Practical Aspects of
Sampling
An Overview
Why Sample?
Why Sample?
Samples
are taken to obtain
information about populations.
Sample
estimators are computed to
estimate parameters of the the
population from which the sample was
drawn.
Advantages
Complete
enumeration of all
sample units in the
entire universe is
often unnecessary
to obtain reasonably
accurate results.
Advantages
An
examination of the
entire population is
often too costly, too
time-consuming, and
impractical (….if not
impossible).
Advantages
In
the case of
destructive testing, the
sample elements or
units must be destroyed
or must be consumed to
obtain necessary
measurements.
Precision
The
standard error [se] is a measure of
precision. A smaller se, other things
remaining the same, means more
precision
.....that is, less variance in the sampling.
Sample Size
for a mean –
n = z2 2 / e2
where:
– e, the sampling error, is the difference
between sample mean and population mean
[e is expressed in units]
Sample Size
for a proportion n = [z2 p (1 – p)] / e2
where:
– e, the sampling error, is the difference
between sample proportion and population
proportion
[ e is expressed in percentage points]
Sample Size
Errors
Sampling
(internal) Error
The fact that a sample was taken, the
sample statistic is expected to deviate
from the population parameter.
Errors
Non-Sampling
(external) Error
Practical considerations in taking a sample.
recording errors
coding errors
processing errors
Errors
Bias
Most insidious to detect ....
poorly defined universe
inadequate sampling design
improperly worded questions
distorted answers
convenience sampling
Errors
 The
sampling error refers to the extent
to which the sample values on some
variable of importance to the research
differ from those of the population
from which it was drawn.
Types of Random
Samples
Simple Random
 with
replacement
 without replacement
…must be able to identify the target population
and ensure each item has an equal likelihood of
being selected…
….use table of random numbers …or computer
generate a series of random numbers…
Stratified
When
the population
is heterogeneous
overall, but within it
there are
homogeneous
populations (strata)
the population is
stratified.
Systematic
Selecting
a random
sample, as opposed
to the simple random
selection technique.
Select the K-th item.
Draw every I-th item.
Cluster
Another
modified
random sample design
-- requires that the
sample unites be
grouped in clusters in
the universe.
Not grouped by
homogeneous strata in
the population.
Multistage
The
selection procedure takes place in
a hierarchy of stages.
–
–
–
–
–
first
second
third
.....
last
primary sample unit
second sample unit
tertiary sample unit
final (or ultimate) sample unit
Multistage - An Example
The president of Supermarkets, Inc.
decided to sample purchases at 150
stores in the US.
The first stage is to select, on the basis of
clustering (save travel time), 15 of the
150 stores.
Multistage - An Example
The researcher recommends that cash register
files be randomly selected at each of the
150 stores. [second stage]
Then select every 20th purchase in a file using
a random start. [final stage]
Comparison of Survey
Sampling Designs
Simple Random
 How
to Select
– assign numbers to
elements using
random numbers
table
 Strengths/Weaknesses
– basic, simple, often
costly
– must assign a number
to each element in
target population
Stratified
 How
to Select
– divide population
into groups that are
similar within and
different between
variable of interest
 Strengths/Weaknesses
– with proper strata, can
produce very accurate
estimates.
– less costly than
simple random
sampling
– must stratify target
population correctly
Stratified

One of the main reasons for using a
stratified sample is that stratifying has the
effect of reducing sampling error for a given
sample size to a level lower than that of a
simple random sample of the same size.
Stratified
This is so because of a very simple
principle: the more homogeneous a
population is on the variables being studied,
the smaller the sample size needed to
represent it accurately.
 Stratifying makes each sub-sample more
homogeneous by eliminating the variation
on the variable that is used for stratifying.

Systematic
 How
to Select
– select every K-th
element are from a
list after a random
start
 Strengths/Weaknesses
– produces very accurate
estimates when
elements in population
exhibit order
– used when pop. size
not known
– simplifies selection
process
Cluster
 How
to Select
– randomly choose
clusters and sample
all elements within
each cluster
 Strengths/Weaknesses
– with proper clusters,
can produce accurate
estimates
– useful when sample
frame not available or
travel costs high
– must cluster target
population correctly
Convenience





in Dining Commons at
dinner…
in Student Union
between classes…
in classes in which you
are enrolled…
data available on the
www…
friend knows somebody
who...
Mini-Cases
Working as a team…
… determine best sampling technique
and explain decision
Scenario 1

You have been hired by the County of
Sacramento to estimate the percentage of
registered voters that favor issuing a bond in
order to finance the construction of a new
bike trail along the Sacramento River. You
want no more than a  4 percentage point
error margin, at the 95% confidence level.
How would you conduct such a survey
using a simple random sample?
Scenario 1
(continued)
 When
going over your sampling design
with the county Parks Director, you are
asked whether you think a stratified sample
would be appropriate? What is your reply?
Why?
 What
about a systematic sample?
Travel Vouchers
Fly the Friendly Skis
Scenario #2
o
The State of California has hired you to
estimate the number of travel vouchers for
legislators that have been filed incorrectly.
The vouchers have been filed as they are
processed.
o
Which sampling technique would you
recommend and why?
Light Rail
Scenario #3

Light Rail has hired you to determine
whether passengers like the convenience of
using the light rail system.

Which sampling technique would you
recommend and why?

Other concerns that might be investigated?
Trucks
Scenario #4
 Marketers,
Inc., has hired you to determine
why so many young drivers, both male and
female, prefer owning a pickup truck as
compared to an automobile.
 Which
sampling technique would you
recommend and why?
Merit Pay
Scenario #5
 You
have been hired to determine how
faculty at a local university feel about the
following statement: “…the union is
seeking to obtain a moratorium on merit
pay.”
 Which
sampling technique would you
recommend and why?
Questions?
References
 Levine,
David, et al. Statistics for
Managers, Second Edition. Upper Saddle
River, NJ: Prentice-Hall, 1999.
 Monette,
Duane R., et al. Applied Social
Research New York: Holt, Rinehart and
Winston, 1986.