Sampling

SAMPLING
(ВЫБОРОЧНОЕ НАБЛЮДЕНИЕ)

QUESTIONS
1. Types of sampling
2. Standard errors of the
sampling

1. TYPES OF SAMPLING
Sampling is the part of
population which uses
when it is difficult to
examine every item in a
population.
Sampling reflects all
properties of population

It is possible to describe
samples and populations
by the same characteristics
such as the mean,
standard deviations,
variance, mode, median
and etc.

These characteristics are
calculated for sampling are
named as statistics, but if
they are calculated for a
population they are named
as parameters.

There are two methods of
selecting samples from a
population:
 Nonrandom or judgment
sampling
 Random or probability
sampling

In judgment sampling personal
knowledge and opinion are used
to identify those items from the
population that are to be
included in the sample. These
samples avoid the statistical
analysis and loses a significant
degree of representativeness.

In random sampling, all items
in the population have a
chance of being chosen in
the sample. These samples
are used for statistical
analysis and support a
significant degree of
representativeness.

There are 4 methods of random sampling:
1. Simple random sampling (собственно
случайная выборка или простая
случайная выборка)
2. Systematic sampling (систематическая
или механическая выборка)
3. Stratified sampling (типическая или
стратифицированная выборка)
4. Cluster sampling (серийная, гнездовая
или кластерная выборка)

Simple random sampling is the most
convenient method, selects samples by
methods that allow each possible sample
to have an equal chance of being
included in the sampling.
The easiest way to select a sample
randomly is to use random numbers.
They can be generated by Excel, or by a
table of random digits

Systematic sampling selects items from a
population at the uniform interval that is
measured by time, order or space.
Systematic sampling differs from simple
random sampling in that each item has
an equal chance of being selected. But in
this case, each sample doesn’t have
equal chance of being selected.
Systematic sampling set proportion of
selection, for example, every 5th item, or
every 10th item and etc.

Stratified sampling is used when population
is divided into typological groups (for
example, education, health, libraries in
public sphere). Each group is called
strata.
Stratified sampling reflects the proportions of
population (for example, population in a
city 1,300,000 people, including 52% of
female and 48% of male. It is needed to
select 10,000 people in the sampling
maintaining the original aspect ratio).

In stratified sampling we have groups of
items, the number of different units but
the same of any characteristics (for
example, groups of people, (the number
of different units), who work in health,
education, libraries (the same sphere for
each group)

In cluster sampling population is divided into
groups, the same number of units, and
the same of all characteristics (for
example, boxes of Coca-cola, boxes of
chocolate and etc.)
Each group is called cluster and then we
select clusters (not items) by simple
random sampling or systematic sampling.

2. STANDARD ERRORS OF THE SAMPLING
Errors occur when we select items or
clusters from a population.
Population distribution can be described by
the mean, standard deviation and other
parameters.
Sampling can be described by the same
characteristics.
But there is the difference between
population mean and sampling mean,
population standard deviation and
sampling standard deviation.

The difference is called error.
The standard error shows not only error that
has been made but also the accuracy of
our results, which will be received in the
sampling analysis .
Standard error allows to extend the
sampling results to the population.
Average consumption of chocolate for
1000 people is 7.5 kg/year. Does it mean
the average consumption of chocolate for
all people who live in this city will be the
same? NO!

We can suppose that the average
consumption of chocolate for all people
who live in this city will be 7.5error.
There are two common equations of
standard error for all types of sampling:
t – confidence coefficient
2 – variance for sampling
n – number of items in
a sampling
n
t
2



N – number of items
in a population
These equations can be changed according
to the type and kind of sampling.
Confidence coefficient t can take on a value
of 1, 2 or 3 according to confidence
probability (68,3%; 95,4%; 99,7%)







N
n
n
t 1
2


 Simple random sampling (absolute measure units,
no proportions). The same equations are used for
systematic sampling – standard error of the mean
 Replicate sampling or population is infinite (N is not
known)
2 - variance
 Non-repeated sampling or population is finite (N is
known)
n
tx
2
~









N
n
n
tx 1
2
~


 Simple random sampling (proportions, just two
characteristics, answer the question – yes or no,
proportion of positive (or negative) answers are
known) – standard error of the proportion
known)
w(1-w) - variance
known)
 
n
ww
tw


1
 









N
n
n
ww
tw 1
1

 Stratified sampling (absolute measure units, no
proportions) – standard error of the mean
known)
- average within-group variance
known)
n
t i
x
2
~









N
n
n
t i
x 1
2
~

2


 Stratified sampling (proportions, just two
characteristics, answer the question – yes or no,
proportion of positive (or negative) answers are
known) – standard error of the proportion
known)
- average within-group variance
known)
 
n
ww
t ii
w


1
 









N
n
n
ww
t ii
w 1
1
 ww 1

 Cluster sampling (absolute measure units or
proportions) – standard error of the mean (or
proportion)
known)
 2 – external variance
r – number of clusters in a sampling
R – number of clusters in a population
known)
r
tx
2
~









R
r
r
tx 1
2
~


To begin the sampling it is needed to find the size of
sampling (number of items in a sampling) – n
To calculate it the size of sampling is expressed from
the equations of standard error.
In a whole size of sampling (number of items or
number of clusters) is counted:
 for replicate sampling
(population is infinite)
 For non-repeated sampling
(population is finite)
2
~
22
x
t
n



222
~
22


tN
Nt
n
x 


Sampling

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