CHAPTER 12
DETERMINING THE SAMPLE
PLAN
Important Topics of This Chapter
Differences between population and sample.
Sampling frame and frame error.
Developing sampling plan.
Basic sampling methods.
Strength and Weaknesses of Basic Sampling
techniques.
Choosing Probability Vs. non-probability
sampling.
Definitions of Important Terms
Population or Universe

The total group of people from whom information is needed.
Census

Data obtained from or about every member of the population of
interest.
Sample

A subset of the population of interest
Sampling Error:


Selection error
Sampling size
Sample Frame and Frame Error:
Sample vs. Census
Types of Study
Conditions Favoring the Use of
Sample
Census
1. Budget
Small
Large
2. Time available
Short
Long
3. Population size
Large
Small
4. Variance in the characteristic
Small
Large
5. Cost of sampling errors
Low
High
6. Cost of nonsampling errors
High
Low
7. Nature of measurement
Destructive
Nondestructive
8. Attention to individual cases
Yes
No
The Sampling Design Process
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process
Steps in Developing a Sampling
Plan
Step 1: Defining the Population:

Bases for defining the population of interest include:




Geography
Demographics
Use
Awareness
Step 2: Choosing a Sampling Frame

Sampling frame

List of population elements from which to select units to be
sampled.
Steps in Developing a Sampling
Plan (cont.)
Step 3: Selecting the Sampling Technique(s):

Probability samples:


Non-probability samples:


Samples in which every element of the population has a
known, nonzero probability of selection.
Include the selection of specific elements from the population
in a nonrandom manner.
Sampling error:

The difference between the sample value and the true value of
the population mean.
Steps in Developing a Sampling
Plan (cont.)
Advantages of
probability samples
Disadvantages of
probability samples
- The researcher can be sure of
obtaining information from a
representative cross section of the
population of interest.
- They are more expensive than
non-probability samples of the
sample size in most cases. The
rules for selection increase
interviewing costs and professional
time must be spent in developing
the sample design.
- Sampling error can be computed.
- The survey results are projectable
to the total population.
- Probability samples take more time
to design and execute than nonprobability samples.
Steps in Developing a Sampling
Plan (cont.)
Advantages of nonprobability samples
- Non-probability samples cost less
than probability samples. This
characteristic of non-probability
samples may have considerable
appeal in those situations where
accuracy is not of critical
importance.
-Non-probability samples
ordinarily can be conducted more
quickly than probability samples.
Disadvantages of nonprobability samples
- Sampling error cannot be computed.
- The researcher does not know the
degree to which the sample is
representative of the population
from which it was drawn.
- The results of non-probability
samples cannot and should not be
projected to the total population.
Steps in Developing a Sampling
Plan (cont.)
Step 4: Determine the Sample Size:
Once the sampling method has been chosen, the
next step is to determine the appropriate sample
size.
 Developing Operational Procedures:


Involves determining whether a probability or nonprobability sample is being used.
Steps in Developing a Sampling
Plan (cont.)
Step 5: Execute the Sampling Process:
The final step in the sampling process involves
execution of the operational sampling plan
discussed in the previous steps.
 It is important that this step include adequate
checking to make sure that specified procedures
are adhered to.

Classification of Sampling Techniques
Sampling Techniques
Non-probability
Sampling Techniques
Convenience
Sampling
Judgment
Samples
Simple random
Sampling
Systematic
Sampling
Probability
Sampling Techniques
Quota
Sampling
Stratified
Sampling
Snowball
Sampling
Cluster
Sampling
Probability Sampling Methods
Simple Random Sampling

Is considered to be the purest form of
probability sampling. A probability sample is a
sample in which every element of the
population has a known and equal probability
of being selected into the sample.
Probability of Selection =
Sample Size
Population Size
Procedures for Drawing
Probability Samples
Simple Random
Sampling
1. Select a suitable sampling frame
2. Each element is assigned a number from 1 to N
(pop. size)
3. Generate n (sample size) different random
numbers between 1 and N
4. The numbers generated denote the elements
that should be included in the sample
Probability Sampling Methods
(cont.)
Systematic Sampling

Probability sampling in which the entire
population is numbered, and elements are
drawn using a skip interval.
Population Size
Skip Interval = Sample Size
Systematic
Sampling
1. Select a suitable sampling frame
2. Each element is assigned a number from 1 to N (pop. size)
3. Determine the sample interval i:i=N/n. If i is a fraction,
round to the nearest integer
4. Select a random number, r, between 1 and i, as explained
in simple random sampling
5. The elements with the following numbers will comprise the
systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i
Probability Sampling Methods
(cont.)
Stratified Samples

Stratified samples are probability samples that
are distinguished by the following procedural
steps:
First, the original or parent population is divided
into two or more mutually exclusive and exhaustive
subsets (e.g., male and female).
 Second, simple random samples of elements from
the two or more subsets are chosen independently
from each other.

Stratified
Sampling
1. Select a suitable frame
2. Select the stratification variable(s) and the number of strata, H
3. Divide the entire population into H strata. Based on the
classification variable, each element of the population is assigned
to one of the H strata
4. In each stratum, number the elements from 1 to Nh (the pop.
size of stratum h)
5. Determine the sample size of each stratum, nh, based on
proportionate or disproportionate stratified sampling, where
H
h=1
nh = n
6. In each stratum select a simple random sample of size nh
Probability Sampling Methods
(cont.)
Cluster Samples

In the case of cluster samples, the sampling
units are selected in groups. There are two basic
steps in cluster sampling:
First, the population of interest is divided into
mutually exclusive and exhaustive subsets.
 Second, a random sample of the subsets is selected.

Cluster
Sampling
1. Assign a number from 1 to N to each element in the population
2. Divide the population in C clusters of which c will be included in
the sample
3. Calculate the sampling interval i, i=N/c (round to nearest integer)
4. Select a random number r between 1 and i, as explained in simple
random sampling
5. Identify elements with the following numbers: r,r+i,r+2i,... r+(c-1)i
6. Select the clusters that contain the identified elements
7. Select sampling units within each selected cluster based on SRS or
systematic sampling
8. Remove clusters exceeding sampling interval i. Calculate new
population size N*, number of clusters to be selected C*= C-1, and
new sampling interval i*.
Types of Cluster Sampling
Cluster Sampling
One-Step
Approach
Two-Step
Approach
Simple Cluster
Sampling
Multistage
Approach
Probability
Proportionate
to Size Sampling
Non-probability Sampling
Methods
Convenience Samples

Non-probability samples used primarily
because they are easy to collect.
Judgment Samples

Non-probability samples in which the selection
criteria are based on personal judgment that the
element is representative of the population
under study.
Non-probability Sampling
Methods (cont.)
Quota Samples

Non-probability samples in which population
subgroups are classified on the basis of
researcher judgment.
Snowball Samples

Non-probability samples in which selection of
additional respondents is based on referrals
from the initial respondents.
Strengths and Weaknesses of Basic Sampling Techniques
Technique
Strengths
Weaknesses
Nonprobability Sampling
Convenience sampling
Least expensive, least
time-consuming, most
convenient
Low cost, convenient,
not time-consuming
Sample can be controlled
for certain characteristics
Can estimate rare
characteristics
Selection bias, sample not
representative, not recommended for
descriptive or causal research
Does not allow generalization,
subjective
Selection bias, no assurance of
representativeness
Time-consuming
Easily understood,
results projectable
Difficult to construct sampling
frame, expensive, lower precision,
no assurance of representativeness.
Can decrease representativeness
Judgmental sampling
Quota sampling
Snowball sampling
Probability sampling
Simple random sampling
(SRS)
Systematic sampling
Stratified sampling
Cluster sampling
Can increase
representativeness,
Easier to implement than
SRS, sampling frame not
necessary
Include all important
subpopulations,
precision
Easy to implement, cost
effective
Difficult to select relevant
stratification variables, not feasible to
stratify on many variables, expensive
Imprecise, difficult to compute and
interpret results
Table 11.4
Choosing Non-probability vs.
Probability Sampling
Factors
Conditions Favoring the Use of
Nonprobability Probability
sampling
sampling
Nature of research
Exploratory
Conclusive
Relative magnitude of sampling and
nonsampling errors
Nonsampling
errors are
larger
Sampling
errors are
larger
Variability in the population
Homogeneous
(low)
Heterogeneous
(high)
Statistical considerations
Unfavorable
Favorable
Operational considerations
Favorable
Unfavorable