This document provides an overview of quantitative analysis techniques for assessing relationships between variables. It discusses concepts related to relationships including presence, nature, direction, and strength of association. It also defines statistical techniques such as ANOVA, cluster analysis, conjoint analysis, discriminant analysis, factor analysis, logistic regression, and multiple regression. Examples are provided to demonstrate calculating explained and unexplained variance in regression, interpreting regression coefficients, and using dummy variables. Steps for conducting regression analysis are outlined including checking assumptions and interpreting residuals plots.

1. Research Design and
Methods
Quantitative Analysis Techniques
FEKD62
Ralf Müller
Tomas Blomquist
School of Business and Economics
Umeå University
Concepts About Relationships
Presence
Nature
Direction
Strength of Association
1

2. Relationship Presence
. . . . assesses whether a systematic
relationship exists between two or more
variables.
If we find statistical significance between
the variables we say a relationship is
present.
Nature of Relationships
Relationships between variables typically are described
as either linear or nonlinear.
•Linear relationship = a “straight line
-
association” between two or more variables.
•Nonlinear relationship = often referred to
as curvilinear, it is best described by a curve
instead of a straight line.
2

3. Direction of Relationship
The direction of a relationship can be either
positive or negative.
Positive relationship = when one variable
increases, e.g., loyalty to employer, then so
does another related one, e.g. effort put
forth for employer.
Negative relationship = when one variable
increases, e.g., satisfaction with job, then a
related one decreases, e.g. likelihood of
searching for another job.
Strength of Association
When a consistent and systematic
relationship is present, the researcher
must determine the strength of
association.
The strength ranges from very strong to
slight.
3

4. Covariation
. . . . exists when one variable
consistently and systematically changes
relative to another variable.
The correlation coefficient is used to
assess this linkage.
Correlation Coefficients
Positive Correlation = when the value of X increases,
+ 1.0
the value of Y also increases. When the value of X
decreases, the value of Y also decreases.
0.0 Zero Correlation = the value of Y does not increase or
decrease with the value of X.
Negative Correlation = when the value of X increases,
- 1.0
the value of Y decreases. When the value of X
decreases, the value of Y increases.
4

5. Rules of Thumb about Correlation Coefficient Size
Coefficient Strength of
Range Association
+/– .91 to +/– 1.00 Very Strong
+/– .71 to +/– .90 High
+/– .41 to +/– .70 Moderate
+/– .21 to +/– .40 Small
+/– .01 to +/– .20 Slight
Pearson Correlation
The Pearson correlation coefficient
measures the linear association between
two metric variables.
It ranges from – 1.00 to + 1.00, with zero
representing absolutely no association.
The larger the coefficient the stronger the
linkage and the smaller the coefficient the
weaker the relationship.
5

6. Coefficient of Determination
The coefficient of determination is the
square of the correlation coefficient, or r2.
It ranges from 0.00 to 1.00 and is the
amount of variation in one variable
explained by one or more other variables.
6

7. Definitions of Statistical Techniques
ANOVA (analysis of variance) is used to examine statistical
differences between the means of two or more groups. The
dependent variable is metric and the independent variable(s) is
nonmetric. One-way ANOVA has a single nonmetric independent
variable and two-way ANOVA can have two or more nonmetric
independent variables.
Cluster analysis enables researchers to place objects (e.g.,
customers, brands, products) into groups so that objects within the
groups are similar to each other. At the same time, objects in any
particular group are different from objects in all other groups.
Conjoint analysis enables researchers to determine the preferences
individuals have for various products and services, and which
product features are valued the most.
Definitions of Statistical Techniques
Discriminant analysis enables the researcher to predict group
membership using two or more metric dependent variables. The
group membership variable is a nonmetric dependent variable.
Factor analysis is used to summarize the information from a large
number of variables into a much smaller number of variables or
factors. This technique is used to combine variables whereas
cluster analysis is used to identify groups with similar
characteristics.
Logistic regression is a special type of regression that can have a
non-metric/categorical dependent variable.
Multiple regression has a single metric dependent variable and
several metric independent variables.
7

8. Calculating the “Explained” and
“Unexplained” Variance in Regression
The explained variance in regression, referred to
as r2, is calculated by dividing the regression
sum of squares by the total sum of squares.
The unexplained variance in regression, referred to
as residual variance, is calculated by dividing the
residual sum of squares by the total sum of
squares.
How to calculate the t-value?
The t-value is calculated by dividing the
regression coefficient by its standard
error.
8

9. How to interpret the regression coefficient
The regression coefficient of .459 for Samouel’s
X1– Food Quality reported in Exhibit 11-11 is
interpreted
as follows: “ . . . for every unit that X1 increases, X17
will increase by .459 units.” Recall that in this
example
X1 is the independent (predictor) variable and X17 is
the
dependent variable.
Dummy Variable
. . . . an independent variable that has two
(or more) distinct levels, which are coded 0
and 1.
9

10. Regression Analysis Terms
Explained variance = R2.
Unexplained variance or error =
residuals.
Regression Assumptions
The error variance is constant over all
values of the independent variables;
The errors are uncorrelated with each of
the independent variables; and
The errors are normally distributed.
10

11. Residuals Plots
Plot of standardized residuals – enables you to
determine if the errors are normally distributed
Normal probability plot – enables you to determine if
the errors are normally distributed. It compares the
observed standardized residuals against the expected
standardized residuals from a normal distribution
Plot of standardized residuals – can be used to identify
outliers. It compares the standardized predicted values
of the dependent variable against the standardized
residuals from the regression equation.
Exhibit A-5 Histogram of
Employee Survey Dependent
Variable X15 – Proud
Histogram
Dependent Variable: X15 -- Proud
10
8
6
4
Frequency
Std. Dev = .97
2
Mean = 0.00
N = 63.00
0
-1.75 -1.25 -.75 -.25 .25 .75 1.25 1.75 2.25
-1.50 -1.00 -.50 0.00 .50 1.00 1.50 2.00
Regression Standardized Residual
11

12. Normal Probability Plot of
Regression Standardized Residuals
Normal P-P Plot of Regression Standardized Residual
Dependent Variable: X15 -- Proud
1.00
.75
Expected Cum Prob
.50
.25
0.00
0.00 .25 .50 .75 1.00
Observed Cum Prob
Scatterplot
Scatterplot
Dependent Variable: X15 -- Proud
Regression Standardized Predicted Value
3
2
1
0
-1
-2
-2 -1 0 1 2 3
Regression Standardized Residual
12

13. Example: Communication Research
Appropriate Formal
Situational Variables
Communication Variables
Organisation Structure
H2 (+) Communication Frequency
Level of organic
Daily, (bi)-weekly,
organisation structure
monthly, at milestone,
phase end, project end
H3
Research Model (+)
H
H4
(-)
)
Methodology Clearness
H6 (+)
Communication Media
Richness
Written,
verbal,
face-to-face
)
H5 (-
Objective Clearness
Relational Norms Communication Contents
Status, changes, issues,
Flexibility, next steps, analysis,
information exchange, measures
solidarity
H2 to H5: Hypothesized relationships
Exploratory investigation
Example: Communication Research
Standard
Deviation
Questionnaire Item(s) Mean
Variable (from Appendix A-3) (SD)
Project Variables
Respondents Role 1 N/A N/A
Project Type 2, 3 N/A N/A
Objective Clearness 4, 5, 6 5.39 (1.15)
Methodology Clearness 7, 8, 9 5.05 (1.32)
Summary statistics Relational Norms 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 5.45 (0.90)
Organisation Structure 68, 69, 70, 71, 72, 73, 74 4.58 (1.05)
Project Performance 65, 66, 67 5.69 (0.96)
Communication Media
Importance of Written Communication 20 6.34 (0.97)
Importance of Verbal Communication 21 6.19 (0.96)
Importance Personal Communication 22 6.21 (1.04)
Communication Frequency
Variable Interval Communication 27, 28, 33, 34, 35, 41, 42 2.83 (0.24)
Fixed Interval Communication 25, 26, 32, 33, 39, 40 3.32 (0.44)
Continuous Communication 23, 24, 30, 38 4.04 (0.79)
Communication Contents
Personal Review 58, 59, 60, 61, 62, 63, 64 5.23 (0.63)
Project Analysis 45, 48, 52, 55, 59, 62 4.40 (0.45)
Written Status 44, 46, 47, 49, 50, 57, 64 5.51 (0.91)
Verbal Update 51, 53, 54, 56 5.47 (0.16)
Demographic Variables
Age 80 42.2 (8.15)
Years of work experience 81 20.2 (8.87)
Years of experience in proj. mgmt. 82 10.3 (6.47)
Years as sponsor 83 5.9 (5.19)
13

14. Example: Communication Research
Frequency Factors
Variable Interval Fixed Interval Continuous
Final Factor Names:
Communication Communication Communication
Factor Eigenvalue 5.760 2.277 1.728
% Variance Explained 29.684 18.309 13.040
Analysis Factor Loading
Variable/Item
Frequency in Communication
Written daily communication 0.007 -0.273 0.583
Written weekly communication -0.077 -0.014 0.688
Written bi-weekly communication -0.087 -0.042
0.803
Written monthly communication 0.349 -0.243
0.641
Written communication at milestone achievement 0.121 -0.186
0.808
Written communication at phase or project end 0.074 -0.117
0.826
No formal written communication*
Verbal daily communication -0.060 -0.107 0.766
Verbal weekly communication**
Verbal bi-weekly communication 0.229 -0.242
0.781
Verbal monthly communication -0.273
0.485 0.570
Verbal communication at milestone achievement 0.196 -0.131
0.847
Verbal communication at phase or project end 0.090 -0.120
0.849
No formal Verbal communication*
Personal daily communication**
Personal weekly communication -0.214 0.146 0.563
Personal bi-weekly communication -0.070 0.309
0.668
Personal monthly communication 0.342 -0.011
0.549
Personal communication at milestone achievement 0.115 0.007
0.821
Personal communication at phase or project end 0.066 -0.027
0.841
No formal Personal communication*
* Items not included because of low preference
** Items dropped because of low MSA or Alpha
Example: Communication Research
Contents Factors
Written status
Personal Project report with Verbal
Final Factor Names:
Factor Analysis Review Analysis possible follow- Update
up
Eigenvalue 5.136 2.487 2.091 1.963
% Variance Explained 15.396 13.999 13.812 12.392
Factor Loading
Variable/Item
Contents in Communication
Written contents: status and achievements 0.036 0.151 0.151
0.489
Written contents: measures and quality metrics -0.078 0.356 -0.171
0.673
Written contents: issues or 'open items' -0.004 0.044 0.212
0.628
Written contents: project changes -0.027 0.186 0.177
0.598
Written contents: trends 0.156 0.364 -0.108
0.663
Written contents: next steps 0.137 -0.095 0.112
0.611
Written contents: other 0.217 0.139 -0.269
0.554
Verbal contents: status and achievements 0.025 0.154 -0.093 0.740
Verbal contents: measures and quality metrics -0.029 0.027 0.353
0.741
Verbal contents: issues or 'open items' 0.150 -0.051 0.154 0.747
Verbal contents: project changes 0.053 0.069 0.115 0.808
Verbal contents: trends 0.047 0.109 0.194
0.759
Verbal contents: next steps 0.301 -0.034 0.350 0.481
Verbal contents: other 0.129 0.137 -0.093
0.548
Personal contents: status and achievements 0.060 -0.114 0.184
0.762
Personal contents: measures and quality metrics -0.104 -0.016
0.560 0.590
Personal contents: issues or 'open items' 0.006 0.272 0.088
0.711
Personal contents: project changes 0.085 0.106 0.304
0.727
Personal contents: trends 0.000 -0.096
0.540 0.624
Personal contents: next steps 0.012 0.367 -0.059
0.750
Personal contents: other 0.186 -0.263
0.465 0.495
14

15. Example: Communication Research
Appropriate Formal
Situational Variables
Communication Variables
Organisation Structure
Level of organic
organisation structure
Communication
H2
(+)
Frequency
Variable Intervals
---
Fixed Intervals
---
Continuous
Methodology Clearness
Revised Research Model
H3
(-)
)
,H
H
6( Communication
+)
4
4(
Contents and Media
Objective Clearness
-)
Personal Review
H5
(+) ---
Project Analysis
---
Written Status
Relational Norms ---
Verbal Update
Flexibility,
information exchange,
solidarity
H2 to H6: Hypothesized relationships
Exploratory investigation
Example: Communication Research
Normal distribution 40
30
of dependent variables 30
20
20
10
10
Std. Dev = 1.00
Std. Dev = 1.00 Mean = 0.00
Mean = 0.00 N = 200.00
0
N = 200.00
0 -1.50 -.50 .50 1.50 2.50
-1.00 0.00 1.00 2.00
-2
-2
-1
-1
-.7
-.2
.2
.7
1.2
1.7
2.2
5
5
.7
.2
.7
.2
5
5
5
5
5
5
5
5
5
Variable Interval Communication
Continuous Communication
30
30 30
20
20 20
10
10 10
Std. Dev = 1.00
Std. Dev = 1.00
Std. Dev = 1.00
Mean = 0.00
Mean = 0.00
Mean = 0.00
N = 200.00
0
N = 200.00
0 N = 200.00
0
-2
-1
-1
-.5
0.0
.5
1.0
1.5
2.0
2.5
0
.0
.5
.0
0
-3
-3
-2
-2
-1
-1
-.5
0.0
.5
1.0
1.5
2.0
0
0
0
0
0
0
0
0
0
.5
.0
.5
.0
.5
.0
-3
-3
-2
-2
-1
-1
-.7
-.2
.2
.7
1.2
1.7
0
0
0
0
0
0
0
0
0
0
0
5
5
.7
.2
.7
.2
.7
.2
5
5
5
5
5
5
5
5
5
5
Fixed Interval Communication
Project Analysis Personal Reviews
15