hw.2

7

Sampling

S
o far, this book has mostly addressed the planning stages of research. Now
we will move into the stages of choosing what variables to observe and
gathering data. In this chapter, we will investigate the issue of sampling.

This chapter looks at different sample options and examines which ones are more
or less likely to offer an adequate representation of a population. We will discuss
sample size, two types of sampling— probability sampling and nonprobability
sampling— and several techniques for sample selection.

W H AT I S S A M P L I N G?

One of the goals of research is to draw conclusions from a sample of observed
cases in a population. In research, a population is a group of people affected
by a research problem or question. You, the researcher, define what the pop-
ulation is that you are going to study. For example, if you are interested in
examining the effects of team- building exercises with children in foster care,
you may select the families in your state who are providing foster care as the
population you are studying. Your sample would be drawn (selected) from
this group.

In most studies it is impossible to study all pertinent cases in a population, so
we must choose a sample of the elements within the population. For example, it
is not possible to study every case of binge drinking on every US college campus
or even on a single campus. When we select a subset from a population, this
group is referred to as a sample. Sampling allows the researcher to make the best
use of time, money, and other resources.

A sample is a group of elements selected from a larger population in the hope
that studying this smaller group will reveal important things about the group and
that it may represent the larger population of that group. Sampling, then, is the
process of selecting elements from which observations will be made. People do
this every day: students take their first social work class and imagine what the rest
of their social work classes will be like. Or you might meet a victim of domestic

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100 R E S E A R C H M E T H O D S F O R S O C I A L W O R K E R S

violence and make generalizations about other instances of domestic violence or
domestic violence victims. While people sample daily, they rarely think about good
and bad sample experiences and can therefore come to inaccurate conclusions.

Social and behavioral sciences research is often conducted on individuals or groups
(e.g., hospitals, schools, and families). A sampling frame is a list of all elements or
other units containing the elements in a population. For example, we are going to
survey all the students living in a dorm about the quality of food on campus, but we
can only obtain a list of the rooms (not the residents) in the dorm. Therefore, we will
be drawing our sample from the dorm rooms, which are called enumeration units,
as opposed to the individual students in each dorm room, who are the elements. An
enumeration unit contains one or more units to be listed in the sampling frame.

There are times when the researcher samples different elements within a sam-
pling frame. For instance, we could sample the dorm rooms about the quality of
food at the university and then sample individual students on campus about the
quality of the food. Both the dorm rooms and the individual students would be
called sampling units. A sampling unit is a population selected for inclusion within
a sampling frame. The dorm rooms are selected in the first stage of sampling and
become the primary sampling units (they are also the elements in the study). The
general student population becomes the secondary sampling units because they
are not necessarily elements of the study as some students do not reside on campus.

R A N D O M S E L E C T I O N A N D R A N D O M A S S I G N M E N T

Researchers can derive a sample using random selection, a means of selecting a
sample from a larger population in which each member of the population has an
equal chance of being selected for a study, or by random assignment, the selec-
tion and placement of individuals from the pool of all potential participants to
either the experimental group or the control group.

For example, let’s say you want to know if studying in a group results in a better
grade in research classes than does studying individually. There are four sections
of a research class offered this semester. Ideally, you would want to survey all the
students in these classes, but, for the purpose of this example, you randomly select
half of them from the class rosters (for instance, every other person on the roster
lists). This is random selection. Then, you randomly assign members into one
of two groups (perhaps by drawing names out of a hat). One group (the experi-
mental group) studies together, and the members of the other group (the control
group) study on their own. This is random assignment.

S A M P L E S I Z E :  H OW M A N Y I S E NOUG H ?

As researchers, we need to be confident that our sample is representative of
the population from which it was drawn. Representativeness is assumed when

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Sampling 101

characteristics of the sample are similar to those of the population from which
the sample was drawn. There are several ways that we can ensure representa-
tiveness. One of the easiest ways is to have a large enough sample. We know
that a very small sample can be misleading. For example, interviewing three
survivors of Hurricane Katrina about their intent to return and rebuild their
homes might reveal that all three do not plan to return to their hometown;
however, a larger sample may reveal that while some report no intention of
returning, many more plan to return and rebuild. Unfortunately, there are no
hard and fast formulas to use to determine the appropriate sample size. There
are, however, some guidelines that you can use. One technique that is widely
utilized (and has gained widespread acceptance) is simply counting the number
of variables in your study and then selecting a certain number of cases for each
variable. Different researchers have different opinions on what that number of
cases should be, but most people agree that between ten and twenty cases per
variable is adequate. Thus, if you had ten variables, you would need a sample size
of between 100 and 200 subjects. Therefore, for many researchers, the challenge
is not having a large enough number of variables in the study but recruiting
enough subjects to participate.

E X T E R N A L A N D I N T E R N A L VA L I D I T Y

One goal of many research studies is to apply findings beyond the group from
which they were drawn. For example, you study the activities of gang members
in one city to try to understand gang activity in all cities. This makes sampling
an important process in conducting research. External validity (sometimes re-
ferred to as generalizability) is the extent to which a study’s findings are appli-
cable or relevant to a group outside the study (often the population from which
the sample was drawn). The more that a study can be generalized to a larger pop-
ulation, the more external validity the study has. Internal validity, in its simplest
form, refers to how confident the researcher can be about the independent var-
iable truly causing a change in the dependent variable (as opposed to outside
influences).

Externa l Va lidity

External validity cannot be quantified in terms of a specific set of guidelines.
However, it can be evaluated in light of several characteristics. One characteristic
is whether the study is explained in enough detail that other researchers could
duplicate the study if they wished. The more a study can be replicated, the more
external validity it assumes. Two other characteristics of external validity are
related to how the sampling was conducted: how the respondents of the measure
were chosen and the size of the sample.

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102 R E S E A R C H M E T H O D S F O R S O C I A L W O R K E R S

Interna l Va lidity

Internal validity is different from the validity of a measure. Internal validity is a
measure of the worth of the overall research design. It exists when a conclusion
that A leads to or results in B is correct. When designing your research study, you
need to keep in mind the following seven threats to internal validity:

1. Extraneous and widespread events that coincide in time with your
study: For example, you are working with students in an after- school
program to teach seventh- graders social empathy skills. How do you
know that the repercussions of the aftermath of recent hurricanes,
wildfires, and other natural disasters and events such as mass shootings
did not affect the student’s empathy?

2. Maturation or the passage of time: The passage of time during a study
(especially for studies lasting months or years) can have an effect. For
example, we know that people commit less crime as they become sick
or weak. Therefore, if you were researching crime among older adults,
factors associated with age alone may account for a lower incidence of
crime in older respondents.

3. Enhanced test- testing skills: After taking a test the first time,
respondents’ performance on subsequent tests often improves. For
example, imagine that we are conducting a workshop for consumers
in a homeless shelter on effective job- interviewing techniques. We give
participants a pretest and then provide a workshop on techniques for
effective job interviewing. After the workshop, we give the participants
the same test again (posttest). If they scored significantly better on the
posttest, we might be tempted to argue that it was the workshop that
made the difference. However, we can’t be certain that taking the pretest
didn’t prepare them to do better on the posttest.

4. Instrumentation: If different measures are used for the pretest and
posttest, how do we know that the posttest is not easier than the pretest?
For example, an easier posttest might inflate the difference in scores
and thus affect the findings of the study. In other words, the results may
be inaccurately reporting that the intervention was effective. Problems
involving instrumentation can also develop when a researcher uses a
measure that is not measuring what it is intended to measure or that is
not normed for the population to whom it was given.

5. Selection bias: Selection bias refers to the differences between groups
that are being compared that occur when group members choose
which group (the treatment group or nontreatment group) to be in.
The differences between the members of the two groups might explain
away any change that occurred after the intervention. For example,
participants who self- select to be in a treatment group dealing with
attitudes toward feminism may already be more politically liberal. It is

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Sampling 103

important to make sure selection bias is eliminated as much as possible
through randomization.

6. Experimental mortality: This refers to subjects dropping out of a study.
This is one of the most common threats to internal validity and can
affect sample size (you may not have enough respondents left at the end
of the study to have a meaningful finding) and generalizability (your
study no longer represents the characteristics of the population your
sample came from).

7. Ambiguity about the direction of causal inference: To establish causation,
the independent variable must precede (cause) the change in the
dependent variable. For example, studies looking at substance abuse
and mental health issues have established that there is a relationship
between the two variables. What is not clear is which variable precedes
the other.

One of the best ways to control for threats to internal validity is to use a group to
compare the study group to, which strengthens the study. By having a nonstudy
group to compare against the study group, the researcher can make a stronger
argument that any change in the study group is due to the intervention, not to
outside influences.

P RO B A B I L I T Y S A M P L I N G

In probability sampling, each and every member of the population has a chance
of being selected for the study (being included in the sample). Probability sam-
pling allows the researcher to make relatively few observations and generalize
from those observations to the wider population. Because everyone in the pop-
ulation has an equal chance of being selected for the study, we can (theoreti-
cally) assume that results from the study can be generalized to the population
studied. We will examine some of the most common techniques for probability
sampling.

P RO B A B I L I T Y S A M P L I N G T E C H N I QU E S

Four types of sampling techniques are used in probability sampling:  simple
random sampling, systematic random sampling, stratified random sampling,
and cluster sampling.

In simple random sampling, each person in the population is assigned a
number and then a sample is generated randomly from this population. This
technique requires the compilation of a list of everyone in the population, such
as all residents in a nursing home. The process for selecting the sample can be as
simple as drawing numbers from a hat that then will be matched to the names

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104 R E S E A R C H M E T H O D S F O R S O C I A L W O R K E R S

on the list. When drawing a sample from a population, one can return or not
return subjects to the sampling space after each draw. Returning a number to
the hat after it is drawn is called sampling with replacement and is a preferred
method. When one is using sampling with replacement, each selection from
the population is independent of the selections already made. For example, if
your population at the nursing home had twenty- five individuals (elements) to
select from and you were to randomly select individual number 4, that indi-
vidual would become part of your sample. Then you go back to your original
twenty- five elements and draw again, leaving the number 4 as an option. If you
draw number 4 again, you return it to the hat and continue to draw until you get
a different number to add to your sample. Drawing a sample without returning
elements to the hat is called sampling without replacement.

For systematic random sampling, every nth number is selected at random (for
example, every third person or every tenth person). In essence, this is identical
to simple random sampling but uses a more organized technique to produce the
sample. Here, simple random sampling is always used to select the first number.
For example, if you want to draw a systematic sample of 1,000 individuals from a
student roster containing 100,000 names, you would divide 100,000 by 1,000 to
get 100, meaning you would select every 100th name on the list. You would start
with a randomly selected number between 1 and 100. For example, if you started
with the number 47, you would then select the 147th name, the 247th name, the
347th name, and so on.

Stratified random sampling is a method for obtaining a greater degree of rep-
resentativeness. Remember, probability sampling theory requires the researcher
to select a set of elements from a population in such a way that those elements ac-
curately portray the parameters of the total population from which the elements
are selected. To do this, you divide your population into subgroups, or strata (for
instance, by sex), then you draw the sample from each stratum using a probabi-
listic procedure.

Cluster sampling (sometimes referred to as multi- stage sampling) is a method
for drawing a sample from a population in two or more stages. This is used when
the researcher cannot get a complete list of everyone in the population but can get
complete lists within clusters of the population (such as the population of a city
from a phonebook). Generally, the researcher wishes to get clusters that are as di-
verse as possible, whereas in stratified random sampling the goal is to find subjects
who are as similar to one another as possible. Cluster sampling is accomplished
through two basic steps:  listing and sampling. Listing entails constructing a list
of a subset of the population. Sampling occurs within your chosen clusters. The
disadvantage is that each stage of the process increases sampling error. In fact, the
margin of error is larger in cluster sampling than in simple random or stratified
random sampling. However, one can compensate for this error by increasing the
sample size.

Perhaps you are examining child maltreatment reports by grade level in your
thirteen- county region. You get a list of the schools for each county (primary

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Sampling 105

cluster list) and identify a random sample of approximately 30% from each
county (secondary cluster list). See Table 7.1 for an example. You will then collect
child maltreatment reports by grade level in each identified school. A sample of
clusters will best represent all clusters if a large enough number is selected and if
all clusters are very much alike.

Table 7.1. Example of Cluster Coding by County

County Number of Elementary
Schools in Each County
(Primary List)

Identified Schools
(Secondary List)

Fargo 6 Jefferson Elementary
Jackson Elementary

Bishop 3 Washington Elementary

Johnson 7 Lincoln Elementary
Carter Elementary

Sewer 5 Clinton Elementary
Bush Elementary

Lake 8 Adams Elementary
Buchanan Elementary

Lincoln 10 Johnson Elementary
Kennedy Elementary
Lincoln Elementary

Norman 2 Roosevelt Elementary

Tulane 6 Reagan Elementary
Grant Elementary

Orange 5 Taft Elementary
Garfield Elementary

Camargo 5 Fillmore Elementary
Harding Elementary

Fisher 9 Hoover Elementary
Hayes Elementary
Tyler Elementary

Newman 5 Harrison Elementary
Wilson Elementary

Angel 5 Nixon Elementary
Reagan Elementary

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106 R E S E A R C H M E T H O D S F O R S O C I A L W O R K E R S

S A M P L I N G E R RO R

A sampling error occurs because only part of the population is directly contacted.
With any sample, differences are likely to exist between the characteristics of the
sampled population and the larger group from which the sample was chosen.
Sampling error can be reduced in two ways. First, the larger the sample is, the
smaller the sampling error. For instance, a sample size of 10% of the population
will have less sampling error than a sample size of 5% of the population because
more of the original population is represented within your sample. Second, a ho-
mogenous population produces samples with smaller sampling errors than does
a heterogeneous population. Stratified random sampling is based on this second
method. Rather than selecting your sample from the total population, you en-
sure that appropriate numbers of elements are drawn from homogenous subsets
of the population. This means you break the sample into smaller sections with
similar qualities such as age, sex, race, and occupation. For example, you want
to measure client satisfaction with the services in a large social service agency.
You suspect that race is a factor in consumer satisfaction. So, you separate your
participants according to race and then randomly select an appropriate number
from each racial category (proportionate to the number of individuals in the cat-
egory). For example, if you had one hundred whites and fifty African- Americans,
you might randomly select twenty whites and ten African- Americans (one- fifth
of each group) to sample. Again, stratified random sampling is used most often
when a simple random sample cannot guarantee enough representation from
small subgroups that are important to your study.

NO N P RO B A B I L I T Y S A M P L I N G

Social work is often conducted in settings where it is not possible to use random
selection of subjects or random assignment to an experimental or comparison
group. This occurs for a variety of reasons. Often, a list of possible respondents
for a particular study does not exist. Also, a researcher is often only able to
find subjects who are willing to volunteer for one group (such as the treatment
group) as opposed to being randomly assigned. Sometimes finding participants
willing to join either group can be a problem. So, a second form of sampling
is available:  nonprobability sampling. Any technique for selecting a sample
in which every individual does not have a greater than zero chance of being
selected is a nonprobability sampling technique. There are four sampling
techniques used in nonprobability sampling:  convenience, purposive, quota,
and snowball sampling.

Convenience sampling is sampling in which one relies on available subjects.
That is, you get information from any source of data you can. This is one of
the most frequently used sampling techniques in social work research. Some
examples of researchers who use this would be a caseworker who studies her own
agency, a college professor who studies students at his college, or a researcher

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Sampling 107

who observes people in her own church. This type of sampling limits the gen-
eralizability of the research to the population from which the sample is drawn.
Another drawback to this method is that it can be subject to sampling error be-
cause of researcher bias (selecting the sample that gives the best outcome).

Purposive sampling (also called judgmental sampling) is simply selecting a
sample based on one’s knowledge of a population or drawing a sample with
some predetermined characteristics in mind. For example, perhaps you are a
caseworker at an agency that assists consumers in obtaining assistance with
utility bills. You need to do a study for a grant that would help quantify the
characteristics of your participants (such as whether they rent or own their
homes, whether they are employed, their level of education, their income level).
Because your study must be completed soon and it is the middle of a cold winter,
you decide to select those individuals who are requesting assistance for electric
bills. You feel that individuals who seek assistance for electric bills reflect the
majority of your clientele, as opposed to clients who seek assistance with tele-
phone payments.

Quota sampling is a means of selecting a stratified nonrandom sample in
which a researcher divides a population into categories and selects a certain
number (a quota) of subjects from each category. Individual subjects from
each category are not selected randomly; they are usually chosen on the basis
of convenience and ease. Imagine that you are studying the treatment of
individuals in a mental health setting. You want to see if professionals with
different professional training treat clients in different ways. So your sample
includes the psychiatrists, psychologists, and social workers who are willing
to participate.

In snowball sampling, the researcher starts with one or more members of the
group being studied to gain access to other members of the same group through
a referral system for the purpose of building the sample. Snowball sampling is
most appropriate when members of a population are difficult to locate. For ex-
ample, if you are studying women who have disabled children and you are having
difficulty locating these mothers, you may find that once you have established
a relationship with one mother, she may be willing to introduce you to other
women who have disabled children. Snowball sampling is also often used when
the group being studied is engaged in an activity that is illegal or considered to be
deviant. For example, to study members of a gang, you need referrals to members
of the gang. The strength of this type of sampling is that it creates access that
allows you to increase the sample. However, because friends and other associates
are usually very similar, there may be little variation in the study.

L I M I TAT I O N S O F N O N P RO B A B I L I T Y S A M P L I N G

Although nonprobability sampling may be more convenient, it is less likely to
be representative of your population than probability sampling techniques.
Remember that nonprobability sampling techniques do not require that every

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108 R E S E A R C H M E T H O D S F O R S O C I A L W O R K E R S

member have a greater than zero chance of being selected. Your study is affected
if those not included in your sample differ in some way from the rest of the pop-
ulation. Therefore, a random sample will have more generalizability than a con-
venience sample or any sample where subjects are self- selecting. For example, it
might be misleading to apply the findings of a researcher who only studies gangs
in Southern California to other areas of the United States because of differences
in population size and characteristics, gang- related laws, law enforcement
capabilities, and gang prevention programs. One question to ask is “How much
does the sample reflect the population from which it was drawn?” For obvious
reasons, a larger sample size would have more generalizability than a smaller one
because the study is taking into account more of the actual population.

So when is nonprobability sampling most useful? Some examples are pilot
studies in which you are doing a trial run, agency- based research, and qualita-
tive investigations in which you’re not striving for generalizability but rather to
reproduce and understand real life.

C A S E S C E N A R I O

As part of your research class assignment, you and three of your fellow students have
been assigned to work together in a group. You have been given the task of finding
out if there is any relationship between how much alcohol students consume on
weekends and their academic majors. To determine this relationship, you and your
group members wait outside one of the residence halls on campus, and, as students
enter and leave the building, you ask if they would be willing to complete your survey.

C R I T I C A L T H I N K I N G QU E S T IO N S

Based on the scenario just presented, answer the following questions:

1. What type of sampling design would you and your group members be
utilizing?

2. Would you consider your sampling to be probability or nonprobability?
State your reasons for your answer.

3. What would you consider to be an adequate sample size? How did you
arrive at this number?

K E Y P O I N T S

• Sampling is the process of selecting a group of subjects from a larger
population in the hope that studying this smaller group (the sample)
will reveal important things about the larger group (the population)
from which it was drawn.

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Sampling 109

• Probability sampling is a method of sampling in which everyone in
the population has an equal chance of being randomly selected for the
study and randomly assigned to either the experimental group or the
comparison group.

• There are four techniques for conducting probability sampling: simple
random sampling, systematic random sampling, stratified random
sampling, and cluster sampling.

• Nonprobability sampling is a method for selecting a sample where every
member does not necessarily have a greater than zero chance of being
selected.

• There are four techniques for conducting nonprobability
sampling: convenience, purposive, quota, and snowball sampling.

• Internal validity refers to how confident the researcher can be about
the independent variable truly causing a change in the dependent
variable. There are seven threats to internal validity: extraneous events,
passage of time, testing effect, instrumentation problems, selection bias,
mortality of sample, and lack of casual direction.

• External validity (referred to as generalizability) is the extent to which a
study’s findings are …