Introduction into Sampling Theory,
Applying Partial Order Concepts
Bardia Panahbehagh and Rainer Bruggemann
1 Introduction
In sampling theory, for estimating some population parameters, each survey based
on a strategy involves two stages; sampling stage and estimation stage (Hajek 1959).
In the sampling stage, we indicate how it is supposed to select the sample units and
in the estimation stage, estimators will be proposed for estimating the respective
parameters.
The development of sampling theory is based on efficiency; i.e. on the search
for high precision, low cost, etc. Searching is mostly based on the two principles;
Randomization and Representation.
• Randomization: Based on randomization, the sampling design should select
the sample units at random such that all the population units have chances to
be selected. We know such designs as probability sampling designs. In contrast
to probability sampling designs, we have non-probability or selective sampling
designs in which the sampling is based on many factors including personal
or expert-oriented ideas, the population situations, budgets of projects, etc.
Probability sampling designs have at least two advantages relative to their nonprobability versions; first, according to the randomize bases of the designs, we
can make inferences about the estimators, second, we decrease the chance of
facing a bias sample result of personal factors of the sampler mind (Sarndal et al.
2003, page 8).
B. Panahbehagh ()
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
e-mail: panahbehagh@khu.ac.ir
R. Bruggemann
Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany
e-mail: brg_home@web.de
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_10
135
Applying Partial Order Concepts
Bardia Panahbehagh and Rainer Bruggemann
1 Introduction
In sampling theory, for estimating some population parameters, each survey based
on a strategy involves two stages; sampling stage and estimation stage (Hajek 1959).
In the sampling stage, we indicate how it is supposed to select the sample units and
in the estimation stage, estimators will be proposed for estimating the respective
parameters.
The development of sampling theory is based on efficiency; i.e. on the search
for high precision, low cost, etc. Searching is mostly based on the two principles;
Randomization and Representation.
• Randomization: Based on randomization, the sampling design should select
the sample units at random such that all the population units have chances to
be selected. We know such designs as probability sampling designs. In contrast
to probability sampling designs, we have non-probability or selective sampling
designs in which the sampling is based on many factors including personal
or expert-oriented ideas, the population situations, budgets of projects, etc.
Probability sampling designs have at least two advantages relative to their nonprobability versions; first, according to the randomize bases of the designs, we
can make inferences about the estimators, second, we decrease the chance of
facing a bias sample result of personal factors of the sampler mind (Sarndal et al.
2003, page 8).
B. Panahbehagh ()
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
e-mail: panahbehagh@khu.ac.ir
R. Bruggemann
Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany
e-mail: brg_home@web.de
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_10
135