Abdm4064 week 09 10 sampling

Research Design :Research Design :
Sampling &Sampling &
Data CollectionData Collection
Research Design :Research Design :
Sampling &Sampling &
Data CollectionData Collection
ABDM4064 BUSINESS RESEARCHABDM4064 BUSINESS RESEARCH
by
Stephen Ong
Principal Lecturer (Specialist)
Visiting Professor, Shenzhen

6-2
Design in the Research ProcessDesign in the Research Process

14-3
Sampling DesignSampling Design
within the Research Processwithin the Research Process

Sampling DesignSampling Design

LEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMES
1. Explain reasons for taking a sample rather than a
complete census
2. Describe the process of identifying a target
population and selecting a sampling frame
3. Compare random sampling and systematic
(nonsampling) errors
4. Identify the types of nonprobability sampling,
including their advantages and disadvantages
After studying this chapter, you should be able to

LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)
5. Summarize the advantages and disadvantages of
the various types of probability samples
6. Discuss how to choose an appropriate sample
design, as well as challenges for Internet sampling
7. Understand basic statistical terminology
8. Interpret frequency distributions, proportions, and
measures of central tendency and dispersion
9. Distinguish among population, sample, and
sampling distributions
10. Summarize the use of confidence interval
estimates
After studying this chapter, you should

14-7
Small Samples Can EnlightenSmall Samples Can Enlighten
““The proof of the pudding is in theThe proof of the pudding is in the
eating.eating.
ByBy a small samplea small sample we may judge of thewe may judge of the
whole piece.”whole piece.”
Miguel de Cervantes SaavedraMiguel de Cervantes Saavedra
authorauthor

14-8
The Nature of SamplingThe Nature of Sampling
PopulationPopulation
Population ElementPopulation Element
CensusCensus
SampleSample
Sampling frameSampling frame

Sampling TerminologySampling Terminology
 Sample
 A subset, or some part, of a larger
population.
 Population (universe)
 Any complete group of entities that share
some common set of characteristics.
 Population Element
 An individual member of a population.
 Census
 An investigation of all the individual
elements that make up a population.

14-10
Why Sample?Why Sample?
GreaterGreater
accuracyaccuracy
AvailabilityAvailability
of elementsof elements
AvailabilityAvailability
of elementsof elements
GreaterGreater
speedspeed
GreaterGreater
speedspeed
SamplingSampling
providesprovides
SamplingSampling
providesprovides
LowerLower
costcost
LowerLower
costcost

14-11
What Is a SufficientlyWhat Is a Sufficiently
Large Sample?Large Sample?
““In recent Gallup ‘Poll on polls,’ . . . When askedIn recent Gallup ‘Poll on polls,’ . . . When asked
about the scientific sampling foundation on whichabout the scientific sampling foundation on which
polls are based . . . most said that a survey ofpolls are based . . . most said that a survey of
1,500 – 2,000 respondents—a larger than average1,500 – 2,000 respondents—a larger than average
sample size for national polls—cannot representsample size for national polls—cannot represent
the views of all Americans.”the views of all Americans.”
Frank NewportFrank Newport
The Gallup Poll editor in chiefThe Gallup Poll editor in chief
The Gallup OrganizationThe Gallup Organization

14-12
When Is a CensusWhen Is a Census
Appropriate?Appropriate?
NecessaryNecessaryFeasibleFeasible

14-13
What Is a Valid Sample?What Is a Valid Sample?
AccurateAccurate PrecisePrecise

Why Sample?Why Sample?
 Pragmatic Reasons
 Budget and time constraints.
 Limited access to total population.
 Accurate and Reliable Results
 Samples can yield reasonably accurate
information.information.
 Strong similaritiesStrong similarities in population elements makesin population elements makes
sampling possible.sampling possible.
 Sampling may beSampling may be more accuratemore accurate than a census.than a census.
 Destruction of Test UnitsDestruction of Test Units
 SamplingSampling reduces the costsreduces the costs of research in finiteof research in finite
populations.populations.

A Photographic Example of How Sampling WorksA Photographic Example of How Sampling Works

16–16
Stages inStages in
thethe
SelectionSelection
of aof a
SampleSample

14-17
Types of Sampling DesignsTypes of Sampling Designs
Element
Selection
Probability Nonprobability
•UnrestrictedUnrestricted • Simple randomSimple random • ConvenienceConvenience
•RestrictedRestricted • Complex randomComplex random • PurposivePurposive
• SystematicSystematic • JudgmentJudgment
•ClusterCluster •QuotaQuota
•StratifiedStratified •SnowballSnowball
•DoubleDouble

14-18
Steps in Sampling DesignSteps in Sampling Design
What is the target population?What is the target population?What is the target population?What is the target population?
What are the parameters ofWhat are the parameters of
interest?interest?
What are the parameters ofWhat are the parameters of
interest?interest?
What is the sampling frame?What is the sampling frame?What is the sampling frame?What is the sampling frame?
What is the appropriateWhat is the appropriate
sampling method?sampling method?
What is the appropriateWhat is the appropriate
sampling method?sampling method?
What size sample is needed?What size sample is needed?What size sample is needed?What size sample is needed?

14-19
When to Use Larger Sample?When to Use Larger Sample?
DesiredDesired
precisionprecision
DesiredDesired
precisionprecision
Number ofNumber of
subgroupssubgroups
Number ofNumber of
subgroupssubgroups
ConfidenceConfidence
levellevel
ConfidenceConfidence
levellevel
PopulationPopulation
variancevariance
Small errorSmall error
rangerange

Practical Sampling ConceptsPractical Sampling Concepts
 Defining the Target Population
 Once the decision to sample has been made,
the first question concerns identifying the
target population.
 What is the relevant population? In many cases
this is easy to answer, but in other cases, the
decision may be difficult.
 At the outset of the sampling process it is
vitally important to carefully define the target
population so that the proper source from
which the data are to be collected can be
identified.
 To implement the sample in the field, tangible
characteristics (e.g. age, gender etc) should be
used to define the population.

(cont’d)(cont’d)
 The Sampling Frame
 In practice, the sample will be drawn from a
list of population elements that often differs
somewhat from the defined target population.
 A sampling frame is a list of elements from
which the sample may be drawn.
 The sampling frame is also called the working
population, because these units will
eventually provide units involved in the
analysis.
 The discrepancy between the definition of the
population and a sampling frame is the first
potential source of error associated with
sample selection.

ExampleExample
 Target population: Students in
Malaysia between 18 years old and 22
years old.
 Sampling frame: students from a
higher education institution.

 The Sampling Frame
 A sampling frame error occurs when
certain sample elements are excluded or
when the entire population is not
accurately represented in the sampling
frame.
 Population elements can be either under-
or overrepresented in a sampling frame.

Sampling UnitsSampling Units
 Sampling Unit
 A single element or group of elements
subject to selection in the sample.
 Primary Sampling Unit (PSU)
 A unit selected in the first stage of sampling.
 Secondary Sampling Unit
 A unit selected in the second stage of
sampling.
 Tertiary Sampling Unit
 A unit selected in the third stage of sampling.

EXAMPLE
Target population: Students in Malaysia
between 18 years old and 22 years old.
Sample frame: students from a higher
education institution.
Sampling units:
 Advanced Diploma students only (primary
sampling unit)
 School of Business Studies only (secondary
sampling unit)
 ABU only (tertiary sampling unit)
16–25

Random Sampling andRandom Sampling and
Nonsampling ErrorsNonsampling Errors
 If a difference exists between the value
of a sample statistic of interest and the
value of the corresponding population
parameter, a statistical error has
occurred.
 Two basic causes of differences
between statistics and parameters:
random sampling errors
systematic (nonsampling) errors

Random Sampling and Nonsampling Errors (cont’d)Random Sampling and Nonsampling Errors (cont’d)
 Random Sampling Error
 Random sampling error is the difference between the
sample result and the result of a census conducted using
identical procedures.
 Random sampling error occurs because of chance
variation in the scientific selection of sampling units.
 Because random sampling errors follow chance variations,
they tend to cancel one another out when averaged.
 This means that properly selected samples are generally
good approximations of the population.
 Random sampling error is a function of sample size.
 As sample size increases, random sampling error
decreases
 It is possible to estimate the random sampling error that
may be expected with various sample sizes.

Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)
 Systematic Sampling Error
 Systematic (nonsampling) errors result
from nonsampling factors, primarily the
nature of a study’s design and the
correctness of execution.
 These errors are not due to chance
fluctuations.
 Sample biases account for a large portion
of errors in research.

Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)
 Less than Perfectly Representative
Samples
 Random sampling errors and systematic
errors associated with the sampling process
may combine to yield a sample that is less
than perfectly representative of the
population.
 Additional errors will occur if individuals
refuse to be interviewed or cannot be
contacted.
 Such nonresponse error may also cause the
sample to be less than perfectly
representative.

EXHIBIT 16.EXHIBIT 16.44 Errors Associated with SamplingErrors Associated with Sampling

Probability versusProbability versus
Nonprobability SamplingNonprobability Sampling
 Several alternative ways to takeSeveral alternative ways to take
a sample are available.a sample are available.
 The main alternative samplingThe main alternative sampling
plans may be grouped into twoplans may be grouped into two
categories:categories:
 1. probability techniques1. probability techniques
 2. nonprobability techniques.2. nonprobability techniques.

Probability versus Nonprobability SamplingProbability versus Nonprobability Sampling
 Probability Sampling
 In probability sampling, every element in
the population has a known, nonzero
probability of selection.
 The simple random sample, in which each
member of the population has an equal
probability of being selected, is the best-
known probability sample.

Probability versus NonprobabilityProbability versus Nonprobability
Sampling (cont’d)Sampling (cont’d)
 Nonprobability sampling
 In nonprobability sampling, the probability of any
particular member of the population being chosen
is unknown.
 The selection of sampling units in nonprobability
sampling is quite arbitrary, as researchers rely
heavily on personal judgment.
 Technically, no appropriate statistical techniques
exist for measuring random sampling error from a
nonprobability sample.
 Therefore, projecting the data beyond the sample is
technically speaking, statistically inappropriate.
 Nevertheless, nonprobability samples are
pragmatic and are used in business research.

14-34
Nonprobability SamplesNonprobability Samples
CostCost
FeasibilityFeasibilityFeasibilityFeasibility
TimeTimeTimeTime
No need toNo need to
generalizegeneralize
LimitedLimited
objectivesobjectives
LimitedLimited
objectivesobjectives

14-35
NonprobabilityNonprobability
Sampling MethodsSampling Methods
ConvenienceConvenienceConvenienceConvenience
JudgmentJudgmentJudgmentJudgment
QuotaQuotaQuotaQuota
SnowballSnowballSnowballSnowball

MethodsMethods
 Convenience Sampling
 Obtaining those people or units that are most
conveniently available.
 Mall interception survey is applying this
method.
 Judgment (Purposive) Sampling
 An experienced individual selects the sample
based on personal judgment about some
appropriate characteristic of the sample
member.
 E.g. Consumer Price Index (CPI)

Nonprobability Sampling (cont’d)Nonprobability Sampling (cont’d)
 Quota Sampling
 Ensures that various subgroups of a population will be
represented on pertinent characteristics to the exact extent that
the investigator desires.
 E.g. SOT – 20, SBS - 30
 Possible Sources Of Bias
 Respondents chosen because they were:
 Similar to interviewer
 Easily found
 Willing to be interviewed
 Middle-class
 Advantages of Quota Sampling
 Speed of data collection
 Lower costs
 Convenience

 Snowball Sampling
 A sampling procedure in which initial
respondents are selected by probability
methods and additional respondents are
obtained from information provided by the
initial respondents.
 E.g. 1 respondent (selected through
probability method) recommended another
5 respondents; then the 5 additional
respondents recommended another 25
respondents.

Probability SamplingProbability Sampling Simple Random Sampling
 Simple random sampling is a sampling procedure
that assures that each element in the population
will have an equal chance of being included in the
sample.
 Drawing names from a hat is a typical example of
simple random sampling; each person has an
equal chance of being selected.
 To use this method, we must have a list of all
members in a population, then we draw lots.
 Systematic Sampling
 A starting point is selected by a random process
and then every nth number on the list is selected.
 E.g. for the list of all members in a population,
every 10th
name will be selected.

14-40
Simple RandomSimple Random
AdvantagesAdvantages
•Easy to implementEasy to implement
with random dialingwith random dialing
DisadvantagesDisadvantages
•Requires list ofRequires list of
population elementspopulation elements
•Time consumingTime consuming
•Larger sampleLarger sample
neededneeded
•Produces largerProduces larger
errorserrors
•High costHigh cost

14-41
SystematicSystematic
•Simple to designSimple to design
•Easier than simpleEasier than simple
randomrandom
•Easy to determineEasy to determine
sampling distributionsampling distribution
of mean or proportionof mean or proportion
•Periodicity withinPeriodicity within
population may skewpopulation may skew
sample and resultssample and results
•Trends in list mayTrends in list may
bias resultsbias results
•Moderate costModerate cost

Proportional versus DisproportionalProportional versus Disproportional
SamplingSampling Stratified Sampling
 Simple random subsamples that are more or less equal on
some characteristic are drawn from within each stratum
(subgroup) of the population.
 E.g. based on the same characteristics, we divide students
into 3 subgroups (e.g. students with straight-pass,
students with re-sit units, students with repeat units), then
we use simple random sampling method to draw a
subsample.
 Proportional Stratified Sample
 The number of sampling units drawn from each stratum
is in proportion to the population size of that stratum.
 Disproportional Stratified Sample
 The sample size for each stratum is allocated according
to analytical considerations.

EXHIBIT 16.EXHIBIT 16.55 Disproportional Sampling: Hypothetical ExampleDisproportional Sampling: Hypothetical Example

14-44
StratifiedStratified
•Control of sample size inControl of sample size in
stratastrata
•Increased statisticalIncreased statistical
efficiencyefficiency
•Provides data toProvides data to
represent and analyzerepresent and analyze
subgroupssubgroups
•Enables use of differentEnables use of different
methods in stratamethods in strata
•Increased error ifIncreased error if
subgroups are selected atsubgroups are selected at
different ratesdifferent rates
•Especially expensive ifEspecially expensive if
strata on population muststrata on population must
be createdbe created
•High costHigh cost

Cluster SamplingCluster Sampling
 The purpose of cluster sampling is to sample
economically while retaining the characteristics of a
probability sample.
 In a cluster sample, the primary sampling unit is no
longer the individual element in the population (e.g.,
grocery stores) but a larger cluster of elements
located in proximity to one another (e.g., cities).
 Cluster sampling is classified as a probability
sampling technique because of either the random
selection of clusters or the random selection of
elements within each cluster.
 Cluster samples frequently are used when lists of the
sample population are not available.

EXHIBIT 16.EXHIBIT 16.66 Examples of ClustersExamples of Clusters

14-47
ClusterCluster
•Provides an unbiasedProvides an unbiased
estimate of populationestimate of population
parameters if properlyparameters if properly
donedone
•Economically moreEconomically more
efficient than simpleefficient than simple
randomrandom
•Lowest cost per sampleLowest cost per sample
•Easy to do without listEasy to do without list
•Often lower statisticalOften lower statistical
efficiency due toefficiency due to
subgroups beingsubgroups being
homogeneous rather thanhomogeneous rather than
heterogeneousheterogeneous
•Moderate costModerate cost

Multistage Area SamplingMultistage Area Sampling
 Multistage Area Sampling
 Involves using a combination of two or
more probability sampling techniques.
 Typically, geographic areas are randomly
selected in progressively smaller (lower-
population) units.
 Researchers may take as many steps as
necessary to achieve a representative sample.
 Progressively smaller geographic areas are
chosen until a single housing unit is selected
for interviewing.

EXHIBIT 16.EXHIBIT 16.88 Geographic Hierarchy Inside Urbanized AreasGeographic Hierarchy Inside Urbanized Areas

14-50
Stratified and Cluster SamplingStratified and Cluster Sampling
StratifiedStratified
•Population divided intoPopulation divided into
few subgroupsfew subgroups
•Homogeneity withinHomogeneity within
subgroupssubgroups
•Heterogeneity betweenHeterogeneity between
subgroupssubgroups
•Choice of elementsChoice of elements
from within eachfrom within each
subgroupsubgroup
ClusterCluster
•Population divided intoPopulation divided into
many subgroupsmany subgroups
•Heterogeneity withinHeterogeneity within
subgroupssubgroups
•Homogeneity betweenHomogeneity between
subgroupssubgroups
•Random choice ofRandom choice of
subgroupssubgroups

14-51
Area SamplingArea Sampling

14-52
Double SamplingDouble Sampling
•May reduce costs ifMay reduce costs if
first stage results infirst stage results in
enough data to stratifyenough data to stratify
or cluster theor cluster the
populationpopulation
•Increased costs ifIncreased costs if
discriminately useddiscriminately used

What Is the AppropriateWhat Is the Appropriate
Sample Design? (cont’d)Sample Design? (cont’d)
 Resources
 The cost associated with the different
sampling techniques varies tremendously.
 If the researcher’s financial and human
resources are restricted, certain options will
have to be eliminated.
 Managers concerned with the cost of the
research versus the value of the information
often will opt for cost savings from a certain
nonprobability sample design rather than
make the decision to conduct no research at
all.

What Is the Appropriate SampleWhat Is the Appropriate Sample
Design? (cont’d)Design? (cont’d) Time
 Researchers who need to meet a deadline or
complete a project quickly will be more likely to
select simple, less time-consuming sample
designs.
 Advance Knowledge of the Population
 In many cases, a list of population elements
will not be available to the researcher.
 A lack of adequate listslack of adequate lists may automatically rule
out systematic sampling, stratified sampling,
or other sampling designs, or it may dictate
that a preliminary study, such as a short
telephone survey using random digit dialing,
be conducted to generate information to build
a sampling frame for the primary study.

What Is the AppropriateWhat Is the Appropriate
Sample Design? (cont’d)Sample Design? (cont’d)
 National versus Local Project
 Geographic proximity of population
elements will influence sample design.
 When population elements are unequally
distributed geographically, a cluster
sample may become much more attractive.

© 2010 South-Western/Cengage
Learning. All rights reserved. May not
be scanned, copied or duplicated, or
posted to a publically accessible
website, in whole or in part.
16–56
EXHIBIT 16.EXHIBIT 16.99 Comparison of Sampling Techniques: Nonprobability SamplesComparison of Sampling Techniques: Nonprobability Samples

16–57
EXHIBIT 16.EXHIBIT 16.1010 Comparison of Sampling Techniques: Probability SamplesComparison of Sampling Techniques: Probability Samples

Determination of sample sizeDetermination of sample size
 Descriptive and Inferential Statistics
There are two applications of
statistics:
(1) to describe characteristics of
the population or sample
(descriptive statistics) and
(2) to generalize from the sample to
the population (inferential
statistics).

Sample Statistics and PopulationSample Statistics and Population
ParametersParameters
 The primary purpose of inferential statistics is to make a
judgment about the population, or the collection of all
elements about which one seeks information.
 The sample is a subset or relatively small fraction of the
total number of elements in the population.
 Sample statistics are variables in the sample or
measures computed from the sample data.
 Population parameters are variables or measured
characteristics of the population.
 We will generally use Greek lowercase letters to denote
population parameters (e.g., μ or σ) and English letters
to denote sample statistics (e.g., X or S).

Making Data UsableMaking Data Usable
 To make data usable, this information
must be organized and summarized.
 Methods for doing this include:
frequency distributions
proportions
measures of central tendency
and dispersion

Making Data Usable (cont’d)Making Data Usable (cont’d)
 Frequency Distributions
 Constructing a frequency table or frequency
distribution is one of the most common means of
summarizing a set of data.
 The frequency of a value is the number of times
a particular value of a variable occurs.
 Exhibit 17.1 represents a frequency distribution
of respondents’ answers to a question asking
how much customers had deposited in the
savings and loan.
 It is also quite simple to construct a distribution
of relative frequency, or a percentage
distribution, which is developed by dividing the
frequency of each

EXHIBIT 17.EXHIBIT 17.11 Frequency Distribution of DepositsFrequency Distribution of Deposits

EXHIBIT 17.EXHIBIT 17.22 Percentage Distribution of DepositsPercentage Distribution of Deposits

EXHIBIT 17.EXHIBIT 17.33 Probability Distribution of DepositsProbability Distribution of Deposits

Population Mean
Making Data Usable (cont’d)Making Data Usable (cont’d)
 Proportion
 The percentage of elements that meet
some criterion
 Measures of Central Tendency
 Mean: the arithmetic average.
 Median: the midpoint; the value below
which half the values in a distribution fall.
 Mode: the value that occurs most often.
Sample Mean

EXHIBIT 17.EXHIBIT 17.44 Number of Sales Calls per Day by SalespersonNumber of Sales Calls per Day by Salesperson

EXHIBIT 17.EXHIBIT 17.55 Sales Levels for Two Products with Identical Average SalesSales Levels for Two Products with Identical Average Sales

Measures of DispersionMeasures of Dispersion
The Range
The distance between the
smallest and the largest
values of a frequency
distribution.

EXHIBIT 17.EXHIBIT 17.66 Low Dispersion versus High DispersionLow Dispersion versus High Dispersion

Measures of Dispersion (cont’d)Measures of Dispersion (cont’d)
 Why Use the Standard Deviation?
 Variance
 A measure of variability or dispersion.
 Its square root is the standard deviation.
 Standard deviation
 A quantitative index of a distribution’s spread, or
variability; the square root of the variance for a
distribution.
 The average of the amount of variance for a
distribution.
 Used to calculate the likelihood (probability) of an
event occurring.

Calculating DeviationCalculating Deviation
Standard Deviation =

EXHIBIT 17.EXHIBIT 17.77 Calculating a Standard Deviation: Number of Sales Calls per Day for EightCalculating a Standard Deviation: Number of Sales Calls per Day for Eight
SalespeopleSalespeople

The Normal DistributionThe Normal Distribution
 Normal Distribution
 A symmetrical, bell-shaped distribution
(normal curve) that describes the expected
probability distribution of many chance
occurrences.
 99% of its values are within ± 3 standard
deviations from its mean.
 Example: IQ scores
 Standardized Normal Distribution
 A purely theoretical probability distribution
that reflects a specific normal curve for the
standardized value, z.

EXHIBIT 17.EXHIBIT 17.88 Normal Distribution: Distribution of Intelligence Quotient (IQ) ScoresNormal Distribution: Distribution of Intelligence Quotient (IQ) Scores

The Normal Distribution (cont’d)The Normal Distribution (cont’d)
 Characteristics of a Standardized Normal
Distribution
1. It is symmetrical about its mean; the tails on
both sides are equal.
2. The mean identifies the normal curve’s highest
point (the mode) and the vertical line about
which this normal curve is symmetrical.
3. The normal curve has an infinite number of
cases (it is a continuous distribution), and the
area under the curve has a probability density
equal to 1.0.
4. The standardized normal distribution has a
mean of 0 and a standard deviation of 1.

EXHIBIT 17.EXHIBIT 17.99 Standardized Normal DistributionStandardized Normal Distribution

The Normal Distribution (cont’d)The Normal Distribution (cont’d)
 Standardized Values, Z
 Used to compare an individual value to the
population mean in units of the standard
deviation
 The standardized normal distribution can be
used to translate/transform any normal variable,
X, into the standardized value, Z.
 Researchers can evaluate the probability of the
occurrence of many events without any
difficulty.

EXHIBIT 17.EXHIBIT 17.1010 Standardized Normal Table: Area under Half of the Normal CurveStandardized Normal Table: Area under Half of the Normal Curveaa

EXHIBIT 17.EXHIBIT 17.1111 StandardizedStandardized
Values can beValues can be
Computed fromComputed from
Flat or PeakedFlat or Peaked
DistributionsDistributions
Resulting in aResulting in a
StandardizedStandardized
Normal CurveNormal Curve

EXHIBIT 17.12EXHIBIT 17.12 Standardized Distribution CurveStandardized Distribution Curve

17–81
Population Distribution, SamplePopulation Distribution, Sample
Distribution, and SamplingDistribution, and Sampling
DistributionDistribution Population Distribution
 A frequency distribution of the elements of a
population.
 Sample Distribution
 A frequency distribution of a sample.
 Sampling Distribution
 A theoretical probability distribution of sample
means for all possible samples of a certain size
drawn from a particular population.
 Standard Error of the Mean
 The standard deviation of the sampling
distribution.

Three Important DistributionsThree Important Distributions

EXHIBIT 17.EXHIBIT 17.1313
FundamentalFundamental
Types ofTypes of
DistributionsDistributions

Central-limit TheoremCentral-limit Theorem
 Central-limit Theorem
 The theory that, as sample size increases,
the distribution of sample means of size n,
randomly selected, approaches a normal
distribution.

17–85
EXHIBIT 17.14EXHIBIT 17.14
The MeanThe Mean
Distribution ofDistribution of
AnyAny
DistributionDistribution
ApproachesApproaches
Normal asNormal as nn
IncreasesIncreases

EXHIBIT 17.15EXHIBIT 17.15 Population Distribution: Hypothetical Product DefectPopulation Distribution: Hypothetical Product Defect

EXHIBIT 17.16EXHIBIT 17.16 Calculation of Population MeanCalculation of Population Mean

EXHIBIT 17.17EXHIBIT 17.17 ArithmeticArithmetic
Means ofMeans of
Samples andSamples and
FrequencyFrequency
DistributionDistribution
of Sampleof Sample
MeansMeans

Estimation of Parameters and ConfidenceEstimation of Parameters and Confidence
Intervals (for inference statistics)Intervals (for inference statistics)
 Point Estimates
 An estimate of the population mean in the form
of a single value, usually the sample mean.
 Gives no information about the possible magnitude
of random sampling error.
 Confidence Interval Estimate
 A specified range of numbers within which a
population mean is expected to lie.
 An estimate of the population mean based on
the knowledge that it will be equal to the sample
mean plus or minus a small sampling error.
 i.e. μ = X + a small sampling error.

 The information can be used to
estimate market demand.
 E.g. with 95 percent confidence, the
average number of unit used per week is
between 2.3 and 2.9.

Confidence IntervalsConfidence Intervals
 Confidence Level
 A percentage or decimal value that tells
how confident a researcher can be about
being correct.
 It states the long-run percentage of
confidence intervals that will include the
true population mean.
 The crux of the problem for a researcher is
to determine how much random sampling
error to tolerate.
 Traditionally, researchers have used the
95% confidence level (a 5% tolerance for
error).

Calculating a ConfidenceCalculating a Confidence
IntervalInterval
Estimation of the sampling error
Approximate location (value) of the population
mean

Calculating a Confidence IntervalCalculating a Confidence Interval

Sample SizeSample Size
 Random Error and Sample Size
 Random sampling error varies with samples
of different sizes.
 Increases in sample size reduce sampling
error at a decreasing rate.
 Diminishing returns - random sampling error is
inversely proportional to the square root of n.

EXHIBIT 17.18EXHIBIT 17.18 Relationship between Sample Size and ErrorRelationship between Sample Size and Error

EXHIBIT 17.19EXHIBIT 17.19 Statistical Information Needed to Determine Sample Size forStatistical Information Needed to Determine Sample Size for
Questions Involving MeansQuestions Involving Means

Factors of Concern in ChoosingFactors of Concern in Choosing
Sample SizeSample Size
 Variance (or Heterogeneity)
 A heterogeneous population has more
variance (a larger standard deviation) which
will require a larger sample.
 A homogeneous population has less
variance (a smaller standard deviation) which
permits a smaller sample.
 Magnitude of Error (Confidence Interval)
 How precise must the estimate be?
 Confidence Level
 How much error will be tolerated? For
business research, 95 percent confidence95 percent confidence
level is used.

Estimating Sample Size forEstimating Sample Size for
Questions Involving MeansQuestions Involving Means
 Sequential Sampling
 Conducting a pilot study to estimate the
population parameters so that another, larger
sample of the appropriate sample size may be
drawn.
 Estimating sample size:

Sample Size ExampleSample Size Example
 Suppose a survey researcher, studying expenditures
on lipstick, wishes to have a 95 percent confidence
level (Z) and a range of error (E) of less than $2.00.
The estimate of the standard deviation is $29.00.
What is the calculated sample size?

Sample Size ExampleSample Size Example
 Suppose, in the same example as the one before,
the range of error (E) is acceptable at $4.00. Sample
size is reduced.

Calculating Sample Size at theCalculating Sample Size at the
99 Percent Confidence Level99 Percent Confidence Level

Determining Sample Size for ProportionsDetermining Sample Size for Proportions

753=
001225.
922.
=
001225
)24)(.8416.3(
=
)035( .
)4)(.6(.)961.(
n
4.q
6.p
2
2
=
=
=
Calculating Example SampleCalculating Example Sample
Size at the 95 PercentSize at the 95 Percent
Confidence LevelConfidence Level

EXHIBIT 17.20EXHIBIT 17.20 Selected Tables for Determining Sample Size When the Characteristic ofSelected Tables for Determining Sample Size When the Characteristic of
Interest Is a ProportionInterest Is a Proportion

EXHIBIT 17.21EXHIBIT 17.21 Allowance for Random Sampling Error (Plus and Minus PercentageAllowance for Random Sampling Error (Plus and Minus Percentage
Points) at 95 Percent Confidence LevelPoints) at 95 Percent Confidence Level

The Nature of FieldworkThe Nature of Fieldwork
 Fieldworker
 An individual who is responsible for
gathering data in the field.
 Typical fieldwork activities:
 Administering a questionnaire door to door
 Telephone interview calling from a central
location
 Counting pedestrians in a shopping mall
 Supervising the collection of data

Making Initial ContactMaking Initial Contact
 Personal Interviews
 Making opening remarks that will convince the
respondent that his or her cooperation is important.
 Telephone Interviews
 Giving the interviewer’s name personalizes the call.
 Providing the name of the research agency is used
to imply that the caller is trustworthy.
 Providing an accurate estimate of the time helps
gain cooperation.
 Internet Surveys
 Respondent may receive an e-mail requesting
assistance.

Gaining ParticipationGaining Participation
 Foot-in-the-Door Compliance Technique
 Compliance with large or difficult task is
induced by first obtaining the respondent’s
compliance with a smaller request.
 Door-in-the-Face Compliance Technique
 A two-step process for securing a high
response rate.
 Step 1: An initial request, so large that nearly
everyone refuses it, is made.
 Step 2: A second request is made for a smaller
favour; respondents are expected to comply with
this more reasonable request.

Asking the QuestionsAsking the Questions
 Major Rules for Asking Questions:
1. Ask questions exactly as they are worded in
the questionnaire.
2. Read each question very carefully and
clearly.
3. Ask the questions in the specified order.
4. Ask every question specified in the
questionnaire.
5. Repeat questions that are misunderstood or
misinterpreted.

Probing When No Response IsProbing When No Response Is
GivenGiven
 Probing
 Verbal attempts made by a field-worker when
the respondent must be motivated to
communicate his or her answers more fully.
 Probing Tactics that Enlarge and Clarify:
 Repeating the question
 Using a silent probe
 Repeating the respondent’s reply
 Asking a neutral question

EXHIBIT 18.EXHIBIT 18.11 Commonly Used Probes and Their AbbreviationsCommonly Used Probes and Their Abbreviations

Recording the ResponsesRecording the Responses
 Rules for recording responses to fixed-alternative
questions vary with the specific questionnaire.
 Rules for recording open-ended answers include:
 Record responses during the interview.
 Use the respondent’s own words.
 Do not summarize or paraphrase the respondent’s answer.
 Include everything that pertains to the question objectives.
 Include all of your probes.
 How answers are recorded can affect researchers’
interpretation of the respondent’s answers.

18–114
EXHIBIT 18.EXHIBIT 18.22 A Completed Portion of a Response Form with NotesA Completed Portion of a Response Form with Notes

Terminating the InterviewTerminating the Interview
 How to close the interview is important:
 Fieldworkers should wait to close the
interview until they have secured all pertinent
information including spontaneous comments
of the respondent.
 Fieldworkers should answer any respondent
questions concerning the nature and purpose
of the study to the best of his or her ability.
 Avoiding hasty departures is a matter of
courtesy.
 It is important to thank the respondent for his
or her time and cooperation as reinterviewing
may be required.

Principles of Good InterviewingPrinciples of Good Interviewing
 The Basics:
1. Have integrity, and be honest.
2. Have patience and tact.
3. Pay attention to accuracy and detail.
4. Exhibit a real interest in the inquiry at hand,
but keep your own opinions to yourself.
5. Be a good listener.
6. Keep the inquiry and respondents’ responses
confidential.
7. Respect others’ rights.

Principles of GoodPrinciples of Good
Interviewing (cont’d)Interviewing (cont’d)
 Required Practices
1. Complete the number of interviews according to the
sampling plan assigned to you.
2. Follow the directions provided.
3. Make every effort to keep schedules.
4. Keep control of each interview you do.
5. Complete the questionnaires meticulously.
6. Check over each questionnaire you have completed.
7. Compare your sample execution and assigned quota with
the total number of questionnaires you have completed.
8. Clear up any questions with the research agency.

Further ReadingFurther Reading
 COOPER, D.R. AND SCHINDLER, P.S. (2011)
BUSINESS RESEARCH METHODS, 11TH
EDN,
MCGRAW HILL
 ZIKMUND, W.G., BABIN, B.J., CARR, J.C. AND
GRIFFIN, M. (2010) BUSINESS RESEARCH
METHODS, 8TH
EDN, SOUTH-WESTERN
 SAUNDERS, M., LEWIS, P. AND THORNHILL, A.
(2012) RESEARCH METHODS FOR BUSINESS
STUDENTS, 6TH
EDN, PRENTICE HALL.
 SAUNDERS, M. AND LEWIS, P. (2012) DOING
RESEARCH IN BUSINESS & MANAGEMENT, FT
PRENTICE HALL.

DETERMINING SAMPLE SIZEDETERMINING SAMPLE SIZE
APPENDIXAPPENDIX

14-120
Random SamplesRandom Samples

14-121
Increasing PrecisionIncreasing Precision

14-122
Confidence Levels & theConfidence Levels & the
Normal CurveNormal Curve

14-123
Standard ErrorsStandard Errors
Standard Error
(Z score)
% of Area Approximate
Degree of
Confidence
1.00 68.27 68%
1.65 90.10 90%
1.96 95.00 95%
3.00 99.73 99%

14-124
Central Limit TheoremCentral Limit Theorem

14-125
Estimates of Dining VisitsEstimates of Dining Visits
Confidence Z
score
% of
Area
Interval Range
(visits per
month)
68% 1.00 68.27 9.48-10.52
90% 1.65 90.10 9.14-10.86
95% 1.96 95.00 8.98-11.02
99% 3.00 99.73 8.44-11.56

14-126
Calculating Sample Size forCalculating Sample Size for
Questions involving MeansQuestions involving Means
PrecisionPrecision
Confidence levelConfidence level
Size of interval estimateSize of interval estimate
Population DispersionPopulation Dispersion
Need for FPANeed for FPA

14-127
Metro U Sample Size for MeansMetro U Sample Size for Means
Steps InformationInformation
Desired confidence level 95% (z = 1.96)95% (z = 1.96)
Size of the interval estimate ±± .5 meals per month.5 meals per month
Expected range in
population
0 to 30 meals0 to 30 meals
Sample mean 1010
Standard deviation 4.14.1
Need for finite population
adjustment
NoNo
Standard error of the mean .5/1.96 = .255.5/1.96 = .255
Sample size (4.1)(4.1)22
/ (.255)/ (.255)22
= 259= 259

14-128
Proxies of theProxies of the
Population DispersionPopulation Dispersion
 Previous research on thePrevious research on the
topictopic
 Pilot test or pretestPilot test or pretest
 Rule-of-thumb calculationRule-of-thumb calculation
 1/6 of the range1/6 of the range

14-129
Metro U Sample Size forMetro U Sample Size for
ProportionsProportions
Steps InformationInformation
Desired confidence level 95% (z = 1.96)95% (z = 1.96)
Size of the interval estimate ±± .10 (10%).10 (10%)
Expected range in population 0 to 100%0 to 100%
Sample proportion with given
attribute
30%30%
Sample dispersion Pq = .30(1-.30) = .21Pq = .30(1-.30) = .21
Finite population adjustment NoNo
Standard error of the
proportion
.10/1.96 = .051.10/1.96 = .051
Sample size .21/ (.051).21/ (.051)22
= 81= 81

14-130
Random SamplesRandom Samples

14-131
Confidence LevelsConfidence Levels

14-132
Metro U. Dining Club StudyMetro U. Dining Club Study

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