J. Software Engineering & Applications, 2010, 3: 384-390
doi:10.4236/jsea.2010.34043 Published Online April 2010 (http://www.SciRP.org/journal/jsea)
Exploring Design Level Class Cohesion Metrics
Kuljit Kaur, Hardeep Singh
Department of Computer Science and Engineering, Guru Nanak Dev University, Amritsar, India.
Received November 17th, 2009; revised December 15th, 2009; accepted January 25th, 2010.
ABSTRACT
In object oriented paradigm, cohesion of a class refers to the degree to which members of the class are interrelated.
Metrics have been defined to measure cohesiveness of a class both at design and source code levels. In comparison to
source code level class cohesion metrics, only a few design level class cohesion metrics have been proposed. Design
level class cohesion metrics are based on the assumption that if all the methods of a class have access to similar pa-
rameter types then they all process closely related information. A class with a large number o f parameter types common
in its methods is more cohesive than a class with less number of parameter types common in its methods. In this paper,
we review the design level class cohesion metrics with a special focus on metrics which use similarity of parameter
types of methods of a class as the basis of its cohesiveness. Basically three metrics fall in this category: Cohesion
among Methods of a Class (CAMC), Normalized Hamming Distance (NHD), and Scaled NHD (SNHD). Keeping in
mind the anomalies in the definitions of the existing metrics, a variant of the existing metrics is introduced. It is
named NHD Modified (NHDM). An automated metric collection tool is used to collect the metric data from an open
source software program. The metric data is then subjected to statistical analysis.
Keywords: Design Metrics, Class Cohesion Metrics, Cohesion among Methods of a Class, Normalized Hamming
Distance, Scaled N H D
1. Introduction
In the object oriented paradigm, cohesion of a class re-
fers to the degree to which members of the class are in-
terrelated. Chidamber and Kemerer defined the first met-
ric to measure cohesiveness of a class [1]. Since then,
several class cohesion metrics have been proposed (dis-
cussed in the next section). Empirical studies report that
class cohesion metrics are useful to assess software de-
sign quality [2,3], to predict fault proneness of classes
[4-6], and to identify reusable components [7,8].Existing
class cohesion metrics mainly fall into two categories –
metrics which can be computed at design level (high
level) and metrics which can be computed one step later
i.e. at source code level (low level). Design level class
cohesion metrics use the limited amount of information
available about a class at this level i.e. only the class at-
tributes, and method signatures. Method implementation
is not completely defined at design level. So some as-
sumptions are made. Different class cohesion metrics
defined at design level are based on different assump-
tions.
1) One school of thought assumes that the types of
method parameters match the types of the attributes ac-
cessed by the method. It is further assumed that the set of
attribute types accessed by a method is the intersection of
this method’s parameter types and the set of parameter
types of all the methods in the class [9,10].
2) Another school of thought assumes that the set of
attribute types accessed by a method is the intersection of
the set of this method’s parameter types and the set of its
class attribute types [11].
In this paper we review the design level class cohesion
metrics based on the first assumption. Keeping in mind
the anomalies in the definitions of the ex isting metrics, a
variant of the metrics is introduced. The paper is organ-
ized as follows: Section 2 reviews the related work. Sec-
tion 3 explains the existing design level class cohesion
metrics and introduces a modified version as well. Sec-
tion 4 presents the statistical analysis of the data col-
lected from an open source project. Section 5 concludes
the paper.
2. Related Work
A number of class cohesion metrics are defined in the
low level metrics category [1,12-26]. However, there are
only a few proposals for design level class cohesion met-
rics [9-11].

Explo r ing Design Level Class Cohesion Me tric s385
The metric, named Cohesion among Methods of a
Class (CAMC) captures the information about parameter
types of methods of a class [9]. A class is cohesive if all
methods of the class use the same set of parameter types.
Methods which use same type of parameter types are
assumed to process related kind of information. CAMC
metric values lie in the range [0, 1]. Counsell et al. point
out some anomalies in definition of this metric, and pro-
pose a new metric named Normalized Hamming Dis-
tance (NHD) [10]. It is a normalized metric which meas-
ures average agreement between each pair of methods on
their parameter types. A variant of the NHD metric
called Scaled NHD (SNHD) is introduced in the same
paper. It addresses shortcomings of both CAMC and
NHD, as claimed by the authors [10]. This research finds
anomalies in the definitions of NHD and SNHD as well,
and proposes a modified version of the NHD metric -
NHD modified (NHDM). The NHDM metric gives sta-
tistically significant results.
Dallal proposes another metric for measuring cohesion
of a class at design level [11]. Similarity based Class
Cohesion (SCC) metric is based on the second assump-
tion discussed above. This metric is not analyzed in this
paper as the automated tool developed for this research
does not support collection of this metric.
3. Design Metrics
This section describes the class cohesion metrics com-
putable with information available at design level. At
design level, information regard ing name of the class, its
attributes (names, and data types), and method signatures
is available. Method signature includes name of the
method and its parameter list which describes names of
the parameters and their data types. A Class does not
have a detailed or algorithmic description of its methods
available at this level.
3.1 CAMC
The CAMC metric measures the extent of intersection of
individual method parameter type lists with the parame-
ter type list of all methods in the class [9]. This metric
computes the relatedness among methods of a class
based upon the parameter list of the methods. It is as-
sumed that methods of a class, having access to similar
parameter types, process closely related information.
The CAMC metric uses a parameter-occurrence matrix
(PO matrix) that has a row for each method and a column
for each data type that appears at least once as the type of
a parameter in at least one method in the class. The value
in row i and column j in the matrix is 1 when the ith
method has a parameter of the jth data type and is 0 oth-
erwise. In the original version of the metric [9], the PO
matrix has an additional column of all 1s. This column
represents the ‘self’ parameter that corresponds to the
type of the class itself which is by default one of the pa-
rameters of every method. In this discussion, the original
version of the metric is referred to as CAMCs (Cohesion
among methods of a class with ‘self’ parameter) and
metric definition without the ‘self’ parameter is named as
CAMC [10].
The CAMC metric is defined as the ratio of the total
number of 1s in the PO matrix to the total size of th e ma-
trix.
11
CAMC(C)where[ ][]
kl
PO ij
kl

 

CAMC suffers from the following anamolies:
1) CAMC gives false positives – the metric gives a
non-zero value for a class with no parameter sharing in
its methods.
2) CAMC can not differentiate between two classes
having same number of 1s but with different patterns of
1s in their PO matrices.
3) Smaller classes take high values for the cohesion
metric than the larger classes with same properties.
3.2 NHD
Counsell et al. [10] suggested an alternative of CAMC. It
is based on the definition of hamming distance. NHD
measures agreement between rows in the PO matrix.
NHD metric for a class with k methods and l unique pa-
rameter types (set obtained from union of parameter
types received by all its methods) is defined as:
1
11
2
NHD( ,)
(1)
kk
jai j
lk k



where a(i,j) is value of the cell at (i,j)th location in the
PO matrix. Another easy way to compute NHD is to first
find the sum of disagreements between methods for all
the parameter types and then subtract it from 1.
1
2
1(
(1)
l)
j
j
N
HDc kc
lk k
 

where cj is the number of 1s in the jth column of the PO
matrix.
A varaint of NHD (with self parameter), NHDs can be
defined for a PO matrix with an additional column of all
1s.
NHD suffers from the following anomalies:
1) NHD metric also gives false positives. The metric
removes the first anomaly of the CAMC for a class with
k = l = 2. The metrics fails to give correct answer for
higher values of k and l (e.g. when k = l = 3, and th ere is
no parameter sharing among methods, NHD metric gives
a non-zero value).
2) NHD does not give different answers for classes
with different properties – metric fails to distinguish a
class with no parameter sharing in its methods from a
class with substantial amount of parameter sharing in its
methods.
3) Class size influences metric value. As size of the
class increases, value of the NHD metric also increases
(even if the PO matrix gets sparser).

Explo r ing Design Level Class Cohesion Me tric s 386
3.3 SNHD
SNHD is the Scaled NHD metric proposed to interpret
values of the NHD metric in a more varied range. Pro-
ponents of the NHD metric are of the opinion that NHD
metric can take values at two extremes: the minimum or
the maximum. But they admit that it is not clear as to
which of these extremes represents a cohesive class.
However without giving any clear explanation they state
that classes at both the extremes may be cohesive. They
define these extreme values as NHDmin and NHDmax re-
spectively [10]. SNHD metric value helps to know how
close the NHD metric is to the maximum value of the
NHD value in comparison to the minimum value. SNHD
is defined as follows:
min max
min
0 ,
1
21,
max min
if NHDNHDandkl
SNHD=if kl
NHD NHDotherwise
NHD NHD














,

The SNHD metric values lies in the range [-1,1]. SNHD
= –1 implies that NHD = NHDmin, and SNHD = 1 implies
that NHD=NHDmax . NHD is closer to its minimum or
maximum value depending upon whether SNHD is get-
ting values close to –1 or +1 respectively. A class is con-
sidered non-cohesive if SNHD metric value for the class
is 0.
SNHDs is defined by considering the ‘self’ parameter.
SNHD suffers from these Anomalies:
1) Difficult to calculate and interpret.
2) False negatives – SNHD metric gives 0 value for a
class with good degree of cohesion.
3.4 NHDM
Keeping in view the anomalies of the cohesion metrics
discussed above, this research prop oses a variation of the
NHD metric. This variat is named as Normalized Ham-
ming Distance Modified (NHDM) metric. The NHD
metric ignores the method pairs with zero values in a
column of the PO matrix. It counts only those methods
pairs which do not agree, and ignores all other method
pairs irrespective of whether they agree on a 0 or a 1.
NHDM counts the method p airs which agree on a 0, as a
disagreement. NHDM for a class with k methods and l
unique parameter types, of all its methods, is defined as:
1
21
1(()(
(1)2
l
jj jj
NHDMc kczz
lk k
 
1))
where cj is the number of ones and zj is the number of
zeroes in the jth column of the PO matrix for the class.
Similarly NHDMs is defined by including the ‘self’
parameter in the PO matrix.
This metric removes the anomalies present in the de-
fintion of CAMC, NHD, and SNHD metrics. NHDM
gives correct results. It gives different results for classes
with different properties. NHDM metric values are inde-
pendent of the class size.
4. Data Analysis
Cohesion metrics discussed above are collected from an
open source software system available at www.source-
forge.net. The software is a JAVA based charting library,
and it consists of 884 classes. For automated collection
of metrics, a tool CohMetric is developed.
4.1 Descriptive Analysis
Histograms in Figures 1 to 4 show metrics distributions.
Table 1 presents the descriptive statistics. It can be ob-
served that majority of the CAMC metric values lie close
to 0 (see Figure 1). On average a class’s cohesion value
is 0.21. NHD metric takes values in a higher range (Fig-
ure 2). Average NHD metric value is 0.66. SNHD is 0
for maximum of the classes. Its values lie more on the
Figure 1. Distribution of CAMC metric
Table 1. Descriptive statistics for cohesion metrics
MetricAverageStd
Dev Metric AverageStd Dev
CAMC0.21 0.18 CAMCs 0.48 0.21
NHD 0.66 0.21 NHDs 0.81 0.12
SNHD -0.43 0.51 SNHDs 0.63 0.42
NHDM0.05 0.16 NHDMs 0.38 0.22
Figure 2. Distribution of NHD metric

Explo r ing Design Level Class Cohesion Me tric s387
Figure 3. Distribution of SNHD metric
Figure 4. Distribution of NHDM metric
left side of 0 which implies that majority of the classes
has NHD more close to NHDmin than NHDmax . Average
SNHD for a class is –0.43 and standard deviation is also
very high (Figure 3). NHDM takes very low values
(Figure 4). For majority of the classes it is 0. Its average
value is just 0.05. As earlier stated, it may be due to the
reason that it does not give false positives.
4.2 Metric Vari ants
Variants of these cohesion metrics are defined on the
basis of the assumption that all the methods of a class by
default receive the class type itself (self) as one of the
parameter types. CAMCs, NHDs, SNHDs and NHDMs
are defined as variants of CAMC, NHD, SNHD, and
NHDM respectively. Cohesion metrics which consider
the ‘self’ parameter are expected to give higher values as
the class methods agree on at least one parameter type.
Table 1 gives a comparison of averages of cohesion met-
rics and their variants. All the metrics in this category
(which consider self parameter type) have higher aver-
ages than their counterp arts. The observation is that met-
ric variants, which consider ‘self’ as one of the parameter
types, take values in higher range.It is also confirmed by
the descriptive analysis of these metrics as shown in
Figures 5 to 8. It is worth noting that SNHDs takes val-
ues in the range from 0 to 1 more frequently, in contrast
to SNHD which takes values in the range from 0 to –1. It
CAMCS
Figure 5. Distribution of CAMCs metric
NHDS
Figure 6. Distribution of NHDs metric
SNHDS
Figure 7. Distribution of SNHDs metric
NHDMS
Figure 8. Distribution of NHDMs metric

Explo r ing Design Level Class Cohesion Me tric s 388
implies that a class whose NHD value is more close to
NHDmax is more cohesive.
4.3 Size Independence
Figures 9 to 12 present the relation between cohe-
sion metrics and class size (measured in terms of number
of methods). CAMC metric value is higher for small
classes and is lower for large classes. NHD takes large
values for classes with larger nu mber of methods. This is
in line with the earlier findings about these two metrics
[10]. As shown in Figure 11, SNHD is close to 1 for
Figure 9. Scatter diagram of CAMC and class size
Figure 10. Scatter diagram of NHD and class size
Figure 11. Scatter diagram of SNHD and class size
Figure 12. Scatter diagram of NHDM and class size
some comparatively small classes. For larger classes,
SNHD lies in the range [-1, 0]. NHDM takes values near
0 for most of the classes. However small classes have
metric value in the higher range. However if size of the
parameter occurrence (PO) matrix is taken into consid-
eration then it is found that it does not have significant
correlation with any of the metrics (see Table 2). Here l
represents the number of parameter types, k is the num-
ber of methods of the class, and lk is the size of the pa-
rameter occurrence matrix. This result is unlike the pre-
vious studies on these metrics [10,27].
4.4 Metrics Inter-Dependencies
The parametric Pearson’s correlation coefficient between
each pair of cohesion metrics is given in Table 3. All the
correlation figures are significant at p = 0.01 level. Met-
ric variants such as CAMCs, NHDs, SNHDs, and NHDMs
are moderately correlated with their counterparts. NHD
and NHDs have the highest correlation coefficien t in this
category. NHDM and CAMC are strongly correlated.
Similar is the case for their variants NHDMs and CAMCs.
SNHD is moderately correlated with NHDMs and
CAMCs. Unlike the previous studies, the correlation
analysis for this data set does not show any significant
correlation in NHD and CAMC [10,27]. However the
scatter plot of values for these two metrics shows a n ega-
tive trend. CAMC and NHD show a negative relationship
in the scatter diagram given in Figure 13. CAM C is ve ry
low for the classes for which NHD is very high. On av-
erage the NHD metric takes values in higher range.This
implies that this metric pair does not have a linear co-
variation.
Principal Component Analysis (PCA) is used to iden-
tify the metrics measuring orthogonal dimensions. Ro-
tated principal components are obtained using the vari-
max rotation technique. Three principal components are
extracted which capture 93.28% of the data set variance
(shown in Table 4). Metrics with significant loading co-
efficients in a particular dimension are highlighted in
bold. An analysis of the table shows that NHDMs and
CAMCs and SNHD contribute significantly to the first

Explo r ing Design Level Class Cohesion Me tric s389
Table 2. Correlation in cohesion metric s and size
CAMC
CAMCs
NHD
NHDs
SNHD
SNHDs
NHDM
NHDMs
l -.222 -.696 .337 .003 -.356 -.539 -.128-.645
k -.307 -.520 .350 .219 -.071 -.179 -.177-.429
lk -.158 -.357 .210 .138 .067 -.223 -.075-.298
Table 3. Correlation analysis among metrics
CAMC CAMCs NHD NHDs SNHD SNHDsNHDM
CAMCs 0.575
NHD -0.267 -0.542
NHDs -0.372 -0.024 0.623
SNHD 0.341 0.654 -0.043 0.334
SNHDs -0.253 0.347 0.271 0.678 0.478
NHDM 0.854 0.466 0.122 0.107 0.403 -0.043
NHDMs 0.456 0.962 -0.356 0.249 0.726 0.5200.480
Figure 13. Scatter diagram shows correlation in CAMC and
NHD metrics
Table 4. Principal Components Matrix
PC1 PC2 PC3
Eigen Value 3.72 2.39 1.35
Percent 46.45 29.93 16.90
Comm. percent 46.45 76.38 93.28
CAMC 0.25 -0.32
0.90
CAMCs 0.91 -0.27 0.30
NHD -0.39
0.89 0.11
NHDs 0.27
0.90 -0.13
SNHD 0.84 0.21 0.27
SNHDs 0.66 0.59 -0.31
NHDM 0.24 0.15 0.95
NHDMs 0.95 -0.01 0.25
dimension: PC1. SNHDs is moderately significant in two
dimensions: PC1 and PC2. NHD and NHDs both load
significantly on PC2. NHDM and CAMC both load sig-
nificantly on PC3.
It is worth mentioning here that NHDM and NHDMs
have the maximum variance among all the metrics in this
analysis. So metrics measuring different dimensions are:
PC1: NHDMs, CAMCs
PC2: NHD, NHDs
PC3: NHDM, CAMC
5. Conclusions
Cohesion is one of the important design properties to
realize a quality software product. Many empirical stud-
ies exist which relate the cohesion deign property with
other properties of interest such as maintainability, reus-
ability, and reliability. Several metrics have been pro-
posed to compute cohesion at class level in object ori-
ented systems. In this paper design level cohesion met-
rics such as CAMC, NHD, SNHD have been investigated
using empirical data. In view of the anomalies present in
the existing metrics’ definitions, a modified version of
the NHD metric is proposed and is named as NHDM
(NHD Modified) ss. Statistical analysis of the metrics
data shows that CAMC and NHD are influenced by the
size of class (measured in terms of number of methods).
None of the studied metrics correlates with the size of the
Parameter Occurence matrix (PO matrix) of the class.
Principal Component Analysis of the data shows that
NHDM and CAMC both give similar results but NHDM
has more variation in its values. Similar is the case for
NHDMs and CAMCs. SNHD or SNHDs does not con-
tribute significantly to any dimension. NHD and NHDs
are not significantly related to any of the other metrics.
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