Basic Statistics Part II

APPLIED
STATISTICS AND
EXPERIMENTAL
DESIGNS
SAMPLING DESIGN: BASIC CONCEPTS
AND PROCEDURE
The goal in sampling is to obtain individuals for a
study in such a way that accurate information
about the population can be obtained.
Two Type of Samples
1. Probability Sample
2. Non – Probability Sample
Probability Samples
• 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.
Probability Samples
• The probabilities of selection are known.

• They are generally referred to as random
samples.
• They allow drawing of valid generalizations
about the universe/population.
Non-Probability Samples
• Samples are obtained haphazardly, selected

purposively or are taken as volunteers.
• The probabilities of selection are unknown.
Non-Probability Samples
• They should not be used for statistical inference.

• The result fro the use of judgment sampling, accidental
sampling, purposively sampling, and the like.
Basic Sampling Technique of Probability
Sampling
• Simple Random Sampling
• Systematic Random Sampling
• Stratified Random Sampling
• Cluster Sampling
• Multi-stage Sampling
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
Simple Random Sampling
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Obtaining a Simple Random Sample
1. Assign a number to each item in the lot.

2. Consult the table of random numbers.
3. Preplan how to select a sequence of digits from
the table so that no bias enters into the selection
process.
Obtaining a Simple Random Sample
4. Select a random number in the preplanned pattern.

5. Arrange the random numbers consecutively in
numerical order.
6. Select as samples those items in the lot corresponding
to the random numbers.
An example of a Table of Random Numbers
Systematic Random Sampling
• It is obtained by selecting every kth individual from the

population.
• The first individual selected corresponds to a random
number between 1 to k.
Systematic Random Sampling
Obtaining a Systematic Random Sample
•1. Decide on a method of assigning a unique serial number, from 1 to N, to
each one of the elements in the population.
2. Compute for the sampling interval
3. Select a number, from 1 to k, using a randomization mechanism. The
element in the population assigned to this number is the first element of
the sample. The other elements of the sample are those assigned to the
numbers and so on until you get a sample of size.
Example:
We want to select a sample of 50 students from

500 students under this method kth item and
picked up from the sampling frame.
Solution:
•
We start to get a sample starting from i and for every kth

unit subsequently. Suppose the random number i is 5,
then we select 5, 15, 25, 35, …
Stratified Random Sampling
• It is obtained by separating the population into non –

overlapping groups called strata and then obtaining a
simple random sample from each stratum.
• The individuals within each stratum should be
homogeneous (or similar) in some way.
Example:
A sample of 50 students is to be drawn from a population

consisting of 500 students belonging to two institutions A
and B. The number of students in the institution A is 200
and the institution B is 300. How will you draw the
sample using proportional allocation?
Solution:
•There
are two strata in this case.
Given:
If and are the sample size,
=(
=(
The sample size are 20 from A and 30 from B. Then the units from each
institution are to be selected by simple random sampling.
Cluster Sampling
• It is a way to randomly select participants from a list

that is too large for simple random sampling.
• The clusters are constructed such that the sampling
units are heterogeneous within the cluster and
homogeneous among the clusters.
Cluster Sampling
Obtaining a Cluster Sample
1. Divide the population into non-overlapping clusters.
2. Number the clusters in the population from 1 to N.
3. Select n distinct numbers from 1 to N using a randomization
mechanism. The selected clusters are the clusters associated
with the selected numbers.
4. The sample will consist of all the elements in the selected
clusters.
Example:
If you wanted to choose 1000 participants from the entire

population of the Philippines, it is likely impossible to
get a complete list of everyone. Instead, the researcher
randomly selects areas (i.e. cities or province) and
randomly selects from within those boundaries.
Example:
The list of all the agricultural farms in a village or district

may not be easily available but the list of village or
district is generally available. In this case, every farm in
sampling unit and every village or district is the cluster.
Multi – Stage Sampling
Selection of the sample is done in two or more

steps or stages, with sampling units varying in each
stage.
Multi – Stage Sampling
Obtaining a Multi – Stage Sampling
1. Organize the sampling process into stages where the

unit of analysis is systematically grouped.
2. Select a sampling technique for each stage.
3. Systematically apply the sampling technique to each
stage until the unit of analysis has been selected.
Obtaining a Multi – Stage Sampling
Second, a Third, a random
First, divide
random sample sample of even
into smaller of smaller areas smaller areas
regions (such (such as (such as
as states), and countries) is neighborhood) is
a random taken from taken from
sample of within each of within each of
the regions the areas chosen
these regions
chosen in the in the second
is collected. first stage. stage.
Basic Sampling Technique of Non-Probability
Sampling
• Accidental Sampling
• Quota Sampling
• Convenience Sampling
• Purposive Sampling
• Judgment Sampling
Cases wherein Non-Probability Sampling is
Useful
• Only few are willing to be interviewed.
• Extreme difficulties in locating or identifying subjects.
• Probability sampling is more expensive to implement.
Exercises:
Identify the sample selection procedure used in each of

the following cases:
1. A tax auditor selects every 1000th income tax return
that is received.
2. 12 people are randomly selected to serve as jurors
from a jury pool of 150 people.
Exercises:
Identify the sample selection procedure used in each of the
following cases:
3. To select a sample of households in province, a sample of
provinces were selected, then a sample of municipalities were
chosen from each of the selected provinces, then a sample of
barangays were chosen from each of the selected municipality,
and all households in the selected barangays were included.
Exercises:
Identify the sample selection procedure used in each of the
following cases:
4. For a survey, a sample of municipalities was selected from
every province in the country and included all child laborers in
the selected municipalities.
5. In the game of lotto, 6 balls are selected from a container with
42 balls.
Sources of Errors in Sampling
1. Non-sampling error is the error that result from the survey
process.
2. Sampling error is the error that resulted from using sampling
to estimate information regarding a population.
Sources of Non-sampling Error
• Non-responses
• Interview error
• Misrepresented Answers
• Data entry errors
Sources of Non-Sampling Error
• Questionnaire Design
• Wording of Questions
• The order of the questions, words, and responses

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APPLIED

• Samples are obtained using some objective chance

• The probabilities of selection are known.

• Samples are obtained haphazardly, selected

• They should not be used for statistical inference.

• Most basic method of drawing a probability sample

1. Assign a number to each item in the lot.

4. Select a random number in the preplanned pattern.

• It is obtained by selecting every kth individual from the

We want to select a sample of 50 students from

We start to get a sample starting from i and for every kth

• It is obtained by separating the population into non –

A sample of 50 students is to be drawn from a population

• It is a way to randomly select participants from a list

If you wanted to choose 1000 participants from the entire

The list of all the agricultural farms in a village or district

Selection of the sample is done in two or more

1. Organize the sampling process into stages where the

Identify the sample selection procedure used in each of

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