Part one: Designing Survey Samples
1.1 Overview: sampling
2016/3/11
www.uic.edu.hk/~xlpeng
1
What is population?
Population: The group of people, items or units under
investigation.
For example,
 All cars built by a particular company in the year 2001,
 All apples sold as Grade I by a particular supermarket,
 All students in a university, all smokers.
2016/3/11
www.uic.edu.hk/~xlpeng
2
What is a sample?
Sampling frame: A list of members of the
population of interest.
Sample: A subset of a population.
Sampling unit: each member of the population.
When the sampling units are people, the
sample is often referred to as a sample survey.
2016/3/11
www.uic.edu.hk/~xlpeng
3
Sampling Frame

It should be comprehensive, complete and
up-to-date.
Examples of sampling frame:
 Electoral Register (选民名册);
 Telephone book of Zhuhai;
 Student namelist of this course.
 Any others?
Why Sample the Population?
The cost of studying all
the items in a population.
The time-consuming
aspect of contacting the
whole population.
The destructive
nature of certain
tests.
The adequacy of
sample results in
most cases.
Sampling design is very important!
Before analyzing data statistically, it is important to
consider if the data were collected appropriately.

Many years of labor and even careers have been
virtually wasted because of fundamental flaws in the data
collection step.

The statistical analysis will only likely be a minor part of
the total expense of a properly conducted experiment, so
time, effort, and money spent ensuring the data are
collected appropriately is certainly well spent.

About the sample size

Theoretically, the larger, the better.
However, observations cost money, time and talent.

If the sample size is too small, we have bought the
inadequate for the time and effort expended and
have again been wasteful.
Probability and Non-Probability Sampling

A probability sample is one in which each
member of the population has an known chance
of being selected.

In a non-probability sample, some people have
a greater, but unknown, chance than others of
selection.
Types of Sampling
Samples
Non-Probability
Samples
Purposive
Quota
Snowball
Convenience
Probability Samples
Simple
Random
Stratified
Systematic
Cluster
Types of Probability Sampling




Simple Random Sampling
Systematic Sampling
Stratified Sampling
Cluster Sampling
Simple Random Sampling
If a sample of size n is drawn from a population of size N in such
a way that every possible sample of size n has the same chance
of selected, the sampling procedure is called simple random
sampling.
For example, randomly pick two different people from a
group of 15:
Number the people from 1 to 15; and write their numbers on
15 different slips of paper.
Thoroughly mix the papers and randomly pick two of them.
The numbers on the slips identifies the people for the
sample.
Drawing the Random Sample
If the population is large, use a table of random numbers.
In large sampling projects, tables of random numbers are
often used to automate the sample selection process.


See Table 1.1 for a table of random numbers.
For a demonstration of the use of random numbers,
-- Use random numbers to randomly select 100
employees from a bank which has 2,136 employees.
Random numbers can be computer-generated.
The Purpose in Example 1.1

A bank bought a 500-minute plan for its 2136
employees, and the bank is going to estimate its
cellular phone cost. However, it is time consuming to
study all 2136 employees’ mobile phone minutes.

Instead, the bank plans to draw some conclusions
on phone cost by studying the number of minutes
used last month by each of 100 randomly selected
employees.
How to Draw a Random Sample in
Example 1.1 ?







The bank makes a numbered list of the 2136 employees
(the list is called a frame).
Use a random number table (see Table 1.1a)
Each number in the table has 5 digits.
Use the last digit if the population size <10.
Use the last two digits if the population size < 100.
…….
As in the example, the size of the poplation is 2136, we
need to use the last four digits.



Arbitrarily select any set of last four digits in the
table which is not greater than 2136, say choose
0511 from 90511, which is the first randomly
selected employee.
Moving in any direction from 0511 (up, down, right,
or left), if the four digits > 2136, ignore it; otherwise
accept it as the next randomly selected employee.
Continuing this procedure until we obtain the entire
random sample of 100 employees (phone users).
Systematic Random Sampling
(系统抽样)
Every kth member of the population is sampled,
with a random start .

The items or individuals of the population
are arranged in some order.
 A random starting point is selected and
then every kth member of the population is
selected for the sample.
它是先将总体中各单位按一定的标志排队，然后每隔一定的距
离抽取一个单位构成样本。
Systematic Random Sampling

Population elements are an ordered
sequence (at least, conceptually).
k=

The first sample element is selected
randomly from the first k population
elements.

Thereafter, sample elements are
selected at a constant interval, k, from
the ordered sequence frame.
N
n
Where:
n = sample size
N = Population size
k = size of selection
interval
Example 1.2 Rating a New Bottle Design



A soft drink company has designed a new
bottle, and wants to know consumer reaction
to the new design.
The company shows the new design to a part
of shoppers in a big shopping mall, and asks
them to rate the bottle image.
The image will be measured by combining
consumers’ response to five items in a survey
form.
How to Draw a Random Sample in
Example 1.2 ?



In the example, it is not possible to list and number
each shopper at the mall while the study is being
conducted. Consequently, we cannot use random
number table and computer codes.
Instead, we can select every kth (say k=100)
shopper passing a specific location in the mall, and
invite him/her to participate in the survey.
A sample obtained by this way is called a systematic
sample.
Systematic Random Sampling: Example





Purchase orders for the previous fiscal year
are serialized 1 to 10,000 (N = 10,000).
A sample of fifty (n = 50) purchases orders is
needed for an audit.
k = 10,000/50 = 200
First sample element randomly selected from
the first 200 purchase orders. Assume the
45th purchase order was selected.
Subsequent sample elements: 245, 445,
645, . . .
Systematic Random Sampling

Systematic random sampling is convenient and relatively
easy to administer, hence less selection errors.

Another example: The historic event leading to the word
decimate, where every 10th Roman soldier was killed, is
a gruesome example of systematic sampling.
Stratified Random Sampling (分层抽样): A
population is first divided into subgroups, called
strata, and a sample is selected from each stratum.
它是按照某一标志，先将总成分成若干组（类），其中每一组
(类)称为一层，再在层内按简单随机抽样方法进行抽样
Example of stratified sampling
If we want to ensure that a sample of 5 students from a group of
50 contains both male and female students in same proportions
as in the full population (i.e. the group of 50) .
we first divide that population into male and female.
To work out the number of males and females in the
sample........

No. of males in sample = (5 / 50) x 22 = 2.2

No. of females in sample = (5 / 50) x 28 = 2.8
“Round" the numbers and we choose 2 males and 3 females in the sample.
These would be selected using simple random or systematic sample methods.
Stratified Random Sampling
Strata 1 : Gender
Male
Female
Strata 2 : Age Strata 3 : Occupation
< 20
professional
20-30
clerical
31-40
blue collar
41-50
other
51-60
> 60
We can acquire about the total population, make
inferences within a stratum or make comparisons
across strata
Stratified Random Sampling
After the population has been stratified, we can use
simple random sampling to generate the complete
sample:
If we only have sufficient resources to sample 400 people total,
we would draw 100 of them from the low income group…
…if we are sampling 1000 people, we’d draw
50 of them from the high income group.
Reasons for using stratified random sampling

Stratification may produce a smaller error of
estimation.

Estimates of population parameters may be
desired and compared for subgroups.
Cluster Sampling (整群抽样): A population is
first divided into primary units then samples are
selected from the primary units.
整群抽样是先将总体按某一标志分成若干组，其中每个组称为一个群
，以群为单位进行简单随机抽样，然后对抽到的每个单位都进行调查
。
Cluster Sampling
is divided into several “clusters,”
each representative of the population.
 Population
A

simple random sample of clusters is selected
All items in the selected clusters can be used, or
items can be chosen from a cluster using another
probability sampling technique
Population
divided into
16 clusters.
Randomly selected
clusters for sample
Other examples for cluster sample:


City blocks are frequently used as clusters of households
or people .
An automobile forms a nice cluster of four tires for
studies of tire safety.
Cluster sampling is an effective design under the following
conditions:
A good frame listing population elements is not easy
or very cost to obtain, while a frame listing clusters is easily
obtained.
Deference between stratified random
sampling and cluster sampling

In stratified random sampling, we take a
simple random sample within each group;

In cluster sampling, we take a simple random
sample of groups and then all items within
the selected groups (clusters).
Identify the type or types of sampling used-George went through the telephone book and called
every 89th person listed.

Four people divided the telephone book evenly and
each randomly sampling from their portion.


All people with a 461 telephone exchange are called.
Every 5th block of 10 students leaving the Eau Claire
High School cafeteria on June 31 is exhaustively sampled
about their faith in random samples.

(Judgement Sampling)
Examples

Hand Picking People at a Shopping Center that Fit a
Particular Description

Soliciting Participation from Students in Just One
Section of a Course when Many Different Sections
are Offered and of Interest

Only Soliciting Participation from UIC Students when
the Population of Interest is College Students in All
of China
Quota Sampling

Selection Procedures are Similar to Purposive
Sampling

Essentially, the Major Difference is that Sample
Representativeness is of Utmost Importance –
Specifically, the Proportion of Various Elements in
the Sample is Supposed to Closely Match that in the
Population (or, at least, our best guess, most trusted
estimate, etc. of those proportions in the population)
Examples

Hand Picking People at a Shopping Center
Until We Obtain (n=70) Female Shoppers &
(n=30) Male Shoppers

Soliciting Participation from UIC Students
Until We Have 2.5 Times as Many DBM
Students as DST Students for Our Study
Examples





People Living with HIV/AIDS
People with Rare Genetic Disorders
Celebrities
Seniors/Elders
Prisoners