RESEARCH METHODOLOGY Notes for Engineering

RESEARCH METHODOLOGY &
STATISTICS

What is research ?
• Research = Re + Search
• It is the process finding solution to a problem.
• It’s the process of arriving as a dependable solution to a problem
through planned & systematic collection , analysis and
interpretation of Data.
• It seeks answer only of those questions which answers can be
given on the basis of available facilities
• It’s a movement from known to unknown.

Conclusion
Phenomena
Collection of Data Analysis
Person
Observes Again and again

DEFINITIONS OF RESEARCH
• V REDMAN & AVH MORY – “Research is a systematized
effort to gain knowledge”
• Emory defines research as “any organized inquiry designed and
carried out to provide information for solving a problem”.

FEATURES OF RESEARCH
• It gathers new knowledge / data from primary / first hand
resources.
• It requires plan.
• It requires expertise.
• Research is patient and un hurried activity.
• It places emphasis upon the discovery of general principles.
• Its an exact systematic and accurate investigation.
• Its logical and objective.
• It Endeavour to oraginze data in quantitaive forms.
• Researcher carefully record and report the data
• Conclusion and generalization are arrived at carefully and
cautiously .

OBJECTIVES OF RESEARCH
1. THEROTICAL OBJECTIVE
• Formulate new theories, principals etc.
• This type of theory is explanatory because it explains the relationship
between variables.
• Its mainly used in Physics, Chemistry, Math's etc
2. FACTUAL OBJECTIVE
• Find out new facts.
• Its of descriptive nature
• These are mainly historical type of research which describes facts or events
which has previously happened.
3. APPLICATION OBJECTIVE
• It doesn't contribute to new knowledge in the fund of human knowledge but
suggest new application, by application here it means improvement and
modification in practice.

GENERAL OBJECTIVES OF
RESEARCH
• To gain familiarity with a phenomenon or to achive new insight
into it,
• To portray accurately the characteristics of particular
individual/ situation/ group.
• To determine the frequency in which something occurs or with
which it is associated with something else.
• To test hypothesis of causal relation ship between variables.

PURPOSE OF RESEARCH
• Research extends knowledge of human beings social life and environment.
• Research reveals the mysteries of nature.
• Research establishes generalizations and general laws and contributes to theory building
in various fields of knowledge.
• Research verifies and tests existing facts and theory.
• Research helps us to improve our knowledge and ability to handle situation.
• Research aims to analyze inter-relationship between variables and to derive causal
explanations, which help us to better understanding of the world in which we live.
• Research aims to finding solutions to the problem, e.g.:- socio-economic problems,
health problems, organizational and human relational problems and so on…
• Research also aims at developing new tools, concepts and theories for better
understanding to unknown phenomena.
• Research helps national planning board to focus our national development. It enables the
planners to evaluate alternative strategies, on-going programs and evaluation etc.,
• Research provides functional data for rational decision making and formulation of
strategies and policies.

• PURE RESEARCH : It is conducted for the purpose of developing
scientific theories, by discovering basic principles / broad generalization
of a discipline rather than for the purpose of solving some immediate
problems.
• APPLIED RESEARCH: The purpose of applied research is to improve a
product or a process and to test theoretical concepts in actual problematic
situation . It seeks an immediate and practical results.
• EXPLORATORY RESEARCH: It is the preliminary study of an
unfamiliar problem about which the researcher has little or no knowledge.
Exploratory research is necessary to get initial insight into the problem
for the purpose of formulating more precise investigation.
• DESCRIPTIVE RESEARCH: It is a fact finding investigation
describing, recording, analyzing and interpreting conditions that exist. it
gives proper basis for understanding current problems, and guides in
planning and formulation of policies
• ANALYTICAL RESEARCH: It’s a system of procedures and
techniques of analysis applied to quantitaive data. This field is used in
different fields in which numerical data are engaged.

• EXPERIMENTAL – This method provides the best approach for the study of
cause and effect relationship under controlled conditions. This is popular in
field of natural sciences.
• HISTORICAL – It is concerned with some past phenomena, in this process
evidence about past is systematically collected, evaluated, verified and
synthesized.
• DIAGNOSTIC – Its is directed towards what is happening, why it is
happening and what can be done about it. It aims at a cause of a problem and
the possible solution for it.
• ACTION – The purpose of action research is to acquire new skill or new
approach to solve a certain problem. A test marketing research for a new
product is good example of action research.
• EVALUATION – Its is done for assessing the effectiveness of social or
economic programs implemented or for assessing the impact of developmental
projects.
• CONCLUSION ORIENTED – Here the researcher is free to pickup a
problem, redesign the enquiry as he or she wants to proceed and is prepared the
conceptualization as he visualize.
• DECISION ORIENTED – It is always for the need of decision maker and the
researcher and here it is free to embark upon researchers inclination for his or
her research.

• ONE TIME RESEARCH – Here the research is confined to only a single
period of time.
• LONGITUIDINAL RESEARCH – Research is carried on over several times
for the purpose of getting a feasible solution.
• CASE STUDY - It is an in-depth comprehensive study of a person, an
episode, a program or a social unit.
• SURVEY RESEARCH - It is a method of research involving collection of
data directly from a population or a sample at a particular period.

APPROACHES
TO RESEARCH
QUANTITATIVE
APPROACH
QUALITATIVE
APPROACH

QUANTITATIVE APPROACH
It is rooted in the philosophy of
rationalism , follows a rigid ,
structured and predetermined set of
procedures to explore ; aims to
quantify the extent of variation in a
phenomenon ; emphasis the
measurement of variables and the
objectivity of process; believes in
substantiation on the basis of large
sample size; gives importance to
validity and reliability of findings
and communicate findings in
aggregate and analytical manner;
drawing conclusion and inferences
that can be generalized
QUALITATIVE APPROACH
It is embedded in the
philosophy of empiricism;
follows an open , flexible and
unstructured approach to
enquiry; aims at explore
diversity rather than to
quantify; emphasizes the
description and narration of
feelings, perception and
experiences rather than their
measurement; and
communicates findings in a
descriptive and narrative
manner rather than analytical;
placing no or less emphasis on
generalization.

Problem
identification
Literature review
Formulation of
objectives
Research Design
A. Problem identification
B. Consideration in selecting a research
Problem
C. Steps in formulating a research problem
A. Need for Literature
B. Sources
C. Steps
A. General and Specific Objectives
B. Hypothesis
C. Variables
B. Types of study
C. Data collection tools and techniques.
D. Sampling
E. Pilot study
F. Data collection
A. Research Design and Plan

Data processing
Data analysis
Report writing
A. Editing
B. Categorizing
C. Coding
D. Summarizing
A. Report writing
B. Stages
C. Content
A. Statistics
B. Uni-variate Analysis
C. Parametric Measures
D. Non parametric Measures
E. Econometrics

Problem identification
• Problem is identified after narrowing down the broad area of topic
to highly specific research problem . Researcher normally selects a
single problem at time because of unique needs and purposes
Steps in formulating a research problem
• identify a broad field or subject area of interest of you
• Dissect the broad area into sub areas.
• Select what is of most interest to you
• Raise research question

Consideration in selecting a research problem
Each problem taken for research has to be judged on the basis of
some criteria
• Relevance
• Avoidance of duplication
• Feasibility
• Political acceptability
• Applicability
• Urgency of data needed
• Ethical acceptability

NEED FOR REVIEW OF
LITERATURE
• Preventing duplicating work that has been done before
• Know what others have learned and reported about the
problem.
• Become more familiar with the various types of methodologies.
• Get good background knowledge about the problem and why
research is needed in this area.
• Helps to know the theoretical perspective of the problem.

SOURCES
• Subject catalogues of libraries.
• Documentation services.
• Bibliographies.
• List of Books and publishers bulletins.
• Journals
• Government reports.
• Research abstract.
• Information on research done.

STEPS IN REVIEWING THE
LITERATURE
• Searching for the existing literature in your area of study.
• Review the selected literature
• Developing a theoretical framework
• Developing a conceptual framework

OBJECTIVES
• General objectives : It states what is expected to be
achieved by the study. It’s the overall thrust of the study.
Its is concerned with the main association and relationship
that a person seeks to discover or establish.
• Specific objectives : it should be numerically listed, worded
clearly and unambiguously. It addresses the various aspects
of the problem and should specify what will be done,
where and for what purpose..

HYPOTHESIS
A hypothesis is a specific statement of prediction.
It describes in concrete terms what a researcher
expects to happen in his/ her study.
Good and Hatt defines it as “ a question which can
be put to test to determine validity “
In short hypothesis , is a tentative solution or
explanation or a guess or assumption or proposition
or a statement to the problem facing by the
researcher

TYPES OF HYPOTHESIS
• Descriptive hypothesis : It intends to describe some characteristics of an
object , a situation ,an individual or even an organization.
• Relational Hypothesis : It intends to describe the relation ship between
variables.
• Empirical / Working Hypothesis : This is a hypothesis framed in early
stages of research. This maybe altered or modified as research proceeds.
• Null Hypothesis: This states that there is no significant difference between
the parameter and statistic that is being compared.
• Alternative hypothesis :they are the research hypothesis which involves the
claim to be tested
• Analytical hypothesis : These are used when one would specify the
relationship between changes in one property leading to change in other.
• Common sense Hypothesis : These are based on what is being observed
with common idea existing among people.
• Statistical hypothesis :These are developed from samples that
measureable. They are of two types:
1. Hypothesis which indicates difference
2. Hypothesis which indicates relationship

VARIABLES
A variable is a characteristics of a person , object or phenomenon that can
take on different values.
Variables are condition or characteristics that experimenter manipulates,
control or observes.
A variable is anything that change.
Types of Variables
• Numerical variables : when variables are expressed in numbers they are
called numerical variables.
• Categorical Variables : When the values of a variable are expressed in
categories, they are called Categorical variables.
• Dependent Variable & Independent Variable : the variable that is used to
measure the problem under study is called the dependent variable.
The variables that re used to describe or measure the factor that are
assumed to cause or at least to influence the problem are called independent
variable.
• Active Variable: The variable that are directly manipulated by the
experiment are called active variables.

• Attribute Variable: they are those characteristics which cannot
be altered by the experiment.
• Intervening Variables : certain factors or variables may influence
the relationship even though they cannot be observed directly
and they are called intervening variables
• Extraneous variables : They are those uncontrolled variables
that may have significant influence upon the results of a study.

RESEARCH DESIGN
A research design a logical and systematic plan prepared for
directing a research study .
It constitutes the blueprint for the collection , measurement and
analysis of data.
It is the plan , structure , strategy of investigation conceived so as
to obtain answers to research question.
Essential of a good research design
• Plan
• Outline
• Blue print
• Scheme

CLASSIFICATION OF
DESIGNS
• Experimental
• Exploratory
• Descriptive
• Historical
• Case studies
• Survey
• Combination of any of these.

RESEARCHPLAN
• A research plan prescribes the boundaries of research activity and
enables the researcher to channel his energies in the right work.
• Various question are needed to be answered while preparing the plan
What the study is about?
Why the study is made?
What is it scope ?
What are the objectives of the study?
What kind of data are needed?
What are the sources ?
What is the sample size?
What are the techniques?
How the data should be processed?
What is the cost involved ? etc.

CONTENTS OF A
RESEARCH PLAN
• Introduction
• Statement of the problem
• Review of the previous studies
• Scope f the studies
• Objective of the study
• Conceptual model
• Hypothesis
• Operational definition of concepts
• Geographical area to be covered
• Reference period
• Methodology
• Sampling plan
• Tools for gathering data
• Plan of analysis
• Chapter scheme
• Time budget
• Financial budget

SAMPLING
Sampling is the statistical process of selecting a subset (called a
“sample”) of a population of interest for purposes of making
observations and statistical inferences about that population.
Sampling, therefore, is the process of selecting a few (a sample)
from a bigger group (the sampling population) to become the
basis for estimating or predicting the prevalence of an unknown
piece of information, situation or outcome regarding the bigger
group.
Characteristics of a good sample
Representativeness
Accuracy
Precision
Size

SAMPLING PROCESS
• Define the population or universe
• State the sampling frame
• Specify the sampling unit
• Selection of sampling method
• Determine the sample size
• Specify the sampling plan
• Select the sample

TECHNIQUES OF SAMPLING
SAMPLING
Probability sampling Non Probability sampling
Simple random sampling
Stratified random sampling
Systematic random sampling
Cluster sampling
Multi stage sampling
Matched pair sampling
Convenience sampling
Judgment sampling
Quota sampling
Snowball sampling

Probability sampling: It is a technique in which every unit in the
population has a chance (non-zero probability) of being selected in the
sample, and this chance can be accurately determined.
All probability sampling have two attributes in common:
• Every unit in the population has a known non-zero probability of
being sampled, and
• The sampling procedure involves random selection at some point.
The different types of probability sampling techniques include:
Simple random sampling. In this technique, all possible subsets of a
population are given an equal probability of being selected. Simple
random sampling involves randomly selecting respondents from a
sampling frame, but with large sampling frames, usually a table of
random numbers or a computerized random number generator is
used.
Stratified sampling. In stratified sampling, the sampling frame is
divided into homogeneous and non-overlapping subgroups (called
“strata”), and a simple random sample is drawn within each subgroup.

• Systematic sampling (also known as interval sampling) relies on
arranging the study population according to some ordering scheme
and then selecting elements at regular intervals through that ordered
list.
• Cluster sampling. If you have a population dispersed over a wide
geographic region, it may not be feasible to conduct a simple random
sampling of the entire population. In such case, it may be reasonable
to divide the population into “clusters” (usually along geographic
boundaries), randomly sample a few clusters, and measure all units
within that cluster.
• Multistage sampling can be a complex form of cluster sampling. Pardo
Fuccboi refers it to sampling plans where the sampling is carried out in
stages using smaller and smaller sampling units at each stage.
• Matched-pairs sampling. Sometimes, researchers may want to
compare two subgroups within one population based on a specific
criterion. matched-pairs sampling technique is often an ideal way of
understanding bipolar differences between different subgroups within
a given population.

Nonprobability sampling is a sampling technique in which some
units of the population have zero chance of selection or where the
probability of selection cannot be accurately determined. Typically,
units are selected based on certain non-random criteria, such as quota or
convenience.
• Convenience sampling. Also called accidental or opportunity
sampling, this is a technique in which a sample is drawn from that part
of the population that is close to hand, readily available, or convenient.
• quota sampling, the population is first segmented into mutually
exclusive sub-groups, just as in stratified sampling. Then judgment is
used to select the subjects or units from each segment based on a
specified proportion.
• Snowball sampling. In snowball sampling, you start by identifying a
few respondents that match the criteria for inclusion in your study, and
then ask them to recommend others they know who also meet your
selection criteria.
• Purposive sampling (also known as judgment, selective or subjective
sampling) is a sampling technique in which researcher relies on his or
her own judgment when choosing members of population to
participate in the study.

PILOT STUDY
• Pilot study is a small scale preliminary study conducted in order
to evaluate feasibility, time, cost, adverse events, and effect size
(Statistical variability) in an attempt to predict an appropriate
sample size and improve upon the study design prior to
performance of a full scale research project.
• Although a pilot study cannot eliminate all systematic errors or
unexpected problems, it reduces the likelihood of making
a Type I or Type II error. Both types of errors make the main
study a waste of effort, time, and money.

SAMPLE SIZE
Before you can calculate a sample size, you need to determine a few things
about the target population and the sample you need:
Population Size — How many total people fit your demographic?
Margin of Error (Confidence Interval) — No sample will be perfect, so you
need to decide how much error to allow. The confidence interval
determines how much higher or lower than the population mean you are
willing to let your sample mean fall. If you’ve ever seen a political poll on the
news, you’ve seen a confidence interval. It will look something like this:
“68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”
Confidence Level — How confident do you want to be that the actual mean
falls within your confidence interval? The most common confidence
intervals are 90% confident, 95% confident, and 99% confident.
Standard of Deviation — How much variance do you expect in your
responses? Since we haven’t actually administered our survey yet, the safe
decision is to use .5 – this is the most forgiving number and ensures that
your sample will be large enough.

• Your confidence level corresponds to a Z-score. This is a constant
value needed for this equation. Here are the z-scores for the most
common confidence levels:
• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576
• If you choose a different confidence level, use this Z-score table* to
find your score.
• Next, plug in your Z-score, Standard of Deviation, and confidence
interval into this equation:**
• Necessary Sample Size = (Z-score)² * Std Dev*(1-StdDev) / (margin of
error)²

DATA COLLECTION
Data are the facts and figures collected for statistical investigation. Data
collection is the process of gathering and measuring information on
targeted variables in an established systematic fashion, which then
enables one to answer relevant questions and evaluate outcomes.
There are two types of data:
• 1. Primary data,
• 2. Secondary data (desk research)
The primary data are those which are collected afresh and for the first
time, and thus happen to be original in character or information
collected or generated by the researcher for the purpose of the project
immediately at hand.
The secondary data are those which have already been collected by
someone else and which have already been passed through the statistical
process. Secondary data refer to the information that have been collected
by someone other than researcher for purposes other than those
involved in the research project at hand. Books, journals, manuscripts,
diaries, letters, etc., all become secondary sources of data as they are
written or compiled for a separate purpose

METHOD OF COLLECTING
DATA
1. Observation method
2. Interview method
3. Survey method
4. Experimentation
6. Projective technique
7. Sociometry
8. Content analysis

Observation
Observation is one of the cheaper and more effective techniques of data
collection. Observation, in simple terms, is defined as watching the
things with some purpose in view. Observation, is a systematic and
deliberate study through eye of spontaneous occurrence at the time, they
occur.
Observation has mainly three components-Sensation, attention and
perception
Types of Observation
• Participant observation: In this observation, the observer is a part of
the phenomenon or group which is observed and he acts as both an
observer and a participant
• Non-Participant observation: In this type of observation, the
researcher does not actually participate in the activities of the group to
be studied. There is no emotional involvement on the part of the
observer

• Controlled observation: This type of observation is found quite
useful in either in the laboratory or in the field. Controlled
observation is carried out observational techniques and exercise
of maximum control over extrinsic and intrinsic variables.
• Uncontrolled observation: If the observation takes place in the
natural settings, it may be termed as uncontrolled observation.
The main aim of this observation is get spontaneous picture of
life.
• Direct observation: In this type of observation, the event or the
behavior of the person is observed as it occurs. This method is
flexible and allows the observer to see and record subtle aspects
of events and behavior as they occur.
• Indirect observation; This does not involve the physical
presence of the observer , and the recording is done by
mechanical, photographic or electronic devices. This method is
less flexible than direct observation.

INTERVIEW
It may be defined as a two way systematic conversation between
an investigator and an informant, initiated for obtaining
information relevant to a specific study.
It involves not only conversation, but also leaning from the
respondents, gestures, facial expression, pauses and his
environment.
Interviewing process
• Preparation
• Introduction
• Developing rapport
• Carrying the interview forward
• Recording the interview
• Closing the interview

Types of interviews
• Structured or directive interview:
This is an interview made with a detailed standardized schedule. The
same questions are put to all the respondents and in the same order.
This type of interview is used for large-scale formalized surveys
• Unstructured or non-directive interview
In this type of interview, a detailed pre-planned schedule is used. Only a
broad interview guide is used. Questions are not standardized and not
ordered in a particular way. This technique is more useful in case studies
rather than large surveys
• Semi-structured or focused interview
The investigator attempt to focus the discussion on the actual effects of a
given experience to which the respondents have been exposed. The
situation is analyzed prior to the interview. An interview guide specifying
topics relating to the research hypothesis is used Interview is focused on
the subjective experiences of the respondent

• Clinical interview
It is concerned with broad underling feelings or motivations or
with the course of the individual’s life experiences. The ‘personal
history’ interview used in social case work, prison administration,
psychiatric clinics and in individuals life history research is the
most common type of clinical interview
• Depth interview
This is an intensive and searching interview aiming at studying the
respondent’s opinion, emotions or convictions on the basis of an
interview guide. This deliberately aims to elicit unconscious as
well as extremely personal feelings and emotions
• Telephone interviews
It is a non-personal method of data collection. It may be used as a
major method or supplementary method
• Group interview
It is a method of collecting primary data in which a number of
individuals with a common interest interact with each other

EXPERIMENTATION
Experimentation is a research process used to observe cause and
effect relationship under controlled condition.
In other words it aims at studying the effect of an independent
variable on dependent variable by keeping other Independent
variable constant through some type of control.
There are broadly two types of experiment
• Laboratory experiment : here the investigator creates a
condition in which he wants to make his study through
manipulation of variables.
• Field experiment :it occurs in real life settings or natural settings
where less control can exerted.

SURVEY METHOD
A survey is a research method for collecting information from a selected group of
people using standardized questionnaires or interviews
It is a non-experimental, descriptive research methods which is used to study large
and small population.
Survey is fact finding study where there is critical inspection to gather information,
often a study of an area with respect to certain condition or its prevalence. There are
two types of survey
• Cross sectional survey are conducted to collect information from the population at
a single point of time. The purpose is to collect a body of data connection with two
or more variables.
• Longitudinal survey : a longitudinal survey is one that takes place over a period of
time. It means the data is gathered over a period of time. there are three types of
longitudinal survey
Trend studies The simplest type of longitudinal analysis of survey data is called trend
analysis, which examines overall change over time.
Cohort studies : A cohort study selects either an entire cohort of people or a
randomly selected sample of them as the focus of data collection.
Panel studies: here the same sample of the population are surveyed repeatedly. Panel
studies are very difficult to

• METHODS OF SURVEY
There are two methods
1. Census method: A complete survey of the population is called
census method. Here the entire population is a subject matter for
conducting survey.
2. Sampling method: a sample is representative of the population
only sample or sub select is selected for conducting survey

PROJECTIVE TECHNIQUE
It involve presentation of ambiguous stimuli to the respondents for
interpretation. In doing so, the respondents reveal their inner characteristics.
This techniques for the collection of data have been developed by
psychologists to use projections of respondents for inferring about
underlying motives, urges, or intentions which are such that the respondent
either resists to reveal them or is unable to figure out himself.
These techniques play an important role in motivational researches or in
attitude surveys.
• Types of projective techniques
Projective techniques may be divided into three broad categories:
1. Visual: to show the respondent a picture and ask him to describe the
persons or objects in the picture.
2. Verbal: this techniques involve use of words both for stimulus and for
response.
3. Expressive: under this technique subjects are asked to improve or act out
a situation in which they have been assigned various roles.

SOCIOMETRY
Sociometry is a quantitative method for measuring social
relationships.
It was developed by psychotherapist Jacob L. Moreno in his
studies of the relationship between social structures and
psychological well-being.
The term sociometry relates to its Latin etymology, socius
meaning companion, and metrum meaning measure. Jacob
Moreno defined sociometry as "the inquiry into the evolution and
organization of groups and the position of individuals within
them."
The basic technique in sociometry is the sociometric test . This is
the test under which each member of a group is asked to choose
from all other members those with whom he prefers to associate
in a specific situation.

CONTENT ANALYSIS
• Human beings communicate through language. Language helps
to convey our emotions, knowledge, opinions, attitudes and
values. Print media, television, radio; movies also communicate
ideas, beliefs and values. The analysis is of communication
content-written and pictorial- has now become a methodological
procedure for extracting data from a wide range of
communications.
• Content analysis is a method of social research that aims at the
analysis of the content qualitative and quantitative- of
documents, books, newspapers. magazines and other forms of
written material.

TOOLS FOR DATA COLLECTION
• The questionnaire
a questionnaire is a research instrument consisting of a set of questions (items) intended to
capture responses from respondents in a standardized manner.
Questions may be unstructured or structured. Unstructured questions ask respondents to
provide a response in their own words, while structured questions ask respondents to select an
answer from a given set of choices.
Characteristics of a Good Questionnaire:
1. It deals with an important or significant topic.
2. Its significance is carefully stated on the questionnaire itself or on its
covering letter.
3. It seeks only that data which cannot be obtained from the resources
like books, reports and records.
4. It is as short as possible, only long enough to get the essential data.
5. It is attractive in appearance, nearly arranged and clearly duplicated
or printed.
6. Directions are clear and complete, important terms are clarified.
7. The questions are objective, with no clues, hints or suggestions.
8. Questions are presented in a order from simple to complex.
9. Double negatives, adverbs and descriptive adjectives are avoided.
10. Double barreled questions or putting two questions in one question
are also avoided.

Response formats. questions may be structured or unstructured. Responses to
structured questions are captured using one of the following response formats:
• Dichotomous response, where respondents are asked to select one of two
possible choices, such as true/false, yes/no, or agree/disagree. An example of
such a question is: Do you think that the death penalty is justified under some
circumstances (circle one): yes / no
• Nominal response, where respondents are presented with more than two
unordered options, such as: What is your industry of employment:
manufacturing / consumer services / retail / education / healthcare / tourism &
hospitality / other.
• Ordinal response, where respondents have more than two ordered options,
such as: what is your highest level of education: high school / college degree /
graduate studies.
• Interval-level response, where respondents are presented with a 5-point or 7-
point Likert scale, semantic differential scale, or Guttman scale.
• Continuous response, where respondents enter a continuous (ratio-scaled)
value with a meaningful zero point, such as their age or tenure in a firm.
These responses generally tend to be of the fill-in-the blanks type.

Types of questions to be avoided.
• Leading questions
• Loaded questions
• Ambiguous questions
• Double barreled questions
• Long questions
• Avoid double negative

SCHEDULES
Schedule as a Data Collection Technique in Research. Schedule
is the tool or instrument used to collect data from the respondents
while interview is conducted. ... The schedule is presented by the
interviewer. The questions are asked and the answers are noted
down by him.
CHECKLIST
this is the simplest form of all devices . It consist prepared list of
items pertinent to an object or a particular task.
The presence or absence of each task my be indicated by
checking yes or no or multi point scale. It ensures complete
consideration of all aspects of an object.
OPINIONNAIRE
This is a list of questions or statements pertaining to an issue or a
program.it is used for studying the opinion of the people .

CHECKING THE VALIDITY AND
RELAIBILTY OF RESEARCH TOOL
Sound measurement must meet the tests of validity, reliability and
practicality. In fact, these are the three major considerations one
should use in evaluating a measurement tool
• Validity
It is the most critical criterion and indicates the degree to which an
instrument measures what it is supposed to measure. Validity can
also be thought of as utility. In other words, validity is the extent to
which differences found with a measuring instrument reflect true
differences among those being tested. But the question arises: how
can one determine validity without direct confirming knowledge?
The answer may be that we seek other relevant evidence that
confirms the answers we have found with our measuring tool.
What is relevant, evidence often depends upon the nature of the
research problem and the judgment of the researcher

• Test of Reliability
The test of reliability is another important test of sound
measurement. A measuring instrument is reliable if it provides
consistent results. Reliable measuring instrument does contribute
to validity, but a reliable instrument need not be a valid
instrument.
Two aspects of reliability viz., stability and equivalence deserve
special mention.
The stability aspect is concerned with securing consistent results
with repeated measurements of the same person and with the
same instrument
The equivalence aspect considers how much error may get
introduced by different investigators or different samples of the
items being studied

• Test of Practicality
The practicality characteristic of a measuring instrument can be
judged in terms of economy, convenience and interpretability.
From the operational point of view, the measuring instrument
ought to be practical i.e., it should be economical, convenient and
interpretable.
Economy consideration suggests that some trade-off is needed
between the ideal research project and that which the budget can
afford
Convenience test suggests that the measuring instrument should
be easy to administer. For this purpose one should give due
attention to the proper layout of the measuring instrument
Interpretability consideration is specially important when persons
other than the designers of the test are to interpret the results

MEASUREMENT AND
SCALING
Measurement
Measurement can be described as a way of obtaining symbols to
represent the properties of persons, objects, events or states under
study - in which the symbols have the same relevant relationship to
each other as do the things represented
Scaling
The ability to assign numbers to objects in such a way that:
• Numbers reflect the relationship between the objects with
respect to the characteristics involved
• It allows investigators to make comparison of amount and
change in the property being measured
Four (4) primary types of scales –
Nominal, Ordinal, Interval and Ratio

NOMINAL SCALE
• Least restrictive of all scales.
• Does not possess order, distance or origin
• Numbers assigned serve only as a label or tags for identifying
objects, properties or events
• Permissible mathematical operations: percentage, frequency,
mode, contingency coefficients
• ORDINAL SCALE
• Possess order but not distance or origin
• Numbers assigned preserve the order relationship (rank) and
the ability to distinguish between elements according to a single
attribute & element
• Permissible mathematical operations: (+) median, percentile,
rank correlation, sign test and run test

• INTERVAL SCALE
• Possess the characteristic of order and distance
• DOES NOT possess origin
• Numbers are assigned in such a way that they preserve both the
order and distance but do not have a unique starting point
• Permissible mathematical operations (+) Mean, average
deviation, standard deviation, correlation, t F
• RATIO SCALE
• Possess the characteristic of order distance and origin
• Numbers are assigned in such a way that they preserve both the
order distance and origin
• .Permissible mathematical operations: ALL

RATING SCALES
In rating or ranking scales the respondent are assigns numerical
positions to an individual specify the degree of his observations
Following are the rating scales
Graphic rating scales
Here different points of the scale run from one extreme of the
attitude to the other . Considering the description of the points
along the scale the rater indicates his rating or preferences by
putting a tick mark on the point determined by him .
Itemized rating scale
It is also known as numerical scales generally 5 point or seven
point are given on the scale to represent different categories of
items. The respondent picks up one of those categories and mark
them on scale. The first point represent lower category and the
last point higher category.

Comparative rating scale
Here the comparative position of an individual is indicated
with reference to other individual .
Rank order scale
It is used for comparative or relative rating. Here an
individual position is indicated inn relation to others. In
case rater himself it is done then it is called as self rating .

Attitude scales
It is used to not to rate the individuals but to
examine their views , agreements or disagreements
of a particular subject . Following are the different scales

Likert Scale
The Likert scale requires the respondents to indicate a degree of
agreement or disagreement with each of a series of statements about the
stimulus objects
The analysis can be conducted on an item-by-item basis (profile
analysis), or a total (summated) score can be calculated.
Semantic Differential Scale
The semantic differential is a seven-point rating scale with end points
associated with bipolar labels that have semantic meaning.
The negative adjective or phrase sometimes appears at the left side of the
scale and sometimes at the right.
This controls the tendency of some respondents, particularly those with
very positive or very negative attitudes, to mark the right- or left-hand
sides without reading the labels.
Individual items on a semantic differential scale may be scored on
either a -3 to +3 or a 1 to 7 scale.

Stapel Scale
The Stapel scale is a unipolar rating scale with ten categories
numbered from -5 to +5, without a neutral point (zero). This
scale is usually presented vertically.
The data obtained by using a Stapel scale can be analyzed in
the same way as semantic differential data.
Differential scale - Thurstone technique
Here attitude scaling is done with the help of judges

PROCESSING THE DATA
Editing
Editing is the first step in data processing. Editing is the
process of examining the data collected in
questionnaires/schedules to detect errors and omissions and
to see that they are corrected and the schedules are ready for
tabulation. Mainly two types of editing are there
Field editing
Central editing

• Classification of Data
Classification or categorization is the process of grouping the
statistical data under various understandable homogeneous groups
for the purpose of convenient interpretation
Classification becomes necessary when there is a diversity in the
data collected for meaningless for meaningful presentation and
analysis. However, it is meaningless in respect of homogeneous
data. A good classification should have the characteristics of
clarity, homogeneity, equality of scale, purposefulness and
accuracy.

Coding of Data
Coding is the process/operation by which data/responses are
organized into classes/categories and numerals or other
symbols are given to each item according to the class in
which it falls. In other words, coding involves two important
operations;
(a) deciding the categories to be used and
(b) allocating individual answers to them.

• Tabulation of Data
Tabulation is the process of summarizing raw data and displaying it in
compact form for further analysis. Therefore, preparing tables is a very
important step. Tabulation may be by hand, mechanical, or electronic.
The choice is made largely on the basis of the size and type of study,
alternative costs, time pressures, and the availability of computers, and
computer programmes. If the number of questionnaire is small, and
their length short, hand tabulation is quite satisfactory.
Table may be divided into:
• (i) Frequency tables,
• (ii) Response tables,
• (iii) Contingency tables
• (iv) Uni-variate tables,
• (v) Bi-variate tables,
• (vi) Statistical table and
• (vii) Time series tables

Data Diagrams
Diagrams are charts and graphs used to present data. These facilitate
getting the attention of the reader more. These help presenting data
more effectively. Creative presentation of data is possible. The data
diagrams classified into:
• Charts: A chart is a diagrammatic form of data presentation. Bar
charts, rectangles, squares and circles can be used to present data. Bar
charts are uni-dimensional, while rectangular, squares and circles are
two-dimensional.
• Graphs: The method of presenting numerical data in visual form is
called graph, A graph gives relationship between two variables by
means of either a curve or a straight line. Graphs may be divided into
two categories. (1) Graphs of Time Series and (2) Graphs of
Frequency Distribution. In graphs of time series one of the factors is
time and other or others is / are the study factors. Graphs on
frequency show the distribution of by income, age, etc. of executives
and so on.

The purpose of analysis is to summarize and organize the
collected data with a view to solve variety of social , economic and
developmental problem which help researcher to bring new ideas
and creative thinking into research investigation and to draw
conclusion and make suggestion for future course of action.
Objects of analysis
• Simplification & summarization
• Comparison
• Forecasting
• Policy formulation

STATISTICS
• It is the science of collecting , organizing , analyzing and
interpreting data
Statistics are of two types
Descriptive
Inferential
Descriptive statistics uses the data to provide descriptions of the
population, either through numerical calculations or graphs or
tables
inferential statistics makes inferences and predictions about a
population based on a sample of data taken from the population
in question.

Probability distribution
They are such distribution which are not obtained by actual
observation or experiments but are mathematically deducted
on certain assumption.
Classification of theoretical distributions.
They are classified into two categories
1. Discrete theoretical distribution
2. Continuous theoretical probability distribution.
Discrete again is divided into two
1. Binomial distribution
2. Poisson distribution
And continuous distribution includes
1. Normal Distribution

Discrete
• Binomial distribution
It is also known as Bernoulli distribution
It is associated with Swiss mathematician James Bernoulli
It is the probability distribution expressing the probability of
one set of dichotomous variables.
That is success or failure
They are used in business decision making situation also in
quality control etc.
There are only two possible outcome in a trail
The trails are independent .

• Poisson distribution
• It was originated by French mathematician Simeon Denis
Poisson
• This is limiting form of binomial distribution
• Binomial can only be used if trails are previously known
• In real life situation one cannot analyze the possible
number of trials
• The Poisson distribution is employed in situation where
the number of success is relatively small
• All Poisson distribution are skewed to right

Continuous Distribution
Normal distribution
• it was described by Abraham De
Moivre
• In a ND Mean=median=mode
• It is a bell shaped curve
• Total area under the curve is 1
• 50% of the values are less than the
mean and50 %of values are above the
mean
• It is symmetrical about the center
• We could use normal curve to predict
the chance of happening something.
• It gives us the idea the what the data
actually look like.
• It also describes that 68.26% of all
observation are within ±1 standard
deviation and95 % are within ± 2std
deviation and 99 % are in ±3 Std
deviation.

UNIVARIATE ANALYSIS
It deals with simple data set pertaining to a single variable . It
includes
• Measures of central tendency
• Measures of dispersion

Measures of central tendency
A measure of central tendency (also referred to as measures of
center or central location) is a summary measure that attempts to
describe a whole set of data with a single value that represents the
middle or center of its distribution. Following are the different
measure of central tendency
• Mean
• Median
• Mode
• Geometric mean
• Harmonic mean
• Quadratic mean

• Mean :The mean is the sum of the value of each observation in a
dataset divided by the number of observations. This is also known as
the arithmetic average.
• Median :The median is the middle value in distribution when the
values are arranged in ascending or descending order.
• Mode :The mode is the most commonly occurring value in a
distribution.
• Geometric mean – the nth root of the product of the data values,
where there are n of these items. This measure is valid only for data
that are measured absolutely on a strictly positive scale
• Harmonic mean – the reciprocal of the arithmetic mean of the
reciprocals of the data values. This measure too is valid only for data
that are measured absolutely on a strictly positive scale
• The Quadratic mean (often known as the root mean square) is
useful in engineering, but is not often used in statistics. This is because
it is not a good indicator of the center of the distribution when the
distribution includes negative values.

RESEARCH METHODOLOGY Notes for Engineering

MEASURES OF DISPERSION
Dispersion in statistics is a way of describing how spread out a set of data
is. When a data set has a large value, the values in the set are widely
scattered; when it is small the items in the set are tightly clustered.
• Range: the difference between the smallest and largest number in a set
of data.
• Standard deviation: It is the probably the most common measure. It
tells you how spread out numbers are from the mean,
• Interquartile range (IQR): It describes where the bulk of the data lies
(the “middle fifty” percent).
• Interdecile range: The difference between the first decile (10%) and
the last decile (90%).
• Variance : It is the expectation of the squared deviation of a random
variable from its mean, and it informally measures how far a set of
(random) numbers are spread out from their mean

Two sets of data
-10, 0 ,10,20,30
Range = 40
Variance = 200
SD = 10
10
2
8,9,10,11,12
Range = 4
Variance = 2
SD=√2

Parametric and Non Parametric
measures
Parametric Measures
Conventional statistical procedures are also called as parametric
tests.
In a parametric test sample statistic is used to estimate population
parameter
The main assumption relying behind parametric testing are the
samples are drawn from normally distributed population.

Testing of Hypothesis
The various steps involved in testing are
• Select a data sample from the population
• Make an assumption that whether the data is normally distributed or
not
• Set up a null hypothesis that is H0: µ= specified value
• Set up an alternative Hypothesis H1 : µ ≠specified value
µ > specified value
µ< specified value
• Choose an alpha or significance level at 5% or 1%
alpha is the probability of having a null hypothesis that is indeed true
but our data says that it is wrong
• Select the test statistic
• Decide the critical value : critical value is the value of test statistics
which separates acceptance region from rejection region.
• Form a decision rule computation of test statistic value
• Conclusion or decision

Here while testing there are two types of hypothesis.
1. Directional
2. Non directional
Directional hypothesis are those type in which the data are either
positively related or negatively related , i.e.; the one tailed test
Non directional hypothesis are the hypothesis used in two tailed test
were we say as there is no significant difference between observed and
expected frequencies.
Also to mention two types of errors can also commit while testing the
hypothesis i.e.,
Type 1 error
Type 2 error
Type 1 error occurs when rejecting the null hypothesis when it is true
Type 2 error occurs when accepting null hypothesis when it is false.
In order to minimize both the errors we are fixing the confidence level as
95 %

Testing normality
Normality: This assumption is only broken if there are large
and obvious departures from normality
• This can be checked by
• Inspecting a histogram
• Skewness and kurtosis ( Kurtosis describes the peak of the curve
Skewness describes the symmetry of the curve.)
• Kolmogorov-Smirnov (K-S) test (sample size is ≥50 )
• Shapiro- Wilk test (if sample size is <50)
(Sig. value >0.05 indicates normality of the distribution)

Parametric measures
• Z test
The Z score is a test of statistical significance that helps you decide whether or
not to reject the null hypothesis. The p-value is the probability that you have
falsely rejected the null hypothesis. Z scores are measures of standard deviation.
A z-test is a statistical test used to determine whether two population means are
different when the variances are known and the sample size is large. The test
statistic is assumed to have a normal distribution, and nuisance parameters such
as standard deviation should be known for an accurate z-test to be performed.
The formula for calculating Z value
= X −𝜇
𝜎 𝑛
Uses
• Testing of hypothesis for means
• Testing significance between the mean of the two samples
• Testing significance of difference between two standard deviation
Assumption
• The random distribution of a statistic is normal
• Sample values are close to parameter values

• Students t test
A t-test is any statistical hypothesis test in which the test statistic follows
a Student's t-distribution under the null hypothesis. It can be used to
determine if two sets of data are significantly different from each other.
Formula for calculating t is as follows
T = X - 𝜇 𝑛
S
Uses of t test
• It is used to test whether the two samples have the same mean when
the samples are small
• It is used to test the significance of mean of a random sample
• It is used to test difference between the means of two dependent
sample
• It is used to test the significance of an observed correlation coefficient
Assumptions
• Normal distribution
• The population standard deviation is not known
• Sample size is less than 30

ANOVA
• The term variance was introduced in the statistical analysis by R.A.Fisher
• F test is the name introduced to honor R.A.Fisher
• F test is used to determine whether the two independent estimates f population
variance significantly differ between themselves or to establish whether both
variables have come from the same universe
Uses of F distribution
• It can be used to test the hypothesis
• It can be used to test the equality of variances of two population when samples are
drawn
• To test the equality of means of three or more population
• It is used for testing the significance of an observed sample multiple correlation
• It is used to test the linearity of regression
Assumption
• Sample follow a normal distribution
• All observation are randomly selected
• the ratio of greater variance and smaller variance should equal to or greater than
one
• F distribution is always formed by the ratio of squared values , therefore it can
never be a negative number
F = Greater variance
Smaller variance

Non parametric
• Non parametric test are used when assumption required by the
parametric test are not met
• All test involving rank data are non parametric
• Non parametric test are distribution free
Assumption of non parametric test
• Sample observation are independent
• The variables are continuous
• Sample drawn is a random sample
• Observation are measured o ordinal scale

Non parametric test
One sample K samples
Two sample
Chi Square
Sign test
Kolmogorov Smirnov
test
Run test
Wilcoxon signed-rank
test
Mann–Whitney U test
Median test
The Wald–Wolfowitz
runs test
Kruskal Wallis test
Median test

Non Parametric tests
Chi square test
• The chi square test was first introduced by Karl Pearson.
• It is a test which explains the magnitude of difference between
observed frequencies and expected frequencies under certain
assumptions.
• Greater the discrepancy b/w observed & expected frequencies, greater
shall be the value of χ2.
Assumptions
• The observation are always assumed to be independent of each other.
• All the events must be mutually exclusive
• A sample with sufficiently large size is assumed
• It look like normal distribution but it starts with zero and is skewed
with long tail to the right

• χ2 test of goodness of fit
By using this test we can find out the deviation between the
observed values and expected values
It is used when the variable is categorical or ordinal
It is a type of binomial test in which we determine who is different
from whom.I.e.. the post hoc test.
• As a test of independence
χ2 is used to find whether one or more attributes are associated or
not
Here the variables are independent or not are tested
• χ2 test a test for homogeneity
It is an extension of test of independence
Here it determines whether the two or more independent random
samples are drawn from the same population or from different
population

SIGN TEST
It is to be applied in case the sample is drawn from a continuous
symmetrical population.
Here the mean is expected to be lied at the center and equal
number of units are to be lied above and below the mean value.
Simple and easy to interpret
Makes no assumptions about distribution of the data
Not very powerful
To evaluate H0 we only need to know the signs of the differences
If half the differences are positive and half are negative, then the
median = 0 (H0 is true).
If the signs are more unbalanced, then that is evidence against H0.

• Kolmogorov Smirnov test
For testing the relationship between an empirical
distribution and some theoretical distribution or between
two empirical distribution goodness of fit test are employed
K-S can be applied to test the relationship between a
theoretical and a sample frequency distribution for one
sample test or between two sample distributions.
RUN TEST for randomness
The run test has been decided to determined whether the
sample is random or not.
The total no. of runs in a sample indicate whether the
sample is random or not.

Median test
The median test is used to determine the significance of difference
between median of two or more independent groups .
The object is to find out whether the median of different sample drawn
randomly are alike or can be taken as drawn from the same population.
It is an application of Chi square test for two variables each having two
subgroups.
Mann–Whitney U test
In statistics, the Mann–Whitney U test (also called the Mann–Whitney–
Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–
Whitney test) is a nonparametric test designed to test the significance of
difference between the result of two samples drawn at random from the
same population but administered differently .
It can be used as an alternative to t test when parametric assumptions
are not met. It is nearly as efficient as the t-test on normal distributions
Here the observation are at least expressed in ordinal scale .

Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a non-parametric statistical
hypothesis test used when comparing two related samples,
matched samples, or repeated measurements on a single sample
to assess whether their population mean ranks differ (i.e. it is
a paired difference test). It can be used as an alternative to
the paired Student's t-test, t-test for matched pairs, or the t-test for
dependent samples when the population cannot be assumed to
be normally distributed.
Run test
The Wald–Wolfowitz runs test , named after Abraham
Wald and Jacob Wolfowitz, is a non-parametric statistical test that
checks a randomness hypothesis for a two-valued data sequence.
More precisely, it can be used to test whether the two samples
were drawn from the same population.

• K sample test
Kruskal – Wallis test
The Mann Whitney U test is used to test the significance of
difference between the result of two independent samples
where dependent variable is measured on ordinal scale .the
K-W extent the use of Mann Whitney U test to three or
more independent groups
Median test
It has already been discussed in two sample test . The same
can be extended to meet further requirement of K samples

• In narrow sense
Econometrics means Economic Measurement.
• In Broader sense
It may be defined as the social science in which the tool of economics
theory , mathematics and statistical inferences are applied to the analysis
of economic phenomena
Types of Econometrics
• Theoretical
Theoretical Econometrics is concerned with the development of
appropriate methods for measuring economic relationships specified by
econometric models.
• Applied
In applied econometrics, we use the tools of theoretical econometrics to
study some special fields of economics and business, such as production
function, investment function, demand and supply function.

Methodology of Econometric
1. Statement of theory or hypothesis
2. Specification of the mathematical model of the theory
3. Specification of the Statistical or Econometric model
4. Obtaining Data
5. Estimation of the parameters of the Econometric Model
6. Hypothesis testing
7. Forecasting or Prediction
8. Using the model for control or policy purpose

Types of Data
• Time Series Data
• Cross Sectional Data
• Pooled Data
• Time Series Data
Time series is a sequence of data points, measured typically at
successive time instants spaced at uniform time intervals. Time
series data have a natural temporal ordering.
• Daily- Weather, Stock Price
• Monthly- Unemployment rate
• Quarterly- GDP
• Yearly- National Budgets
• Decennially- Population Census

• Cross Sectional Data
Cross-sectional data or cross section is a type of one-dimensional data
set. It refers to data collected by observing many subjects such as
individuals, firms or countries/regions at the same point of time, or
without regard to differences in time.
For example, we want to measure the mobile uses for a particular brand
in this campus. We could draw a sample of 100 students randomly from
the population, measure their mobile use, and calculate what percentage
of that sample is used of that brand. For example, 60% of our samples
were used that particular branded mobile. This cross-sectional sample
provides us with a snapshot of that population, at that one point in time.
Note that we do not know based on one cross-sectional sample if the
uses of this brand are increasing or decreasing; we can only describe the
current proportion.
Pooled Data
In Pooled or combined data are the element of both time series and
cross-sectional data.

CORRELATIONAL ANALYSIS
• Correlation analysis is an attempt to determine the degree of
relationship between variables. It is the analysis of co variation between
two variables.
• The coefficient of correlation ranges between -1 and +1 and quantifies
the direction and strength of the linear association between the two
variables.
• The correlation between two variables can be positive (i.e., higher
levels of one variable are associated with higher levels of the other) or
negative (i.e., higher levels of one variable are associated with lower
levels of the other).
Significance of correlational analysis
• It is used as basis for the study of regression
• In business it helps the management to estimate costs, sales, price,
and other variables.
• It helps to reduce the range of uncertainty associated with decision
making

Assumption of correlation
• Cause and effect relationship exist between the variables .
• The relation ship between the variable is linear
• The variables follows a normal distribution.
Classification of correlation
Correlation
On the basis of
Direction
On the basis of
linearity
On the basis of
variables
Positive correlation
Negative correlation
Linear
Non linear
Simple correlation
Partial correlation
Multiple correlation

• Positive correlation
If the variables are moving and varying in the same direction. It is called
positive correlation. I.e.. increase in value of one variable lead to
increase in other variable.
E.g.
P : 5 10 15 20 25 30
Q: 15 20 25 30 35 40
Negative correlation
Here the variables are moving in the opposite direction .
E.g.
X : 2 3 4 5 6 7
Y : 6 5 4 3 2 1
Linear correlation and non linear correlation
The distinction between linear and non linear correlation is based upon
the consistency of the ratio of changes between the variable understudy.
If the amount of change in one variable follows a constant change of
other variable then the correlation is said to be linear

Simple correlation
An analysis were relationship exist between two variables ;one
independent ad other dependent is known as simple correlation
analysis.
Simple correlation measures strength and type of the relationship
between two variables on the assumption that no other variable
come into play as such and it is need not to be taken.
It is also called as ‘Zero order correlation’
The statistical measure of simple correlation is known as ‘
Coefficient of Linear correlation’ with symbol ‘r’.
It can be either positive or negative.
Coefficient of simple determination with symbol r2 gives the
proportion of variation in the dependent variable (y) accounted
for the repressor (x).
For e.g. if the value of r2 = .81 , this means 81 % of the variation
in dependent variable has been explained by repressor.

• Partial correlation
It represent the relationship between two variables after the
effect of one or more other distracting variable , if any has
been eliminated.
Determination of partial correlation is essential to
understand the cause effect relationship between variables
under observation.
For e.g. ,
In a study it was observed that the correlation between
education and income was positive. But it might be entirely
due to a third variable say the persons economic status .
People with higher economic status earns more money.
Accordingly education and income may have high
correlation .

• Multiple correlation
Coefficient of multiple correlation determines the nature
and extent of proximity in the relationship between one
dependent variable and two or more independent variable.
The statistical measure of such a relationship is known as
coefficient of multiple correlation, with a symbol R.

METHODS OF STUDYING
CORRELATION
a) Scatter diagram
b) Karl Pearson's coefficient of correlation
c) Spearman’s Rank correlation coefficient
d) Method of least squares
Karl Pearson's Coefficient of Correlation
„Pearson’s ‘r’ is the most common correlation coefficient. „Karl
Pearson’s Coefficient of Correlation denoted by- ‘r’ The coefficient of
correlation ‘r’ measure the degree of linear relationship between two
variables say x & y.
Karl Pearson's Coefficient of Correlation „
When deviation taken from actual mean:
r(x, y)= Σxy / √ Σx² Σy² „
When deviation taken from an assumed mean:
r = N Σdxdy - Σdx Σdy
√N Σdx²-( Σdx)² √N Σdy²-( Σdy)²

• Spearman’s Rank Coefficient of Correlation „
When statistical series in which the variables under study
are not capable of quantitative measurement but can be
arranged in serial order, in such situation Pearson's
correlation coefficient can not be used in such case
Spearman Rank correlation can be used.
„R = 1- (6 ∑ D2 ) / N (N 2 – 1) „
R = Rank correlation coefficient
„D = Difference of rank between paired item in two series. „
N = Total number of observation.

• Scatter Diagram Method „
Scatter Diagram is a graph of observed plotted points where each
points represents the values of X & Y as a coordinate. It portrays
the relationship between these two variables graphically.

REGRESSION ANALYSIS
In statistical modeling, regression analysis is a statistical process for
estimating the relationships among variables.
More specifically, regression analysis helps one understand how
the typical value of the dependent variable (or 'criterion variable')
changes when any one of the independent variables is varied,
while the other independent variables are held fixed.
Regression analysis is widely used for prediction and forecasting
Regression line is the line which gives the best estimate of one
variable from the value of any other given variable. „
The regression line gives the average relationship between the two
variables in mathematical form
Regression can be simple linear regression or multiple linear
regression

Simple linear regression
It is a causal relation in which it describe how does a dependent
variable changes because of a change independent variable while
all other variables are held constant
Simple linear regression is representing a set of clustered data
points with best fit line
The line of best fit which represent the data set with the smallest
distance between the line and each of the data points.
For a linear regression to work the data set must have two
variables that are correlated.
• Simple linear regression has 2main objectives
1. Establish if there is a relationship between variables
2. Forecast new observation.

• Standard form for simple linear regression
y= 𝛽0 + 𝛽1 𝑥 + 𝜀
Y = dependent variable
𝛽0 = 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝛽1 = 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒
𝜀 = error term

Multiple linear regression model
It is about modeling a data a set with two or more independent
variable and one dependent variable .
Here the dependent variable is expressed as a function of two or
more independent variables in a single equation.
• Assumption of multiple linear regression
1. Only relevant variables are included
2. A linear relationship is required
3. Causality of variables
4. All variables are normally distributed
5. Homoscedasticity is assumed.
6. Absence of multicollinearity is assumed in the model.

• Standard form for multiple regression model is
Y=𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝛽3𝑥3 … . +𝛽𝑛𝑥𝑛

MULTICOLLINEARITY
Multicollinearity refers to a situation in which two or more
explanatory variables in a multiple regression model are highly
linearly related. We have perfect multicollinearity if, for example
as in the equation above, the correlation between two independent
variables is equal to 1 or −1.
a multiple regression model with correlated predictors can
indicate how well the entire bundle of predictors predicts
the outcome variable, but it may not give valid results about any
individual predictor, or about which predictors are redundant with
respect to other
Multicollinearity. It's good to have a relationship between
dependent and independent variables, but it's bad to have a
relationship between independent variables. Effect of single
variable hard to measure.

Heteroskedasticity
• Heteroskedasticity, in statistics, is when the standard deviations of a
variable, monitored over a specific amount of time, are non constant.
Heteroskedasticity often arises in two forms: conditional and
unconditional
Conditional Heteroskedasticity identifies non constant volatility when future
periods of high and low volatility cannot be identified. Unconditional
Heteroskedasticity is used when futures periods of high and low volatility can
be identified.
• Unconditional Heteroskedasticity
Unconditional Heteroskedasticity is predictable, and most often relates to
variables that are cyclical by nature. This can include higher retail sales
reported during the traditional holiday shopping period, or the increase in
air conditioner repair calls during warmer months.
.

In finance, conditional Heteroskedasticity is often seen in the prices of
stocks and bonds. The level of volatility of these equities cannot be
predicted over any period of time. Unconditional Heteroskedasticity can
be used when discussing variables that have identifiable
seasonal variability, such as electricity usage.
As it relates to statistics, Heteroskedasticity, also spelled
Heteroskedasticity, refers to the error variance, or dependence of scatter,
within a minimum of one independent variable within a particular
sample. These variations can be used to calculate the margin of error
between data sets, such as expected results and actual results, as it
provides a measure for the deviation of data points from the mean value.

FACTOR ANALYSIS
• Factor analysis identifies correlation between and among
variables to bind them into one underlying factor
• Factor analysis reduces larger number of variables into
smaller amount of factors.
• E.g. , in a set of variables (V1,V2,V3,V4,V5,V6)
• A correlational relationship may be found between
V1,V2,V3
• So these variables can be identified as factor because there
is higher degree of relationship between these three things.
• Accordingly large no. of variables will be reduced to
several small no.of factors.
• Factor analysis is also referred to as data reduction.

• Factor analysis consider either pairs of responses or pairs of variables
I.e. Q type and R type factor.
• The important terminology used in factor analysis is a factor which is
the weighted linear combination of the variables understudy.
• The factor loading in factor analysis indicates the extent of closeness of
relationship among variables constituting a factor
• Another term that is needed to be pointed out in factor analysis is
Commonality which indicates the extent of a variable has been
accounted for by underlying factor taken together. Higher the value of
commonality the variable has been considered by the factor and lower
if it left out.
• Eigen value : the sum of squares of factor loading relating to factor is
called as eigenvalue . It indicates the relative importance of factor in
account for the set of variables considered.
• Factor rotation: it is done to reveal different structures in data.
Different structures give different results but they are statistically equal.
There 2 types of rotation Orthogonal and oblique.

• Assumption of factor analysis
No outliers in data set
Adequate sample size
The data set must posses no perfect multicollinearity
Homoscedasticity is not required
Linearity of variables
The data must be at least interval data

CLUSTER ANALYSIS
• Cluster analysis is a process of identifying natural homogenous
group existing in data , so that similarity within group and
difference among group may be used for understanding the
basic character of the data.
• It is applied to large set of data which may consist of many
variables.
• It is applied to data recorded on interval scale
• Here internal homogeneity and external heterogeneity is
determined
• There are basically two types of clusters
Hierarchical cluster
Non hierarchical cluster

• Hierarchical cluster : here first two closest objects are
grouped and treated as single cluster . Then the same
process is carried out until there is a single cluster
containing all the items .
• Non hierarchical clusters.: here the items are disbursed
into predetermined groups successively in integrative
process finally some defined group emerges.
Linkage function of clustering : it is used to find out the
distance between two clusters there are two types of linkages
Simple linkage
Complete linkage

CONJOINT ANALYSIS
• It is a technique useful in determining relative value of different
attributes of an item
• In marketing research it helps to find out most desirable
combination of a product or service that is existing or proposed
to be introduced in the market.
• Conjoint analysis is applied to categorical variables
• It is done to analyze most important feature of a product.
• It gives relative importance to the factor that are taken for
consideration.
• It helps us to develop alternative sets of combination of different
levels of product.
• The respondents are given a chance to rate or rank accordingly

It is applied in the following fields
• New product development
• Transport industry

DISCRIMINANT ANALYSIS
• It is a statistical technique useful in classification of individuals or
observation into two or more mutually exclusive groups, on the basis
of set of predictor variables.
• In DA there is one nominal dependent variable and two or more
interval scaled independent variables.
• IV have certain common characteristic features which are useful in
discriminating among individuals
• The main object of DA is to classify the observed cases into two or
more groups.
• DA is applied in following areas
1. Credit rating
2. Prediction of sickness
3. Portfolio selection
4. Market research
5. Classification of various attributes

• Discriminant function
• Linear discriminant function
It is a linear function of predictive variables weighted in such a way
that it will discriminate among groups minimizing errors. In case
the dependent variable is classified into only two groups this is
known as simple discriminant analysis
In case dependent variable is classified into more than two groups
it is termed as multiple discriminant function
Bi variate discriminate analysis for two groups
If the no.of variables included in the discriminant function is 2 ,
there is a straight line classification boundary . An individual on
one side belong to group 1 and on the other side belong to group
2

DECOMPOSTION
ANALYSIS
• It means analysis of as set of data to reveal its composition and thereby
express it in terms of extent of change over time in its components.
• It reveals the extent of change in structure , the composition and the
intensity of a set of data
• It is suitable for large mass of data such as financial statements,
performance reports , budget etc.
• It reveals significant changes in the structure of data over a period of
time or from one organization to another.
• It pinpoints the area of change
• With availability of computers now large data based statements can be
subjected to decomposition analysis
DA can be applied in the following areas
Business data analysis
Prediction of financial distress

REPORT WRITING
• Research report is a research document that contains basic
aspects of the research project
• Research report is the systematic, articulate, and orderly
presentation of research work in a written form.
• It may be in form of hand-written, typed, or computerized.

Report writing stages
• Understanding the report brief
• Gathering and selecting information
• Organizing your material
• Analyzing your material
• Writing the report
• Reviewing and redrafting
• Presentation

Content of research report
Research report is divided into three parts as:
I. First Part (Formality Part):
(i) Cover page
(ii) Title page
(iii) Certificate or statement
(iv) Index (brief contents)
(v) Table of contents (detailed index)
(vi) Acknowledgement
(vii) List of tables and figures used
(viii) Preface/forwarding/introduction
(ix) Summary report

II. Main Report (Central Part of Report):
(i) Statement of objectives
(ii) Methodology and research design
(iii) Types of data and its sources
(iv) Sampling decisions
(v) Data collection methods
(vi) Data collection tools
(vii) Fieldwork
(viii) Analysis and interpretation (including tables, charts, figures, etc.)
(ix) Findings
(x) Limitations
(xi) Conclusions and recommendations
(xii) Any other relevant detail

III. Appendix (Additional Details):
(i) Copies of forms used
(ii) Tables not included in findings
(iii) A copy of questionnaire
(iv) Detail of sampling and rate of response
(v) Statement of expenses
(vi) Bibliography – list of books, magazines, journals, and
other reports
(vii) Any other relevant information

References
• Research methodology - K.R Sharma
• Methodology of research in social science –
-Dr O R Krishnaswamy , Dr M Ranganathan
• Business research methods – Naval Bajpai
• Research methodology , A step by step guide fro beginners –
Ranjith Kumar
• Introduction to Econometrics –G S Maddala & Kajal Lahiri
• Quantitative techniques Dr K venugopalan
• www.wikipedia.org

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