Transcript Chapter 10 File

Chapter 10 – Quantitative Data Analysis
Chapter Objectives
 Understand differences in measurement scale
○ How to code measurements on the spread sheet
 Understand different analysis methods for different scales
 Understand how to read and interpret results
 Develop your own research with appropriate analysis
method
Scales
Different Measurement Scales
Type of Scales
Nominal
Ordinal
Key Characteristics
Examples
• Key characteristics of • Sex
objects or individuals
• Colour of eye or hair
• Categories or groups
• Occupation
• Department of employees
• Importance attached or • Preference of hotel brands
preference for certain • Preference of courses
variables
• Rank-orders
Interval
• Numbers
with
same • Temperature
intervals
• Five-point (or seven-point
• Distance between any two or any number of points)
points on the scale
scale (i.e., Likert Scale)
Ratio
• Absolute value
• Sales turnover
• Size of the objects or • Number of customers
individuals
• Weight
• Time
Nominal Scale
 Nominal
○ Categories or groups
○ Gender, occupation, department of employees in an
organization
What was the type of restaurant that you have dined most recently?
 Fast food restaurant
 Casual dining restaurant
 Upscale restaurant
Ordinal Scale
 Ordinal
○ Rank orders the categories
○ An individual’s preference of hotel brands (rank)
○ A hospitality student’s preference of courses (rank)
Service Quality Dimensions
1. Tangibles
2. Reliability
3. Responsiveness
4. Assurance
5. Empathy
Ranking of Importance
________
________
________
________
________
Interval Scale
 Interval Scale
○ Numbers with same intervals
• Distance from 1 to 2 is same as the distance from 2 to 3
○ Measure the distance between any two points on the scale
 Likert Scale
○ A psychometric scale commonly used in research that employs
questionnaires
○ The most widely used approach to scaling in survey research, such that
the term is often used interchangeably rating scale
○ It is a statement which the respondent is asked to evaluate according to
any kind of subjective or objective criteria
• The level of agreement or disagreement is measured
Example of Likert Scale
 Many research in social science utilize Likert scale for mean comparison,
regression analysis, and so forth
 Most common form of Likert scale is 5-point or 7-point Likert scale
 Example of 5-point Likert scale
This question is asking how important you perceive service quality dimension
of a restaurant. Please indicate the extent to which you agree or disagree with
the following dimensions by checking the option you prefer
Tangibles of a restaurant
Reliabilities of service
Responsiveness of employees
Assurance of service
Empathy from employees
Strongly
Disagree
Somewhat
Disagree
j
j
j
j
j
k
k
k
k
k
Neutral
Somewhat
Agree
Strongly
Agree
l
l
l
l
l
m
m
m
m
m
n
n
n
n
n
Ratio Scale
 Ratio Scale
○ Has unique ‘zero’ origin
○ Multiplication & division
1a. What was the sales turnover for the start-up year?
1b. What is the sales turnover for 2006?
2a. How many people did you employ in the start-up year?
2c. How many people do/did you employ in 2006?
£______________
£______________
_______________
_______________
Coding / Entering Data for Analysis
 Variable
○ An indicator of interest in a research
○ May take any of a specified set of values, perceptions,
attitudes, and attributes
Measurement
What was the type of restaurant that you have dined most recently?
 Fast food restaurant
 Casual dining restaurant
 Upscale restaurant
Entering Data
What was the type of restaurant that you have dined most recently?
 Fast food restaurant
 Casual dining restaurant
 Upscale restaurant
Entering Data
Tangibles of a restaurant
Reliabilities of service
Responsiveness of employees
Assurance of service
Empathy from employees
Strongly
Disagree
Somewhat
Disagree
j
j
j
j
j
k
k
k
k
k
Neutral
Somewhat
Agree
Strongly
Agree
l
l
l
l
l
m
m
m
m
m
n
n
n
n
n
Analysing Quantitative Data
Outline of Analysis Methods
Scale
Nominal
Ordinal
Central Tendency
Dispersion
Mode
Variance
Mode, Median
Variance
Interval*
Mode, Median,
Mean
Standard
Deviation
Ratio
Mode, Median,
Mean
Standard
Deviation
•
•
•
•
•
•
•
•
•
Methods
Chi Square (χ2)
Chi Square (χ2)
t-test
Correlation
ANOVA
t-test
Correlation
ANOVA
Regression
• Even though Interval scale is not designed for regression analysis, it is often
considered continuous scale
• It is common to conduct regression analysis with interval scale
Descriptive Statistics #1
 Mean
○ Sum of all values divided by their number
x1 + x2 +... + xn
○
x=
n
 Standard Deviation
○ The amount of variation or dispersion from the average
(mean)
○
1 N
2
s=
(x
x
)
å i
N -1 i=1
Descriptive Statistics #2
 Median
○ Middle piece of data
○ 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6.
○ Median = 4
 Mode
○ Most frequently observed value in the dataset
○ 4, 6, 1, 2, 6, 3, 4, 5, 2, 6, 6, 3, 3, 3, 6, 4, 6, 4, 2, 6
○ Mode = 6
SPSS Example
(Descriptive Statistics)
 Analyze  Descriptive Statistics  Descriptives...
 Enter Variables  Options
SPSS Example
(Descriptive Statistics)
 Descriptive Statistics
Descriptive Statistics
N Min Max Mean Std. Deviation Variance
Price Reduction
296 1
5 3.54
0.780
0.608
New Product Development 298 1
5 3.70
0.808
0.653
Advertising
297 1
5 3.28
0.915
0.837
Relationship Marketing
297 1
5 3.06
0.805
0.648
Valid N (listwise)
292
 Price Reduction
○ Min = 1, Max = 5
○ Mean = 3.54
○ Standard Deviation = 0.780
○ Variance = 0.608
SPSS Example
(Frequencies)
 Analyse  Descriptive Statistics  Frequencies
 Statistics or Charts
SPSS Example
(Frequency)
 Frequency
○ 41.5% (n=124) of employees work at Housekeeping
department
○ 24.4% (n=73) of employees work at Food & Beverage
department
SPSS Example #2
 Bar Chart Example
Exploring Relationships between Variables
b. Relationships
1. Cross-Tabulation (χ2 test)
 Cross-tabulation
○ The representation of two variables in a matrix where all
answers in one variable (e.g., gender) are presented in rows,
and all answers in other (e.g., customer opinion) are presented
in columns
○ χ2 test is possible
SPSS Example
(Cross-Tabulation)
 Hypothesis
○ H0: Employment status (part-time vs. full-time) does not differ according to the
hotel brand scale
 Analyze  Descriptive Statistics  Crosstabs…
 Statistics  Select Chi-square
SPSS Example
(Cross-Tabulation)
 Results
○ Pearson Chi-Square = 9.719 (p < .05)
• Null Hypothesis can be rejected
• Employment status (part-time vs. full-time) differs according to the hotel brand
scale
2. Correlation
 Pearson Correlation
○ The degree to which a change in a variable is related to a
change in one or more other variable(s)
○ Identify the strength of relationship
○ Cannot tell the causal relationship
 One-tailed vs. Two-tailed
○ Specific direction is hypothesized  One-tailed
○ Non-directional hypotheses  Two-tailed
SPSS Example
(Correlation)
 Hypothesis
○ H1: Service performance is negatively related to service performance but
positively correlated to time spent training
 Analyze  Correlate  Bivariate…
 Option  Pearson Correlation Coefficient
SPSS Example
(Correlation)
 Results
○ rPerformance and Anxiety = -0.424 (p < .05) ; rPerformance and Time = 0.379 (p < .05)
• Null Hypothesis can be rejected
• Performance is negatively correlated to service anxiety but positively correlated
to time spent training
Exploring Relationships between Variables
b. Mean Comparison
Independent Sample t-test
 Independent Sample t-test
○ Compares the mean values of two different groups (μ1 = μ2)
○ If the mean values of two different groups are different (i.e.,
μ1 – μ2 = 0), t-value will be significant (p < .05)
 Dependent Variable
○ Measured by at least interval scale
 Independent Variable
○ Measured by categorical variable (e.g., male/female, parttime/full-time, etc.)
SPSS Example
(Independent Sample t-test)
 Hypothesis
○ H0: There is no significant difference between the check-in service speed of
male and female employees
 Analyze  Compare Means  Independent Samples T Test…
You need to define groups
In this case, male=1 and female=2
SPSS Example
(Independent Sample t-test)
 Results
○ Equal variance assumption check
• If F-value is not significant (p > .05), read ‘Equal variances assumed’ row
• If F-value is significant (p < .05), read “Equal variance not assumed’ row
○ t-value = –2.981 (p < .05)
• Null Hypothesis can be rejected
• Speed of check-in service differs according to the gender of employees
Paired Sample t-test
 Paired Sample t-test
○ Compares mean values of one group but measured at different
times
 Independent Sample t-test vs. Paired Sample t-test
○ Independent sample t-test
• Group: 2 different groups
• Mean value: one for each group
○ Paired sample t-test
• Group: 1 group
• Mean value: two mean values measured at different times
SPSS Example
(Paired Sample t-test)
 Hypothesis
○ H0: Potential customers’ attitudes toward a restaurant do not differ after they
are exposed to a new advertisement
 Analyze  Compare Means  Paired-Samples T Test…
You need to define two variables
(Before or After advertisement)
SPSS Example
(Paired Sample t-test)
 Results
Pair 1
Before - After
Mean
-.696
Std. Deviation
.995
Paired Samples Test
Paired Differences
95% Confidence Interval of the Difference
Std. Error
Mean
Lower
Upper
.058
-.809
-.582
t
-12.084
df
298
○ t-value = –12.084 (p < .05)
• Null Hypothesis can be rejected
• Potential customers’ attitudes toward a restaurant differs after they are exposed to a
new advertisement
Sig.
(2-tailed)
.000
One-Way ANOVA
 One-Way ANOVA
○ Mean comparison of more than two groups (or factor)
 Independent Sample t-test vs. One-Way ANOVA
○ Independent sample t-test
• Mean comparison between two groups
○ One-way ANOVA
• Mean comparison among more than two groups
SPSS Example
(One-Way ANOVA)
 Hypothesis
○ H0: Restaurant customers’ overall satisfaction does not differ according to the
type of restaurant
 Analyze  Compare Means  One-Way ANOVA…
‘Post Hoc…’ to identify specific
difference
SPSS Example
(One-Way ANOVA)
 Results #1 (ANOVA)
○ F-value = 16.499 (p < .05)
• Null Hypothesis can be rejected
• Restaurant customers’ overall satisfaction differs according to the type of restaurant
 Results #2 (Post-Hoc test)
○ Fast Food < Limited Service < Upscale Restaurant
Two-Way ANOVA
 Two-Way ANOVA
○ Compares the mean differences between groups that can be
split on two independent variables (factors)
○ Commonly used to identify interaction effects
Interaction Effect
• Male Low vs. Female High
• Female High vs. Male Low
Gender
Male
Female
Mean
Education Level
High
Low
μ Male High
μ Male Low
μ Female High μ Female Low
μ High
μ Low
Mean
μ Male
μ Female
μ Total
Main Effect
• High vs. Low
• Male vs. Female
Exploring Relationships between Variables
c. Causal Relationship
SPSS Example
(Two-Way ANOVA)
 Hypothesis
○ H1: The overall performance of employee would differ according to the gender
of an employee
○ H2: The overall performance of employee would differ according to the
education level of an employee
○ H3: There will be an interaction effect of gender and education level on overall
performance of employee
 Analyze  General Linear Model  Univariate…
SPSS Example
(Two-Way ANOVA)
 Step #1: Descriptive Statistics
○ Results #1 (Descriptive Statistics)
 Step #2: Table Construction
○ Construct table for descriptive statistics
Education Level
High School Undergraduate
Gender
3. Gender * Education Level
Dependent Variable: Overall Performance
95% Confidence Interval
Gender Education Level Mean Std. Error Lower Bound Upper Bound
Male
Undergraduate 3.443
.103
3.240
3.646
Graduate
3.147
.148
2.855
3.439
High School
3.071
.133
2.809
3.334
Female Undergraduate 3.796
.118
3.565
4.028
Graduate
3.289
.140
3.014
3.565
High School
2.831
.112
2.609
3.052
Graduate Mean
Male
3.071
3.443
3.147
3.220
Female
Mean
2.831
2.951
3.796
3.620
3.289
3.218
3.305
SPSS Example
(Two-Way ANOVA)
 Step #3: Between-Subjects Effects
Tests of Between-Subjects Effects
Dependent Variable: Overall Performance
Source
Type III Sum of Squares
df Mean Square
a
Corrected Model
30.603
5
6.121
Intercept
2964.513
1
2964.513
Gender
.503
1
.503
Education
24.884
2
12.442
Gender * Education
4.842
2
2.421
Error
217.202 291
.746
Total
3442.000 297
Corrected Total
247.805 296
a. R Squared = .123 (Adjusted R Squared = .108)
F
8.200
3971.757
.673
16.669
3.243
Sig.
.000
.000
.413
.000
.040
○ H1: F-value = 0.673 (p > .05)
• The overall performance of employee does not differ according to the gender of an
employee
○ H2: F-value = 12.442 (p < .05)
• The overall performance of employee differs according to the education level of an
employee
○ H3: F-value = 2.421 (p < .50)
• There is an interaction effect of gender and education level on overall performance of
employee
SPSS Example
(Two-Way ANOVA)
 Step #4: Graphical Illustration of Interaction Effect
○ Choose ‘Plots…’
Female undergraduate > Male undergraduate
Female High School < Male High School
Multiple Regression
 Multiple Regression
○ Examine the simultaneous effects of several independent
variables on a dependent variable
 Correlation vs. Regression
○ Correlation
• No causal relationship
○ Regression
• Causal relationship
• A  B (A causes B)
Multiple Regression
 Y = β0 + β1X1 + β2X2 + β3X3 + ε
○ Y: Dependent variable
○ X1, X2, and X3: Independent variables
○ β0: Intercept
○ β1, β2, and β3: Regression coefficients
○ ε: Error term
 Regression is an approach for modeling the relationship between a dependent
variable and one or more independent variables
○ The case of one independent variable is called simple linear regression
○ The case of more than one independent variables is called multiple linear
regression
 Correlation vs. Regression
○ Regression can explain causal relationship but correlation cannot
Multiple Regression
(Concepts to know)
 R2
○ The proportion of the original variance in dependent variable
that is explained by the regression equation
 Multicollinearity
○ A problem referring to correlated independent variables
• Causes unexpected signs
• Small t-value
○ Can be detected by VIF and Tolerance
SPSS Example
(Multiple Regression Analysis)
 Hypotheses
○ H1: Perceived quality of atmospherics will increase the overall satisfaction of
restaurant customer
○ H2: Perceived quality of food will increase the overall satisfaction of restaurant
customer
○ H3: Perceived quality of service will increase the overall satisfaction of
restaurant customer
 Analyze  Regression  Linear…
 Statistics  Collinearity diagnostics
SPSS Example
(Multiple Regression Analysis)
 Results #1 (Model Summary)
○ R2 = .311
• 31.1% of total variance in Y has been explained by regression equation
 Results #2 (Post-Hoc test)
○ F-value = 43.535 (p < .05)
• At least one coefficient is not equal to zero
SPSS Example
(Multiple Regression Analysis)
 Result #3: Coefficients and Multicollinearity Diagnostics
No multicollinearity detected
• VIF < 10
• Tolerance > .10
○ H1: t-value = 6.620 (p < .05)
• One unit increase in atmospheric quality significantly increases 0.329 unit in overall
satisfaction
• H1: Supported
○ H2: t-value = 6.081 (p < .05)
• One unit increase in food quality significantly increases 0.277 unit in overall satisfaction
• H2: Supported
○ H3: t-value = 1.108 (p > .05)
• Increase in service quality does not significantly increase overall satisfaction
• H1: Not Supported
Exploring Relationships between Variables
d. Advanced Methodologies
Factor Analysis
 Factor Analysis
○ Define the underlying structure among the variables
○ Reduce the number of variables that will be used
• Reduces multiple and similar measurement items to one dimension
(variable)
 Correlation Table
Factor 1
(Physical Environment)
Factor 2
(Service Quality)
SPSS Example
(Factor Analysis)
 14 measurement items related to the quality of coffee shops
○ Examining whether these measurement items can be reduced to few dimensions
 Analyze  Dimension Reduction Factor…
○ Extraction  Principal component
○ Rotation  Varimax
SPSS Example
(Factor Analysis)
 Result #1: Communalities
○ The variance accounted for by the factors
 Result #2: Total Variance Explained
○ 4 Factors were identified and 67.03% of total variance was explained
 Result #2: Total Variance Explained
○ 4 Factors were identified (# of factors with Eigen value > 1)
○ 67.03% of total variance was explained by four factors
Initial Eigenvalues
Component Total % of Variance Cumulative %
1
3.308
23.630
23.630
2
2.861
20.434
44.064
3
1.945
13.896
57.960
4
1.269
9.066
67.026
5
.946
6.760
73.786
6
.769
5.493
79.279
7
.704
5.031
84.310
8
.535
3.819
88.128
9
.404
2.887
91.015
10
.307
2.195
93.211
11
.281
2.009
95.220
12
.252
1.799
97.019
13
.226
1.617
98.636
14
.191
1.364
100.000
Extraction Method: Principal Component Analysis.
Total Variance Explained
Extraction Sums of Squared Loadings
Total % of Variance Cumulative %
3.308
23.630
23.630
2.861
20.434
44.064
1.945
13.896
57.960
1.269
9.066
67.026
Rotation Sums of Squared Loadings
Total % of Variance Cumulative %
2.817
20.121
20.121
2.527
18.048
38.169
2.289
16.351
54.520
1.751
12.506
67.026
SPSS Example
(Factor Analysis)
 Result #3: Factor Loadings
○ Loadings lower than 0.4 was not displayed
 Name each factor based on the measurement items included
○
○
○
○
Factor 1: Value
Factor 2: Advertisement
Factor 3: Accessibility
Factor 4: Coffee Quality
Utilization of Factors
 Utilization of Extracted Factors
○ Extracted factors in the previous example can be used for multiple
regression analysis
 Things to consider
1. Utilization of factor scores
• Standardized score
– Mean = 0, Standard Deviation = 1
2. Utilization of mean value
• Calculate mean value for measurement items included in each
factor
– Mean ≠ 0, Standard Deviation ≠ 1
SPSS Example
(Factor Score + Multiple Regression Analysis)
 Hypotheses
○ H1: Perceived value will increase the overall satisfaction of coffee shop
customer
○ H2: Perceived quality of advertisement will increase the overall satisfaction of
coffee shop customer
○ H3: Perceived quality of accessibility will increase the overall satisfaction of
coffee shop customer
○ H4: Perceived quality of coffee will increase the overall satisfaction of coffee
shop customer
 Analyze  Dimension Reduction  Factor…  Score
○ Save as variables
 Analyze  Regression  Linear… (Move factor scores as independent variables)
SPSS Example
(Factor Score + Multiple Regression Analysis)
 Results
○ R2 = 0.314
○ F-value = 32.337
○ VIF, Tolerance = 1 (No multicollinearity)
• Varimax rotation minimizes correlation between dimensions
 Hypotheses Testing
○ H1: Perceived value significantly increase the overall satisfaction (Supported)
○ H2: Perceived quality of advertisement does not have significant influence on the
overall satisfaction (Not supported)
○ H3: Perceived quality of accessibility does not have significant influence on the
overall satisfaction (Not supported)
○ H4: Perceived quality of coffee significantly increase the overall satisfaction
(Supported)
SPSS Example
(Mean Value + Multiple Regression Analysis)
 How to calculate mean value in SPSS?
 Transform  Compute Variable…
○ Select ‘Statistical’ and ‘Mean’
SPSS Example
(Mean Value + Multiple Regression Analysis)
 Type variable name you want to create
 Numeric Expression
○ MEAN (m7, m5, m6, m8)
○ Generate mean value for each factor
SPSS Example
(Factor Score vs. Mean Value)
 Comparison of Results
○ Mean Value
Coefficientsa
Unstandardized
Standardized
Coefficients
Coefficients
Model
B
Std. Error
Beta
1 (Constant)
-.651
.476
Value
.401
.074
.269
Advertisement
-.144
.082
-.093
Accessibility
.009
.084
.005
Coffee Quality
1.049
.116
.486
a. Dependent Variable: Satisfaction
t
Sig.
-1.367 .173
5.393 .000
-1.768 .078
.106 .915
9.043 .000
Collinearity
Statistics
Tolerance
VIF
.990
.892
.921
.851
1.010
1.121
1.086
1.175
○ Factor Score
Model
1 (Constant)
Unstandardized
Coefficients
B
Std. Error
3.663
Value
.358
Advertisement
-.022
Accessibility
.062
Coffee Quality
.609
a. Dependent Variable: Satisfaction
Coefficientsa
Standardized
Coefficients
Beta
.062
.062
.062
.062
.062
.283
-.017
.049
.481
t
Sig.
58.837
.000
5.740
-.352
.996
9.761
.000
.725
.320
.000
Collinearity
Statistics
Tolerance
VIF
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
SPSS Example
(Factor Score vs. Mean Value)
 Similarity
○ Standardized β
○ Sign of coefficients
○ Significance level
 Differences
○ Unstandardized coefficients
○ t-value
○ Collinearity diagnostics
• Varimax Rotation: No collinearity at all
• Mean Value: Collinearity may exist
 Utilization of factor score or mean score depends on researcher’s decision