br lecture 10-12 data analysis-upload

8/8/2019 BR Lecture 10-12 Data Analysis-Upload

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William G. Zikmund

Barry J. Babin

William G. Zikmund

Barry J. Babin

9th Edition9th Edition

Hypothesis testingUnivariate & Bivariate

Statistical Analysis


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13MGT 3940 Business Research Methods: Asst. Prof Dr. Nucharee S.

Types ofhypothesesTypes ofhypotheses

Null hypothesisNull hypothesis Statement about the status quoStatement about the status quo

No differenceNo difference

Alternative hypothesisAlternative hypothesis

Statement that indicates the opposite of the null hypothesisStatement that indicates the opposite of the null hypothesis


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Linear Transformation ofAny Normal VariableLinear Transformation ofAny Normal VariableInto a Standardized Normal VariableInto a Standardized Normal Variable

-2 -1 0 1 2

Sometimes thescale is stretched

Sometimes the

scale is shrunk

QQ

WW

X

WQ!

x

z

x 1SD 2SD 3SD-3SD -2SD -1SD


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2.14%

13.59%

34.13% 34.13%

13.59%

2.14%

0 1 2 3-3 -2 -1

Standardized Normal DistributionStandardized Normal Distribution

Z


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Region ofRejectionRegion ofRejection

Q x

UPPER LIMITLOWER LIMIT

95%


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Hypothesis Test: an exampleHypothesis Test: an example

,, ! !

,,

! !

X = 3.28, SD=0.1,

95% Confident level

2.804 3.196Q X = 3.28

P-value


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,, ! !

,,

! !

X = 3.18, SD=0.1,

95% Confident level

P-value is exceeding 0.05, Null hypothesis is failed to reject.The measurement score is not statistical differencefrom 3.00.


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,, ! !

,,

! !

X = 3.78, SD=0.1,

95% Confident level

! X = 3.782.804 3.196

P-value is less than 0.05, Null hypothesis can be rejected. Population parameter is statistically different

from 3.00


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Accept null Reject null

Null is true

Null is false

CorrectCorrect--no errorno error

Type IType Ierrorerror

Type IIType II

errorerror

CorrectCorrect--

no errorno error

Type I and Type II ErrorsType I and Type II Errors


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Choosing the Appropriate Statistical TechniqueChoosing the Appropriate Statistical Technique

Type of question to be answeredType of question to be answered

Number of variablesNumber of variables

UnivariateUnivariate

BivariateBivariate

MultivariateMultivariate

Scale of measurementScale of measurement

PARAMETRIC

STATISTICS

NONPARAMETRIC

STATISTICS


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Questionnaire: An ExampleQuestionnaire: An ExampleStarbucks Survey1. Do you know Starbucks?

Yes No

2. Which of the following coffee shop have you used to go?

Starbucks Coffee World

Ban Rai Blue Mountain

Au Bon Pain Other, specify _________3. How many times did you go to Starbucks last month ?

Less than 1 time. 1-2 times.

3-4 times. More than 4 times

4. How would you rate the quality of the following attributes of Starbucks?

1. Reputation2. Rational Price

3. Atmosphere

4. Service

5. Accessibility to the shop

6. Sales promotion

7. Advertisement

8. Taste9. Quality of products

10. Variety of products

HighHigh

High

High

High

High

High

HighHigh

High

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LowLow

Low

Low

Low

Low

Low

LowLow

Low

5. How do feel with the following sales promotions offered by Starbucks?

1. Discount Coupon

2. Member Card

3. Premium

4. Collecting point

Interesting

Interesting

Interesting

Interesting

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Unattractive

Unattractive

Unattractive

Unattractive

6. In the next time, if you need to go to a coffee shop, will you choose Starbucks?

Yes not sure No


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Personal Data

7. Gender Male Female

8. Age

Less than 20 years old. 20-25 years old.

26-30 years old. 31-35 years old.



Over 55 years old.

9. Education Primary school. Secondary/high school.

Bachelor. Master/ Ph.D.

10. Occupation

Student. Employee.

Housewife. Governor.

Business Owner. Other, specify _________.

11. Income_____________ Baht.

Less than 10,000 10,000-20,000 20,001-30000 More than 30,000

Questionnaire: An ExampleQuestionnaire: An Example


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Hypothesis Test Using the tHypothesis Test Using the t--DistributionDistribution

3. How would you rate the quality of the following attributes of Starbucks?

11. Reputation. Reputation

22. Rational Price. Rational Price

33. Atmosphere. Atmosphere

44. Service. Service

55. Accessibility. Accessibility

66. Sales promotion. Sales promotion77. Advertisement. Advertisement

88. Taste. Taste

99. Quality of products. Quality of products

1010. Variety of products. Variety of products

HighHigh

HighHigh

HighHigh

HighHigh

HighHigh

HighHighHighHigh

HighHigh

HighHigh

HighHigh

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LowLow

LowLow

LowLow

LowLow

LowLow

LowLowLowLow

LowLow

LowLow

LowLow

HYPOTHESIS:

Consumers perceive the quality of Starbucks as high

H0: = 3.5

Ha: 3.5


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T-TestOne-Sample Statistics

80 3.30 1.036 .116

80 3.46 .993 .111

80 3.78 1.006 .112

80 3.90 .922 .103

80 3.75 .834 .093

80 3.09 .697 .078

80 3.91 .679 .076

80 4.24 .716 .080

80 4.35 .929 .104

80 3.70 1.107 .124

Reputation

Price

Atmosphere

Services

Place

Sales promotion

Advertisement

Taste

Quality of products

Variety of products

N Mean Std. Deviation

Std. Error

Mean

One-Sample Test

-1.727 79 .088 -.200 -.43 .03

-.338 79 .736 -.038 -.26 .18

2.445 79 .017 .275 .05 .50

3.879 79 .000 .400 .19 .61

2.680 79 .009 .250 .06 .44

-5.293 79 .000 -.413 -.57 -.26

5.436 79 .000 .413 .26 .56

9.214 79 .000 .738 .58 .90

8.182 79 .000 .850 .64 1.06

1.616 79 .110 .200 -.05 .45

Reputation

Price

Atmosphere

Services

Place

Sales promotion

Advertisement

Taste

Quality of products

Variety of products

t df Si . (2-tailed)

Mean

Difference Lo er pper

95%

onfidence

nterval of the

Difference

Test Value 3.5

From the table, t-values of

atmosphere, services, place,

sales promotion,

advertisement, taste, andquality of products are

exceeding 1.96, with p-

values of less than 0.05,

therefore, those null

hypotheses could be

rejected. Thus, consumers

perceive Starbucks

atmosphere, services, place,

sales promotion,

advertisement, taste, and

quality of products assignificantly high while

consumers perception on

reputation, price, and

variety of product are nothigh.


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MGT 3940 Business Research Methods: Asst. Prof Dr. Nucharee S.

Differences Between Groups when Comparing MeansDifferences Between Groups when Comparing Means

Ratio/Interval scaled dependent variablesRatio/Interval scaled dependent variables tt--test for comparing meanstest for comparing means

When groups are smallWhen groups are small

When population standard deviation is unknownWhen population standard deviation is unknown

Null Hypothesis About Mean Differences BetweenNull Hypothesis About Mean Differences Between

GroupsGroups

21

21XX

St

''!

X1 = mean for Group 1X2= mean for Group 2

SX1-X2= the pooled or combined standard error

of difference between means.


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Hypothesis: Frequent and non frequent customers perceive the quality ofStarbucks

differently.


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Grou Statistics

37 2.8

.023 .

68

43 3.72 .854 .

30

37 3.38

.

63 .

9

43 3.53 .827 .

26

37 3.38

.037 .

7043 4.

2 .85

.

30

37 3.78

.

09 .

82

43 4.00 .724 .

0

37 3.62 .68

.

2

43 3.86 .94

.

43

37 3.05 .664 .

09

43 3.

2 .731 .111

37 3.68 .626 .103

43 4.12 .662 .101

37 4.38 .758 .125

43 4.12 .662 .101

37 4.08 1.140 .187

43 4.58 .626 .095

37 3.54 1.216 .200

43 3.84 .998 .152

T

f cst

r

N

-fr

t c

st

rs

Fr

t c

st

rs

N

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t c

st

rs

Fr

t c

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rs

N

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t c

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rsFr

t c

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rs

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t c

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t c

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ric

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rtis

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st

lit

fr

cts

ri

t

fr

cts

N

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.

i

ti

t

.!

rr

r

Inde endent Sam les Test

2.171 .145 -4.337 78 .000

-4.278 70.429 .000

4.508 .037 -.701 78 .486

-.683 63.767 .497

2.811 .098 -3.496 78 .001

-3.444 69.745 .001

10.703 .002 -1.046 78 .299

-1.015 60.284 .314

3.737 .057 -1.282 78 .204

-1.312 75.901 .193

.469 .496 -.396 78 .693

-.399 77.745 .691

.168 .683 -3.043 78 .003

-3.056 77.286 .003

2.408 .125 1.650 78 .103

1.634 72.126 .107

5.774 .019 -2.478 78 .015

-2.379 54.006 .021

3.415 .068 -1.198 78 .234

-1.181 69.772 .242

Equal"

arianc#s assumed

Equal"

ariances not assumed

Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Equal"

ariances assumed

Equal"


Reputatio

n

Price

Atmosphe

re

Ser"

ices

Place

Sales

promotion

Advertise

ment

Taste

Qualit$of

products%

ariet$of

products

F Sig.

Levene's Test

forEqualit$of

%

ariances

t df Sig.&2-tailed) Di

t-test forEqualit$ofM

H pothesis:

Ho: 1=

2

Ha: 1 2

Conclusion:..


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Ratio/interval scaled dependent variablesRatio/interval scaled dependent variables

Analysis of VarianceAnalysis of Variance

Hypothesis when comparing three groupsHypothesis when comparing three groups

,,QQ11

!Q!

Q!

Q!

Q,,

%%t least one group is different from others.t least one group is different from others.

Differences among groups when comparing meansDifferences among groups when comparing means

groupswithinVariance

groupsbetweenVarianceF

!


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AN A

Discount coupon

121.080 3 40.360 27.558 .000

111.307 76 1.465

232.388 79

Between Groups

Within Groups

Total

Sum of

Squares df Mean Square F Sig.

Homogeneous Subsets

Discount cou on

Scheffea,

7 1.43

7 1.86

25 4.64

41 4.98

.869 .932

Income

More than 30,000 Baht

20,001 - 30,000 Baht

10,000 - 20,000 Baht

Less than 10,000 Baht

Sig.

N 1 2

Subset for

alpha = .05

Means for groups in homogeneous subsets are displayed.

Uses Harmonic Mean Sample Size = 11.425.a.

The group sizes are unequal. The harmonic mean

of the group sizes is used. Type I error levels are

not guaranteed.

b.

Ho: 1 = 2 = 3= 4Ha: At least one is not equal

Conclusions: .


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Measures ofAssociationMeasures ofAssociation

A general term that refers to a number ofA general term that refers to a number ofbivariate statistical techniques used tobivariate statistical techniques used to

measure the strength of a relationshipmeasure the strength of a relationship

between two variables.between two variables.

Relationships Among VariablesRelationships Among Variables Correlation analysisCorrelation analysis

Bivariate regression analysisBivariate regression analysis


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Correlation CoefficientCorrelation Coefficient

is a statistical measure of the covariation oris a statistical measure of the covariation or

association between two variables.association between two variables.

The Correlation coefficient for two variables, X and Y isThe Correlation coefficient for two variables, X and Y is rr

Regression analysisRegression analysis

is a measure of linear association that

investigates a straight line relationship Useful in forecasting


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Bivariate Linear RegressionBivariate Linear Regression

A measure of linear association that investigates a straightA measure of linear association that investigates a straight--linelinerelationshiprelationship

Y = a + bX or Y =Y = a + bX or Y = 00 ++ X +X + wherewhere

Y is the dependent variableY is the dependent variable

X is the independent variableX is the independent variable

a and ba and b 00 ++ ) are two constants to be estimated unstandardized) are two constants to be estimated unstandardized ))

a = Y intercepta = Y intercept which is an intercepted segment of a linewhich is an intercepted segment of a line

The point at which a regression line intercepts the YThe point at which a regression line intercepts the Y--axisaxis

b Slopeb Slope

The inclination of a regression line as compared to a base lineThe inclination of a regression line as compared to a base line Rise over runRise over run

Can be positive or negative directionCan be positive or negative direction


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Simple Regression AnalysisSimple Regression Analysisaria les ntered/Remo ed'

Reputationa . Enter

Model

1

Variables

Entered

Variables

Removed Method

All requestedvariables entered.a.

Dependent Variable: Purchare Intentionb.

Model Summary

.540a .292 .283 .420

Model

1

R R Square

Adjusted

R Square

Std.Errorof

theEstimate

Predictors: Constant), Reputationa.

AN A

5.656 1 5.656 32.126 .000a

13.732 78 .176

19.388 79

RegressionResidual

Total

Model

1

Sumof


Predictors: Constant), Reputationa.

Dependent Variable: Purchare Intentionb.

oefficientsa

1.735 .158 11.017 .000

.258 .046 .540 5.668 .000

Constant)

Reputation

Model

1

B Std.Error

nstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Purchare Intentiona.


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Mode Su ar

.797a .635 .583 .320

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

Predictors: ( onstant) Variety of products,

Advertisement, Taste, Services, Sales promotion,

Place, Reputation, Price, Atmosphere, Quality of

products

a.

AN A

12.318 10 1.232 12.023 .000

a

7.069 69 .102

19.388 79

Regression

Residual

Total

Model

1

Sum of


Predictors: ( onstant), Variety of products, Advertisement, Taste,

Services, Sales promotion, Place, Reputation, Price, Atmosphere,

Quality of products

a.

Dependent Variable: Purchare Intentionb.oefficientsa

1.712 .442 3.877 .000

.137 .040 .287 3.398 .001

-.021 .044 -.043 -.482 .631

.138 .044 .280 3.166 .002

-.127 .049 -.237 -2.597 .011-.093 .052 -.156 -1.790 .078

.078 .056 .110 1.407 .164

.145 .057 .199 2.537 .013

-.236 .056 -.340 -4.239 .000

.179 .049 .335 3.631 .001

.062 .038 .139 1.624 .109

( onstant)

Reputation

Price

Atmosphere

ServicesPlace

Sales promotion

Advertisement

Taste

Quality of products

Variety of products

Model

1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Purchare Intentiona.

Mu tip e Regression Ana sisMu tip e Regression Ana sis


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HYPOTHESIS:HYPOTHESIS:The numbers of customers who went to Starbucks in the last month withThe numbers of customers who went to Starbucks in the last month withdifferent frequency are different.different frequency are different.

HHoo:: The numbers of customers who went to Starbucks in the last month withThe numbers of customers who went to Starbucks in the last month with

different frequency are equal.different frequency are equal.

HHaa:: The numbers of customers who went to Starbucks in the last month withThe numbers of customers who went to Starbucks in the last month with

different frequency are different.different frequency are different.

ChiChi--Square Test: an exampleSquare Test: an example

Starbucks Survey2.How many times did you go to Starbucks last month ?

Less than 1 time. 1-2 times.

3-4 times. More than 4 times


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ChiChi--square testsquare test

Less thanLess than 11 time.time. ExpectedExpectedcountscounts

ObservedObservedcountscounts

ExpectedExpectedcountscounts






11--22 times.times.

33--44 times.times.

More thanMore than 44 timestimes

!i

ii)(

E

EOx

x= chi-square statistics

Oi= observed frequency in the ith cell

Ei= expected frequency on the ith cell


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ChiChi--Square Test: an exampleSquare Test: an example

How many times did you go to Starbucks in the last month?

37 46.3 46.3 46.3

18 22.5 22.5 68.8

10 12.5 12.5 81.3

15 18.8 18.8 100.0

80 100.0 100.0

Less than 1 time

per week

1 time per week

2- 3 times per week

More than 3 times

per week

Total

Valid

(requency Percent Valid Percent

Cumulative

Percent

How many times did you go to Starbucks in the last month?

37 20.0 17.0

18 20.0 -2.0

10 20.0 -10.0

15 20.0 -5.0

80

Less than 1 time per week

1 time per week

2- 3 times per week

More than 3 times per week

Total

bserved N Expected N Residual

Test Statistics

20.900

3

.000

Chi-Square a

df

Asymp.Sig.

How many times did you go to

Starbucks in the last month?

0 cells (.0%) have expected frequencies less than

5. The minimum expected cell frequency is 20.0.

a.

From the table, chi-square value is

20.9 with a p-value of less than 0.05,

therefore, the null hypothesis could

be rejected and alternative

hypothesis is accepted. Thus, the

numbers of customers who went toStarbucks in the last month with

different frequency are significantlydifferent


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Differences Between GroupsDifferences Between Groups Contingency TablesContingency Tables

CrossCross--TabulationTabulation

ChiChi--Square allows testing for significant differences betweenSquare allows testing for significant differences betweengroupsgroups

Goodness of itGoodness of it

!i

ii

)(

E

EOx

n

CR

E

ji

ij !

Ri= total observed frequency in the ith row

Cj= total observed frequency in the jth column

n = sample size

d.f. = (R-1)(C-1)

x= chi-square statistics

Oi= observed frequency in the ith cell

Ei= expected frequency on the ith cell


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Hypothesis: The frequency to visit Starbucks is different among

various income groups.


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How many times did you go to Starbucks in the last month? * Income Crosstabulation

22 13 2 0 37

53.7 52.0 28.6 .0 46.311 4 2 1 18

26.8 16.0 28.6 14.3 22.5

6 3 0 1 10

14.6 12.0 .0 14.3 12.5

2 5 3 5 15

4.9 20.0 42.9 71.4 18.8

41 25 7 7 80

100.0 100.0 100.0 100.0 100.0

Count

within IncomeCount

within Income

Count

within Income

Count

within Income

Count

within Income

Less than 1 time

per week1 time per week

2- 3 times per week

More than 3 times

per week

How many

times did yougo to Starbucks

in the last

month

Total

Less than

10,000 Baht

10,000 -

20,000 Baht

20,001-

30,000 Baht

More than

30,000 Baht

Income

Total

Chi S uare Tests

23.317a 9 .006

24.357 9 .004

15.631 1 .000

80

earson Chi-Square

Likelihood atio

Linear-by-Linearssociation

of alid Cases

alue dfAsymp. Sig.

(2-sided

10 cells (62.5 ha e e pected count less than5. The minimum e pected count is .88.

a.

Error collapse scale


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To transform data by

collapsing the scale,

recode commandwould be used


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Hypothesis: The frequency to visit Starbucks is different among thegroup of customers with different income levels.


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Doyou have toperform anyotherDoyou have toperform anyotherdata analyses?data analyses?

RankingRanking

Multiple response analysis (for the checklist)Multiple response analysis (for the checklist)Etc.Etc.

br lecture 10-12 data analysis-upload

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