TEACHING SURVEY SAMPLING THEORY AND
METHODOLOGY AT THE UNIVERSITY OF
LATVIA
Natalja Budkina
University of Latvia, Latvia
e-mail: budkinanat@gmail.com
Abstract
The paper deals with teaching the theory and methodology of survey sampling at the University
of Latvia. The overview of the programme of professional studies in Mathematical Statistics is
given. The short program of the course of survey sampling in this programme is presented. The
problems that arose during teaching the course and the perspectives of development are
mentioned.
1 Introduction
Sample surveys are essential tools in a modern society to provide accurate information to
politicians, businesses and the general public about living conditions and opinions.
Unfortunately, the Baltic countries started to develop survey statistics only after gaining their
independence. Now the course Survey Sampling is given in the programme of professional
studies in Mathematical Statistics of the University of Latvia.
2 Programme of professional studies in mathematical statistics
The programme of professional studies in Mathematical Statistics has been running at the
Department of Mathematics, University of Latvia since 1997/1998 academic year. In 2001 it
was accredited for the period till December 2007 and reaccredited in 2007 for the period till
2013. During whole period 2001-2008 the programme remained the most popular among all
mathematical programmes at the University of Latvia. The reaccredited programme is 4,5
years long, to compare with the previous 5 years long programme. Naturally, this transition
required a serious rework and modernization of the programme. The modernization of the
programme was necessary in order to keep the educational process up to day in spite of
reduction of number of hours and courses. Besides, it was essential to introduce new actual
courses in some branches of modern mathematical statistics and to apply new software. Now
this programme is valued at 180 national credit points (70 of them are common with Bachelor
Programme in Mathematics).
Now the programme foresees the following modules of the courses and requested activities of
our students:

a module of Pure Mathematics;

a module of Mathematical Statistics and Probability Theory;

a module of Analysis of Social and Economic Processes;

a module of Software Provision for Statistical and Numerical Problems;

a module of General Subjects;

probation work;

a Diploma Thesis.
The module of Pure Mathematics aims at two mutually connected goals and tasks. First, to
guarantee the students, after successfully mastering the module, to have knowledge and
professional skills in different areas of Pure Mathematics which are necessary in order to
acquire speciality courses in probability, statistics, econometrics, decision making and others.
Second, to give the students an opportunity to continue studies at the second, master level in
one of the four offered directions in Mathematics at our university (Probability Theory and
Mathematical Statistics, Mathematical Simulation, Mathematical Didactics and Modern
Elementary Mathematics, Pure Mathematics, orientated towards Algebra, Topology and
Analysis).
The aim of the module of Mathematical Statistics and Probability Theory is to educate
specialists of high level of proficiency in Mathematical Statistics, whose knowledge and
professional skills would be sufficient in order to make statistical analysis in all areas of
modern economics, social and scientific activities.
The module of Analysis of Social and Economic Processes provides students with principles
and methods in simulation and decision making.
There are courses in the software provision for statistical and numerical problems in the
fourth module.
The module of General Subjects is relatively small and foresees a course in professional
English and a course in Natural Sciences.
The probation period is increased from 4 months in the previous programme to 26 weeks in
the modernized programme. The problem to organize fruitfully the probation work for
students is quite difficult. The staff of the Department tries to develop the collaboration with
enterprises where the probation for the students could be successfully organized.
Diploma work constitutes an essential part of the programme. By defending the Diploma a
student demonstrates that his/her theoretical knowledge and developed skills are sufficient to
start professional activities. The subjects of Diploma work for graduates of our programme
are usually related to Probability Theory, Mathematical Statistics, Applied Statistics and
Actuary Sciences as well as to Mathematical Simulation of Social and Financial Processes.
One of the principal criteria to accept the work for defence is its mathematical correctness.
3 The teaching programme of survey sampling
3.1 Course in Survey Sampling
The special course in Survey Sampling was introduced at the Department of Mathematics in
1996 by Dr. Math. J. Lapiņš. It was intended for the students of the programme of the
professional studies in Mathematical Statistics in the fourth-fifth year of studies. For the
reaccreditation of this programme in 2007 the course was reworked. The changes were not
very essential, but they were important taking into account the development of Survey
Sampling Theory and Methodology during the last years. Now this course consists of 54
hours of lectures and 10 hours of practical lessons during the autumn semester in the fourth
year of studies.
The lectures on Survey Sampling are based mostly on the book by W. G. Cochran (1) and S.
L. Lohr (), which are available in the library of the Faculty of Physics and Mathematics of the
University of Latvia. Unfortunately, we do not have a good literature on survey sampling in
Latvian. For example, the overview of some sampling designs is given in Z. Goša (2003),
O.Krastiņš (1998), O.Krastiņš, I.Krūmiņa (1993). Most of the students can use the
methodological materials by N. Budkina.
3.2 The programme of the course "Survey Sampling"
Course plan is as follows:
1.
Introduction to sampling theory and methodology (the main concepts and
definitions of Survey Sampling Theory, the main stages of modernization and
realization of survey, types of sampling).
2.
Simple random sampling with and without replacement (sampling scheme,
definitions and notions, estimators of total, mean, proportion in the population and in
domain, estimators of variance, sample size).
3.
Sampling with Unequal Probability (description of the techniques, estimators).
4.
Stratified sampling (sampling scheme, allocation of the sample size, estimators of
total, mean, proportion, poststratifcation).
5.
Ratio and regression estimators (description, estimators).
6.
Systematic sampling (description, estimators, population with linear trend,
population in random order, population with periodic variation).
7.
Single-stage and multistage cluster sampling (description, estimators for the case of
sampling with equal and unequal probabilities wit and without replacement, optimum
selection of sampling rates, Jackknife method).
8.
Double sampling (description, estimators).
9. Errors in surveys, their sources and Methods of their reduction. (nonresponse).
Practical works
During the course each student must work out 3 home works and control work. The practical
works, the home works and the control work give 40% of the final mark.
Control work consists of short theoretical question and the numerical problems. Numerical
problems are solved without using a computer during the practical lectures and the control
work. Two home works consist of two common tasks and the one individual. The third home
work is individual for each student. The Statvillage data of C. J. Schwarz (1997) and the
exercises of S. L. Lohr (1999) are used for the preparation of the variants for these
home works. Therefore a computer is needed for the solution of some numerical problems
from home works. Most of the students use SPSS and Excel. The results of home works are
discussed during the practical lectures.
The main problem that arises in teaching Survey Sampling is the lack of practical training.
More practical work is needed for students and a possibility to provide the students with real
data is needed for teachers.
3.3. Probation work and Diploma Thesis
During the whole period of teaching the course “Survey Sampling” it has been popular
among the students. Every year there is at least one student choosing a theme on Survey
Sampling for his/her probation work or Diploma paper.
Probation work
As it was mentioned above, Mathematical statistics programme foresees an essential increase
in the role of probation work. The problem to successfully organize a half year long probation
work is difficult. The tasks which the students have to fulfil are essentially different but a lot
of students choose themes connected with survey sampling. A long period of probation work
gives the possibility for the students to participate in real sampling projecting, carrying it out
and its analysis.
There have been cases when the students themselves offered the companies to carry out a
survey and got the support. The aim of these surveys was to find out the opinion of the clients
and partners of the companies about different aspects of cooperation, to find out the opinion
of the workers of the companies about working conditions, to estimate some parameter. In
carrying out these surveys different types of sampling have been applied: simple random
sampling, stratified random sampling, single-stage cluster sampling and two-stage cluster
sampling.
Unfortunately, there have been some cases when the probation work was connected with
statistical data processing, when these data were restricted and the problem to let the students
use these data was aroused.
Diploma Thesis
Since the course “Survey Sampling” is intended for the students of the programme of
professional studies, most of the Diploma Papers have practical purpose. It is common
(however not obligatory) that the subject of the Diploma is closely related to the work which
a student has fulfilled in the result of the probation work.
Since 1996 22 Diploma Theses on Survey Sampling have been defended by students of the
speciality “Mathematician-Statistician” of the University of Latvia. There have been
theoretical, practical and methodological works, which have been written under the
supervision of J. Lapiņš, N. Budkina, S. Bāliņa, K. Lece and M. Liberts. 9 Master Theses
have been defended under the supervision of J. Lapiņš, I. Priedola, S. Bāliņa.
4 Conclusions
The course „Survey Sampling” is very important and interesting for the students of
Programme of Professional Studies in Mathematical Statistics at the University of Latvia. It
could be developed by introducing new methods and modern techniques, the number of hours
for practical works should be increased.
References
Cochran, W. G. (1977) Sampling techniques. Wiley and Sons.
Goša, Z. (2003) Statistka, LU, Rīga
Krastiņš, O. (1998) Statistika un ekonometrija: mācību grāmata augstskolām. Latvijas Republikas
Centrālā statistikas pārvalde, Rīga.
Krastiņš, O. and Krūmiņa I. (1993) Izlases metode. LU, Rīga.
Lohr, S. L. (1999) Sampling: Design and Analysis. Duxbury Press, Pacific Grove.
Schwarz C. J. (1997) StatVillage: An On-Line, WWW-Accessible, Hypothetical City Based on Real Data for Use
in an Introductory Class in Survey Sampling. Journal of Statistics Education, 5(2).
http://www/amstat.org/publications/jse/v5n2/schwarz.html