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An introduction to measurement theory, focusing on scales and measures used in software metrics. It covers the classification of scales, including nominal, ordinal, interval, and ratio scales, and discusses basic measures such as ratio, proportion, percentage, and rate. The document also explores issues related to making a measurement plan and the importance of reliability and validity in measurement. Additionally, it touches upon six sigma and the concept of validity, including construct, content, and criterion-related validity.
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Department of Computer & Information Sciences Department of Computer & Information SciencesPakistan Institute of Engineering and Applied SciencesPakistan Institute of Engineering and Applied Sciences
Lecture 9Lecture 9
Umar Faiz
http://www.pieas.edu.pk/umarfaiz/cis
Software Quality
To describe the current state of the art in the ^
To
describe
the
current
state
‐of
‐the
‐art
in
the
measurement
of
software
products
and
process.
http://www.pieas.edu.pk/umarfaiz/cis
Measurement is the process by which numbers or symbols ^
Measurement
is
the
process
by
which
numbers
or
symbols
are
assigned
to
attributes
of
entities
in
the
real
world
in
such
a
way
as
to
describe
them
according
to
clearly
d fi
d
bi
l
d
efined
unambiguous
rules
http://www.pieas.edu.pk/umarfaiz/cis
In classifying we attempt to sort elements into categories ^
In
classifying
we
attempt
to
sort
elements
into
categories
with
respect
to
a
certain
attribute.
Five
types
of
scales
can
be
described
that
are
characterized
by
their
admissible
t^
f^
ti
transformations
^
Nominal ^
Ordinal ^
Ordinal ^
Interval ^
Ratio ^
Absolute
http://www.pieas.edu.pk/umarfaiz/cis
In a nominal scale
the two key requirements for the
In a nominal scale, the two key requirements for thecategories are jointly exhaustive and mutually exclusive.
^
Mutually
exclusive
means
a
subject
can
be
classified
into
one
and
y^
j
only
one
category.
^
Jointly
exhaustive
means
that
all
categories
together
should
cover
all possible categories of the attribute If the attribute has moreall
possible
categories
of
the
attribute
.^ If
the
attribute
has
more
categories
than
we
are
interested
in,
an
"other"
category
is
needed
to
make
the
categories
jointly
exhaustive.
http://www.pieas.edu.pk/umarfaiz/cis
An ordinal scale is a measurement scale that assigns values ^
An
ordinal
scale
is
a
measurement
scale
that
assigns
values
to
objects
based
on
their
ranking
with
respect
to
one
another.
^
For
example,
we
may
classify
families
according
to
socio
‐economic
status:
upper
class,
middle
class,
and
lower
class.
The ordinal measurement scale is at a higher level than ^
The
ordinal
measurement
scale
is
at
a
higher
level
than
the
nominal
scale
in
the
measurement
hierarchy.
An
ordinal
scale
is
asymmetric
in
the
sense
that
if
is
true
th
A i
f l
It h
th
t^
iti it
t^
i^
th t if
th
en
is
f
alse.
It
h
as
th
e
t
ransitivity
property
in
th
at
if
and
then
http://www.pieas.edu.pk/umarfaiz/cis
Ratio scales are like interval scales except they have true ^
Ratio
scales
are
like
interval
scales
except
they
have
true
zero
points. ^
A^
good
example
is
the
Kelvin
scale
of
temperature.
This
scale
has
g^
p^
p
an
absolute
zero.
Thus,
a
temperature
of
300
Kelvin
is
twice
as
high
as
a
temperature
of
150
Kelvin
http://www.pieas.edu.pk/umarfaiz/cis
Basic measures such as ratio proportion percentage and ^
Basic
measures
such
as
ratio
,^ proportion
,^ percentage
,^ and
rate,
are
frequently
used
in
various
activities
associated
with
software
development
and
software
quality.
http://www.pieas.edu.pk/umarfaiz/cis
Ratios are also used in software metrics The most often ^
Ratios
are
also
used
in
software
metrics
The
most
often
used,
perhaps,
is
the
ratio
of
number
of
people
in
an
independent
test
organization
to
the
number
of
those
in
th
d
l^
t^
Th
t^
t/d
l^
t h
d
th
e
d
evelopment
group.
Th
e
t
est/development
h
ead
count
ratio
could
range
from
to
depending
on
the
management
approach
to
the
software
development
process.
http://www.pieas.edu.pk/umarfaiz/cis
Proportion is different from ratio in that the numerator in ^
Proportion
is
different
from
ratio
in
that
the
numerator
in
a
proportion
is
a
part
of
the
denominator:
P^
=^
a a+b
Proportion
also
differs
from
ratio
in
that
ratio
is
best
used
f^
t^
h
ti
i^
d f
lti l
for
t
wo
groups,
whereas
proportion
is
used
f
or
multiple
categories
(or
populations)
of
one
group.
http://www.pieas.edu.pk/umarfaiz/cis
When the numerator and the denominator are integers ^
When
the
numerator
and
the
denominator
are
integers
and
represent
counts
of
certain
events,
then
p
is
also
referred
to
as
a
relative
frequency.
For
example,
the
f ll
i^
i^
th
ti
f^
ti fi d
t^
f
following
gives
th
e
proportion
of
satisfied
customers
of
the
total
customer
set:
Number of satisfied customersNumber
of
satisfied
customers
Total
number
of
customers
of
a
software
product
The
numerator
and
the
denominator
in
a
proportion
need
not
be
integers.
They
can
be
frequency
counts
as
well
as
measurement
units
on
a
continuous
scale.
When
the
measurement
unit
is
not
integer,
proportions
are
called
fractions.
http://www.pieas.edu.pk/umarfaiz/cis
The concept of rate is associated with the dynamics ^
The
concept
of
rate
is
associated
with
the
dynamics
(change)
of
the
phenomena
of
interest;
generally
it
can
be
defined
as
a
measure
of
change
in
one
quantity
(y)
per
it
f^
th
tit
hi h th
f^
unit
of
another
quantity
x)
on
which
th
e
f
ormer
y)
depends. ^
Usually the x variable is time It is important that the timeUsually
the
x
variable
is
time
.^ It
is
important
that
the
time
unit
always
be
specified
when
describing
a
rate
associated
with
time.
http://www.pieas.edu.pk/umarfaiz/cis
1 Schedule:1.
Schedule:
^
Can
we
expect
it
to
be
done
on
time?
2 Cost:2.
Cost:
^
Can
we
afford
to
fi
nish this
project,
or
will
it
end
up
costing
more
than
it
is
worth?
Size:
^
How
big
is
the
product
so
far?
Is
the
scope
stable?
http://www.pieas.edu.pk/umarfaiz/cis
4 Quality :4.
Quality
^
Is
the
product
being
made
well,
with
few
bugs?
5 Ability :5.
Ability
^
How
much
design/coding/debugging/etc.
can
this
team
do
per
month?
Performance
^
Is
the
program
fast
enough,
using
reasonable
resources?
http://www.pieas.edu.pk/umarfaiz/cis
