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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
Establishing Relationships Among Chidamber and
Kemerer’s suite of Metrics Using Field Experiments
Ezekiel U. Okike Adenike O. Osofisan
Department of computer Science Department of computer Science
University of Ibadan University of Ibadan
Ibadan, Nigeria Ibadan, Nigeria
euokike@gmmail.com ao.osofisan@mail.ui.edu.ng
Abstract— Chidamber and Kemerer suite of metrics were relationship between cohesion and coupling, inheritance
used in the study of 3250 classes from five JAVA based and coupling (CBO), coupling and size
industrial systems. System 1 had 34 classes, System 2 had
318 classes, System 3 383 classes, System 4 1055 classes, Keywords-software measurement; cohesion, coupling,
and System 5 1460 classes. Metric values were computed inheritance, Chidamber and Kemerer metrics
for the Lack of Cohesion in Methods (LCOM), Coupling
between Object Classes (CBO), Response For a Class I. INTRODUCTION
(RFC), Number of Children (NOC), Depth of Inheritance Chidamber and Kemerer [3,4] defined a basic set of object-
(DIT), Weighted Methods per Class (WMC), Number of oriented measures which seem to be widely accepted [11]. The
Public Methods (NPM) and Afferent Coupling (CA). suite of metrics include the Lack of Cohesion in Methods
LCOM was used as cohesion variable; CBO, RFC, CA as (LCOM), Coupling between Object Classes (CBO), Response
coupling variables; WMC, NPM, NOC as size variables For a Class (RFC), Number of Children (NOC), Depth of
and DIT as inheritance variable. Descriptive statistics and Inheritance (DIT), and Weighted Methods per Class (WMC).
correlation analysis were used to analyze the results. Tests The Lack of Cohesion in Methods (LCOM) metric measures
of hypotheses were carried out to examine if there were the dissimilarity of methods in a class by instance variables or
significant relationships between cohesion and coupling attributes. A highly cohesive module should stand alone; high
variables, cohesion and size variables, cohesion and cohesion is an indication of good class subdivision. Lack of
inheritance variables, coupling and inheritance variables, cohesion or low cohesion increases complexity, thereby
coupling and size variables, inheritance and size variables. increasing the likelihood of errors during the development
The results of the study showed that in System 1, there process. It is suggested that classes with low cohesion could
were strong significant relationships between cohesion and be divided into two or more subclasses with increased
coupling (CBO, RFC), cohesion and size (WMC,NPM), cohesion [4]. A critical evaluation of this is already presented
coupling and size variables (WMC, NPM), and a weak in [7]
relationship between Affarent coupling CA and
inheritance (DIT). In System 2, there were strong Coupling between Objects (CBO) is a count of the number of
significant relationship between cohesion and coupling other classes to which a class is coupled. It is measured by
(CBO, RFC), cohesion and size variables (WMC, NPM), counting the number of distinct non-inheritance related class
coupling and size (WMC, NPM); a low relationship hierarchies on which a class depends. Excessive coupling is
between coupling by CA and WMC, NOC, and a weak detrimental to modular design and prevents reuse. The more
relationship between inheritance DIT and WMC, RFC, independent a class is, the easier it is reused in another
NPM. In System 3, there were strong significant application. Hence, the larger the number of couples, the
relationship between cohesion and coupling (CBO, RFC), higher the sensitivity to changes in other parts of the design
cohesion and size (WMC, NPM), coupling and size (WMC, and therefore maintenance is more difficult. Strong coupling
NPM); a low relationship between coupling by CA. In complicates a system since a class is hard to understand,
System 4, there were strong significant relationship change or correct by itself if it is interrelated with other
between cohesion and coupling (RFC), cohesion and size classes. Complexity can be reduced by designing systems with
(WMC, NPM), size WMC and Size NPM. There were low the weakest possible coupling between classes. This improves
relationships between cohesion and coupling (CBO, CA) modularity and promotes encapsulation [1,2,5].
and weak relationships between inheritance DIT and CA,
inheritance and size (WMC). In System 5, there were Response for a Class (RFC) is a count of the set of all
strong significant relationship between cohesion and size methods that can be invoked in response to a message to an
(WMC, NPM), coupling and size (WMC, NPM); a low object of the class or by some method in the class. This
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
include all methods assessable within the class hierarchy. RFC Specifically, the research questions investigated by this
metric combines the complexity of a class through the number study are the following:
of methods and the amount of communication with other • Is there any significant relationship between cohesion
classes. The larger the number of methods that can be invoked variables and coupling variables?
from a class through messages, the greater the complexity of
• Is there any significant relationship between cohesion
the class. If a large number of methods can be invoked in
and the size of a class?
response to a message, the testing and debugging of the class
becomes complicated since a greater level of understanding on • Is there any significant relationship between cohesion
the part of the tester is required. A worst case value for and the level of inheritance in a class?
possible responses will assist in the appropriate allocation of
• Is there any significant relationship between coupling
testing time .
variables and the size of a class?
• Is there any significant relationship between coupling
Number of Children (NOC) is the number of immediate variables and inheritance?
subclasses subordinate to a class in the hierarchy. It is an
indicator of the potential influence a class can have on the • Is it true that the larger the number of methods, the
design and on the system. The greater the number of children, lower the cohesiveness, and the higher the coupling of
the greater the likelihood of improper abstraction of the parent the class?
and may be a case of misuse of sub classing. But the greater
the number of children, the greater the reuse since inheritance C. Statemment of Research Hypotheses
is a form of reuse. If a class has a large number of children, it • H0: There is no significant relationship between class
may require more testing of methods of that class, thus cohesion and coupling.
increases the testing time.
H1: There is significant relationship between class
Depth of Inheritance Tree (DIT) of a class within the cohesion and coupling.
inheritance hierarchy is the maximum number of steps from
the class node to the root of the tree and is measured by the • H0: There is no significant relationship between class
number of ancestor classes. The deeper a class is within the cohesion and the size of a class
hierarchy, the greater the number of methods it is likely to H1: There is significant relationship between class
inherit making it more complex to predict its behavior. cohesion and the size of a class.
Deeper trees constitute greater design complexity, since more
methods and classes are involved, but the greater the potential • H0: There is no significant relationship between class
cohesion and inheritance.
for reuse of inherited methods. A support metric for DIT is the
number of methods inherited . H1: There is significant relationship between class
Weighted Method Per Class (WMC) is a count of the methods cohesion and inheritance.
implemented within a class or the sum of the complexities of
• H0: There is no significant relationship between
the methods (method complexity being measured by coupling and inheritance.
cyclomatic complexity). It is difficult to implement WMC by
the cyclomatic complexity method because not all methods are H1: There is significant relationship between coupling
assessable within the class hierarchy due to inheritance. The and inheritance.
number of methods and the complexity of the methods
involved is a predictor of how much time and effort is required D. Methodology
to develop and maintain the class. The larger the number of Chidamber and Kemerer’s Lack of Cohesion in Methods
methods in a class, the greater the potential impact on (LCOM) metric was experimentally examined using a
children; children inherit all methods defined in the parent metric tool that computes Chidamber and Kemerer
class. Classes with large number of methods are likely to be metric (ckjm), and a Java based Scanning program. The
more application specific, limiting the possibility of Chidamber and Kemerer metric tool and the Java based
reuse[1,2,5] . scanning program were applied in the experimental
study of 3250 classes from five Java based industrial
A. Aims and Objectives systems in order to measure class cohesion, coupling,
and inheritance in the selected systems. The choice of
The overall aims and objectives of this study were to Chidamber and Kemerer metric as the base metric for
investigate the relationship among Chidamber and Kemerer this study was informed by the fact that the components
suite of metrics : LCOM, CBO, RFC, NOC, DIT, WMC and of the metric enabled the measurement of all variables
their implication in software design and implementation. needed in this study such as Lack of Cohesion in
Methods (LCOM), Coupling Between Object classes
B. Research Questions (CBO), Weighted Methods per Class (WMC), Depth of
Inheritance Tree (DIT), Number of Children (NOC),
Identify applicable sponsor/s here. (sponsors)
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
and Response For a Class (RFC). Two other metrics, Table 1.1. Some characteristics of the selected test
although not part of Chidamber and Kemerer were used
systems
namely: Number of Public methods (NPM), and
Afferent Coupling (CA). The decision to incorporate Sys1 Sys2 Sys3 Sys4 Sys5 Total
the use of NPM and CA metrics in this study was
informed by the need to have a measure of the number
of public methods as well as a measure of afferent No of 34 318 383 1055 1460 3254
coupling in the systems. Moreover the metric tool used
classes
to compute the Chidamber and Kemerer metrics already
incorporated NPM and CA measures. Cohesion is No of 30 3388 685 22000 223066 249179
measured by LCOM; coupling measured by CBO, RFC,
methods
CA; size is measured by WMC, NPM; inheritance is
measured by DIT, NOC. (Pro&Pub
No of 21 2536 266 6232 6414 15476
In the experiment, a maximum number of Java classes
in the selected systems were examined. The considered public
systems varied not only in size but also in domain.
methods
System 1, a small compiler project system has 34
classes. System 2, an open source GNU Java Server Size 3.9 172.9 180 770 1030 2157.9
Pages (JSP) has 318 classes. System 3, a metric system
in
for calculating Chidamber and Kemerer metrics has 383
classes. System 4, a Java based tool from OpenCms (KB)
systems has 1055 classes. System 5, a mathematical
database tool has 1460 classes. Some of the
characteristics of the selected systems are presented in
Table1.1. The environment for the computation of the
Chidamber and Kemerer metric consist of a Java
Scanning tool to scan the system source codes used in
this study in order to extract data about classes such as
System System Metric
the number of classes in the system, number of
attributes, number of methods, and the size in repository Measures
of the systems. This information was treated in a second
phase by a Chidamber and Kemerer metric tool [ 9] System
which was used to compute metric values for Source Code
LCOM,CBO, WMC, DIT, NOC, RFC, NPM and CA. (Java)
The metric calculation process is presented in Figure1.2.
Descriptive Statistics (mean, median, minimum,
maximum, standard deviation) and correlation analysis Result
Java
(Spearman’s Correlations) were used to analyze the
Scanner
results. Tests of hypotheses were carried out to examine
if there were relationships between cohesion and
coupling variables, cohesion and class size variables,
cohesion and inheritance, coupling and class size
variables, coupling variables and number of children, Metric
ClassesData
coupling and inheritance variables. Tool
. Figure 1.2 Metric calculation process
The remainder of this study is organized as follows: section 2
examines the approaches to measuring software complexity.
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Section 3 presents the empirical study. Section 4 presents the A method with a low cyclomatic complexity is generally
result and discussion . better. According to Rosenberg [6] this may imply decreased
testing and increased understandability or that decisions are
deferred through message passing, not that the method is not
complex . Cyclomatic complexity cannot be used to measure
II. MEASURING SOFWARE COMPLEXITY the complexity of a class because of inheritance, but the
cyclomatic complexity of individual methods can be combined
A. Linesof code, Statement counts and Related Metrics with other measures to evaluate the complexity of the class.
The lines of code measure counts the number of lines of Other measures of software complexity are WMC, RFC,
code in a program and uses that number as a measure of LCOM, CBO, DIT, NOC as explained in section 1.
complexity. If then bugs appear at 1% per line, a 1000 line
program should have 10 bugs at least. If it takes an average of
say 20 tests to find a bug, the expected number of tests needed III. EMMPIRICAL STUDY
per line of code can be inferred from this empirically. Some of
the difficulties with lines of code can be overcome by using A. Cohesion
statement counts instead. The problem of using statement Class Cohesion is a measure of the degree of relatedness
counts is that there is no unique way to count statements in among the members of a class (or module). In object-oriented
some languages, and there is no simple rule for defining programming the module is the individual class (or component
statements across different languages. In addition, just as there in the context of software reuse). Ideally, a class should
is subjectivity in applying lines of code, there is also represent a single responsibility. A class is cohesive when all
subjectivity in deciding what is and what is not to be called a elements are related to the performance of a single function. A
statement for some languages. class that is not cohesive poses several problems. First, it is
difficult to understand; second, it assumes that the abstractions
B. Size
that it represents are always in a one-to one correspondence;
The Size of a class is used to evaluate the ease of lastly one may have to specialize (through inheritance) a class
understanding of code by developers and software along different dimensions. A cohesive class on the other hand
maintainers. Size can be measured in a variety of ways such as offers the following:
counting all physical lines of code, the number of statements, • A cohesive class or a class with high cohesion allows
the number of blank lines, and the number of comment lines. ease of maintainability, reusability. Hence, the
Non comment Non Blank (NCNB) is sometimes referred to as cohesion of a class allows measurement of its structure
Source Lines of Code and counts all lines that are not quality .
comments and not blanks. Executable Statement (EXEC) is a
count of executable statements regardless of number of • High cohesion indicates good class subdivision. A
highly cohesive module should stand alone. Therefore
physical lines of code.
high cohesion is a desirable property of software
C. Comment Percentage components.
The comment percentage is calculated by the total number Lack of cohesion (or low cohesion) increases the likelihood
of comments divided by the total lines less the number of of errors during the software development process. Classes
blank lines. Since comments assist developers and with low cohesion could probably be subdivided into two or
maintainers, higher comment percentages increase more subclasses with increased cohesion [3,4].
understandability and maintainability.
B. Coupling
D. Maccabe’s Metric (Cyclomatic Complexity)
Coupling is the degree of interconnection between software
This metric is used to evaluate the complexity of an
classes (or modules). One objective of any good design is to
algorithm in a method. It is the count of the number of test
minimize coupling between modules. Being able to quantify
cases that are needed to test the method comprehensively. The
and measure coupling is one of the ways to assess the quality
formula for calculating the cyclomatic complexity is the
of a software using coupling as a design attribute. The
number of edges minus the number of nodes plus 2. For a
definition of coupling applies to Myer’s view of coupling [10]
sequence where there is only one path, no choices or option,
and his five fold classification of coupling from the non-
only one test case is needed. An IF loop however, has two
desirable case to the best desirable case. Design guidelines
choices, if the condition is true, one path is tested; if the
suggest that data coupling is the desirable form of class (or
condition is false, an alternative path is tested. Examples of
module) communication. In general, coupling between classes
calculations of cyclomatic complexity for some basic
(or modules) has been said to affect reuse, extendibility
programming structures are discussed in [6,8]. Hence,
(flexibility), and comprehensibility of systems in the following
Cyclomatic Complexity => Number of independent test paths
ways:
= No. of edges – No. of nodes + 2 • The higher the degree / level of coupling, the harder it
is to make changes to individual classes (modules)
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since the changes are likely to affect a large number of
other modules.
B. Descriptive Statistics for System 2
• The higher the level of coupling, the lower the reuse of Table 4.2 Descriptive statistics for system 2
class (or module) Statistics W D N C R L C N
• The higher the level of coupling, the harder the class M I O B F C A P
(or module) is understood C T C O C OM M
N 318 318 318 318 318 318 318 318
C. Measures of Size
Valid 318 318 318 318 318 318 318 318
Several measures have been classified as size measures
Missing 3 3 3 3 3 3 3 3
[2]. With respect to code measures, there are: Lines of
Code(LOC), No of statements, Number of Modules, Number Mean 9.71 1.16 4.09E- .75 18.17 93.94 .56 7.97
of procedures, Halstead’s length, Number of occurrences of 02
operators, Number of unique operators. Number of executable Median 5.00 1.00 .00 .00 7.00 3.00 .00 4.00
statements (NStms) is also used for code level assessment of Std. Dev 12.52 2.25 .25 2.18 28.07 490.02 1.53 8.36
lines of code.With respect to design level measurement, No
Min 0 1 0 0 0 0 0 0
of Methods (NM), or Number of Public methods (NPM) and
No. of Attributes (Natt) are size measures . Other size Max 118 41 3 16 182 6075 10 40
measures which although are meant to capture other concepts, Cohesion: [0≤median≤1]
but are indeed size measures include, Weighted Methods Per
Class (WMC), and No of Children (NOC).
C. Descriptive Statistics for System 3
Table 4.3 Descriptive statistics system 3
IV. RESULT FROM THE TEST SYSTEMS
Statistics WMC DIT NOC CBO RFC LCOM CA NPM
Descriptive statistics and correlation analysis results of
applying a Chidamber and Kemerer metric tool in the N 383 383 383 383 383 383 383 383
experimental study of the selected test systems are presented. Valid 383 383 383 383 383 383 383 383
Missing 0 0 0 0 0 0 0 0
Descriptive statistics were used to obtain the minimum,
Mean 8.24 2.14 .58 8.33 20.93 150.40 5.70 6.97
maximum, mean, median, and standard deviation values for the
test systems as shown in tables 4.1–4.5. In case of Median 3.00 2.00 .00 5.00 10.00 1.00 3.00 2.00
measurement for cohesion, the LCOM value lies between a Std. Dev 19.16 1.16 3.00 20.07 31.14 1318.02 14.02 18.63
range [0, maximum]. From Chidamber and Kemerer’s Min 0 1 0 0 0 0 0 0
interpretation of their LCOM metric, a class is cohesive if its Max 118 5 36 195 265 16290 157 181
LCOM =0. Using descriptive statistics, a median value in this
Cohesion: [0≤median≤1]
range [0≤median≤1] shows the class is cohesive. Hence
systems 1,3,5 are cohesive while systems 2, 4 are not cohesive.
A detailed discussion on this is already presented in [7,8].
D. Descriptive Statistics for System 4
Table 4.4 Descriptive statistics system 4
A. Descriptive Statistics for System 1
Table 4.1 Descriptive statistics for system 1 Statistics WMC DIT NOC CBO RFC LCOM CA NPM
Statistic W D N C R L CA N N 1055 1055 1055 1055 1055 1055 1055 1055
s M I O B F C P Valid 1055 1055 1055 1055 1055 1055 1055 1055
C T C O C OM M Missing 0 0 0 0 0 0 0 0
N 34 34 34 34 34 34 34 34 Mean 7.96 1.42 .36 6.25 26.49 44.91 1.69 5.91
Valid 34 34 34 34 34 34 34 34 Median 5.00 1.00 .00 3.00 16.00 6.00 .00 4.00
Missing 3 3 3 3 3 3 3 3 Std. Dev 9.40 .62 3.00 7.55 30.93 180.45 5.83 6.82
Mean 7.8 1.4 .41 5.5 22. 79.0 4.2 6.1 Min 0 1 0 0 0 0 0 0
Median 4.0 1.0 .00 5.0 18. .00 2.0 4.0 Max 109 4 64 65 210 2744 71 61
Std. Dev 13. .50 1.5 5.8 24. 440. 4.7 8.6 Cohesion : [0≤median≤1]
Min 0 1 0 0 0 0 0 0
Max 74 2 8 31 12 2531 22 45
Cohesion: [0≤median≤1]
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E. Descriptive Statistics for System 5 H. Correlation Analysis for System 3
Table 4.5 Descriptive statistics system 5 In System 3, there were strong significant relationship
Statistics W D N C R L CA N between cohesion and coupling (CBO, RFC), cohesion and
M I O B F C P size (WMC, NPM), coupling and size (WMC, NPM); a low
relationship between coupling by CA. (table 5.3)
C T C O C OM M
N 1460 1460 1460 1460 1460 1460 1460 1460
1460 1460 1460 1460 1460 1460 1460 1460
I. Correlation Analysis for System 4
Valid
Missing 0 0 0 0 0 0 0 0
In System 4, there were strong significant relationship between
cohesion and coupling (RFC), cohesion and size (WMC, NPM),
Mean 5.51 1.26 .20 4.34 15.78 25.29 1.78 4.39
size WMC and Size NPM. There were low relationships
Median 3.00 1.00 .00 3.00 8.00 1.00 1.00 2.00 between cohesion and coupling (CBO, CA) and weak
Std. Dev 8.20 .61 1.42 5.37 20.33 283.08 3.79 7.53 relationships between inheritance DIT and CA, inheritance and
Min 0 1 0 0 0 0 0 0 size (WMC) (table 5.4).
Max 141 5 35 56 270 9870 50 141
Cohesion: [0≤median≤1] J. Correlation Analysis for System 5
In System 5, there were strong significant relationship
Using Pearson correlation coefficients, tests of between cohesion (LCOM) and size (WMC, NPM),
hypotheses were carried out to examine if there were coupling (CBO, RFC) and size (WMC, NPM); a low
significant relationships between cohesion and coupling: relationship between cohesion and coupling,
LCOM and CBO, LCOM and RFC, LCOM and CA; cohesion inheritance (DIT) and coupling (CBO), coupling and
and size: LCOM and WMC, LCOM and NPM; and coupling size (table 5.5)
and size: CBO and WMC, CBO and NPM, RFC and WMC,
RFC and NPM, CA and WMC, CA and NPM; coupling by TABLE 5.1 CORRELATION ANALYSIS FOR SYSTEM 1
CBO and RFC; coupling by CBO and CA; coupling by RFC
and CA; coupling and number of children: CBO and NOC, Correlations
RFC and NOC, CA and NOC; cohesion and inheritance: WMC DIT NOC CBO RFC LCOM CE NPM
LCOM and DIT; coupling and inheritance: CBO and DIT, WMC Pearson Corre 1.000 -.234 -.063 .897** .926** .881** -.054 .984**
RFC and DIT,CA and DIT; size by WMC and NPM; size and Sig. (2-tailed) . .183 .721 .000 .000 .000 .760 .000
inheritance: WMC and DIT, NPM and DIT (Tables N 34 34 34 34 34 33 34 34
DIT Pearson Corre -.234 1.000 -.230 -.054 -.170 -.155 -.442** -.244
5.1-5.5). The relationship is established at the 0.01 level (2 Sig. (2-tailed) .183 . .191 .761 .337 .388 .009 .165
tailed) because software systems measured at code level are akin N 34 34 34 34 34 33 34 34
to medical systems while the 0.05 level is suited for social NOC Pearson Corre -.063 -.230 1.000 -.110 -.102 -.047 .280 -.082
systems and survey studies as established in [8]. Additionally, at Sig. (2-tailed) .721 .191 . .537 .566 .797 .109 .643
the 0,01 level of significance, relationships could strong (p≥.5), N 34 34 34 34 34 33 34 34
CBO Pearson Corre .897** -.054 -.110 1.000 .968** .769** -.251 .895**
low (0≤p≤.5), and weak (p.< 0). Sig. (2-tailed) .000 .761 .537 . .000 .000 .153 .000
N 34 34 34 34 34 33 34 34
RFC Pearson Corre .926** -.170 -.102 .968** 1.000 .785** -.140 .924**
F. Correlation Analysis for System 1 Sig. (2-tailed) .000 .337 .566 .000 . .000 .429 .000
N 34 34 34 34 34 33 34 34
There were strong significant relationships between LCOMPearson Corre .881** -.155 -.047 .769** .785** 1.000 -.113 .800**
cohesion and coupling (CBO, RFC), cohesion and size Sig. (2-tailed) .000 .388 .797 .000 .000 . .530 .000
(WMC,NPM), coupling and size variables (WMC, N 33 33 33 33 33 33 33 33
NPM), and a weak relationship between Affarent CE Pearson Corre -.054 -.442** .280 -.251 -.140 -.113 1.000 -.045
coupling CA and inheritance (DIT) (table 5.1). Sig. (2-tailed) .760 .009 .109 .153 .429 .530 . .802
N 34 34 34 34 34 33 34 34
G. Correlation Analysis for System 2 NPM Pearson Corre .984** -.244 -.082 .895** .924** .800** -.045 1.000
Sig. (2-tailed) .000 .165 .643 .000 .000 .000 .802 .
In System 2, there were strong significant relationship N 34 34 34 34 34 33 34 34
between cohesion and coupling (CBO, RFC), cohesion and **.Correlation is significant at the 0.01 level (2-tailed).
size variables (WMC, NPM), coupling and size (WMC,
NPM); a low significant relationship between coupling by
CA and WMC, NOC, and a weak relationship between
inheritance DIT and WMC, RFC, NPM (table 5.2).
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TABLE 5.2 CORRELATION ANALYSIS FOR SYSTEM 2 TABLE 5.4 CORRELATION ANALYSIS FOR SYSTEM 4
Correlations
Correlations
WMC DIT NOC CBO RFC LCOM CA NPM
WMCPearson Corr 1.000 .049 -.040 .265** .792** .810** .102 .786** WMC DIT NOC CBO RFC LCOM CA NPM
Sig. (2-tailed) . .381 .478 .000 .000 .000 .069 .000 WMCPearson Corr 1.000 -.104** .102** .420** .758** .765** .212** .846**
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) . .001 .001 .000 .000 .000 .000 .000
DIT Pearson Corr .049 1.000 -.012 .064 .044 -.013 .012 .081 N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .381 . .835 .257 .437 .821 .834 .150 DIT Pearson Corr -.104** 1.000 -.043 .077* -.016 -.040 -.136** -.057
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) .001 . .162 .012 .613 .191 .000 .064
NOC Pearson Corr -.040 -.012 1.000 -.010 -.039 -.018 .038 -.080 N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .478 .835 . .861 .488 .746 .495 .156 NOC Pearson Corr .102** -.043 1.000 .062* .050 .077* .518** .114**
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) .001 .162 . .045 .106 .013 .000 .000
CBO Pearson Corr .265** .064 -.010 1.000 .716** .092 .281** .077 N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .000 .257 .861 . .000 .103 .000 .169 CBO Pearson Corr .420** .077* .062* 1.000 .793** .298** .055 .270**
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) .000 .012 .045 . .000 .000 .075 .000
RFC Pearson Corr .792** .044 -.039 .716**1.000 .571** .211** .523** N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .000 .437 .488 .000 . .000 .000 .000 RFC Pearson Corr .758** -.016 .050 .793** 1.000 .610** .084** .572**
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) .000 .613 .106 .000 . .000 .006 .000
LCO Pearson Corr .810** -.013 -.018 .092 .571**1.000 .033 .343** N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .000 .821 .746 .103 .000 . .554 .000 LCO Pearson Corr .765** -.040 .077* .298** .610** 1.000 .090** .654**
N 318 318 318 318 318 318 318 318 Sig. (2-tailed) .000 .191 .013 .000 .000 . .003 .000
CA Pearson Corr .102 .012 .038 .281** .211** .033 1.000 .027 N 1055 1055 1055 1055 1055 1055 1055 1055
Sig. (2-tailed) .069 .834 .495 .000 .000 .554 CA Pearson Corr .212** -.136** .518** .055 .084** .090** 1.000 .188**
. .634
N Sig. (2-tailed) .000 .000 .000 .075 .006 .003 . .000
318 318 318 318 318 318 318 318
N 1055 1055 1055 1055 1055 1055 1055 1055
NPM Pearson Corr .786** .081 -.080 .077 .523** .343** .027 1.000
NPM Pearson Corr .846** -.057 .114** .270** .572** .654** .188** 1.000
Sig. (2-tailed) .000 .150 .156 .169 .000 .000 .634 .
Sig. (2-tailed) .000 .064 .000 .000 .000 .000 .000 .
N 318 318 318 318 318 318 318 318
N 1055 1055 1055 1055 1055 1055 1055 1055
**.
Correlation is significant at the 0.01 level (2-tailed).
**.
Correlation is significant at the 0.01 level (2-tailed).
*.Correlation is significant at the 0.05 level (2-tailed).
TABLE 5.3 CORRELATION ANALYSIS FOR SYSTEM 3 TABLE 5.5 CORRELATION ANALYSIS FOR SYSTEM 5
Correlations
Correlations WMC DIT NOC CBO RFC LCOM CA NPM
WMCPearson Cor 1.000 .014 .094** .309** .833** .625** .243** .967**
WMC DIT NOC CBO RFC LCOM CA NPM
WMCPearson Cor 1.000 -.211** .002 .889** .849** .822** .268** .992** Sig. (2-tailed . .593 .000 .000 .000 .000 .000 .000
Sig. (2-tailed . .000 .968 .000 .000 .000 .000 .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 DIT Pearson Cor .014 1.000 .017 .080** .040 -.016 .065* .023
DIT Pearson Cor -.211**1.000 -.027 -.131* -.268** -.105* -.130* -.191** Sig. (2-tailed .593 . .507 .002 .129 .539 .012 .389
Sig. (2-tailed .000 . .595 .010 .000 .041 .011 .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 NOC Pearson Cor .094** .017 1.000 .045 .065* .032 .497** .096**
NOC Pearson Cor .002 -.027 1.000 .000 -.006 -.017 .249** -.014 Sig. (2-tailed .000 .507 . .089 .014 .217 .000 .000
Sig. (2-tailed .968 .595 . .993 .914 .740 .000 .791 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 CBO Pearson Cor .309** .080** .045 1.000 .661** .091** .231** .238**
CBO Pearson Cor .889** -.131* .000 1.000 .807** .782** .225** .892** Sig. (2-tailed .000 .002 .089 . .000 .000 .000 .000
Sig. (2-tailed .000 .010 .993 . .000 .000 .000 .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 RFC Pearson Cor .833** .040 .065* .661**1.000 .385** .252** .759**
RFC Pearson Cor .849** -.268** -.006 .807**1.000 .547** .144** .813** Sig. (2-tailed .000 .129 .014 .000 . .000 .000 .000
Sig. (2-tailed .000 .000 .914 .000 . .000 .005 .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 LCO Pearson Cor .625** -.016 .032 .091** .385**1.000 .089** .625**
LCO Pearson Cor .822** -.105* -.017 .782** .547**1.000 .332** .843** Sig. (2-tailed .000 .539 .217 .000 .000 . .001 .000
Sig. (2-tailed .000 .041 .740 .000 .000 . .000 .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 CA Pearson Cor .243** .065* .497** .231** .252** .089**1.000 .174**
CA Pearson Cor .268** -.130* .249** .225** .144** .332**1.000 .274** Sig. (2-tailed .000 .012 .000 .000 .000 .001 . .000
Sig. (2-tailed .000 .011 .000 .000 .005 .000 . .000 N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 NPM Pearson Cor .967** .023 .096** .238** .759** .625** .174**1.000
NPM Pearson Cor .992** -.191** -.014 .892** .813** .843** .274**1.000 Sig. (2-tailed .000 .389 .000 .000 .000 .000 .000 .
Sig. (2-tailed .000 .000 .791 .000 .000 .000 .000 . N 1460 1460 1460 1460 1460 1460 1460 1460
N 383 383 383 383 383 383 383 383 **.
Correlation is significant at the 0.01 level (2-tailed).
**.
Correlation is significant at the 0.01 level (2-tailed). *.Correlation is significant at the 0.05 level (2-tailed).
*.Correlation is significant at the 0.05 level (2-tailed).
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
V. DISCUSSION
REFERENCES
Using Pearson Correlation, and the research questions and
hypotheses investigated in section 1.3 and 1.4 as well as the
[1] R. Adammov, and L. Richter, “A proposal for structural complexity
correlation results shown in tables 5.1-5.5, it can be of program, “ . Journal of Systems and Software vol. 12, 1990,
concluded as follows: pp. 55-70.
[2] V. R. Basili, L. C. Briand, and W. Melo, “A validation of Object
• There is significant correlation between the cohesion oriented design metrics as qaulity indicators” , IEEE Trans. On software
variable LCOM and coupling variables CBO and/or engineering, vol. 22, no. 10, 1996, pp. 751-761
RFC, CA across the systems . This confirms research [3] S. R. Chidamber and C. F. Kemerer, “Towards a metric suite for Object
oriented design,” object oriented programming systems, languages and
question 1. The Significance means that the applications, special issue of SIGPLAN notices 26, vol. 10, 1991, pp.
relationship is not merely statistical (not by chance); it 197-211.
is a real relationship due to the underlying behavior of [4] S. R. Chidamber and C. F. Kemerer, “A metric suite for Object oriented
the systems. It is expected that high cohesion should design,” IEEE trans. on software engineering vol. 26, no. 6, 1994, pp.
mean low coupling and vice versa. For systems 1, 3, 476-493.
and 5, at least 50% of the total number of classes were [5] N. Gorla and R. Ramakrishnan , “Effect of Software Structure
cohesive (see table 4.1- 4.5). It should be observed that attributes on software development, ” Journal of systems and software
vol. 36, no. 2. 1997, pp. 191-199.
the median values from descriptive statistics for these
cohesive system are either 0 or 1 whereas the median
values for systems 2 and 4 are 3.0 and 6.0 respectively. [6] L. H. Rosenberg, “Applying and interpreting object oriented metrics “
retrieved October 10, 2005 from
• There is significant correlation between cohesion and http://www.satc.gsfc.nasa.gov/support/STC_APR98/apply_OO/apply_O
O.html
number of methods in a class NPM across the systems
[7] E. Okike, “A pedagogical evaluation and discussion about the Lack of
(research question (ii)). Tables 5.1 show significant Cohesion in Methods metric (LCOM) using field experiments, “
correlations between LCOM and WMC, NPM. A high International Journal of computer science issues, vol. 2, no. 3, march
number of methods in a class should mean low 2010, pp. 36-43.
cohesion. This is confirmed in [8] . Classes with high [8] E. U. Okike, “Measuring class cohesion in object oriented systems
number of public methods NPM are not cohesive, using Chidamber and Kemerer metrics and Java as case study,”
while classes with low NPM (at least less than 5) are unpublished Ph.D thesis, Department of computer science, university of
Ibadan, xvii+ 133pp, 2007.
cohesive. This agrees with the suggestion that in the
design of classes, less than 5 methods should be in the [9] D. Spinellis, “Ckjm – A tool for calculating Chidamber and Kemerer
Java metrics, ” retrieved December 15, 2005 from
class to be cohesive, otherwise the class could be split
http://www.spinellis.gr/sw/ckjm/doc/indexw.html
into two or more classes [3,4].
• There is no significant correlation between cohesion [10] W. Stevens, G. Myers and L. Constantine, “Structured design, “ IBM
and inheritance (research question (iii)), as shown in systems Journal, vol. 13, no. 2, 1974, pp. 115-139.
tables 5.1– 5.5. [11] H. Zuse, “A framework for software mmeasurement. New York: Walter
de Gruyter, 1989.
• There is significant correlation between coupling and
number of methods (see tables 5.1-5.5). High coupling
AUTHORS PROFILE
could mean high number of methods and vice versa.
Ezekiel U Okike is a Senior Lecturer in the Department of commputer
From the tables 5.1-5.5, CBO correlates significantly science, University of Ibadan, Nigeria. He holds a B. S computer
with WMC and NPM; RFC correlates significantly Science, MInf (Information Science) and a Ph. D in computer science
with NPM (research question iv). A high number of from the University of Ibadan, Nigeria.
public methods in a class could mean high coupling Adenike O. Osofisan is a Professor of Computer Science and Head,
[8]. Also in table 5.6, most classes with high RFC Department of Computer Science, University of Ibadan, Nigeria.
values also had high NPM values.
• There is low or weak correlation between coupling and
inheritance as shown in tables 5.1-5.5.
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