This document outlines the key steps and components of the research process for a study titled "A Study on Pragmatic Approaches and Quality Initiatives for Enhancing Teachers’ Caliber in Post Graduate Institutes offering MBA Programme under Bangalore University". The research methodology section defines different types of research and the scientific research process. It also provides details on key aspects of research design including objectives, hypotheses, sampling, data collection and analysis. The document concludes by mentioning the final steps of report writing and research reporting.

1. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
1
Paper
1
Exam
Sheet
Research
Methodology
and
Statistics
Shivananda
R
Koteshwar
TITLE:
A
Study
on
Pragmatic
Approaches
and
Quality
Initiatives
for
Enhancing
Teachers’
Caliber
in
Post
Graduate
Institutes
offering
MBA
Programme
under
Bangalore
University
Under
the
Guidance
of
Dr.
T.V.
Raju
Director,
RV
Institute
of
Management,
Bangalore
CANARA
BANK
SCHOOL
OF
MANAGEMENT
STUDIES
BANGALORE
UNIVERSITY

2. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
2
RESEARCH METHODOLOGY
Life cycle of Research.................................. 3
Scientific Research..................................... 3
Research Process........................................ 4
Research Report......................................... 5
Good measurement characteristics........................ 7
Research Problem........................................ 8
Hypothesis.............................................. 8
Case Study............................................. 11
Sampling............................................... 11
Data Preparation Process............................... 12
STATISTICS
Characteristics of a statistical data.................. 13
Arithmetic Mean........................................ 13
Median................................................. 14
Mode................................................... 14
Standard Deviation and Variance........................ 14
Coefficient of Variation............................... 15
Range and Coefficient of Range......................... 15
Trend Analysis (Straight Line Analysis)................ 15
Standard Normal Curve (SNC)............................ 16
Non parametric test – (χ2) kai2 test ................... 16
ANNOVA – Analysis of Variance.......................... 17
Coefficient of Correlation............................. 20
Regression............................................. 20
Small Sample Test...................................... 21
IMPORTANT QUESTIONS

3. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
3
Life cycle of Research
• Hypothesis,
Prediction,
Formulation
of
question,
Sampling,
Experimentation,
Observation,
Recording,
Measurement,
Analyzing,
Formulation,
Testing,
Modification
and
Conclusion
Types of Research (PAD DEEA) (ASHE)
• Either
based
on
Intent
or
based
on
method
• Intent
Based:
Pure,
Applied,
Exploratory,
Action,
Descriptive,
Diagnostic,
Evaluation
• Method
Based:
Experimental,
Analytical/Statistical,
Historical,
Survey/Fact
Finding
o Pure:
Undertaken
for
the
sake
of
knowledge
without
any
intention
to
apply
it
in
practice.
Aims
at
extension
of
knowledge
o Applied:
Problem
oriented
and
action
directed.
Gives
conceptual
clarity
o Exploratory:
Formulative
Research.
Study
of
an
unfamiliar
problem
about
which
the
researcher
has
little
or
no
knowledge.
Usually
takes
the
form
of
a
pilot
study
o Descriptive:
Fact
finding
investigation.
More
specific
than
exploratory
research.
o Diagnostic:
Similar
to
descriptive
but
with
a
different
focus.
Directed
towards
discovering
what
is
happening,
why
is
it
happening
and
what
can
be
done
about
o Evaluation:
Type
of
Applied
research.
Made
for
assessing
the
effectiveness
of
social
or
economic
programmes
implemented
o Action:
It’s
a
type
of
evaluation
study.
It
is
a
concurrent
evaluation
of
an
action
programme
launched
for
solving
a
problem
for
improving
an
existing
situation
o Experimental:
Assessing
the
effects
of
a
particular
variables
on
a
phenomenon
by
keeping
the
other
variables
constant
or
controlled
o Analytical:
Known
as
Statistical
Method.
System
of
procedures
and
techniques
of
analysis
applied
to
a
quantitative
data
o Historical:
Study
of
past
records.
Tries
to
discover
the
trends
in
the
past
o Survey:
Fact
finding
study.
Purpose
is
to
provide
information,
explain
phenomenon
to
make
comparisons
and
concerned
with
cause
and
effect
relationships
Scientific Research
• A
method
or
procedure
consisting
of
systematic
observation,
measurement,
and
experiment,
and
the
formulation,
testing,
and
modification
of
hypotheses”
• Requires
replication,
external
review
and
data
recording
&
sharing
• The
key
elements
of
scientific
research
(articles
of
faith)
are

4. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
4
o Ethical
neutrality
(Eliminate
personal
opinion)
o Reliance
on
empirical
Evidence
o Use
of
relevant
concept
o Commitment
of
Objectivity
o Generalization
o Validity
&
Reliability
o Logical
Reasoning
process
• Scientific
research
method
is
inquiry
based
on
empirical
and
measurable
evidence
subject
to
specific
principles
of
logic
reasoning
• Effective
Methodology:
Question

Observe

Hypothesis

Prediction

Test

Analyze

Interpret

Publish

Retest
Research Process
• Research
Area/Theme/Problem/Idea
• Tentative
hypothesis
• Literature
Review
• Research
Title/Topic
• Research
Questions
• Research
Proposal
o Need
for
study
o Limitation
of
Research
o Scope
of
Research
o Budget
o Responsibilities
and
Obligations
of
stake
holders
o Place
and
Period
of
study
• Research
Proposal
Approval
• Objectives
• Hypothesis
• Operational
definition
• Research
Method/
Research
Design
(Type,
Purpose,
Timeframe,
Scope
and
environment)
o Research
Type
 Experimental,
Historical
and
Inferential
Designs
 Exploratory,
Descriptive
and
Causal
Designs
 Experimental
and
Post
facto
 Historical
method,
Case
study,
Clinical
Study
 Sample
Surveys,
Field
studies,
Experiments
in
field
settings,
Laboratory
experiments
 Exploratory,
Descriptive,
Experimental
studies
 Exploratory,
Descriptive,
Casual
 Experimental,
Quasi-­‐Experimental
Designs
 True
Experimental,
Quasi-­‐Experimental
and
Non
experimental
designs
 Experimental,
Pre-­‐Experimental,
Quasi-­‐Experimental
designs,
Survey
Research
o Research
question
or
purpose
o Research
timeframe
o Data
Collection
Design

5. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
5
 Variables
 Data
collection
methods
o Sampling
Design
 Sample
Population
and
Sampling
Size
 Sample
Distribution
Decision
 Sampling
Method/Technique
 Sampling
Unit/Frame
o Instrument
Development
 Introduction
and
Instructions
for
participants
 Target
Questions
(AIM)
• Administrative
Questions
• Investigative
questions
• Measurement
Questions
 Preliminary
Analysis
plan
o Pilot
testing
• Data
collection
and
preparation
• Data
Analysis
o Findings
(Testing
of
hypothesis)
o Interpretation
and
Conclusions
• Report
writing
/
Research
Reporting
Note:
Research
type
is
categorized
based
on
the
different
perspectives
from
which
any
given
study
can
be
viewed.
They
are:
• The
degree
of
formulation
of
the
problem
(Exploratory
or
Formalized)
• The
topical
scope-­‐breadth
and
depth
of
the
study
(Case
or
statistical
study)
• The
research
environment
(Field
Setting/Survey
or
laboratory
experiment)
• The
time
dimension
(one-­‐time
or
longitudinal)
• The
mode
of
data
collection
(Observational
or
survey)
• The
nature
of
relationship
among
variables
(Descriptive
or
casual)
Research Report
Broad
Divisions
Individual
Sections
Title
of
Report
Table
of
Contents
Preliminary
material
Abstract/Synopsis
Introduction
Literature
Review
Methodology
Results
Discussion
Conclusion
Body
of
report
Recommendations
References
or
Bibliography
Supplementary
material
Appendices

6. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
6
Levels of Measurement / Measurement
Scales (NOIR)
(ODO)
• Nominal:
Consists
of
assigning
numerals
or
symbols
to
different
categories
of
a
variable.
They
are
just
like
labels
and
have
no
quantitative
value.
E.g.:
Male
and
Female
applicants
of
a
MBA
program
• Ordinal:
Persons
or
objects
are
assigned
numerals,
which
indicate
ranks
with
respect
to
one
or
more
properties
either
in
ascending
or
descending
order.
E.g.:
Ranking
of
individual
based
on
socio-­‐economic
class,
which
might
be
a
combination
of
income,
education,
occupation
and
wealth
• Interval:
It’s
ranking
with
equality
in
distance.
So
it’s
not
possible
to
multiply
or
divide
the
numbers
on
an
interval
scale.
E.g.:
The
centigrade
temperature
gauge.
A
temperature
of
50degrees
is
exactly
10
degrees
hotter
than
40
degrees
and
10
degrees
cooler
than
60
degrees
• Ratio:
This
has
absolute
zero
point.
Since
there
is
natural
zero,
it
is
possible
to
multiply
and
divide
the
numbers
on
a
ratio
scale.
E.g.:
Height,
weight,
distance
and
area
MEASUREMENT
ORDER
DISTANCE
ORIGIN
STATISTICAL
TOOL
USED
SCALES
USED
Nominal
NO
NO
NO
None
Simple
Category,
Multiple
choice,
Single
Response,
Multiple
Choice,
Multiple
response,
Graphic
Rating
scale
Ordinal
YES
NO
NO
Median,
Rank
order
correlation
coefficient
Stapel
Scale
Interval
YES
YES
NO
Standard
Deviation,
Product
Moment
correlation,
“t”
tests,
“F”
tests
Likert
scale
summated
Rating,
Semantic
Differential
Scale,
Numerical
Scale,
Multiple
rating
list
scale,
Staple
scale,
Graphic
Rating
scale
Ratio
YES
YES
YES
Standard
Deviation,
Product
Moment
correlation,
“t”
tests,
“F”
tests,
Geometric
Mean,
Coefficient
of
variation
Constant
sum
scale,
Graphic
Rating
Scale

7. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
7
• The
measurement
scales,
commonly
used
in
marketing
research,
can
be
divided
based
on
number
of
dimensions:
o Comparative
and
Non
comparative
scales
 Comparative
scales
involve
the
respondent
in
signaling
where
there
is
a
difference
between two
or
more
producers,
services,
brands
or
other
stimuli.
Examples
of
such
scales
include;
paired
comparison,
dollar
metric,
unity-­‐sum-­‐gain
and
line
marking
scales.
 Non-­‐comparative
scales,
described
in
the
textbook,
are;
continuous
rating
scales,
line-­‐marking
scales,
itemized
rating
scales,
semantic
differential
scales
and
Likert
scales.
o Uni-­‐dimensional
Scale
and
Multi-­‐dimensional
scale
o Balanced
or
unbalanced
scale
o Forced
or
Un
forced
choice
scale
o Simple
Category
scale
(Dichotomous
scale),
Multiple
choice
single
response
scale
and
Multiple
choice
Multiple
response
scale
(multiple
choice
scale)
o Likert
scale
(Summated
rating
scale)
and
Semantic
Differential
Scale
(SD
Scale)
SCALE
MEASUREMENT
Simple
Category
Scale
Nominal
Multiple
Choice
Single
Response
Scale
Nominal
Multiple
Choice
Multi
Response
Scale
Nominal
Likert
Scale
summated
rating
Interval
Semantic
Differential
Scale
Interval
Numerical
Scale
Ordinal
or
Interval
Multiple
Rating
List
scale
Interval
Constant
Sum
Scale
Ratio
Stapel
Scale
Ordinal
or
Interval
Graphic
Rating
Scale
Ordinal
or
Interval
or
Ratio
Good measurement characteristics
• Uni-­‐dimensionality
• Linearity
• Validity:
(ConPreCon)
o Validity
refers
to
how
effective
an
instrument
is
in
measuring
a
property
it
intends
to
measure.
o Three
types
of
validity
are
Content
Validity
(Face
Validity
and
Sampling
Validity),
Predictive
Validity
and
Construct
Validity
o Content
Validity-­Face
Validity:
Subjective
evaluation
of
a
measuring
scale.
E.g.
a
researcher
may
develop
a
scale
to
measure
consumer
attitude
towards
a
brand
and
pre-­‐test
the
scale
among
a
few
experts.
If
the
researchers
are
satisfied,
the
researcher
may
conclude
that
the
scale
has
face
validity
o Content
Validity
–
Sampling
Validity:
Refers
to
how
representative
the
content
of
the
measuring
instrument
is.
E.g.
If
attitude
is
the
characteristic
being
measured,
its
content
universe

8. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
8
may
comprise
statements
and
questions
indicating
which
aspects
of
attitude
need
to
be
measured.
This
is
also
based
on
judgment
o Predictive
Validity:
Refers
to
the
extent
to
which
one
behavior
can
be
predicted
based
on
another.
E.g.
In
the
case
of
admission
test
designed
for
prospective
MBA
students,
the
predictive
validity
of
the
test
would
be
determined
by
the
association
between
the
scores
on
the
test
and
the
grade
point
average
secured
by
students
during
the
first
semester
of
study.
Correlation
of
coefficient
can
be
computed
to
determine
the
predictive
validity
of
the
admission
test.
Predictive
validity
is
strong
if
correlation
of
coefficient
is
greater
than
0.5
o Construct
Validity:
Is
a
conceptual
equation
that
is
developed
by
the
researcher
based
on
theoretical
reasoning.
The
instrument
may
be
considered
to
have
construct
validity
only
if
the
expected
relationships
(between
variable
under
study
and
other
variables)
are
found
to
be
true
• Reliability
• Accuracy/Precision
• Simplicity
• Predictability
Research Problem
• Sources
of
Choosing
a
Problem:
Review
of
literature,
academic
experience,
daily
experience,
exposure
to
field
situations,
consultations,
Brain
storming,
Research
and
Intuition
• Formulation
of
problem:
o Internal
Criteria:
Researcher’s
interest,
Researchers
competence
and
Researcher’s
own
resource
o External
Criteria:
Research
ability
of
the
problem,
Importance
and
urgency,
Novelty
of
the
problem,
Feasibility,
Facilities,
Usefulness
&
social
relevance
and
Research
personnel
• Criteria
for
good
research
problem:
Verifiable
evidence,
Accuracy,
precision,
systematization,
objectivity,
recording,
controlling
conditions
and
training
investigators
Hypothesis
• Tentative
statement/assumption
asserting
a
relationship
between
certain
facts
• Its
intended
to
be
tested,
verified
or
rejected
• It
contains
variables
that
are
measurable
and
specifying
how
they
are
related
• Criteria
o Not
a
form
of
a
question
o Empirically
testable
o Specific
and
Precise
o Shouldn’t
be
contradictory

9. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
9
o Should
specify
variables
between
which
the
relationship
is
to
be
established
o Should
describe
only
one
relationship
• Nature
of
Hypothesis
o Accurately
reflect
the
relevant
sociological
fact
o Not
be
in
contradiction
with
approved
relevant
statements
of
other
scientific
disciplines
o Must
consider
the
experience
of
other
researchers
• Characteristics
of
Good
Hypothesis
o Conceptual
Clarity
o Specificity
o Testability
o Availability
of
techniques
o Theoretical
relevance
o Consistency
o Objectivity
o Simplicity
• Types:
o Null
Hypothesis
(H0)
If
we
are
to
compare
method
A
with
method
B
about
its
superiority
and
if
we
proceed
on
the
assumption
that
both
methods
are
equally
good,
then
this
situations
is
termed
as
null
hypothesis.
E.g.
If
we
want
to
test
the
hypothesis
that
the
population
mean
is
equal
to
the
hypothesis
mean
equal
to
100.
Then
null
hypothesis
would
be
H0
:µ=µ
H0
=
100
o Alternative
Hypothesis
(Ha)
If
our
sample
results
do
not
support
this
null
hypothesis,
we
should
conclude
that
something
else
is
true.
What
we
conclude
rejecting
the
null
hypothesis
is
known
as
alternative
hypothesis.
E.g.
For
the
same
example,
the
alternate
hypothesis
are:
 Ha:
µ≠µ
H0
-­‐
Population
mean
is
not
equal
to
100
 Ha:
µ>µ
H0
-­‐
Population
mean
is
greater
than
100
 Ha:
µ<µ
H0
-­‐
Population
mean
is
lesser
than
100
• Level
of
Significance:
If
we
take
level
of
significance
as
5%,
then
this
implies
that
researcher
is
willing
to
take
as
much
as
5%
risk
rejecting
the
null
hypothesis
when
it
happens
to
be
true
• Decision
Rule
of
Test
of
Hypothesis:
Making
rule,
which
is
known
as
decision
rule
according
to
which
we
accept
Null
hypothesis
(rejecting
alternative
hypothesis)
or
reject
null
hypothesis
(accepting
alternative
hypothesis).
E.g.
If
Null
hypothesis
states
that
a
certain
lot
is
good
(less
defective
items)
and
alternate
hypothesis
is
that
the
lot
is
not
good
(many
defective
items).
In
this
case,
we
need
to
decide
the
number
of
items
to
be
tested
and
the
criterion
for
accepting
or
rejecting
the
hypotheses.
We
might
test
10
items
in
the
lot
and
plan
our
decision
saying
that
if
there
are
none
or
only
1
defective
item
among
the
10,
then
we
will
accept
Null
hypothesis
else
we
will
reject
Null
Hypothesis
(and
accept
alternative
hypothesis).
This
sort
of
basis
is
known
as
decision
rule
• Type
1
and
Type
2
Errors
(Type
1
error
is
also
called
as
level
of
significance
of
test)
DECISION

10. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
10
Accept
NULL
Reject
NULL
Null
Hypothesis
(TRUE)
Correct
Decision
Type
1
Error
(α
error)
Null
Hypothesis
(FALSE)
Type
II
Error
(β
error)
Correct
Decision
• Two
Tailed
Test
and
One
Tailed
Test:
o Two
tailed
test
rejects
the
Null
hypothesis
if,
we
say,
the
sample
mean
is
significantly
higher
or
lower
than
the
hypothesized
value
of
the
mean
of
the
population
o One
tailed
test:
When
we
have
to
say
the
population
mean
is
either
lower
than
or
higher
than
some
hypothesized
value
• Testing
Hypothesis:
o Make
a
formal
statement
-­‐
State
NULL
hypothesis
as
well
as
ALTERNATIVE
hypothesis
o Specify
the
level
of
significance
o Decide
the
correct
sampling
distribution
o Decide
the
sampling
distribution
to
use
o Sample
a
random
sample
and
workout
an
appropriate
value
o Calculate
the
probability
that
sample
result
would
diverge
as
widely
as
it
has
from
expectations,
if
NULL
hypothesis
were
true
o Compare
the
probability
-­‐
If
the
probability
equal
to
or
smaller
than
the
Alpha
value
in
case
of
one
tailed
test
or
equal
to
Alpha/2
in
case
of
two-­‐tailed
test,
reject
NULL
hypothesis
else
accept
NULL
hypothesis
• Tests
of
Significance
or
Tests
of
Hypothesis:
o Parametric
Tests
(Standard
Tests)
–
Assume
certain
properties
of
the
parent
population
from
which
we
draw
samples.
E.g.
sample
size,
population
parameters
like
mean,
variants
etc.
All
tests
are
based
on
the
assumption
of
normality
(Source
of
data
is
considered
to
be
normally
distributed)
o Non
Parametric
Test
or
Distribution
(Free
test
of
hypothesis)
–
Statistical
method
o Important
Parametric
tests
 z-­Test:
Used
generally
for
comparing
the
mean
of
a
sample
to
some
hypothesis
mean
for
the
population
in
case
of
large
sample,
or
when
population
variance
is
known.
Based
on
normal
probability
distribution
and
is
used
to
judging
the
significance
of
several
statistical
measures,
particularly
the
mean.
Test
is
also
used
for
both
binomial
distribution
and
t-­‐distribution.
 t-­test:
Used
in
case
of
small
sample
when
population
variance
is
unknown.
Based
on
t-­‐distribution
and
is
considered
an
appropriate
test
for
judging
the
significance
of
sample
mean
or
for
judging
significance
of
difference
between
the
two
means
of
the
two
samples.
 x2
test:
Used
for
comparing
a
sample
variance
to
a
theoretical
population
variance
is
unknown.
Based
on
chi-­‐square
distribution

11. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
11
 f-­test:
Used
to
compare
the
variance
of
the
two
independent
samples.
This
test
is
also
used
in
the
context
of
variance
(ANOVA)
for
judging
the
significance
of
more
than
2
sample
means
at
the
same
time
and
also
for
judging
the
significance
of
multiple
coefficients.
This
is
based
on
f-­‐distribution
Case Study
• Case
study
is
a
method
of
exploring
and
analyzing
the
life
of
a
social
unit
or
entity,
be
it
a
person,
a
family,
an
institution
or
a
community
• The
aim
of
case
study
method
is
to
locate
or
identify
the
factors
that
account
for
the
behavior
patterns
of
a
given
unit
and
its
relationship
with
the
environment
• It
depends
upon
the
wit,
commonsense
and
imagination
of
the
person
doing
the
case
study.
• Efforts
should
be
made
to
ascertain
the
reliability
of
life
history
data
through
examining
the
internal
consistency
of
the
material.
A
judicious
combination
of
techniques
of
data
collection
is
a
prerequisite
for
securing
data
that
are
culturally
meaningful
and
scientifically
significant
• In-­‐depth
analysis
of
selected
cases
is
of
particular
value
to
business
research
when
a
complex
set
of
variables
may
be
at
work
in
generating
observed
results
and
intensive
study
is
needed
to
unravel
the
complexities
Sampling
• A
part
of
the
population
is
known
as
sample.
The
method
consisting
of
the
selecting
for
study,
a
portion
of
the
universe
with
a
view
to
draw
conclusions
about
the
universe
or
population
is
known
as
sampling
• Census
(Total
Population)

Target
Population
(Whom
we
are
concerned
with)

Sample
Frame
(Criteria
through
which
we
will
be
selecting)

Sample
Unit
(Categories)

Sample
Element

Sample
Size
• Sample
size
depends
on
o Variability
of
population
(standard
deviation)
–Can
be
found
out
by
Pilot
study
o Confidence
attached
to
the
estimate
(Confidence
Interval)
o Allowable
error
or
margin
of
error
(Tolerable
Error)
• Sample
Size
o Determining
Sample
size
in
case
of
continuous
and
interval
scale
 n
=
(Z2
(Std
Dev)2
)
/
(e2)
where
Z
=
Value
of
given
confidence
interval,
n
=
sample
size,
Std
Dev
=
Range/6
and
Range=
Max
Value
-­‐1
o For
Dichotomy
questions
 n
=
(Z2
(pq
))
/
(e2)
where
p=probability
of
success
(frequency
of
people
saying
yes)
 If
p
is
not
known,
then
n
=
(¼)(Z2
/
(e2)

12. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
12
• Sample
Techniques
o Non
Probabilistic:
Convenience
(Accidental),
Judgmental
(Expert
Opinion
or
Purposive),
Quota,
Snowball
(Going
through
references)
o Probabilistic:
Simple
Random,
Systematic
Sample
(E.g.:
Every
5th,
11th,
16th
etc),
Stratified
(homogenous),
Cluster
(Heterogeneous)
o Stratified
can
be
either
proportionate
or
disproportionate
o In
scientific
research
only
probabilistic
sampling
technique
need
to
be
used
o Quota
vs.
Stratified
 Quota
is
non
probabilistic
and
Stratified
is
probabilistic
 Both
are
homogeneous
within
Quota/Strata
and
heterogeneous
across
Quota/Strata
 Both
are
2-­‐stage
process.
In
first
step
Quota
and
Stratified
are
same.
Once
its
Quota
or
stratified,
next
step
would
employ
different
methods.
In
Quota
it
would
be
non
probability
method
and
in
Stratified,
it
would
be
probabilistic
• Quota:
Convenience,
Judgmental
or
Snow
ball
sampling
• Stratified:
Simple
Random
or
Systematic
Random
o Cluster
vs.
Stratified
 Heterogeneity
within
Cluster
and
Homogenous
across
cluster
 Homogeneous
within
Strata
and
heterogeneous
across
Strata
o Multi
stage
sampling:
Cluster

Stratified

Systematic/Simple
Random
Data Preparation Process
• Check
Questionnaire:
Edit,
Code,
Transcribe,
Clean
• Statistically
Adjust
data
/
Statistical
Analysis.
The
two
types
are:
o Descriptive
(Data)
o Inferential
(Hypothesis)

13. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
13
STATISTICS
Distribution:
o Normal
Distribution
o Frequency
Distribution
(Poisson,
Binomial,
Normal)
• Discrete
Frequency
Distribution
x
f
74
4
83
3
93
8
• Continuous
Frequency
Distribution
x
f
0-­‐10
4
10-­‐20
3
20-­‐30
8
o For
more
Probability
Distribution:
http://en.wikipedia.org/wiki/Probability_distribution
Characteristics of a statistical data
• Central
Tendency:
Measured
by
statistical
averages
o Mathematical
Average:
Arithmetic
Mean,
Geometric
Mean,
Harmonic
Mean
o Positional
Average:
Median,
Mode
• Dispersion
• Skewness
• Kurtosis
Arithmetic Mean
o AM=∑X/N
where
∑X
=
Sum
of
the
item
and
N
is
the
number
of
items
o If
frequency
is
given,
then
AM=∑fx/∑f
where
∑fx
=
sum
of
the
values
multiplied
by
the
corresponding
frequency
and
∑f
is
sum
of
frequency
o Arithmetic
mean
of
58,67,68,84,93,98,100
 ∑X
=
58+67+68+84+93+98+100
=
560
 N
=
number
of
items
=
7
 AM
=
∑X/N
=
560/7
=
80
o Arithmetic
mean
of
following
50
workers
according
to
their
daily
wages
 Daily
Wage:
15,
18,
20,
25,
30,
35,
40,
42,
45
 Number
of
workers:
2,
3,
5,
10,
12,
10,
5,
2,
1
Wages
(x)
Frequency
(F)
fx
15
2
30

14. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
14
18
3
54
20
5
100
25
10
250
30
12
360
35
10
350
40
5
200
42
2
84
45
1
45
 ∑fx
=
473
and
∑f
=
50
 AM
=∑fx/∑f
=
473/50
=
29.46
o Arithmetic
mean
for
the
following
distribution
 Marks
10-­‐20
20-­‐30
30-­‐40
40-­‐50
50-­‐60
60-­‐70
80-­‐90
 Number
of
students:
6
12
18
20
20
14
8
2
Marks
Frequency
(F)
Mid
Value
(x)
Mean
fx
10-­‐20
6
15
90
20-­‐30
12
25
300
30-­‐40
18
35
630
40-­‐50
20
45
900
50-­‐60
20
55
1100
60-­‐70
14
65
910
70-­‐80
8
75
600
40-­‐90
2
85
170
 ∑fx
=
4700
and
∑f
=
100
 AM
=
=∑fx/∑f
=
4700/100
=
47
Median
• Size
of
the
middlemost
value
• 80,
86,
74,
465,
3,
984,
22:
Median
is
465
• Median
of
Indian
age
is
26
means,
50%
of
India’s
population
will
be
less
than
26years
of
age
and
50%
will
be
more
than
26yrs
of
age
Mode
• Most
occurring
number
Standard Deviation and Variance
o Deviation
from
Mean
o It’s
a
relative
number
and
not
an
absolute
number
o Lesser
the
Standard
Deviation,
higher
the
reliability
o σ
=
√(∑(x-­‐xb)2
/
N)
x
(x-­‐xb)2
15
64
20
9
22
1
28
25

15. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
15
30
49
∑x
=
115
∑(x
–xb)2
=
148
• xb
=
∑x/N
=
115/5
=
23
• σ
=
√(148/5)
=
5.44
• Variance
=
σ2
=
29.59
Coefficient
of
Variation
• Lesser
the
confidence
of
variation,
the
reliability
is
higher
• V
=
σ
/xb*100
• For
the
above
example,
it
would
be
equal
to
5.44/23*100
=
23.65
• Lesser
the
CV,
higher
the
reliability
Range
and
Coefficient
of
Range
• Range
=
L-­‐S
• Coefficient
of
Range
=
(L-­‐S)/(L+S)
Trend Analysis (Straight Line
Analysis)
• Least
Square
Method
(Forecasting
Method)
Year
Sales
(y)
year-­midyear
x
x2
xy
yc
bx
+
a
2006
42
-­‐3.5
12.25
-­‐147
36.11
2007
40
-­‐2.5
6.25
-­‐100
41.97
2008
36
-­‐1.5
2.25
-­‐54
47.83
2009
58
-­‐0.5
0.25
-­‐29
53.69
2010
62
0.5
0.25
31
59.55
2011
60
1.5
2.25
90
65.41
2012
70
2.5
6.25
175
71.27
2013
80
3.5
12.25
280
77.13
∑y=453
∑x=0
∑x2=42
∑xy
=
246
∑yc
=452.96
• Mid
year
=
2009.5
• Deviation
from
Arithmetic
mean
will
be
least
in
this
method,
hence
its
called
least
square
method
• yc
=
bx
+
a
• ∑y
=
b∑x
+
Na
• ∑y
=
b
(0)+
Na
=
Na
• a
=
∑y
/N
• a
=
453/8
=
56.62
• ∑xy
=
a∑x
+
b∑x
2
• 246=
56.62
(0)
+
b
(42)
• b
=
5.86
• Forecast
for
2014,
x
=
4.5
o yc
=
bx
+
a
o yc
=
5.86
(4.5)
+
56.62
=
82.99

16. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
16
• Forecast
for
2015,
x
=
5.5
o yc
=
bx
+
a
o yc
=
5.86
(5.5)
+
56.62
=
88.85
• ∑yc
=
∑y
(Verification
Technique)
Standard
Normal
Curve
(SNC)
1. Assume
mean
height
of
soldier
is
68.22
inches
with
a
variance
of
10.8
inches.
How
many
soldiers
in
a
regiment
of
1000
would
you
expect
to
be
over
6ft
tall
• σ
2
=
10.8
• σ
=
3.29
• x
=
6
feet
=
72
inches
• xb
=
68.22
(mean)
• z
=
SNC
=
(x-­‐xb)/σ
=
(72-­‐68.22)/3.29
=
1.15
• From
the
Statistical
Table
for
1.15
its
=>
0.5
–
0.3759
=
0.1251
• 0.1251*1000
=125
soldiers
are
taller
than
1000
2. 1000
light
bulbs
with
a
mean
life
of
120
days
are
installed
in
a
new
factory.
They
have
length
of
life
is
normally
distributed
with
Standard
deviation
of
20
days.
How
many
bulbs
will
expire
in
less
than
90
days?
How
many
bulbs
will
burn
for
more
than
125
days?
• N
=
1000
• xb
=
120
• σ
=
20
• x
=90
• Z
=
SNC
=
(x-­‐xb)/σ
=
(90-­‐120)/20
=
-­‐1.5
• From
the
statistical
table
for
-­‐1.5
its
=>
0.5
-­‐0.4332
=
0.0668
• 0.0668*1000
=
67
Bulbs
• N
=
1000
• xb
=
120
• σ
=
20
• x
=125
• Z
=
SNC
=
(x-­‐xb)/σ
=
(125-­‐120)/20
=
0.25
• From
the
statistical
table
for
0.25
its
=>
0.5
-­‐0.0987
=
0.4013
• 0.4013*1000
=
401
bulbs
Non parametric test – (χ2) kai2 test
o χ2
=
kai2
=
∑
(O-­‐E)2/E2
where
O
=
Observed
Frequency
and
E
=
Expected
frequency
o In
a
certain
area
in
Bangalore,
the
corporation
distributed
pills
to
combat
CG.
From
the
data
given
below
analyze
whether
the
pills
given
were
effective
or
not
in
combating
the
disease

17. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
17
Fell
Ill
Not
Ill
Took
Pills
345
620
Dint
take
pills
545
450
o Null
Hypothesis:
Given
pills
are
not
effective
in
controlling
the
said
disease
Table
of
Observed
Frequency
(O)
345
620
965
(Row
1
Total)
545
450
995
(Row
2
Total)
890
(Column1
Total)
1070
(Column
1
Total)
1960
(Grand
Total)
• E
=
(RT
*
CT)
/
GT
• Table
of
Expected
Frequency
(E)
• E345
=
965*890
/
1960
=
438.19
• E620
=
965*1070
/
1960
=
526.81
• E545
=
995*890
/
1960
=
451.81
• E450
=
995*1070/
1960
=
543.19
438.19
526.81
965
451.81
543.19
995
890
1070
1960
O
E
(O-­E)2/E2
345
438.19
0.045
545
451.81
0.042
620
526.81
0.032
450
543.19
0.029
∑
(O-­‐E)2/E2
=
0.148
• χ2
=
Kai2
=
0.148
• Degree
of
freedom
=
(r-­‐1)
(c-­‐1)
=
(2-­‐1)(2-­‐1)
=
1
• Taking
the
significance
level
to
be
5%
(Confidence
level
as
95%),
from
the
statistical
table,
we
can
find
that
the
table
value
is
3.84
• As
calculated
hypothesis
=
0.1484
is
less
than
the
table
value
of
3.84,
Null
hypothesis
is
accepted
ANNOVA – Analysis of Variance
1. 5
salesmen
work
in
4
cities.
Based
on
the
data
given
determine
whether
there
is
a
significance
difference
in
the
sales
performance
of
different
cities
Salesmen
A
B
C
D
S1
14
12
13
15
S2
15
14
12
11

18. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
18
S3
16
17
15
10
S4
12
16
15
14
S5
10
11
15
17
• Null
Hypothesis:
There
is
no
significance
difference
in
the
sale
performance
of
different
cities
X1
X2
X3
X4
14
12
13
15
15
14
12
11
16
17
15
10
12
16
15
14
10
11
15
17
∑X
67
70
70
67
Xb
=
∑X/N
(N=5)
13.4
14
14
13.4
• Grand
Mean
=
Xbb
=
∑Xb/N
=
(13.4
+
14
+
14
+
13.4)/4
=
13.7
• Variance
between
samples
(X1b-­
X1bb)2
(X2b-­
X2bb)2
(X3b-­
X3bb)2
(X4b-­X4bb)2
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
∑
0.45
0.45
0.45
0.45
• Sum
of
Squares
=
0.45
+
0.45
+
0.45
+
0.45
=
1.8
• Degree
of
Freedom
(d.f)
γ1
=
4
-­‐1
=
3
• Mean
of
sum
of
squares
=
1.8/3
=
0.6
• Variance
within
samples
(X1-­X1b)2
(X2-­X2b)2
(X3-­X3b)2
(X4-­X4b)2
0.36
4
1
2.56
2.56
0
4
5.76
6.76
9
1
11.56
1.96
4
1
0.36
11.56
9
1
12.96
∑
23.2
26
1
33.2
• Sum
of
Squares
=
23.2
+
26
+
1
+
33.2
=
90.4
• Degree
of
Freedom
(d.f)
γ2
=
Total
number
of
observations
–
Number
of
samples
=
(5*4)
–
4
=
16
• Mean
of
sum
of
squares
=
90.4/16
=
5.65
•
• “f”
test
(Fisher)
for
5%
significance
level
• f
test
=
F=
(variation
between
samples)/(variation
within
samples)
=
0.6/5.65
=
0.106
• From
the
table,
m=γ1
and
n=γ2
,
m=3
and
n=16,
value
of
F=3.2389

19. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
19
• Calculated
value
F=0.106
is
less
than
the
table
value
3.2389
so
Null
Hypothesis
is
accepted
2. 5
salesmen
work
in
4
cities.
Based
on
the
data
given
determine
whether
there
is
a
significance
difference
between
the
sales
performance
of
different
salesmen
Salesmen
A
B
C
D
S1
14
12
13
15
S2
15
14
12
11
S3
16
17
15
10
S4
12
16
15
14
S5
10
11
15
17
S1
S2
S3
S4
S5
City1
14
15
16
12
10
City2
12
14
17
16
11
City3
13
12
15
15
15
City4
15
11
10
14
17
∑X
54
52
58
57
53
Xb=∑X/N
(N=4)
13.5
13
14.5
14.25
13.25
• Grand
Mean
=
Xbb
=
∑Xb/N
=
(13.5
+
13
+
14.5
+
14.25
+
13.25)/5=
13.7
• Variance
between
samples
(X1b-­X1bb)2
(X2b-­X2bb)2
(X3b-­
X3bb)2
(X4b-­
X4bb)2
(X5b-­
X5bb)2
0.04
0.49
0.64
0.3
0.2
0.04
0.49
0.64
0.3
0.2
0.04
0.49
0.64
0.3
0.2
0.04
0.49
0.64
0.3
0.2
∑
0.16
1.96
2.56
1.2
0.8
• Sum
of
Squares
=
0.16
+
1.96
+
2.56
+
1.2
+
0.8
=
6.68
• Degree
of
Freedom
(d.f)
γ1
=
5
-­‐1
=
4
• Mean
of
sum
of
squares
=
6.68/4
=
1.67
• Variance
within
samples
(X1-­X1b)2
(X2-­X2b)2
(X3-­X3b)2
(X4-­X4b)2
(X5-­X5b)2
0.25
4
2.25
5.06
10.56
2.25
1
6.25
3.06
5.06
0.25
1
0.25
0.56
3.06
2.25
4
20.25
0.06
14.06
∑
5
10
29
8.74
32.74
• Sum
of
Squares
=
5
+
10
+
29
+
8.74
+
32.74
=
85.48
• Degree
of
Freedom
(d.f)
γ2
=
Total
number
of
observations
–
Number
of
samples
=
(5*4)
–
5
=
15

20. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
20
• Mean
of
sum
of
squares
=
85.48/15
=
5.7
•
• “f”
test
(Fisher)
for
5%
significance
level
• f
test
=
F=
(variation
between
samples)/(variation
within
samples)
=
1.67/5.7
=
0.29
• From
the
table,
m=γ1
and
n=γ2
,
m=4
and
n=15,
value
of
F=3.0556
• Calculated
value
F=0.29
is
less
than
the
table
value
3.0556
so
Null
Hypothesis
is
accepted
Coefficient of Correlation
• Carls
Coefficient
Method
• r
=
∑xy
/
(√(∑x2
*
∑y2)
where
x
=
X-­‐Xb
and
y
=
Y-­‐Yb
• Calculate
the
coefficient
of
correlation
for
the
following
value
X
Y
24
16
36
22
32
34
38
48
40
60
X
Y
x=X-­‐Xb
y=Y-­‐Yb
x2
y2
xy
24
16
-­‐10
-­‐20
100
400
200
36
22
+2
-­‐14
4
196
-­‐28
32
34
-­‐2
-­‐2
4
4
4
38
48
4
4
16
144
48
40
60
6
6
36
576
144
∑
170
180
160
1320
368
• Xb
=
∑X/N
=
170/5
=
34
• Yb
=
∑Y/N
=
180/5
=
36
• r
=
∑xy
/
(√(∑x2
*
∑y2)
=
368/(√(160*1320)
=
0.8
Regression
o x
on
y
 X-­‐Xb=
bxy
(Y-­‐Yb)
 bxy
=
∑xy
/
∑y2
o y
on
x
 Y-­‐Yb=
byx
(X-­‐Xb)

byx
=
∑xy
/
∑x2
o Calculate
the
regression
for
the
following
table
X
Y
32
12
48
15
24
18

21. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
21
26
25
30
20
X
Y
x=X-­‐Xb
y=Y-­‐Yb
x2
y2
xy
32
12
-­‐0
-­‐6
0
36
0
48
15
16
-­‐3
256
9
-­‐48
24
18
-­‐8
0
64
0
0
26
25
-­‐6
7
36
49
-­‐42
30
20
-­‐2
2
4
4
-­‐4
∑
160
90
360
98
-­‐94
• Xb
=
∑X/N
=
160/5
=
32
• Yb
=
∑Y/N
=
90/5
=
18
• x
on
y
• bxy
=
∑xy
/
∑y2
=
-­‐94/
98
=
-­‐
0.96
• X-­‐Xb=
bxy
(Y-­‐Yb)
• X-­‐32
=
-­‐0.96(Y-­‐18)
=>
X=
-­‐0.96Y
+
49.28
• y
on
x
• byx
=
∑xy
/
∑x2
=
-­‐94/360
=
-­‐0.26
• Y-­‐Yb=
byx
(X-­‐Xb)
• Y-­‐18
=
-­‐0.26(X-­‐32)
=>
Y
=
-­‐0.26X
+
26.32
Small Sample Test
o T
Test
(Student
Test)
when
sample
size
is
less
than
30
o t
=
(Xb
-­‐
µ0)
/
(s/√n-­‐1)
1. The
mean
percentage
of
passes
in
all
the
schools
of
a
town
was
found
to
be
83%.
A
random
sample
of
17
schools
revealed
that
86%
pass
with
standard
deviation
of
3%.
Test
a
1%
level
of
significance
whether
the
mean
percentage
of
passes
is
more
than
83%
• µ
=
83%
• n
=
17
• Xb
=
86%
• s=
3%
• Degree
of
freedom
=
n-­‐1
=
16
• Level
of
Significance
=
1%
• Null
Hypothesis
(H0):
Mean
percentage
of
passes
is
less
than
83%
• Alternate
Hypothesis
(Ha):
Mean
percentage
of
passes
is
more
than
83%
• tcal
=
(Xb
-­‐
µ0)
/
(s/√n-­‐1)
=
(86-­‐83)
/
3/√(17-­‐1)
=
4
• From
the
statistics
table,
ttable
=
2.583
(For
Degree
of
freedom
=
16
and
Level
of
significance
of
1%)

22. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
22
• ttable
<
tcal
implies
that
the
Null
Hypothesis
is
in
critical
region
so
its
not
accepted
so
Ha
is
accepted

23. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
23
IMPORTANT QUESTIONS
1. Distinguish
between
probability
and
non
probability
sampling
methods’
by
giving
suitable
examples
2. Research
refers
to
ends
and/or
means.
Discuss
this
statement
3. Hypothesis
is
the
guiding
force
in
any
research
study?
Justify
and
explain
the
process
of
hypothesis
formulation
and
testing
it
with
suitable
example
4. Briefly
describe
the
contents
of
a
research
report
5. Briefly
describe
the
various
methods
used
for
descriptive
analysis
of
data
6. What
is
sampling?
List
the
similarities
and
differences
between
stratified
sampling
and
quota
sampling
7. How
are
research
design
classified?
What
are
the
distinguishing
features
of
each?
Differentiate
by
giving
appropriate
examples
8. What
do
you
mean
by
measurement?
Explain
four
key
levels
of
measurement
with
suitable
examples
and
also
give
details
of
what
statistical
technique
can
be
used
with
data
from
each
type
of
scale?
9. What
is
scaling?
Describe
the
various
comparative
and
non
comparative
scaling
techniques
used
in
business
research
with
suitable
examples
10. How
do
you
edit
a
questionnaire?
What
are
the
precautions
that
a
research
must
take
while
editing
and
coding
a
questionnaire?
Give
suitable
example
11. Explain
various
Parametric
and
Non
Parametric
Test
with
examples
12. Discus
the
various
types
of
research
and
their
features
13. Find
the
correlation
of
coefficient
for
the
following
data
and
comment
on
its
significance?
X
24
26
36
35
43
45
47
Y
47
48
54
58
59
59
65
14. Perform
ANOVA
with
5%
level
of
significance
to
determine
whether
there
is
a
significant
difference
in
the
mean
speed
of
four
different
machines
Hours
Machine
A
Machine
B
Machine
C
Machine
D
1
15
14
30
35
2
20
16
25
30
3
25
22
24
32
4
20
28
26
28
15. From
the
data
given
below
about
the
treatment
of
patients
suffering
from
cold,
state
whether
the
new
treatment
is
superior
to
that
of
the
conventional
treatment.
You
can
use
Kai2
test
for
evaluation
Treatment
Favorable
Not
Favorable
New
280
60
Conventional
120
40

24. Paper1: Research Methodology Exam Sheet
Shivananda
R
Koteshwar,
PhD
Research
Scholar,
Bangalore
University
24
16. Calculate
the
straight
line
trend
for
the
following
data
and
forecast
the
production
figures
for
the
next
two
years
Year
2006
2007
2008
2009
2010
2011
2012
2013
Production
43
67
34
76
71
85
88
96
17. A
cooperative
wishes
to
test
whether
the
preference
of
consumers
for
its
products
its
dependent
on
income
levels.
Use
the
Chi
square
test
to
decide.
You
may
use
a
5%
significance
level
Product
Preferred
Income
Product
A
Product
B
Product
C
Product
D
Low
185
45
95
325
Medium
65
40
75
180
High
35
25
70
130
Total
285
110
240
635