Basic Stats Sampling Techniques

Note: The Slides were taken from Elementary
Statistics: A Handbook of Slide Presentation
prepared by Z.V.J. Albacea, C.E. Reano, R.V.
Collado, L.N. Comia and N.A. Tandang in 2005
for the Institute of Statistics, CAS, UP Los
Banos
Training on Teaching
Basic Statistics for
Tertiary Level Teachers
Summer 2008
BASIC CONCEPTS IN
SAMPLING AND
SAMPLING TECHNIQUES

Session 3.2
TEACHING BASIC STATISTICS ….
Sampling
Process
Sample
Data
Universe
Inferences/Generalization
(Subject to Uncertainty)
INFERENTIAL STATISTICS

Session 3.3
Basic Terms
UNIVERSE – the set of all entities under study
VARIABLE – attribute of interest observable on
each entity in the universe
POPULATION – the set of all possible values of
the variable
SAMPLE – subset of the universe or the
population

Session 3.4
SAMPLING – the process of selecting a sample
PARAMETER – descriptive measure of the
population
STATISTIC – descriptive measure of the sample
INFERENTIAL STATISTICS – concerned with
making generalizations about parameters using
statistics
Basic Terms

Session 3.5
WHY DO WE USE SAMPLES?
1. Reduce Cost
2. Greater Speed or Timeliness
3. Greater Efficiency and Accuracy
4. Greater Scope
5. Convenience
6. Necessity
7. Ethical Considerations

Session 3.6
TWO TYPES OF SAMPLES
1. Probability sample
2. Non-probability sample

Session 3.7
Samples are obtained using some
objective chance mechanism, thus
involving randomization.
They require the use of a complete
listing of the elements of the
universe called the sampling
frame. (Session_5_DEFINING A SAMPLING FRAME.pptx)
PROBABILITY SAMPLES

Session 3.8
The probabilities of selection are
known.
They are generally referred to as
random samples.
They allow drawing of valid
generalizations about the
universe/population.
PROBABILITY SAMPLES

Session 3.9
Samples are obtained unevenly,
selected purposively or are taken
as volunteers.
The probabilities of selection are
unknown.
NON-PROBABILITY SAMPLES

Session 3.10
They should not be used for
statistical inference.
They result from the use of
judgment sampling, accidental
sampling, purposively sampling,
and the like.
NON-PROBABILITY SAMPLES

Session 3.11
BASIC SAMPLING TECHNIQUES
Simple Random Sampling
Stratified Random Sampling
Systematic Random Sampling
Cluster Sampling
Slide No. 3.20

Session 3.12
SIMPLE RANDOM SAMPLING
Most basic method of drawing a
probability sample
Assigns equal probabilities of
selection to each possible sample
Results to a simple random sample

Session 3.13
STRATIFIED RANDOM SAMPLING
The universe is divided into L
mutually exclusive sub-universes
called strata.
Independent simple random
samples are obtained from each
stratum.

Session 3.14
ILLUSTRATION
C
D
B
A
B
Slide No. 3.13

Session 3.15
Steps in Stratified Random Sampling
1.Identify and define the population (sampling
frame)
2.Determine the desired sample size
3.Identify the variable and subgroups (strata) for
which you want to guarantee appropriate
representation (either proportional or equal)
4.Classify all members of the population as
members of one of the identified subgroups
5.Randomly select the individuals from each
subgroup (using the table of random numbers
or lottery)

Formula:
with
= sample size of subgroup k
n = Total sample size (determined using
the specified methods)
= Population size of subgroup k
N = Total population size
Session 3.16
1 1
L L
h h
h h
N N n n
Computation of Sample Size in SRS

Session 3.17
Example: The researcher would like to conduct a
study on administrators’ performance in State
Colleges and Universities in Caraga from which the
distribution of population is given in the table.
Suppose the researcher would like to get 80
samples.
State University/
College
Number of
Administrators
State University/
College
Number of
Administrators
SUC1 7 SUC5 36
SUC2 9 SUC6 29
SUC3 14 SUC7 15
SUC4 45 SUC8 25
Computation of Sample Size in SRS

Session 3.18
Advantages of Stratification
1. It gives a better cross-section of the population.
2. It simplifies the administration of the survey/data
gathering.
3. The nature of the population dictates some inherent
stratification.
4. It allows one to draw inferences for various subdivisions
of the population.
5. Generally, it increases the precision of the estimates.

Session 3.19
SYSTEMATIC SAMPLING
Adopts a skipping pattern in the selection
of sample units
Gives a better cross-section if the listing is
linear in trend but has high risk of bias if
there is periodicity in the listing of units in
the sampling frame
Allows the simultaneous listing and
selection of samples in one operation

Session 3.20
Population
Systematic
Sample
ILLUSTRATION

Session 3.21
CLUSTER SAMPLING
It considers a universe divided into N
mutually exclusive sub-groups called
clusters.
A random sample of n clusters is selected
and their elements are completely
enumerated.
It has simpler frame requirements.
It is administratively convenient to
implement.
Slide No. 3.19
Slide No. 3.11

Session 3.22
ILLUSTRATION
Population
Cluster Sample
Slide No. 3.18

Steps in Cluster Sampling
 Identify and define the
population (sampling frame)
 Determine the desired
sample size
 Identify and determine a
logical cluster
 List all clusters that
comprise the population
 Estimate the average
population per cluster
 Determine the number of
clusters needed by dividing the
sample size by the estimated
average population per cluster
 Randomly select the
needed number of
clusters
 All members in the
selected cluster are
included as sample units
Session 3.23

Example of Cluster Sampling
 Let us see how the superintendent would get a sample
of teachers if cluster sampling were used.
1. The population is 5000 teachers in the
superintendent’s school system.
2. The desired sample size is 500.
3. A logical cluster is a school.
4. There are 100 schools in the list.
5. Although the schools vary in the number of teachers,
there is an average number of teachers per school.
Session 3.24

Example of Cluster Sampling
6. Suppose the average number of teachers per school is 50.
So the number of clusters (schools) needed is:
7. There are 10 schools in the sample, which will be selected
randomly from the 100 schools.
8. All teachers in each of the 10 schools are in the sample (if
the desired sample size is not reached, add one cluster
from the population, which will be chosen randomly from
the 90 schools left).
Session 3.25

Session 3.26
SIMPLE TWO-STAGE SAMPLING
In the first stage, the units are grouped into N sub-
groups, called primary sampling units (psu’s) and
a simple random sample of n psu’s are selected.
Illustration:
A PRIMARY SAMPLING
UNIT





Session 3.27
SIMPLE TWO-STAGE SAMPLING
In the second stage, from each of the n psu’s
selected with Mi elements, simple random sample
of mi units, called secondary sampling units ssu’s,
will be obtained.
Illustration:
A SECONDARY
SAMPLING UNIT
SAMPLE

 Accidental or Incidental Sampling
Getting a subject of study that is
only available during the period
 Quota Sampling
Getting a sample of subject of study
using through quota system
 Ex. All PolSci students of the different
HEI’s in Caraga
Non-Probability Sampling
Techniques

 Purposive Sampling
The researcher simply picks out the
subjects that are representatives of
the population depending on the
purpose of the study
Non-Probability Sampling
Techniques

 End of Presentation
Session 3.30

Basic Stats Sampling Techniques

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