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11414-4-41-1Copyright©
2019
by
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rights
reserved.Chapter
14S
T
A
G
E
4
:
H
Y
P
O
T
H
E
S
I
S
T
E
S
T
I
N
G11414-4--2-2Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Learning
ObjectivesUnderstand
.
.
.The
nature
and
logic
of
hypothesis
testing.A
statistically
significant
differenceThe
six-step
hypothesis
testing
procedure.The
differences
between
parametric
andnonparametric
tests
and
when
to
use
each.The
factors
that
influence
the
selection
of
anappropriate
test
of
statistical
significance.How
to
interpret
the
various
test
statistics.1414-4-3-3-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Research
Thought
Leader“A
fact
is
a
simple
statement
that
everyonebelieves.
It
is
innocent,
unless
found
guilty.
Ahypothesis
is
a
novel
suggestion
that
no
onewants
to
believe.
It
is
guilty,
until
foundeffective.”Edward
Teller,
theoretical
physicist,“father
of
the
hydrogen
bomb”(1908–2003)Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.17-4Hypothesis
TestingDeductionReasoningInductionReasoning141414-4-5-5Copyright©
2019
by
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Companies,
Inc.
All
rights
reserved.Reasoning
and
Hypotheses=Inductions
are
an
inferential
leapfrom
the
evidence
presented.14141-4-4-6-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Reasoning
and
HypothesesDeductions
are
only
as
good
asthe
premises
on
which
they
are
based.=REGISTEREDCopyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.17-7Statistical
ProceduresDescriptiveStatisticsInferentialStatistics1414-4-48-8Copyright©
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by
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Companies,
Inc.
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rights
reserved.HypothesisTesting
andtheResearchProcess1414-4-9-9-Copyright©
2019
by
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Companies,
Inc.
All
rights
reserved.The
“Ah-Ha”
MomentWhen
researcherssift
through
thechaos
and
find
whatmatters.14-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Approaches
to
Hypothesis
TestingClassical
statisticsObjective
view
ofprobabilityEstablishedhypothesis
is
rejectedor
fails
to
be
rejectedAnalysis
based
onsample
dataBayesian
statisticsExtension
of
classicalapproachAnalysis
based
onsample
dataAlso
considersestablished
subjectiveprobability
estimates14-1-11411-1Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Significance
&
HypothesesStatistical
SignificancePractical
Significance141-1-41412-2Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Null
vs.
Alternative
HypothesesNull·
H0:=60
mpg·
H0:<60
mpg·
H0:>60
mpgAlternativeHA:HA:HA:≠
60
mpg>
60
mpg<
60
mpg141-14141-3-3Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
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rights
reserved.Two-Tailed
Test
of
Significance141-14141-4-4Copyright©
2019
by
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Companies,
Inc.
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rights
reserved.One-Tailed
Test
of
Significance14-1-14145-5-Copyright©
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by
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Companies,
Inc.
All
rights
reserved.Decision
RuleTake
no
corrective
action
if
theanalysis
shows
that
one
cannotreject
the
null
hypothesis.14-1-1416-6-Copyright©
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by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Statistical
Decisions141-1-1417-7Copyright©
2019
by
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Companies,
Inc.
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rights
reserved.Probability
of
Making
a
Type
IError141-14141-8-8Copyright©
2019
by
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Companies,
Inc.
All
rights
reserved.Critical
Values141-1-1419-9Copyright©
2019
by
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Companies,
Inc.
All
rights
reserved.Probability
of
Making
A
Type
IErrorCopyright©
2019
by
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Companies,
Inc.
All
rights
reserved.17-20Factors
Affecting
Probability
ofCommitting
a
ErrorTrue
value
of
parameterAlpha
level
selectedOne
or
two-tailed
test
usedSample
standard
deviationSample
size141-1-242-1-1Copyright©
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by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Probability
of
Making
A
Type
IIError141-1-4242-2-2Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Statistical
Testing
ProceduresObtain
criticaltest
valueInterpret
thetestStagesChoosestatistical
testState
nullhypothesisSelect
level
ofsignificanceComputedifferencevalueCopyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.17-23Tests
of
SignificanceNonparametricParametricCopyright©
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by
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Companies,
Inc.
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rights
reserved.17-24Assumptions
for
Using
Parametric
TestsIndependent
observationsNormal
distributionEqual
variances
Interval
or
ratio
scales14-1-2425-5-Copyright©
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by
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Inc.
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rights
reserved.Probability
Plot14-1-2426-6-Copyright©
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by
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Companies,
Inc.
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rights
reserved.Probability
Plot14-1-2427-7-Copyright©
2019
by
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Companies,
Inc.
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rights
reserved.Probability
Plot14-1-24248-8-Copyright©
2019
by
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Companies,
Inc.
All
rights
reserved.Advantages
of
Nonparametric
TestsEasy
to
understand
and
useUsable
with
nominal
dataAppropriate
for
ordinal
dataAppropriate
for
non-normalpopulation
distributions14-1-2429-9-Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.How
to
Select
a
TestHow
manysamplesare
involved?Are
the
individual
casesindependent
or
related?Is
the
measurementnominal,
ordinal,
interval,
or
ratiIf
>
214-1-1343-0-0Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Recommended
Statistical
TechniquesTwo-Sample
Tests_k-Sample
Tests_Measurement
ScaleOne-SampleCaseRelatedSamplesIndependentSamplesRelatedSamplesIndependentSamplesNominalBinomialx2
one-sampletestMcNemarFisherexacttestx2
two-samplestestCochran
Qx2
for
ksamplesOrdinalKolmogorov-Smirnov
one-sample
testRunstestSign
testWilcoxonmatched-pairstestMedian
testMann-Whitney
UKolmogorov-SmirnovWald-WolfowitzFriedmantwo-wayANOVAMedianextensionKruskal-Wallisone-way
ANOVAIntervalandRatiot-testZ
testt-testforpairedsamplest-testZ
testRepeated-measuresANOVAOne-wayANOVAn-wayANOVA14-1-14341-1-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Questions
Answered
byOne-Sample
TestsDifference
between
observed
andexpected
frequencies?Difference
between
observed
andexpected
proportions?Significant
difference
between
somemeasure
of
central
tendency
and
thepopulation
parameter?141-1-3432-2-Copyright©
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by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Parametric
Testst-testZ-test14-1-34343-3Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.One-Sample
t-Test
ExampleNullHo:
=
50
mpgStatistical
testt-testSignificance
level.05,
n=100Calculated
value1.786Critical
test
value1.66(from
Appendix
C,Exhibit
C-2)14-1-13434-4-Copyright
©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.One
Sample
Chi-Square
Test
ExampleLiving
ArrangementIntendto
JoinNumberInterviewedPercent(no.
interviewed/200)ExpectedFrequencies(percent
x
60)Dorm/fraternity16904527Apartment/roominghouse,
nearby13402012Apartment/roominghouse,
distant16402012Live
athome1530159Total6020010060Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.17-35One-Sample
Chi-Square
ExampleNullHo:
0
=
EStatistical
testOne-sample
chi-squareSignificance
level.05Calculated
value9.89Critical
test
value7.82(from
Appendix
C,
Exhibit
C-3)14-1-3434-6-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Sample
Parametric
Tests141-143437-7Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Sample
t-Test
ExampleA
GroupB
GroupAveragehourly
salesX1
=$1,500X2
=$1,300Standarddeviations1
=
225s2
=
251141-13434-8-Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Sample
t-Test
ExampleNullHo:
A
sales
=
B
salesStatistical
testt-testSignificance
level.05
(one-tailed)Calculated
value1.97,
d.f.
=
20Critical
test
value1.725(from
Appendix
C,
Exhibit
C-2)141-1-434-9-9Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Sample
Nonparametric
Tests:Chi-SquareOn-the-Job-AccidentCell
DesignationCountExpected
ValuesYesNoRow
TotalSmoker1,11,2Heavy
Smoker12,4168.247.752,12,2Moderate96157.737.273,13,2Nonsmoker13223518.0316.97Column
Total343266141-14-0-0Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Sample
Chi-SquareExampleNullThere
is
no
difference
indistribution
channel
for
agecategories.Statistical
testChi-squareSignificance
level.05Calculated
value6.86,
d.f.
=
2Critical
test
value5.99(from
Appendix
C,
Exhibit
C-3)141-14-1-Copyright©
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by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.SPSS
Cross-Tabulation
Procedure14-1-42-2-Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-Related-Samples
TestsNonparametricParametric141-143-3Copyright
©
20199
bbyy
TThhee
MMccGGrraaww--HHiillll
CCoommppaanniieess,,
IInncc..
AAlll
rriigghhttss
rreesseerrvveedd..Sales
Data
forPaired-Samples
t-TestCompanySalesYear2SalesYear
1Difference
DD2GM126932123505342711744329GE5457449662491224127744Exxon8665678944771259474944IBM6271059512319210227204Ford9614692300384614971716AT&T3611235173939881721Mobil502204811121094447881DuPont350993242726326927424Sears5379449975381914584761Amoco239662077931871015696914-1-144-4Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Paired-Samples
t-Test
ExampleNullYear
1
sales
=
Year
2
salesStatistical
testPaired
sample
t-testSignificance
level.01Calculated
value6.28,
d.f.
=
9Critical
test
value3.25(from
Appendix
C,
Exhibit
C-2)14-1-45-5Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.SPSS
Outputfor
Paired-Samplest-Test141-14-6-6Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Related
Samples
Nonparametric
Tests:McNemar
TestBeforeAfterDo
Not
FavorAfterFavorFavorABDo
Not
FavorCD14-1-47-7-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Related
Samples
Nonparametric
Tests:McNemar
TestBeforeAfterDo
Not
FavorAfterFavorFavorA=10B=90Do
Not
FavorC=60D=4014-1-148-8-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.k-Independent-Samples
Tests:
ANOVATests
the
null
hypothesis
that
the
means
of
threeor
morepopulations
are
equal.One-way:
Uses
a
single-factor,
fixed-effectsmodel
to
compare
the
effects
of
a
treatment
orfactor
on
a
continuous
dependent
variable.141-1-4-9-9Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.ANOVA
Example
Model
Summary
Sourced.f.Sum
ofSquaresMean
SquareF
Valuep
ValueModel(airline)211644.0335822.01728.3040.0001Residual(error)5711724.550205.694Total5923368.583
Means
Table
CountMeanStd.
Dev.Std.
ErrorLufthansa2038.95014.0063.132MalaysiaAirlines2058.90015.0893.374Cathay
Pacific2072.90013.9023.108All
dataare
hypothetical141-1-54540-0-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.ANOVA
Example
ContinuedNullA1
=
A2
=
A3Statistical
testANOVA
and
F
ratioSignificance
level.05Calculated
value28.304,
d.f.
=
2,
57Critical
test
value3.16(from
Appendix
C,
Exhibit
C-9)141-1-454-1-1Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Post
Hoc:
Scheffe’s
S
MultipleComparison
ProcedureVersesDiffCrit.Diff.p
ValueLufthansaMalaysiaAirlines19,95011.400.0002CathayPacific33.95011.400.0001MalaysiaAirlinesCathayPacific14.00011.400.0122141-1-54542-2-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Multiple
Comparison
ProceduresTestComplexComparisonsPairwiseComparisonsEqualn’sOnlyUnequaln’sEqualVariancesAssumedUnequalVariancesNotAssumedFisher
LSDXXXBonferroniXXXTukey
HSDXXXTukey-KramerXXXGames-HowellXXXTamhane
T2XXXScheffé
SXXXXBrown-ForsytheXXXXNewman-KeulsXXDuncanXXDunnet’s
T3XDunnet’s
CX14-1-1454-3-3Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.ANOVA
Plots141-145454-4Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-WayANOVAExample
Model
Summary
Sourced.f.Sum
ofSquaresMeanSquareF
Valuep
ValueAirline211644.0335822.01739.1780.0001Seat
selection13182.8173182.81721.4180.0001Airline
by
seatselection2517.033258.5171.7400.1853Residual548024.700148.606MeansTable
Effect:
Airline
by
Seat
SelectionCountMeanStd.
Dev.Std.
ErrorLufthansaeconomy1035.60012.1403.839Lufthansabusiness1042.30015.5504.917MalaysiaAirlineseconomy1048.50012.5013.953MalaysiaAirlinesbusiness1069.3009.1662.898CathayPacificeconomy1064.80013.0374.123CathayPacificbusiness1081.0009.6033.037All
data
are
hypothetical141-1-5455-5Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Two-way
Analysis
of
Variance
Plots141-14545-6-6Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.k-Related-Samples
TestsMore
than
two
levels
ingrouping
factorObservations
are
matchedData
are
interval
or
ratio14-1-5457-7-Copyright©
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by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.SummaryTablesforRepeated-MeasuresANOVA Model
Summary
Sourced.f.Sum
ofSquaresMeanSquareF
Valuep
ValueAirline23552735.5017763.77567.1990.0001Subject
(group)5715067.650264.345Ratings1625.633625.63314.3180.0004Ratings
byair22061.7171030.85823.5920.0001Ratings
bysubj572490.65043.696Means
Table
Effect:
RatingsCountMeanStd.
Dev.Std.
ErrorRating
16056.91719.9022.569Rating
26061.48323.2082.996
Means
Table
by
Airline
CountMeanStd.
Dev.Std.
ErrorRating
1,
Lufthansa2038.95014.0063.132Rating
1,Malaysia
Airlines2058.90015.0893.374Rating
1,
Cathay
Pacific2072.90013.9023.108Rating
2,
Lufthansa2032.4008.2681.849Rating
2,Malaysia
Airlines2072.25010.5722.364Rating
2,
Cathay
Pacific2079.80011.2652.519All
dataare
hypothetical.14-1-5454-8-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Repeated
Measures
ANOVA
Plot14-Copyright©
2019
by
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McGraw-Hill
Companies,
Inc.
All
rights
reserved.Key
Termsa
priori
contrastsAlternative
hypothesisAnalysis
of
variance(ANOVA)Bayesian
statisticsChi-square
testClassical
statisticsCritical
valueF
ratioInferential
statisticsK-independent-samples
testsK-related-samples
testsLevel
of
significanceMean
squareMultiple
comparison
tests(range
tests)Nonparametric
testsNormal
probability
plotNull
hypothesisObserved
significance
levelOne-sample
testsOne-tailed
test14-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Key
Termsp
valueParametric
testsPower
of
the
testPractical
significanceRegion
of
acceptanceRegion
of
rejectionStatistical
significancet
distributionTrialst-testTwo-independent-samples
testsTwo-related-samples
testsTwo-tailed
testType
I
errorType
II
errorZ
distributionZ
test141-1464-1-Copyright©
2019
by
The
McGraw-Hill
Companies,
Inc.
All
rights
reserved.Photo
AttributionsSlideSourceSlideSource6©walenga/123RF28©
Shutterstock
/
Anton
Gepolov6©MedicalRF.com29©
Image
Source/Takahiro
Igarashi7©CostinT/Getty
Images32©
Monalyn
Gracia/Fancy/age
fotostock
RF7©
Image
Source,
all
rights
reserved.53©
Blend
Images
/
Alamy
Stock
Photo9©Caiaimage/Glow
Images63©
VStock
/
Alamy
Stock
Photo11©
McGraw-Hill
Education/Mark
Dierker64©
Janne
Tervonen
/
Alamy12©
McGraw-Hill
Education/Mark
Dierker65©
Jukeboxhero/iStock/Getty
Images24©
Anatolii
Babii
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Alamy66Purestock/SuperStockC
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