

Research
Methods STA630
VU
Lesson
28
TYPES
OF PROBABILITY SAMPLING
Probability
samples that rely on random
processes require more work
than nonrandom ones.
A
researcher
must identify specific
sampling elements (e.g. persons) to
include in the sample.
For
example,
if conducting a telephone survey, the
researcher needs to try to
reach the specific
sampled
person,
by calling back several times, to get an accurate
sample.
Random
samples are most likely to
yield a sample that truly
represents the population. In
addition,
random
sampling lets a researcher statistically
calculate the relationship between the sample and
the
population
that is the size of sampling
error. A
nonstatistical definition of the
sampling error is the
deviation
between sample result and a population
parameter due to random process.
Simple
Random Sample
The
simple random sample is both the
easiest random sample to understand and
the one on which other
types
are modeled. In simple random
sampling, a research develops an accurate
sampling frame, selects
elements
from sampling frame
according to mathematically random procedure,
then locates the exact
element
that was selected for
inclusion in the sample.
After
numbering all elements in a
sampling frame, the researcher uses a
list of random numbers to
decide
which elements to select. He or
she needs as many random
numbers as there are elements to
be
sampled:
for example, for a sample of
100, 100 random numbers are
needed. The researcher can
get
random
numbers from a random number table, a
table of numbers chosen in a
mathematically random
way.
Randomnumber tables are available in
most statistics and research
methods books. The
numbers
are
generated by a pure random process so
that any number has an equal
probability of appearing in
any
position.
Computer programs can also
produce lists of random number.
A
random starting point should be
selected at the outset.
Random
sampling does not guarantee
that every random sample
perfectly represents the
population.
Instead,
it means that most random
samples will be close to the
population most of the time, and
that
one
can calculate the probability of a
particular sample being inaccurate. A
researcher estimates
the
chance
that a particular sample is
off or unrepresentative by using
information from the sample
to
estimate
the sampling distribution. The
sampling distribution is the key
idea that lets a
researcher
calculate
sampling error and confidence
interval.
Systematic
Random Sample
Systematic
random sampling is simple random sampling
with a short cut for random selection.
Again,
the
first step is to number each element in
the sampling frame. Instead of
using a list of random
numbers,
researcher calculates a sampling
interval, and the
interval becomes his or her
own quasi
random
selection method. The sampling interval
(i.e. 1 in K
where K is some number) tells
the
researcher
how to select elements from
a sampling frame by skipping elements in
the frame before one
for
the sample.
Sampling
intervals are easy to compute. We
need the sample size and the
population size. You
can
think
of the sample interval as the inverse of
the sampling ratio. The
sampling ratio for 300
names out
of
900 will be 300/900 = .333 =
33.3 percent. The sampling
interval is 900/300 = 3
Begin
with a random start. The easiest
way to do this is to point
blindly at a number from those
from
the
beginning that are likely to
be part of the sampling
interval.
When
the elements are organized in
some kind of cycle or
pattern, the systematic sampling
will not give
a
representative sample.
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Research
Methods STA630
VU
Stratified
Random Sample
When
the population is heterogeneous, the use
of simple random sample may
not produce representative
sample.
Some of the bigger strata
may get over representation while
some of the small ones
may
entirely
be eliminated. Look at the variables
that are likely to affect
the results, and stratify
the
population
in such a way that each
stratum becomes homogeneous group
within itself. Then draw
the
required
sample by using the table of random
numbers. Hence in stratified random
sampling a sub
sample
is drawn utilizing simple random
sampling within each stratum.
(Randomization is not done
for
quota
sampling).
There
are three reasons why a
researcher chooses a stratified random
sample: (1) to increase a
sample's
statistical
efficiency, (2) to provide
adequate data for analyzing
the various subpopulations, and (3)
to
enable
different research methods and
procedures to be used in different
strata.
1.
Stratification
is usually more efficient statistically
than simple random sampling
and at worst it
is
equal to it. With the
ideal stratification, each stratum is
homogeneous internally and
heterogeneous
with other strata. This
might occur in a sample that
includes members of several
distinct
ethnic groups. In this instance,
stratification makes a pronounced
improvement in
statistical
efficiency.
Stratified
random sampling provides the assurance
that the sample will accurately
reflect the
population
on the basis of criterion or criteria
used for stratification.
This is a concern
because
occasionally
simple random sampling yields a
disproportionate number of one group or
another,
and
the sample ends up being
less representative than it could
be.
Random
sampling error will be
reduced with the use of
stratified random sampling
Because
each group is internally
homogeneous but there are
comparative differences
Between
groups. More technically, a smaller
standard error may result
from stratified
Sampling
because the groups are adequately
represented when strata are
combined.
2.
It
is possible when the researcher wants to
study the characteristics of a certain
population
subgroups.
Thus if one wishes to draw some
conclusions about activities in different
classes of
student
body, stratified sampling
would be used.
3.
Stratified
sampling is also called for
when different methods of
data collection are applied
in
different
parts of the population. This
might occur when we survey company
employees at the
home
office with one method but mist
use a different approach with employees
scattered over
the
country.
Stratification
Process
The
ideal stratification would be
based on the primary variable
(the dependent variable) under
study.
The
criterion is identified as an efficient
basis for stratification.
The criterion for
stratification is that it
is
a characteristic of the population elements
known to be related to the dependent
variable or other
variables
of interest. The variable
chosen should increase
homogeneity within each stratum and
increase
heterogeneity
between strata.
Next,
for each separate subgroup or stratum, a
list of population elements
must be obtained.
Serially
number
the elements within each stratum.
Using a table of random numbers or
some other device, a
separate
simple random sample is taken
within each stratum. Of course the
researcher must
determine
how
large a sample must be drawn
from each stratum
Proportionate
versus Disproportionate
If
the number of sampling units drawn
from each stratum is in proportion to the
relative population
size
of
the stratum, the sample is proportionate
stratified sampling. Sometime, however, a
disproportionate
stratified
sample will be selected to
ensure an adequate number of sampling
units in every stratum
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Research
Methods STA630
VU
In
a disproportionate, sample size
for each stratum is not
allocated in proportion to the population
size,
but
is dictated by analytical
considerations.
Cluster
Sampling
The
purpose of cluster sampling is to sample
economically while retaining the
characteristics of a
probability
sample. Groups or chunks of elements
that, ideally, would have
heterogeneity among the
members
within each group are
chosen for study in cluster
sampling. This is in contrast to
choosing
some
elements from the population as in
simple random sampling, or
stratifying and then choosing
members
from the strata, or choosing every
nth case in the population in
systematic sampling.
When
several
groups with intragroup heterogeneity
and intergroup homogeneity
are found, then a
random
sampling
of the clusters or groups can ideally be
done and information gathered from each
of the
members
in the randomly chosen
clusters.
Cluster
samples offer more heterogeneity
within groups and more homogeneity among
and
homogeneity
within each group and
heterogeneity across groups.
Cluster
sampling addresses two problems:
researchers lack a good
sampling frame for a
dispersed
population
and the cost to reach a sampled element
is very high. A cluster is unit
that contains final
sampling
elements but can be treated
temporarily as a sampling element itself.
Researcher first
samples
clusters,
each of which contains elements,
then draws a second a second
sample from within the
clusters
selected
in the first stage of sampling. In
other words, the researcher randomly
samples clusters, and
then
randomly samples elements
from within the selected
clusters. He or she can
create a good
sampling
frame of clusters, even if it is
impossible to create one for
sampling elements. Once
the
researcher
gets a sample of clusters,
creating a sampling frame
for elements within each
cluster becomes
more
manageable. A second advantage for
geographically dispersed populations is
that elements within
each
cluster are physically closer to
each other. This may produce
a savings in locating or reaching
each
element.
A
researcher draws several samples in
stages in cluster sampling. In a
threestage sample, stage 1
is
random
sampling of big clusters;
stage 2 is random sampling of small
clusters within each
selected big
cluster;
and the last stage is
sampling of elements from
within the sampled within the
sampled small
clusters.
First, one randomly samples
the city blocks, then
households within blocks, then
individuals
within
households. This can also be an
example of multistage
area sampling.
The
unit costs of cluster sampling
are much lower than
those of other probability
sampling designs.
However,
cluster sampling exposes itself to
greater biases at each stage of
sampling.
Double
Sampling
This
plan is adopted when further
information is needed from a
subset of the group from
which some
information
has already been collected
for the same study. A
sampling design where initially a
sample
is
used in a study to collect
some preliminary information of interest,
and later a subsample of
this
primary
sample is used to examine the matter in
more detail, is called double
sampling.
What
is the Appropriate Sample
Design?
A
researcher who must make a
decision concerning the most
appropriate sample design for a
specific
project
will identify a number of sampling
criteria and evaluate the
relative importance of each
criterion
before
selecting a sample design. The most
common criteria
Degree
of Accuracy
Selecting
a representative sample is, of course,
important to all researchers.
However, the error
may
vary
from project to project,
especially when cost saving
or another benefit may be a tradeoff
for
reduction
in accuracy.
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Research
Methods STA630
VU
Resources
The
costs associated with the
different sampling techniques vary
tremendously. If the researcher's
financial
and human resources are restricted, this
limitation of resources will
eliminate certain
methods.
For
a graduate student working on a master's
thesis, conducting a national
survey is almost always
out
of
the question because of limited
resources. Managers usually
weigh the cost of research
versus the
value
of information often will
opt to save money by using
nonprobability sampling design rather
than
make
the decision to conduct no research at
all.
Advance
Knowledge of the
Population
Advance
knowledge of population characteristics,
such as the availability of lists of
population
members,
is an important criterion. A lack of
adequate list may
automatically rule out any
type of
probability
sampling..
National
versus Local Project
Geographic
proximity of population elements
will influence sample design.
When population
elements
are
unequally distributed geographically, a
cluster sampling may become more
attractive.
Need
for Statistical Analysis
The
need for statistical
projections based on the sample is
often a criterion. Nonprobability
sampling
techniques
do not allow researcher to
use statistical analysis to project the
data beyond the
sample.
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