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11414-4-41-1Copyright©

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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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Companies,

Inc.

All

rights

reserved.17-4Hypothesis

TestingDeductionReasoningInductionReasoning141414-4-5-5Copyright©

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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

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McGraw-Hill

Companies,

Inc.

All

rights

reserved.Reasoning

and

HypothesesDeductions

are

only

as

good

asthe

premises

on

which

they

are

based.=REGISTEREDCopyright©

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by

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McGraw-Hill

Companies,

Inc.

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rights

reserved.17-7Statistical

ProceduresDescriptiveStatisticsInferentialStatistics1414-4-48-8Copyright©

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Inc.

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rights

reserved.HypothesisTesting

andtheResearchProcess1414-4-9-9-Copyright©

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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

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McGraw-Hill

Companies,

Inc.

All

rights

reserved.Significance

&

HypothesesStatistical

SignificancePractical

Significance141-1-41412-2Copyright©

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by

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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

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McGraw-Hill

Companies,

Inc.

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rights

reserved.Two-Tailed

Test

of

Significance141-14141-4-4Copyright©

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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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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©

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by

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Inc.

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rights

reserved.Critical

Values141-1-1419-9Copyright©

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Inc.

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rights

reserved.Probability

of

Making

A

Type

IErrorCopyright©

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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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Companies,

Inc.

All

rights

reserved.Probability

of

Making

A

Type

IIError141-1-4242-2-2Copyright©

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by

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McGraw-Hill

Companies,

Inc.

All

rights

reserved.Statistical

Testing

ProceduresObtain

criticaltest

valueInterpret

thetestStagesChoosestatistical

testState

nullhypothesisSelect

level

ofsignificanceComputedifferencevalueCopyright©

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by

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McGraw-Hill

Companies,

Inc.

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rights

reserved.17-23Tests

of

SignificanceNonparametricParametricCopyright©

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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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rights

reserved.Probability

Plot14-1-2426-6-Copyright©

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rights

reserved.Probability

Plot14-1-2427-7-Copyright©

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Inc.

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rights

reserved.Probability

Plot14-1-24248-8-Copyright©

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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©

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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©

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by

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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©

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by

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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©

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by

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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

©

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by

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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©

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by

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Inc.

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rights

reserved.Two-Sample

Parametric

Tests141-143437-7Copyright©

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by

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Companies,

Inc.

All

rights

reserved.Two-Sample

t-Test

ExampleA

GroupB

GroupAveragehourly

salesX1

=$1,500X2

=$1,300Standarddeviations1

=

225s2

=

251141-13434-8-Copyright©

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by

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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©

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by

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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©

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by

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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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rights

reserved.SPSS

Cross-Tabulation

Procedure14-1-42-2-Copyright©

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by

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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©

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by

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Companies,

Inc.

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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©

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by

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Inc.

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rights

reserved.SPSS

Outputfor

Paired-Samplest-Test141-14-6-6Copyright©

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by

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Companies,

Inc.

All

rights

reserved.Related

Samples

Nonparametric

Tests:McNemar

TestBeforeAfterDo

Not

FavorAfterFavorFavorABDo

Not

FavorCD14-1-47-7-Copyright©

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by

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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©

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by

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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

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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©

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by

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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©

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by

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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©

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by

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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©

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by

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Companies,

Inc.

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rights

reserved.ANOVA

Plots141-145454-4Copyright©

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by

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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©

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by

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rights

reserved.Two-way

Analysis

of

Variance

Plots141-14545-6-6Copyright©

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by

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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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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©

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by

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rights

reserved.Repeated

Measures

ANOVA

Plot14-Copyright©

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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©

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by

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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©

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by

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McGraw-Hill

Companies,

Inc.

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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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