(Reminder: Don’t forget to utilize the concept maps and
study questions as you study this and the other chapters.)
The purpose of Chapter 7 it to help you to learn about
sampling in quantitative and qualitative research. In other words, you will
learn how participants are selected to be part of empirical research studies.
Sampling refers to drawing a sample (a subset) from a population (the
usual goal in sampling is to produce a representative sample (i.e.,
a sample that is similar to the population on all characteristics, except
that it includes fewer people because it is a sample rather than the
a perfect representative sample would be a "mirror image" of the
population from which it was selected (again, except that it would include
Here are some important terms used in sampling:
sample is a set of elements taken from a larger population.
sample is a subset of the population which is the full set of
elements or people or whatever you are sampling.
- A statistic
is a numerical characteristic of a sample, but a parameter is a
numerical characteristic of population.
error refers to the difference between the value of a sample
statistic, such as the sample mean, and the true value of the population
parameter, such as the population mean. Note: some error is always present
in sampling. With random sampling methods, the error is random rather than
- The response
rate is the percentage of people in the sample selected for the study
who actually participate in the study.
- A sampling
frame is just a list of all the people that are in the population.
Here is an example of a sampling frame (a list of all the names in my population,
and they are numbered). Note that the following sampling frame also has
information on age and gender included in case you want to draw some
samples and do some calculations.
Random Sampling Techniques
The two major types of sampling in quantitative research are
random sampling and nonrandom sampling.
former produces representative samples.
latter does not produce representative samples.
Simple Random Sampling
The first type of random sampling is called simple random
the most basic type of random sampling.
is an equal probability sampling method (which is abbreviated by EPSEM).
that EPSEM means "everyone in the sampling frame has an equal chance
of being in the final sample."
should understand that using an EPSEM is important because that is what
produces "representative" samples (i.e., samples that represent
the populations from which they were selected)!
You will see below
that, simple random samples are not the only equal probability sampling
method (EPSEM). It is the most basic and well know, however.
experts recommend random sampling "without replacement" rather
than random sampling "with replacement" because the former is a
little more efficient in producing representative samples (i.e., it
requires slightly fewer people and is therefore a little cheaper).
“How do you draw a simple random sample?"
- One way is to put all the names from
your population into a hat and then select a subset (e.g., pull out 100
names from the hat).
the chapter we demonstrate the use of a table of random numbers.
days, researchers often use computer programs to randomly select their
is a program the you can easily use for simple random sampling, just click here.
- To use a computer program (called a
random number generator) you must make sure that you give each of the
people in your population a number. Then the program will give you a list
of randomly selected numbers within the range you give it. After getting
the random numbers, you identify the people with those randomly selected
numbers and try to get them to participate in your research study!
you decide to use a table of random numbers such as the one shown on page
201 of the book, here’s what you need to do. First, pick a place to start, and then move in
one direction (e.g., move down the columns). Use the number of digits in the table
that is appropriate for your population size (e.g., if there are 2500
people in the population then use 4 digits). Once you get the set of randomly
selected numbers, find out who those people are and try to get them to
participate in your research study. Also, if you get the same
number twice, just ignore it and move on to the next number.
Systematic sampling is the second type of random
- It is an equal probability sampling
- Remember simple random sampling was also
involves three steps:
determine the sampling interval, which is symbolized by "k," (it is
the population size divided by the desired sample size).
randomly select a number between 1 and k, and include that person in your
include each kth element in your sample. For example if k is 10 and
your randomly selected number between 1 and 10 was 5, then you will select
persons 5, 15, 25, 35, 45, etc.
When you get to
the end of your sampling frame you will have all the people to be included in
(but rarely occurring) problem is called periodicity (i.e., there is a
cyclical pattern in the sampling frame). It could occur when you attach
several ordered lists to one another (e.g., if you had took lists from multiple
teachers who had all ordered their lists on some variable such as IQ). On the
other hand, stratification within one overall list is not a problem at all
(e.g., if you have one list and have it ordered by gender, or by IQ).
Basically, if you are attaching multiple lists to one another, there could be a
problem. It would be better to reorganize the lists into one overall list
(i.e., sampling frame).
The third type of random sampling is called stratified
- First, stratify your sampling frame
(e.g., divide it into the males and the females if you are using gender as
your stratification variable).
- Second, take a random sample from each
group (i.e., take a random sample of males and a random sample of
females). Put these two sets of people together and you now have your
final sample. (Note that you could also take a systematic sample
from the joined lists if that’s easier.)
There are actually two different types of stratified
The first type of
stratified sampling, and most common, is called proportional stratified
- In proportional stratified sampling you
must make sure the subsamples (e.g., the samples of males and females) are
proportional to their sizes in the population.
- Note that proportional stratified
sampling is an equal probability sampling method (i.e., it is EPSEM),
which is good!
The second type of
stratified sampling is called disproportional stratified sampling.
disproportional stratified sampling, the subsamples are not proportional to
sizes in the population.
Here is an example showing the difference between
proportional and disproportional stratified sampling:
that your population is 75% female and 25% male. Assume also that you want
a sample of size 100 and you want to stratify on the variable called gender.
- For proportional stratified sampling,
you would randomly select 75 females and 25 males from the population.
- For disproportional stratified sampling,
you might randomly select 50 females and 50 males from the population.
Cluster Random Sampling
In this type of
sampling you randomly select clusters rather than individual type units
in the first stage of sampling.
- A cluster has more than one unit
in it (e.g., a school, a classroom, a team).
We discuss two types of cluster sampling in the chapter,
one-stage and two-stage (note that more stages are possible in multistage
sampling but are left for books on sampling).
The first type of
cluster sampling is called one-stage cluster sampling.
- To select a one-stage cluster sample,
you first select a random sample of clusters.
- Then you include in your final sample
all of the individual units that are in the selected clusters.
The second type of
cluster sampling is called two-stage cluster sampling.
- In the first stage you take a random
sample of clusters (i.e., just like you did in one-stage cluster
- In the second stage, you take a random
sample of elements from each of the clusters you selected in stage one
(e.g., in stage two you might randomly select 10 students from each of the
15 classrooms you selected in stage one).
about cluster sampling:
- Cluster sampling is an equal probability
sampling method (EPSEM) ONLY if the clusters are approximately the same
size. (Remember that EPSEM is very important because that is what
produces representative samples.)
- When clusters are not the same size, you
must fix the problem by using the technique called "probability
proportional to size" (PPS) for selecting your clusters in stage one.
This will make your cluster sampling an equal probability sampling method
(EPSEM), and it will, therefore, produce representative samples.
The other major type of sampling used in quantitative
research is nonrandom sampling (i.e., when you do not use one of the ransom sampling
techniques). There are four main types of nonrandom sampling:
first type of nonrandom sampling is called convenience sampling
(i.e., it simply involves using the people who are the most available or
the most easily selected to be in your research study).
second type of nonrandom sampling is called quota sampling (i.e.,
it involves setting quotas and then using convenience sampling to obtain
those quotas). A set of quotas might be given to you as follows: find 25
African American males, 25 European American males, 25 African American
females, and 25 European American females. You use convenience sampling to
actually find the people, but you must make sure you have the right number
of people for each quota.
third type of nonrandom sampling is called purposive sampling
(i.e., the researcher specifies the characteristics of the population of
interest and then locates individuals who match those
characteristics). For example, you
might decide that you want to only include "boys who are in the 7th
grade and have been diagnosed with ADHD" in your research study. You
would then, try to find 50 students who meet your "inclusion
criteria" and include them in your research study.
fourth type of nonrandom sampling is called snowball sampling (i.e.,
each research participant is asked to identify other potential research
participants who have a certain characteristic). You start with one or a
few participants, ask them for more, find those, ask them for some, and
continue until you have a sufficient sample size. This technique might be
used for a hard to find population (e.g., where no sampling frame exists).
For example, you might want to use snowball sampling if you wanted to do a
study of people in your city who have a lot of power in the area of
educational policy making (in addition to the already known positions of
power, such as the school board and the school system superintendent).
and Random Assignment
In random selection (using an equal
probability selection method), you select a sample from a population using one
of the random sampling techniques discussed earlier.
resulting random sample will be like a "mirror image" of the
population, except for chance differences.
- For example, if you randomly select
(e.g., using simple random sampling) 1000 people from the adult population
in Ann Arbor, Michigan, the sample will look like the adult population of
random assignment, you start with a set of people (you already have a sample,
which very well may be a convenience sample), and then you randomly divide that
set of people into two or more groups (i.e., you take the full set and randomly
divide it into subsets).
- You are taking a set of
people and “assigning” them to two or more groups.
groups or subsets will be "mirror images" of each other (except
for chance differences).
- For example, if you start with a
convenience sample of 100 people and randomly assign them to two groups of
50 people, the two groups will be "equivalent" on all known and
- Random assignment generates similar
groups, and it is used in the strongest of the experimental research
- To see exactly how to do random
- You can also use this randomizer program
for random assignment, just click here.
When Random Sampling is Used
Would you like to know the answer to the question "How
big should my sample be?"
I will start with my four "simple" answers to your
to get as big of a sample as you can for your study (i.e., because the
bigger the sample the better).
your population is size 100 or less, then include the whole population
rather than taking a sample (i.e., don't take a sample; include the whole
at other studies in the research literature and see how many they are
an exact number, just look at Figure 7.5 which shows recommended sample
are many sample size calculators on the web but they generally require you
to learn a little bit of statistics first. Here is one click here.
I’ll list more when we get to the chapter on statistics.
I want to make a few more points about sample size in this
chapter. In particular, note that you will need larger samples under
the population is very heterogeneous.
you want to breakdown the data into multiple categories.
you want a relatively narrow confidence interval (e.g., note that
the estimate that 75% of teachers support a policy plus or minus 4% is
more narrow than the estimate of 75% plus or minus 5%).
you expect a weak relationship or a small effect.
you use a less efficient technique of random sampling (e.g.,
cluster sampling is less efficient than proportional stratified sampling).
you expect to have a low response rate. The response rate is the
percentage of people in your sample who agree to be in your study.
Sampling in qualitative research is usually purposive
(see the above discussion of purposive sampling). The primary goal in
qualitative research is to select information rich cases.
There are several specific purposive sampling techniques
that are used in qualitative research:
variation sampling (i.e., you select a wide range of cases).
sample selection (i.e., you select a small and homogeneous case or set
of cases for intensive study).
case sampling (i.e., you select cases that represent the extremes on
sampling (i.e., you select typical or average cases).
sampling (i.e., you select cases that are known to be very important).
sampling (i.e., you purposively select cases that disconfirm your
generalizations, so that you can make sure that you are not just
selectively finding cases to support your personal theory).
sampling (i.e., you select useful cases as the opportunity arises).
purposeful sampling (i.e., you can mix the sampling strategies we have
discussed into more complex designs tailored to your specific needs).
For a little more information on sampling in qualitative
here. (Hit the right arrow key to move from slide to slide.)