampling. John Wiley & Sons, 1992.


Practicals

The lecture topic is followed by

solution of short numeric problems without using computer,control works consisting of

short theoretical questions,definitions,numeric problems.

Sources:Krapavickaite, Plikusas (2005)Ardilly and Tillè (2006)originally created problems


Self-sustaining work at VU

Practical problem is being solved by the students using some dataset provided by the lecturer

The problem includes:• Construction of the survey design• Calculation of various different estimates, their variances• Comparison of sampling designs and estimators by simulation• Report writing• Presentation of the results during the lecture when thenumber of students is not too big


Examples of the topics

Regression estimator and its comparison with Horvitz-Thompsonestimator

Stratified sampling, optimal allocation of the sample size

Determination of the stratification boundaries

Linear combination of ratio and regression estimators


Example of the data set for self-sustaining work

Household variables:

1. Number of Children (<15 years old)2. Number of Youth (15-24 years old)3. Number of individuals in the household4. Annual income of the household5. Expenditure on clothing6. Expenditure on furnishings and equipment7. Total expenditure8. Territory

Population size 2300.


Additional comments

• Students can choose the topic for the practical problem bythemselves (to some extent)• Students are free to choose software for calculation (R is themostly frequent)• All students work with the same data set and sometimesinteresting comparisons of the results can be made• The weight of the practical problem varies between 20 and 40percent in the final grade• The stronger the students are, the more freedom in thesolution of practical problem can be given


Example of the exam problems at VU

Problem 1.

The population U = {1, 2, 3, 4} is given.

Possible samples and their selection probabilities are:s1 = {1, 2, 3}, p(s1) = 1/3,s2 = {1, 2}, p(s2) = 1/6,s3 = {3, 4}, p(s3) = 1/6,s4 = {2, 3, 4}, p(s4) = 1/3.

For each population element k, find it’s inclusion probabilityπk = P(k ∈ s), k = 1, 2, 3, 4.


Exam problem 2 at VU

Problem 2.

Two variables y and x are defined on some finite population.The values of the variable x are known.The product estimator of the total of the variable y is defined asfollows:

ty prod =ty txtx

.

Here ty ir tx are Horvitz-Thompson estimators of the totals

ty =N∑

k=1yk , tx =

N∑k=1

xk

of the variables y and x .


Exam problem 2 a), b)

a) Find the approximate variance of ty prod by Taylorlinearization.

b) When the approximate variance of the product estimator islower than approximate variance of the ratio estimator?Hint: The approximate variance of ratio estimator

ty rat =tytx

tx

may be expressed as:

AVar(ty rat) = Var(ty )+R2Var(tx )−2R Cov(ty , tx ), R = ty/tx .


Exam problem 2 c)

c) Find the expression of the approximate variance for

ty prod

in the case of simple random samplingvia variances and coefficient of correlation between variables xand y :

s2y , s2x , ρxy .

Find the condition under which the approximate variance ofthe product estimator ty prod is lower than approximatevariance of the ratio estimator.


Course works at VGTU. The SURVEY exercisesStephen County consists of 75 districts with households living inthe private houses (Lohr, 1999).

Number Mean AssestedArea Districts of Houses Population House ValuationRural 1-43 7 932 29 985 65 511Small towns 44-46 1 157 4 257 56 706Eavesville 47-50 3 236 33 694 59 649Lockhart City 51-75 19 664 57 505 71 117Stephens County 1-75 31 989 103 441 68 045

The TV company is carrying out the sample survey of thepopulation in order to find out which programs should betranslated and what payment from the citizens may be received forcable TV service.

The Fortran computer programs for sample selection and datacollection are available.


Map of Stephen County


The Interview questionaire

1. How many persons ≥ 12 yrs live at this address?2. How many persons ≤ 11 yrs live at this address?3. How many TV sets are in this household?4. If cable TV service cost $ 5 (10, 15, 20, 25) would your

household subscribe?5. How many hours did you spend watching TV last weak?

6-9. How many hours did you spend watching special TV programslast weak?

Students are askedto draw the samples,to estimate the parameters,to find the strategy for the best accuracy of the estimators.


StatVillage data setMicrodata on StatVillage consists of anonymous responses toCanadian Population Census in 1991 (Schwarz, 1997).

34 variables are grouped:- demographic variables,- income variables,- dwelling characteristics,- characteristics of the adults in the household – age, gender,education, occupation...

Possible choice of village consisting of 32, 64, 128 blocks, formedby 8 dwellings each.

The students make a survey with the aim to build

Leisure Center,Kindergarden,Supermarket...


Statvillage map


After the sample of households is drawn, households are accessedby pointing at the map the households selected and indicating "Getthe sample units". As the result

the sample interview data set is constructed,SAS Data step program for data input is build.

Tasks for the students:

To estimate totals, ratios, proportions using various estimatorsand various sampling designs,To compare efficiency of the estimators.

Each student is solving the same problems with the own sample.

After the students have presented their works, the review of alltheir results is done by the lecturer showing the distributions of theestimates by tables and graphs and discussing them.

SAS, R, Excel computer software are used by students.


Control works for basic course at VGTU

There are 3 control works per semester under the topics

1. Probability theory.2. Probablistic sampling. Design-based estimators of total,

mean, proportion in the case of simple random sampling.3. Stratified simple random sampling, estimators of total, mean.

Estimators of the ratio and ratio estimators of total, mean inthe case of simple random sampling.

Each of them consists of

2 theoretical questions,2 numeric problems.


Exam work at VGTU

It consists of 7 questions:

Questions 1, 2, 3 – concepts, definitions, formulations,Questions 4, 5 – short propositions with proofs,Questions 6, 7 – numeric problems.

Evaluation=1/3(Control works + Course work + Exam work)orEvaluation1=1/3 Control works + 2/3 Exam workEvaluation2=Course work


Courses for employees of Statistics Lithuania

Two types of courses are sometimes given at Statistics Lithuania:

• the basic course for beginners,• the advanced course for those who already had attended thebasic course.

The advanced course in 2009 has included the following topics:

• determination of stratification boundaries,• dealing with nonresponse,• calibration,• estimation of the regression model parameters using SASprocedure surveyreg,• computer software CLAN (by Inga and Milda).


Other courses

Experience of the basic survey sampling courses in Russian isgained.

The courses have been delivered for the statisticians fromMoldova,Kaliningrad region of Russia,Uzbekistan.

Theoretical problems and examples, the real surveys have beendiscussed.

Materials prepared by the lecturers in Russian have been given forthe listeners.


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