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SamplingSampling

ChapterChapter 77

INTRODUCTION INTRODUCTION 161161

THE THE NANATURE TURE OF OF SAMPLES SAMPLES 163163

OVEROVERVIEWVIEW OF OF PROBABILITY PROBABILITY SAMPLING SAMPLING 164164

PROBABILITYPROBABILITY SAMPLING SAMPLING METHODS METHODS 167167

NONPROBABILITYNONPROBABILITY SAMPLING SAMPLING 170170

CENTRALCENTRAL LIMIT LIMIT THEOREM THEOREM 173173

APPLICAAPPLICATIONS TIONS OF OF THE THE CENTRAL CENTRAL LIMIT LIMIT THEOREM THEOREM 177177

SOURCES SOURCES OF OF BIAS BIAS AND AND ERROR: ERROR: AA REPRISE REPRISE 183183

RESEARCH RESEARCH IN IN ACTION: ACTION: SAMPLING SAMPLING MAMATTERS TTERS 186186

It It is is a a capital capital mistake mistake to to theorize theorize before before one one has has data.data.

—Sir —Sir Arthur Arthur Conan Conan DoyleDoyle

INTRODUCTIONINTRODUCTION

Much Much of of what what we we know know we we learn learn from from studying studying samples samples of of larger larger “populations.” “populations.”

Consider Consider some some common common examples. examples. When When someone someone asks asks you you whether whether the the lunches lunches

at at a a restaurant restaurant are are good, good, you you use use your your experiences experiences to to answer answer the the question. question. The The

meals meals you you have have eaten eaten at at that that restaurant restaurant represent represent a a sample sample of of all all the the possible possible meals meals

that that you you and and others others could could have have eaten eaten at at that that restaurant. restaurant. The The establishment establishment may may

produce produce thousands thousands of of meals meals and and has has served served hundreds hundreds of of customers customers since since its its

opening. opening. YYou ou have have no no way way of of being being sure sure that that each each meal meal was was prepared prepared well well and and

enjoyed. enjoyed. YYet, et, based based on on your your experience experience with with the the restaurant, restaurant, you you make make a a single single and and

confident confident conclusion, conclusion, “The “The food food here here is is good.”good.”

161161

Understanding Understanding and and Conducting Conducting Research Research in in the the Health Health SciencesSciences, , First First Edition. Edition. Christopher Christopher J. J. L. L. Cunningham, Cunningham, Bart Bart L. L. WWeathington, eathington, and and David David J. J. PittengerPittenger.. © © 2013 2013 John John Wiley Wiley & & Sons, Sons, Inc. Inc. Published Published 2013 2013 by by John John Wiley Wiley & & Sons, Sons, Inc.Inc.

162162 Chapter Chapter 7 7 SamplingSampling

The The same same is is true true when when you you meet meet a a person person for for the the first first time. time. Social Social psycholo-psycholo-

gists gists telltell us us that that we we make make long-lasting long-lasting conclusions conclusions based based on on our our first first impressions impressions

of of people. people. Think Think for for a a moment moment of of what what happens happens in in such such situations. situations. After After a a mere mere

five five minutes, minutes, many many people people are are willing willing to to state state confidently confidently that that they they have have formed formed

a a good good impression impression of of another another person; person; that that is, is, an an extremely extremely small small sample sample of of behav-behav-

ior ior creates creates a a lasting lasting impression impression of of that that person. person. Given Given the the complexity complexity of of human human

behaviorbehavior, , this this is is an an amazing amazing conclusion conclusion based based on on such such a a limited limited sample.sample.

As As you you will will recall recall from from Chapter Chapter 1, 1, Bacon Bacon warned warned about about the the idols idols of of the the cave, cave,

relying relying too too much much on on our our personal personal experience experience for for seeking seeking truth. truth. Objective Objective or or sci-sci-

entific entific sampling sampling is is a a way way of of overcoming overcoming the the idols idols of of the the cave cave because because it it ensures ensures

that that our our experiences experiences are are as as broad broad and and representative representative as as possible. possible. MoreoverMoreover, , as as you you

learned learned in in Chapter Chapter 3, 3, having having a a representative representative sample sample of of the the population population in in a a study study

helps helps to to ensure ensure the the external external validity validity of of the the conclusions conclusions we we draw draw from from the the data data to to

other other members members of of the the population.population.

What What are are the the common common features features of of samples samples and and sampling? sampling? First, First, we we use use samples samples

to to describe describe and and compare compare things. things. ConsiderConsider, , as as an an example, example, the the challenge challenge of of describ-describ-

ing ing someone’someone’s s personalitypersonality. . Each Each of of us us is is affected affected by by many many things, things, ranging ranging from from

situational situational factors factors to to interactions interactions with with others, others, and and myriad myriad other other variables variables too too

numerous numerous to to list. list. Even Even for for an an individual, individual, it it would would be be impossible impossible to to observe observe all all the the

things things he he or or she she would would do do under under different different situations. situations. However, However, based based on on a a repre-repre-

sentative sentative sample sample of of that that person’person’s s behaviorbehavior, , we we may may be be able able to to predict predict how how he he or or

she she will will react react to to specific specific situations. situations. This This observation observation leads leads us us to to the the second second feature feature

of of sampling.sampling.

WWe e use use samples samples to to help help us us make make predictions predictions and and conclusions conclusions about about other other

things things or or conditions. conditions. As As the the quotation quotation at at the the start start of of this this chapter chapter suggests, suggests, our our

theories theories are are the the product product of of the the data data we we collect. collect. Perhaps, Perhaps, by by extension, extension, we we can can also also

suggest suggest that that no no theory theory is is any any better better than than the the data data that that either either inspired inspired its its creation creation

or or are are used used to to test test it.it.

How How can can we we be be sure sure tthat hat what what we we observe observe in in a a sample sample accurately accurately represents represents

the the broader broader population? population? This This is is a a critical critical question. question. As As you you learned learned in in Chapter Chapter 3, 3,

such such a a question question is is at at the the heart heart of of external external validityvalidity. . If If the the sample sample is is not not representa-representa-

tive tive of of the the population, population, then then the the data data will will be be of of little little value value to to us us because because they they do do

not not support support inferences inferences about about the the population.population.

Therefore, Therefore, the the purpose purpose of of this this chapter chapter is is to to examine examine the the foundations foundations of of samples samples

and and sampling. sampling. In In the the following following pages, pages, we we will will examine examine the the methods methods researchers researchers

use use to to collect collect accurate accurate samples samples of of the the population. population. In In addition, addition, we we will will review review how how

statistics, statistics, based based on on sample sample data, data, allow allow us us to to make make inferences inferences about about population population

parameters. parameters. Hence, Hence, we we will will begin begin with with a a more more detailed detailed analysis analysis of of the the charactercharacter–

istics istics of of samples. samples. WWe e assume assume that that you you have have had had a a course course in in statistics statistics and and under-under-

stand stand the the foundations foundations of of descriptive descriptive statistics statistics such such as as measures measures of of central central tendency tendency

(e.g., (e.g., mean mean and and median), median), measures measures of of dispersion dispersion (e.g., (e.g., variance variance and and standard standard

deviation deviation [[ ]), ]), and and basic basic standard standard or or -scores. -scores. If If you you are are not not familiar familiar with with these these SDSD zz

statistics, statistics, or or wish wish to to brush brush up up on on your your skills, skills, you you might might benefit benefit from from reviewing reviewing

Appendix Appendix A.A.

The The Nature Nature of of SamplesSamples 163163

THE THE NATURE NATURE OF OF SAMPLESSAMPLES

There There are are several several ways ways that that we we can can define define samples. samples. The The primary primary feature feature of of a a

“good” “good” sample sample for for research research is is that that the the sample sample actually actually represents represents that that population population

from from which which it it was was selected. selected. One One way way to to define define a a sample sample is is to to contrast contrast samples samples

with with things things that that are are not not samples. samples. WWe e can can also also define define samples samples by by the the methods methods used used

to to create create them. them. As As you you may may recall recall from from our our previous previous discussions discussions of of validityvalidity, , we we

cannot cannot directly directly assess assess the the external external validity validity or or the the representativeness representativeness of of a a sample. sample.

RatherRather, , we we examine examine the the methods methods used used to to create create the the sample sample to to infer infer its its validityvalidity. .

ConsequentlyConsequently, , researchers researchers work work hard hard to to ensure ensure that that their their sampling sampling techniques techniques

produce produce useful useful data.data.

Scientific Scientific Samples Samples versus versus Anecdotal Anecdotal EvidenceEvidence

What What is is the the difdifference ference between between sample-based sample-based data data and and other other types types of of infoinformation? rmation?

WWe e can can begin begin by by considering considering personal personal experiences experiences and and anecdotal anecdotal evidence evidence and and

then then compare compare them them to to a a scientific scientific sample. sample. Imagine Imagine a a person person who who traveled traveled to to Paris Paris

for for a a short short vacation vacation and and then then pronounces pronounces the the French French to to be be rude rude and and inconsiderate inconsiderate

people. people. Such Such a a conclusion conclusion is is indefensible. indefensible. AA moment’moment’s s thought thought will will reveal reveal that that

many many factors factors bias bias this this unflattering unflattering conclusion. conclusion. SpecificallySpecifically, , a a stranger stranger traveling traveling

abroad, abroad, spending spending a a short short time time in in a a small small portion portion of of the the countrycountry, , and and interacting interacting

with with a a minuscule minuscule proportion proportion of of the the population, population, cannot cannot come come to to a a meaningful meaningful con-con-

clusion clusion about about the the manners manners of of a a nation nation of of people.people.

Anecdotal Anecdotal evidenceevidence and and personal personal experience experience are are not not sampling sampling in in the the technical technical

sense sense of of the the word. word. Our Our hypothetical hypothetical traveler traveler probably probably did did meet meet several several rude rude and and

inconsiderate inconsiderate people, people, an an experience experience likely likely to to occur occur when when traveling traveling to to any any large large

citycity. . Therefore, Therefore, we we cannot cannot deny deny the the person’person’s s experiences. experiences. WWe e do do deny deny the the validity validity

of of the the conclusion, conclusion, howeverhowever, , because because we we do do not not consider consider that that one one person’person’s s encoun-encoun-

ters ters to to be be representative representative of of the the population.population.

WWe e can can use use the the criteria criteria of of representativeness representativeness to to distinguish distinguish anecdotal anecdotal evidence evidence

and and personal personal experience experience from from scientific scientific samples samples and and empirical empirical conclusions. conclusions. The The

goal goal of of scientific scientific research research is is to to identify identify and and collect collect data data from from samples samples of of partici-partici-

pants pants that that represent represent the the population population that that we we studystudy. . In In an an experimental experimental scenario, scenario,

researchers researchers are are also also interested interested in in creating creating treatment treatment groups groups that that are are equivalent equivalent on on

all all variables variables other other than than the the independent independent variable(s) variable(s) of of interest. interest. From From these these samples samples

and and treatment treatment groups, groups, researchers researchers collect collect data data and and then then have have to to generate generate reasonable reasonable

and and valid valid conclusions conclusions regarding regarding these these data. data. When When we we collect collect the the data, data, we we use use

procedures procedures that that ensure ensure that that the the samples samples will will be be free free of of bias bias and and thereby thereby represent represent

the the population. population. By By contrast, contrast, anecdotal anecdotal evidence evidence is is typically typically a a haphazard haphazard collection collection

of of personal personal experiences experiences that that may may be be biased.biased.

UnfortunatelyUnfortunately, , anecdotal anecdotal evidence evidence too too easily easily sways sways many many pepeople’ople’s s opinions, opinions, an an

observation observation that that Bacon Bacon noted noted when when he he described described the the idols idols of of the the tribe tribe and and idols idols of of

the the cave. cave. Social Social psychologists psychologists have have long long studied studied the the poor poor decision-making decision-making

164164 Chapter Chapter 7 7 SamplingSampling

processes processes that that many many people people follow follow (Plous, (Plous, 1993). 1993). AA well-known well-known phenomenon phenomenon is is the the

“person-who” “person-who” effect effect that that occurs occurs when when someone someone uses uses anecdotal anecdotal evidence evidence to to discount discount

a a statistical statistical generalization. generalization. For For example, example, a a smoker smoker may may dismiss dismiss the the risk risk of of smoking smoking

by by noting noting that that his his or or her her father father smoked smoked two two packs packs of of cigarettes cigarettes a a day day and and lived lived to to

be be 75. 75. In In this this case, case, the the person person seems seems to to ignore ignore the the larger larger body body of of evidence evidence that that

people people who who smoke smoke have, have, on on average, average, a a shorter shorter life life expectancy expectancy and and an an increased increased risk risk

of of health health problems.problems.

The The problem problem we we all all must must confront confront in in research research and and in in life life is is the the pervasive pervasive nature nature

of of anecdotal anecdotal evidence evidence and and its its influence influence on on decision decision making. making. As As researchers, researchers, we we

must must remain remain vigilant vigilant to to ensure ensure that that our our data data are are representative representative of of the the population. population.

FinallyFinally, , you you should should recognize recognize that that the the plural plural of of is is not not . . Anecdotes, Anecdotes, anecdoteanecdote datadata

even even a a whole whole collection collection of of them, them, like like rumors, rumors, cannot cannot be be trusted trusted to to be be accurate, accurate,

reliable, reliable, or or valid.valid.

OVERVIEW OVERVIEW OF OF PROBABILITY PROBABILITY SAMPLINGSAMPLING

Before Before we we delve delve into into the the topic topic of of sampling sampling any any furtherfurther, , we we must must define define an an impor-impor-

tant tant term. term. TTo o say say that that an an outcome outcome is is means means that that each each possible possible outcome outcome randomrandom

has has an an equal equal probability probability of of occurring occurring and and that that the the outcome outcome of of one one event event has has no no

influence influence on on the the probability probability of of subsequent subsequent outcomes. outcomes. Imagine Imagine a a balanced balanced six-six-

sided sided die. die. Each Each time time you you throw throw the the die, die, the the probability probability of of any any one one side side landing landing

faceup faceup is is always always one-sixth. one-sixth. In In addition, addition, each each time time you you throw throw the the die, die, the the results results

of of the the previous previous tosses tosses have have no no effect effect on on the the current current toss. toss. That That one one of of these these events events

has has no no effect effect on on the the other other possible possible events events is is an an illustration illustration of of the the principle principle of of

independenceindependence. . Random Random sampling sampling is is also also an an example example of of independence independence because because

when when used used in in sample sample selection, selection, selecting selecting one one object object from from the the population population will will not not

influence influence the the selection selection of of other other objects.objects.

Understanding Understanding randomness randomness is is important important for for sampling sampling because because it it allows allows us us to to

link link individual individual samples samples to to the the population. population. According According to to the the law law of of large large numbersnumbers, ,

any any larlarge ge number number of of items items chosen chosen at at random random from from a a population population will will have, have, on on

average, average, the the same same characteristics characteristics as as the the population. population. This This law law is is the the cornerstone cornerstone of of

probability probability sampling sampling and and allows allows us us to to infer infer that that what what is is true true of of a a randomly randomly selected selected

sample sample is is also also true true of of the the population. population. In In this this section, section, we we will will examine examine how how we we can can

use use random random events events and and other other procedures procedures to to create create samples samples that that represent represent the the

population.population.

Populations Populations and and SamplesSamples

In In Chapter Chapter 3, 3, we we introduced introduced you you to to the the concepts concepts of of the the population population and and the the sample. sample.

As As you you should should recall, recall, the the population population consists consists of of all all the the individuals individuals or or things things that that

the the researcher researcher wants wants to to describe. describe. Researchers Researchers define define the the population population by by developing developing

the the criteria criteria that that determine determine membership membership in in the the population. population. Defining Defining the the population population

is is essential essential as as it it determines determines the the conclusions conclusions that that the the researcher researcher may may draw draw from from the the

data data (W(Wilkinson, ilkinson, 1999).1999).

Overview Overview of of Probability Probability SamplingSampling 165165

When When referring referring to to a a population, population, many many researchers researchers refer refer to to the the target target popula-popula-

tiontion universeuniverse or or the the . . For For example, example, a a medical medical researcher researcher may may want want to to study study the the

rates rates of of obesity obesity among among teenagers teenagers between between the the ages ages of of 13 13 and and 18. 18. In In this this example, example,

the the target target population population is is children children between between the the ages ages of of 13 13 and and 18, 18, inclusive.inclusive.

In In some some cases, cases, it it is is impractical impractical or or impossible impossible to to draw draw a a representative representative sample sample

from from the the tartarget get population. population. ConsequentlyConsequently, , researchers researchers will will draw draw their their sample sample from from

a a smaller smaller subset subset of of the the population population called called a a . . For For our our pur-pur-sampling sampling populationpopulation

poses, poses, a a sampling sampling population population consists consists of of an an accessible accessible group group of of people people who who share share

the the same same characteristics characteristics as as the the target target population. population. In In most most health health sciences sciences research, research,

the the sampling sampling population population consists consists of of people people who who live live or or work work near near the the researcherresearcher. .

When When they they report report their their results, results, researchers researchers define define the the characteristics characteristics of of the the sam-sam-

pling pling population. population. Doing Doing so so allows allows the the reader reader to to determine determine wwhether hether the the sampling sampling

population population is is representative representative of of the the target target population.population.

Some Some researchers researchers pull pull their their study study samples samples from from an an existing existing , , a a subject subject poolpool

group group of of people people to to whom whom the the researcher researcher has has easy easy access. access. At At many many colleges colleges and and

universities, universities, the the academic academic departments departments maintain maintain a a subject subject pool pool of of students students enrolled enrolled

in in introductory-level introductory-level courses courses who who may may receive receive extra extra credit credit for for participating participating in in a a

studystudy. . In In other other cases, cases, people people who who have have a a known known medical medical condition, condition, for for example, example,

may may agree agree to to have have their their name name added added to to a a list list of of potential potential participants participants for for controlled controlled

studies.studies.

AA related related concept concept is is the the sampling sampling frameframe, , which which is is the the set set of of individuals individuals within within

a a population population who who can can actually actually be be reached reached for for a a specific specific research research purpose, purpose, for for

example, example, a a list list of of names names that that identifies identifies the the members members of of the the population population is is a a sampling sampling

frame frame (Babbie, (Babbie, 1998). 1998). Consider Consider a a study study conducted conducted by by WWashington, ashington, Sun, Sun, and and

Canning Canning (2010) (2010) in in which which they they created created a a sampling sampling frame frame to to better better examine examine medical medical

care care received received by by veterans. veterans. As As they they noted noted in in their their studystudy, , most most veterans veterans do do not not

receive receive health health care care from from the the Department Department of of VVeterans eterans Affairs Affairs (V(VA). A). Therefore, Therefore, using using

data data drawn drawn exclusively exclusively from from VVAA data data sets sets may may be be incomplete incomplete and and biased. biased. TTo o

address address this this potential potential problem, problem, they they created created a a sampling sampling frame frame using using data data from from the the

VVeterans eterans Health Health Administration, Administration, VVeterans eterans Benefits Benefits Administration, Administration, and and Depart-Depart-

ment ment of of Defense. Defense. WWashington ashington et et al. al. found found that that the the sampling sampling frame frame provided provided a a

wider wider range range of of cases cases than than would would have have been been examined examined had had they they used used only only the the VVAA

data data set. set. Therefore, Therefore, samples samples generated generated using using this this sampling sampling frame frame provides provides

researcher researcher access access to to data data that that are are more more likely likely to to generalize generalize to to the the health health care care and and

status status of of male male and and female female veterans.veterans.

Detailed Detailed descriptions descriptions of of the the characteristics characteristics of of the the population, population, sampling sampling popu-popu-

lation, lation, and and sampling sampling frame frame help help us us evaluate evaluate the the external external validity validity of of inferences inferences

made made from from a a sample. sample. As As you you have have seen seen in in the the previous previous example, example, WWashington ashington et et

al. al. (2010) (2010) were were concerned concerned that that researresearch ch based based exclusively exclusively on on VVAA data data would would be be

incomplete incomplete and and not not representative representative of of the the population population of of veterans. veterans. By By expanding expanding the the

sampling sampling frame frame to to include include other other data data sets, sets, they they demonstrated demonstrated that that samples samples from from

this this sampling sampling frame frame would would be be far far more more inclusive inclusive and and representative representative of of the the popula-popula-

tion tion of of American American veterans.veterans.

The The connection connection among among external external validity validity and and the the sampling sampling population, population, subject subject

pool, pool, and and sampling sampling frame frame is is important. important. If If any any of of these these subgroups subgroups is is not not

166166 Chapter Chapter 7 7 SamplingSampling

representative representative of of the the population, population, then then this this threatens threatens the the external external validity validity of of any any

conclusions conclusions that that are are based based on on the the data data collected collected from from the the sample. sample. For For these these

reasons, reasons, researchers researchers spend spend considerable considerable time time designing designing careful careful sampling sampling plans plans and and

analyzing analyzing and and describing describing the the sources sources of of their their data. data. Doing Doing so so allows allows the the researcher researcher

to to establish establish a a connection connection between between the the sample sample statistics statistics and and the the population population param-param-

eters. eters. With With these these concerns concerns in in mind, mind, we we can can turn turn our our attention attention to to the the business business of of

creating creating samples.samples.

Characteristics Characteristics of of Probability Probability SamplingSampling

There There are are many many ways ways to to secure secure a a representative representative sample sample of of a a population. population. WWe e can can

use use techniques techniques known known as as simple simple random random sampling, sampling, stratified stratified sampling, sampling, systematic systematic

sampling, sampling, or or cluster cluster sampling, sampling, to to name name just just a a fewfew. . Although Although there there are are many many types types

of of sampling sampling procedures, procedures, all all of of those those mentioned mentioned earlier earlier have have one one thing thing in in common: common:

They They are are statistical statistical or or techniques.techniques.probability probability samplingsampling

All All probability probability sampling sampling techniques techniques share share common common features. features. First, First, they they treat treat

each each member member of of the the population population as as a a potential potential member member of of a a sample. sample. This This is is a a criti-criti-

cal cal feature feature as as it it ensures ensures that that the the sampling sampling technique technique does does not not systematically systematically

exclude exclude portions portions of of the the population population from from the the eventual eventual study study sample, sample, thereby thereby biasing biasing

the the results. results. By By implication, implication, the the procedures procedures employed employed in in true true probabilistic probabilistic sampling sampling

procedures procedures are are objective objective and and systematic. systematic. All All sampling sampling procedures procedures involve involve follow-follow-

ing ing a a set set of of rules, rules, known known as as a a prprotocolotocol, , for for selecting selecting members members of of the the population. population.

In In some some cases, cases, the the protocol protocol for for samsampling pling may may be be minimal; minimal; in in other other cases, cases, the the

sampling sampling protocol protocol may may be be extremely extremely elaborate. elaborate. Researchers Researchers follow follow the the sampling sampling

rules rules specified specified in in these these types types of of protocols protocols to to ensure ensure that that the the data data they they ultimately ultimately

collect collect are are not not biased.biased.

The The second second feature feature of of probability probability sampling sampling techniques techniques is is that that when when used used

appropriatelyappropriately, , they they make make it it possible possible for for researchers researchers to to determine determine the the probability probability

that that any any one one sample sample of of a a population population would would be be selected. selected. In In addition, addition, these these tech-tech-

niques niques make make it it easier easier for for the the researcher researcher to to test test whether whether the the sample sample that that was was studied studied

really really is is representative representative of of the the broader broader population population of of interest interest (Cochran, (Cochran, 1977). 1977). This This

may may sound sound a a bit bit strange, strange, but but it it is is an an important important assumption assumption that that allows allows us us to to connect connect

the the results results of of the the sample sample to to the the parameters parameters of of the the population. population. Consider Consider the the follow-follow-

ing ing example example of of probability probability sampling.sampling.

Assume Assume that that you you have have a a population population containing containing the the whole whole numbers numbers 1–6. 1–6. Using Using

sampling sampling without without replacement, replacement, and and with with a a sample sample size size of of 2, 2, you you could could create create the the

15 15 potential potential samples samples listed listed in in TTable able 7.1. 7.1. If If we we use use probability probability sampling, sampling, we we can can

TTable able 7.1 7.1 All All Potential Potential Samples Samples of of Size Size 2 2 Drawn Drawn from from a a

Population Population Consisting Consisting of of VValues alues 1–61–6

SS11 (1,2)(1,2) SS 22 (1,3)(1,3) SS33 (1,4)(1,4) SS44 (1,5)(1,5) SS55 (1,6)(1,6)

SS66 (2,3)(2,3) SS 77 (2,4)(2,4) SS88 (2,5)(2,5) SS99 (2,6)(2,6) SS1010 (3,4)(3,4)

SS1111 (3,5)(3,5) SS 1212 (3,6)(3,6) SS1313 (4,5)(4,5) SS1414 (4,6)(4,6) SS1515 (5,6)(5,6)

Probability Probability Sampling Sampling MethodsMethods 167167

determine determine the the proba proba bility bility that that we we will will select select any any one one of of these these samples. samples. In In this this

example, example, there there is is an an equal equal likelihood likelihood that that we we will will select select any any one one of of the the samples. samples.

SpecificallySpecifically, , for for each each sample, sample, 1/15 1/15 or or .0667. .0667. The The probability probability (( ) ) that that we we pp == pp == pp will will select select any any one one of of these these samples samples is is approximately approximately 6.67%.6.67%.

YYou ou may may object object and and say say that that we we rarely rarely know know the the true true nature nature of of the the population, population,

and and if if we we did, did, why why would would we we need need sampling? sampling? YYou ou are are correct; correct; we we rarely rarely know know the the

parameters parameters of of the the population. population. This This illustration illustration shows shows the the logic logic of of probability probability sam-sam-

pling. pling. For For any any given given population, population, we we can can draw draw an an infinite infinite number number of of samples. samples. Using Using

mathematical mathematical techniques techniques that that we we will will soon soon reviewreview, , we we can can estestimate imate the the probability probability

of of selecting selecting any any one one of of those those samples. samples. Armed Armed with with this this knowledge, knowledge, we we can can then then

make make several several interesting interesting inferences inferences about about the the population. population. YYou ou read read about about these these

inferences inferences all all the the time. time. For For example, example, various various research research agencies agencies report report “consumer “consumer

confidence” confidence” based based on on samples samples of of consumers consumers that that they they can can judge judge to to be be representa-representa-

tive tive of of the the broader broader population population of of consumers.consumers.

PROBABILITY PROBABILITY SAMPLING SAMPLING METHODSMETHODS

There There are are many many methods methods of of drawing drawing samples samples from from the the population. population. Each Each method method

shares shares a a common common goal: goal: to to ensure ensure that that the the sample sample is is an an unbiased unbiased depiction depiction of of the the

population. population. In In this this section, section, we we will will review review several several of of the the more more frequently frequently used used

sampling sampling methods methods that that are are based based on on the the probability probability theory theory just just discussed, discussed, including including

simple simple random random sampling, sampling, sequential sequential sampling, sampling, stratified stratified sampling, sampling, and and cluster cluster

sampling. sampling. This This section section can can provide provide only only a a general general introduction introduction to to sampling sampling

methods. methods. Sampling Sampling itself itself is is a a science, science, and and there there are are many many sophisticated sophisticated techniques techniques

researchers researchers use use for for specific specific purposes purposes (see (see also also Babbie, Babbie, 1998; 1998; Cochran, Cochran, 1977; 1977;

Salant Salant & & Dillman, Dillman, 1994).1994).

Simple Simple Random Random SamplingSampling

Simple Simple random random samplingsampling is is the the most most basic basic of of the the sampling sampling procedures. procedures. Simple Simple

random random sampling sampling occurs occurs whenever whenever each each member member of of the the population population has has an an equal equal

probability probability of of selection selection into into the the sample. sample. The The steps steps involved involved in in conducting conducting a a simple simple

random random sample sample are are clear-cut. clear-cut. First, First, estimate estimate the the size size of of the the population. population. Second, Second,

generate generate random random numbers numbers to to associate associate with with each each person person in in the the population, population, and and

third, third, use use those those numbers numbers to to determine determine which which members members of of the the population population are are

included included in in the the sample. sample. In In the the final final stage, stage, collect collect and and analyze analyze the the data.data.

Figure Figure 7.1 7.1 illustrates illustrates random random sampling sampling conceptuallyconceptually. . The The block block of of circles circles on on

the the left left represents represents members members of of a a population. population. The The block block of of circles circles on on the the right right

represents represents a a random random sample sample of of the the population. population. In In this this example, example, there there are are five five types types

of of circle, circle, each each represented represented by by a a difdifferent ferent shade. shade. Because Because there there is is no no bias bias in in the the

sampling sampling procedure,procedure, the the sample sample should should be be similar similar to to the the population, population, and and any any dif-dif-

ference ference between between the the sample sample and and the the population population represents represents chance chance or or random random

factors. factors. In In simple simple random random sampling, sampling, each each circle circle in in the the block block on on the the left left has has an an

equal equal chance chance of of selection selection into into the the sample sample (the (the block block on on the the right).right).

168168 Chapter Chapter 7 7 SamplingSampling

Imagine Imagine that that you you want want to to conduct conduct a a survey survey of of student student eating eating habits habits at at your your

college. college. The The college’college’s s institutional institutional review review board board approved approved your your research, research, and and you you

are are ready ready to to collect collect the the data. data. The The first first step step is is to to determine determine the the size size of of the the college’college’s s

student student population. population. This This should should be be relatively relatively easyeasy. . Go Go to to the the college’college’s s records records

office office and and ask ask the the registrar registrar for for the the number number of of students students currently currently enrolled enrolled at at the the

college. college. For For the the sake sake of of the the illustration, illustration, assume assume that that there there are are 7584 7584 students students

enrolled enrolled at at your your college college and and that that you you have have decided decided that that you you will will pull pull a a random random

sample sample of of 250 250 students students for for your your research.research.

For For the the next next step, step, you you will will need need 250 250 . . Random Random numbers numbers are are random random numbersnumbers

a a series series of of numbers numbers with with no no order order or or pattern. pattern. TTechnicallyechnically, , random random numbers numbers are are

independent independent of of each each otherother. . Independence Independence means means that that each each number number has has an an equal equal

chance chance of of selection selection and and the the selection selection of of one one number number has has no no effect effect on on the the selection selection

of of another another numbernumber. . Before Before the the advent advent of of personal personal computers, computers, many many researchers researchers

used used a a random random number number table table created created by by the the Rand Rand Corporation Corporation (1955) (1955) that that contains contains

1 1 million million random random digits. digits. The The creators creators of of that that table table went went to to great great pains pains to to build build and and

test test a a machine machine that that produced produced random random digits.digits.

Many Many researchers researchers now now use use their their personal personal computers computers to to generate generate random random

numbers. numbers. Different Different computer computer programs programs can can produce produce a a string string of of random random numbers numbers

between between specific specific values. values. In In the the current current example, example, we we need need 250 250 random random numbers numbers

between between 1 1 and and 7584, 7584, inclusive. inclusive. Once Once you you have have generated generated the the 250 250 random random numbers, numbers,

you you could could sort sort the the entire entire data data file file in in order order of of these these numbers numbers and and select select the the first first

250 250 individuals individuals in in the the sorted sorted list list of of all all the the stustudents dents in in the the population population at at this this college. college.

If If everyone everyone in in this this randomly randomly selected selected sample sample cooperates cooperates with with your your request request to to

complete complete the the questionnaire, questionnaire, your your sample sample will will be be an an unbiased unbiased representation representation of of the the

population.population.

In In case case you you are are interested, interested, many many computer computer programs programs generate generate random random numbers, numbers,

but but most most do do this this based based on on a a preset preset random random number number “seed” “seed” or or starting starting point. point.

Researchers Researchers call call these these numbers numbers numbers numbers because because of of this, this, but but in in pseudorandompseudorandom

most most research research cases, cases, using using pseudorandom pseudorandom numbers numbers is is sufficient sufficient to to ensure ensure repre-repre-

sentativeness sentativeness within within a a sample sample (Pashley(Pashley, , 1993).1993).

Sequential Sequential SamplingSampling

Although Although simple simple random random sampling sampling is is the the gold gold standard standard of of probability probability sampling, sampling,

many many researchers researchers find find other other techniques, techniques, such such as as , , more more sequential sequential samplingsampling

Figure Figure 7.1 7.1 Random Random

sampling.sampling.

Probability Probability Sampling Sampling MethodsMethods 169169

Figure Figure 7.2 7.2 Stratified Stratified

sampling.sampling.

practical practical (Babbie, (Babbie, 1998). 1998). For For a a sequential sequential sample, sample, we we list list the the members members of of the the

sampling sampling population population and and then then select select each each th th member member from from the the list.list.kk

The The steps steps for for sequential sequential sampling sampling are are straightforward. straightforward. First, First, we we need need to to deter-deter-

mine mine the the that that identifies identifies which which members members of of the the list list to to select. select. sampling sampling intervalinterval

The The sampling sampling interval interval is is merelymerely

Sample Sample intervalinterval Size Size of of populationpopulation

Desired Desired sizesize of of samplesample == (7.1)(7.1)

In In our our example, example, we we wanted wanted to to create create a a sample sample of of 250 250 from from a a population population of of

7584 7584 students. students. Therefore, Therefore, the the sampling sampling interval interval is is 30 30 (7584/250 (7584/250 30.336). 30.336). Now Now == all all you you need need to to do do is is obtain obtain a a current current list list of of all all students students and and then then select select every every 30th 30th

student student on on the the list. list. This This procedure procedure assumes assumes that that the the list list you you select select students students from from

represents represents the the entire entire sampling sampling frame.frame.

Stratified Stratified SamplingSampling

Stratified Stratified sampling sampling is is another another variation variation on on simple simple random random sampling. sampling. This This tech-tech-

nique nique is is especially especially useful useful in in situations situations where where the the population population contains contains different different

subgroups subgroups that that the the researcher researcher wants wants to to compare compare or or studystudy. . AA fine fine example example of of strati-strati-

fied fied sampling sampling is is in in a a report report by by Robb Robb et et al. al. (2010), (2010), which which examines examines differences differences

among among ethnic ethnic groups groups regarding regarding brbreast east and and cervical cervical cancers cancers in in England. England. TTo o conduct conduct

the the studystudy, , the the researchers researchers used used stratified stratified sampling sampling of of the the six six largest largest ethnic ethnic groups—groups—

Indian, Indian, Pakistani, Pakistani, Bangladeshi, Bangladeshi, Caribbean, Caribbean, African, African, and and Chinese—to Chinese—to identify identify 1500 1500

participants participants who who then then completed completed a a number number of of surveys surveys regarding regarding cancer cancer awareness. awareness.

Robb Robb et et al. al. found found that that there there were were notable notable differences differences among among the the groups groups regarding regarding

knowledge knowledge of of the the forms forms of of cancer cancer and and previous previous screenings screenings for for the the cancers.cancers.

Figure Figure 7.2 7.2 illustrates illustrates how how stratified stratified sampling sampling works. works. In In this this example, example, the the

population population contains contains five five distinct distinct subgroups subgroups of of different different sizes. sizes. The The researcher researcher wants wants

to to include include a a sample sample of of each each subgroup subgroup in in the the sample. sample. In In order order not not to to bias bias the the sample, sample,

the the size size of of the the subgroups subgroups in in the the sample sample should should equal equal the the relative relative size size of of the the sub-sub-

groups groups in in the the population.population.

The The box box on on the the left left represents represents a a population population consisting consisting of of smaller smaller subgroups subgroups

of of strata. strata. The The researcher researcher randomly randomly selects selects from from each each stratum stratum to to create create the the sample. sample.

170170 Chapter Chapter 7 7 SamplingSampling

The The sample sample will will have have approximately approximately the the same same proportions proportions of of the the subgroups subgroups as as the the

population.population.

Figure Figure 7.2 7.2 offers offers a a hint hint of of how how a a researcher researcher would would conduct conduct stratified stratified random random

sampling. sampling. First, First, the the researcher researcher would would identify identify the the specific specific subgroups subgroups in in the the popula-popula-

tion tion and and attempt attempt to to estimate estimate their their relative relative size. size. Second, Second, the the researcher researcher can can use use

simple simple random random or or sequential sequential sampling sampling within within each each subgroup. subgroup. The The result result is is a a rep-rep-

resentative resentative sample. sample. If If all all goes goes well, well, the the size size of of the the subgroups subgroups in in the the sample sample will will

be be the the same same relative relative size size as as the the population.population.

Cluster Cluster SamplingSampling

Researchers Researchers use use when when it it is is not not convenient convenient to to pull pull one one or or two two cluster cluster samplingsampling

people people out out of of their their environment environment for for the the research research or or when when other other methods methods of of sam-sam-

pling pling are are impractical. impractical. Researchers Researchers often often use use this this technique technique when when working working with with

intact intact groups. groups. An An example example would would be be a a research research project project examining examining the the effectiveness effectiveness

of of different different teaching teaching techniques.techniques.

Imagine Imagine that that Figure Figure 7.3 7.3 represents represents students students enrolled enrolled in in 20 20 different different sections sections

of of the the same same course. course. The The researcher researcher mmay ay want want to to know know whether whether differences differences in in the the

teaching teaching method method affect affect students’students’ performance performance in in the the course. course. It It may may be be impractical impractical

to to randomly randomly select select students students and and create create special special sections sections of of the the course. course. As As an an alter-alter-

native, native, the the researcher researcher can can select select different different sections sections at at random random for for the the research. research. In In

Figure Figure 7.3, 7.3, the the researcher researcher randomly randomly selected selected five five different different clusters.clusters.

The The small small blocks blocks of of individuals individuals in in the the left left square square identify identify separate separate clusters clusters of of

individuals. individuals. The The researcher researcher selects selects several several clusters clusters for for the the sample.sample.

In In other other cases, cases, the the clusters clusters may may represent represent cities, cities, neighborhoods, neighborhoods, schools, schools, or or

other other naturally naturally occurring occurring clusters. clusters. The The researcher researcher can can then then select select clusters clusters randomly randomly

or or systematicallysystematically. . If If the the researcher researcher knows knows that that particular particular clusters clusters contain contain important important

portions portions of of the the population, population, he he or or she she may may then then purposely purposely select select those those clusters.clusters.

NONPROBABILITY NONPROBABILITY SAMPLINGSAMPLING

Although Although probability probability sampling sampling is is the the ideal, ideal, it it is is often often beyond beyond the the budget, budget, time, time,

and and personal personal resources resources of of the the researcherresearcher. . Therefore, Therefore, in in many many situations, situations, researchers researchers

Figure Figure 7.3 7.3 Cluster Cluster sampling.sampling.

Nonprobability Nonprobability SamplingSampling 171171

will will resort resort to to . . YYou ou will will also also see see this this type type of of sampling sampling nonprobability nonprobability samplingsampling

referred referred to to as as sampling sampling since since it it is is not not statistical statistical or or based based on on statistical statistical judgmentaljudgmental

rules. rules. These These methods methods are are often often more more convenient convenient for for the the researcherresearcher, , but but the the results results

of of studies studies using using samples samples of of this this sort sort need need to to be be interpreted interpreted with with caution. caution. As As you you

should should recall recall from from your your reading reading in in previous previous chapters, chapters, using using a a nonprobability nonprobability sam-sam-

pling pling method method may may limit limit the the inferences inferences that that you you can can make make from from the the data. data. HoweverHowever, ,

these these methods methods can can produce produce useful useful data data when when collected collected and and interpreted interpreted under under the the

right right conditions conditions (Cochran, (Cochran, 1977).1977).

Convenience Convenience SamplingSampling

The The most most common common type type of of nonprobability nonprobability sampling sampling is is . . In In convenience convenience samplingsampling

contrast contrast to to probability probability sampling, sampling, convenience convenience sampling sampling means means that that the the researcher researcher

uses uses members members of of a a population population who who are are easy easy to to find. find. Interviewing Interviewing people people coming coming

to to a a clinic clinic or or visiting visiting a a patient patient at at a a hospital hospital is is an an example example of of convenience convenience sampling. sampling.

In In thesethese cases, cases, the the researcher researcher allows allows the the individual’individual’s s behavior behavior to to determine determine who who

will, will, and and more more importantly importantly who who will will not, not, be be a a part part of of the the studystudy..

Do Do you you see see the the difference difference between between probability probability sampling sampling and and convenience convenience

sampling? sampling? For For all all forms forms of of probability probability sampling, sampling, the the rresearesearchercher’’s s methodmethod of of sam-sam-

pling pling determines determines who who will will be be a a potential potential member member of of a a sample. sample. For For convenience convenience

sampling, sampling, the the individuals’individuals’ behaviorsbehaviors determine determine whether whether they they could could become become part part

of of a a study’study’s s sample. sample. ConsequentlyConsequently, , convenience convenience sampling sampling can can bias bias the the results results and and

interpretation interpretation of of the the data. data. Imagine Imagine that that you you wanted wanted to to conduct conduct a a survey survey of of students students

at at your your college. college. Do Do you you think think you you would would get get different different results results if if you you surveyed surveyed

students students lounging lounging around around the the college’college’s s student student union union versus versus students students studying studying in in

the the library? library? In In many many ways, ways, convenience convenience sampling sampling suffers suffers the the same same problems problems as as

anecdotal anecdotal evidence evidence because because the the sample sample does does not not represent represent the the population. population. Indeed, Indeed,

when when researchers researchers use use random random sampling sampling techniques, techniques, they they will will review review characteris-characteris-

tics tics of of the the sample sample in in the the hope hope to to confirm confirm that that those those who who volunteered volunteered appear appear to to

match match the the general general characteristics characteristics of of the the sampling sampling population.population.

Despite Despite these these drawbacks, drawbacks, howeverhowever, , there there are are times times when when a a convenience convenience sample sample

may may be be the the only only realistic realistic sampling sampling strategystrategy. . Many Many good good research research studies studies have have been been

conducted conducted using using a a convenience convenience sample. sample. HoweverHowever, , the the specific specific results results of of any any one one

particular particular study study may may be be an an artifact artifact of of the the sample. sample. The The growth growth of of science science is is depen-depen-

dent dent on on a a body body of of knowledge knowledge that that builds builds on on preexisting preexisting research. research. This This is is especially especially

true true for for convenience convenience samples, samples, and and the the results results of of individual individual studies studies should should be be

examined examined in in light light of of existing existing and and future future research.research.

Snowball Snowball SamplingSampling

SadlerSadler, , Lee, Lee, Lim, Lim, and and Fullerton Fullerton (2010) (2010) outline outline the the benefits benefits of of snowball snowball sampling sampling

for for a a population population of of participants participants that that may may be be otherwise otherwise difficult difficult to to contact contact using using

traditional traditional sampling sampling techniques. techniques. Sometimes Sometimes the the members members of of a a cohort cohort are are difficult difficult

to to find find and and recruit recruit for for research. research. The The members members of of the the cohort cohort mmay ay wish wish to to remain remain

172172 Chapter Chapter 7 7 SamplingSampling

anonymous, anonymous, or or there there is is no no list list identifying identifying the the members members of of the the cohort. cohort. Imagine Imagine

you you wanted wanted to to study study active active users users of of a a controlled controlled substance substance such such as as methamphet-methamphet-

amine amine or or examine examine the the health health of of homeless homeless teens. teens. These These people people may may not not be be difficult difficult

to to find find using using standard standard techniques. techniques. Consider Consider another another example, example, people people who who seek seek

medical medical treatment treatment from from alternative alternative sources sources (e.g., (e.g., folk folk remedies). remedies). Indeed, Indeed, as as

Sadler Sadler et et al. al. note, note, proba proba bility bility sampling sampling will will most most likely likely not not produce produce a a representa-representa-

tive tive sample sample of of these these populations.populations.

The The concept concept of of is is relatively relatively simple simple but but may may require require con-con-snowball snowball samplingsampling

siderable siderable skill skill to to accomplish. accomplish. In In its its simple simple format, format, the the researcher researcher gains gains the the trust trust

of of one one or or more more members members of of the the population. population. AA healthcare healthcare provider provider may may know know that that

women women in in a a specific specific ethnic ethnic group group use use indigenous indigenous or or folk folk medicine medicine during during their their

pregnancypregnancy. . In In this this example, example, the the researcher researcher would would first first need need to to find find a a suitable suitable

method method to to contact contact women women in in this this group group and and to to develop develop a a level level of of trust trust such such that that

the the women women will will introduce introduce the the researcher researcher to to other other women women in in the the group. group. Building Building

upon upon this this trust, trust, the the additional additional participants participants can can then then be be encouraged encouraged to to recruit recruit addi-addi-

tional tional participants participants from from the the population. population. Snowball Snowball sampling sampling has has been been used used success-success-

fully fully to to study study human human behavior behavior in in populations populations as as diverse diverse as as gangs, gangs, illicit illicit drug drug users, users,

and and other other hard-to-reach hard-to-reach populations. populations. For For those those interested interested in in other other techniques techniques

researchers researchers use use to to study study difficult-to-find difficult-to-find populations, populations, we we recommend recommend Kendall Kendall

et et al. al. (2008).(2008).

KNOWLEDGE KNOWLEDGE CHECKCHECK

1. 1. What What are are the the differences differences between between anecdotal anecdotal evidence evidence and and scientific scientific

sampling?sampling?

2. 2. What What are are the the potential potential problems problems with with relying relying on on personal personal experience experience to to

make make decisions?decisions?

3. 3. Describe Describe the the similarities similarities and and differences differences among among simple simple random random sampling, sampling,

sequential sequential sampling, sampling, stratified stratified sampling, sampling, and and cluster cluster sampling.sampling.

4. 4. Anne Anne is is selecting selecting courses courses for for next next semester semester and and must must take take an an English English

literature literature course course but but does does not not know know whwhich ich professor professor she she should should select. select. TTo o

solve solve her her dilemma, dilemma, she she decides decides to to ask ask three three of of her her friends, friends, who who are are English English

majors, majors, for for their their recommendations.recommendations.

a. a. What What type type of of sampling sampling is is Anne Anne using?using?

b. b. Describe Describe the the factors factors that that may may bias bias the the information information Anne Anne receives.receives.

5. 5. The The dean dean of of academic academic affairs affairs at at a a small small college college wants wants to to examine examine the the study study

habits habits of of students students attending attending the the college. college. He He randomly randomly selects selects 50 50 students students

from from the the college college and and asks asks them them to to record record the the number number of of hours hours they they work work

on on homework homework each each day day for for 1 1 week week (assume (assume that that all all the the students students participate participate

and and answer answer honestly). honestly). According According to to the the results, results, the the typical typical student student studies studies

an an average average of of 3.2 3.2 hours hours a a dayday..

a. a. Can Can we we conclude conclude that that the the dean dean has has a a valid valid estimate estimate of of the the students’students’

study study habits?habits?

b. b. Are Are there there factors factors that that can can bias bias the the results results of of the the data?data?

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