Final PPT
Business Research Process
Research –Definition
McGraw-Hill/Irwin
Strategic Management, 10/e
By Anubhav Singh Copyright © 2007 The McGraw-Hill Companies, Inc. All rights reserved.
“Research ; may be defined as the systematic and objective analyze and
recording of controlled observation that may lead to the developments or
generalizations, principles or theories, resulting in prediction and possibility
ultimate control of events”.
Sometimes research is defined as a movement, a movement from the known to
the unknown. It is an effort to discover something. Some people say that
research is a on effort to know “more and more about less and less”.
RESEARCH MEANING
Research is a serious academic activity with a set of objectives to explain
or analyse or understand a problem or finding solution(s) for the problem(s)
by adopting a systematic approach in collecting, organizing and analyzing
the information relating to the problem.
According to CLIFFORD WOODY,
Research comprises, defining and redefining problems
formulating hypothesis or suggested solutions; collecting
organizing and evaluating data; making deductions and
reaching conclusions; and at as carefully testing the conclusions
to determine whether they fit the formulating a hypothesis.
Research may also be defined ”Any organized enquiry discussed
and carried out to provide information for solving a problem”.
OBJECTIVES OF RESEARCH:
Research is a conscious approach to find out the truth which is hidden and
which has not been discovered by applying scientific procedure. Therefore
each research has its own focus. This is stated in terms of objectives (or)
purposes of conducting research. Objectives are like guide points in
research, that the researcher does not nose his focus it is also believed
that the objectives determine the nature of data to be compiled, the scope
of collection, target group sample size and several other crucial aspects
which ultimately decide the success or failure, adequacy or in failure,
adequacy or research. The objectives or a research will be explained in the
following words;
It develops Focus
The research may be to understand for become familiar with some
phenomena or to get to know more in depth it.
For example, since the days of steam engine, the research
continued to come up with more powerful locomotive which could
be operated with alternative sources of energy like diesel, electricity
etc.
It reveals characteristics:
To clearly reveal the characteristics of an individual or a situation or a
group like a society is another type of research objective. For example in
these days before a criminal is sentenced efforts are taken to study why he
had turned criminal. This helps develops an approach to create
opportunities for criminals to cha ge themselves and join the main stream
of life.
It determines frequency of occurrence:
To determine the frequency with which something occurs or
with which it associated with something else. In social research
one of the major areas of repeated and continuous research is
analysis of poverty and unemployment.
It tests hypothesis:
To test a hypothesis about the casual relationship between
variable being studied. This type of research is mainly to
determine the relationship between various factors so that
necessary policy options could be framed. For example, the
reasons for several malpractices adopted in public distribution
outlets include low salary and absence of regulation of service
of the staff in such outlets. This is turn make them to feel
insecure and they resort to mal practices. Having found this the
Govt., had taken a policy to improve the salary structure of
these staff ad regularize their services. Hence the study of
casual relationship might help in formulation of policies.
Understanding the Criteria of Good Research
1. Clarity and Preciseness
Good research begins with clear objectives and research questions. It’s imperative to
articulate what the research intends to achieve and what it seeks to explore. Specific
Objectives
•Define the goals of your research.
•Ensure they are clear, focused, and attainable. WellFormulated Research Question
•Craft a question that guides your research path.
•It should be precise and manageable in scope.
2. Relevance and Significance
Research must contribute value to its field. It should address a gap in knowledge or solve a
specific problem.
Identifying the Gap
•Understand what has already been studied.
•Identify areas that require further exploration. Impact of Research
•Evaluate how your research contributes to the field.
•Consider its practical applications and theoretical implications.
Understanding the Criteria of Good Research
3. Methodological Rigor
The methodology is the blueprint of your research. It should be systematic, appropriate, and reproducible.
Appropriate Method Selection
•Choose methods suited to your research question and objectives.
•Justify your methodological choices.
Reproducibility
•Ensure that others can replicate your study.
•This enhances the reliability and validity of your results.
4. Ethical Considerations
Research must be conducted with integrity and respect for ethical norms.
Informed Consent
•Obtain consent from participants, ensuring they are well-informed about the research.
•Respect their privacy and confidentiality.
Avoiding Bias
•Recognize and mitigate potential biases in your study.
•Strive for objectivity and fairness.
RESEARCH PROCESS
By Prof. Anubhav Singh
Faculty Interna onal Business and Strategy
By Prof. Anubhav Singh
Faculty Interna onal Business and Strategy
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Faculty Interna onal Business and Strategy
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
By Prof. Anubhav Singh
Strategy
Faculty Interna onal Business and
What is research design ?
•The research design refers to the overall strategy that
you choose to integrate the different components of the
study in a coherent and logical way, thereby, ensuring
you will effectively address the research problem; it
constitutes
the
blueprint
for
the
collection,
measurement, and analysis of data.
• Note that the research problem determines the type of
design you should use, not the other way around!
•
Research design
The function of a research design is to ensure that the evidence obtained enables
you to effectively address the research problem logically and as unambiguously
as possible. In social sciences research, obtaining information relevant to the
research problem generally entails specifying the type of evidence needed to test
a theory, to evaluate a program, or to accurately describe and assess meaning
related to an observable phenomenon.
With this in mind, a common mistake made by researchers is that they begin their
investigations far too early, before they have thought critically about what
information is required to address the research problem. Without attending to
these design issues beforehand, the overall research problem will not be
adequately addressed and any conclusions drawn will run the risk of being weak
and unconvincing. As a consequence, the overall validity of the study will be
undermined.
•Identify the research problem clearly and justify its selection, particularly
in relation to any valid alternative designs that could have been used,
•Review and synthesize previously published literature associated with the
research problem,
•Clearly and explicitly specify hypotheses [i.e., research questions] central
to the problem,
•Effectively describe the information and/or data which will be necessary
for an adequate testing of the hypotheses and explain how such
information and/or data will be obtained, and
•Describe the methods of analysis to be applied to the data in determining
whether or not the hypotheses are true or false.
Why is Research Ethics
• *ItImportant has become the norm as an
expectation for
research activity
• *…. a professional requirement for practitioners in
some disciplines e.g. psychology
• *… a requirement for access to participants in
others e.g. health
• *… and a requirement to comply with external
REF’s to obtain funding e.g. ESRC
FUNDAMENTAL (OR) BASIC RESEARCH:
Pure or Basic research is a search for broad principles and
synthesis without and immediate utilization objectives. It is not
concerned with solving any practical problems of policy but with
designing and fascinating tools of analysis and with discovering
underlying and if possible universal laws and theories.
Eg. John Robinson‟s imperfect competition and chamberlains
monopolistic competition.
Applied (or)Action Research:
Applied research also known as action research is associated
with particular project and problem. Such research, being of
practical value may release to current activity (or) immediate
practical situation it aims at finding a solution for an immediate
problems facing a society practically all social science research
undertaken in India is of the applied variety and more
particularly of the type which helps formulation of policy.
Descriptive Research:
It is designed to describe something such as demographic
characteristics of consumers who use the product. It is designed
to describe something, such as demographic characteristics of
consumers who use the product. It deals with determining
frequency with which something occurs or how two variables
vary together. This study is also guided by a initial hypothesis.
For example an investigation of the trends in consumption of
soft drinks in relation to ration-economic characteristics as age,
sex, ethnic group, family income, education level, geographic
location, and so on would be descriptive study.
Merits:
This approach helps to test the conclusion and findings arrived at on the basis of laboratory
studies. By using this approach, it is possible to substan ate exis ng theories and
conclusions on modifying them.
Direct contact between the researcher and the respondent is brought about in this
approach. This is very significant because, the researcher would be able to understand
himself clearly the problem to be studied.
With the possibility of direct contract with the respondent, the researcher is able to elicit all
the relevant informa on and eliminate irrelevant facts.
Limita ons:
Unless the researcher is experienced there is every possibility of the approach
being misused. Hurried conclusions and generaliza ons may be formed based
on the inaccurate field data.
As this approach involves collec on of field data enormous me and efforts
are required to plan and execute the field survey
This approach also involves incurring heavy cost on data collec on.
Unless the respondents are co-opera ve. It is not possible to collect data
through this approach.
HISTORICAL RESEARCH:
As the name suggests in this approach historical data is given importance to undertake analysis and
interpret the results. Following this approach a researcher would collect past data for his research.
A scholar using this approach has to depend on libraries for referring to the magazines or periodicals
for collec ng data.
Merits:
This approach alone is relevant in certain types of research work. For examples to understand the
trend in India‟s exports. One has to collect the export data for a period of say 20 years and them
analyze it similarly to study the impact of the liberaliza ons policy one has to collect informa on
from 1991 ll date.
Historical approach makes research possible as it is firmly believed that once we understand the
past, out understanding of the present and expecta ons of the future could be predicted to some
extent. Hence historical research provides the insight into the past and facilitates looking into the
future.
Qualita ve and Quan ta ve Research Design
EXPLORATORY RESEARCH:
Most of the marke ng research projects begin with exploratory. It is conducted
to explore the possibili es of doing a par cular project. The major emphasis is
on the discovery of ideas and insights.
For example, a so drinks firm might conduct an exploratory study to generate
possible explana ons. The exploratory study is used to spilt the broad and
vague problem into smaller, more precise sub problem statements, in the form
of specific hypothesis. An exploratory study is conducted in the following
situa ons.
To design a problem for inves ga ons and to formulate the hypothesis.
To determine the priori es for further research.
To gather data about the prac cal problems for carrying out research on par cular
conjectural statements.
To increase the interest of the analyst towards the problems and
To explain the basic concepts.
Exploratory study is more flexible and highly informal. There is no formal
approach in exploratory studies. Exploratory studies do not employ detailed
ques onnaire. These studies will not involve probability sampling plans. The
following are the usual methods of conduc ng exploratory research
Literature Survey
Experience Survey and
Analysis of insight s mula ng cases
EXPERIMENTAL RESEARCH:
This is a very scien fic approach. In this approach the researcher first
determines the problem to be studied. Then he iden fies the factors that cause
the problem. The problem to be probed is quan fied and taken as the
dependent variable. The factors causing to the problem will be taken as
independent variable. Then the researcher studies the casual rela onship
between the dependent and independent variable. He is also able to specify
to what extent the dependent variable. He is also able to specify to what extent
the dependent variable is influenced by each independent variable.
For examples suppose food produc on is taken as the problem for a research
study. then the scholar would determine the factors that will affect food
produc on. Viz size of the land cul vated(x) rainfall (y) quan ty of fer lizer
applied (z) etc. These factors x,y and z are called independent variable,. Food
produc on [A] is called dependent variable. Then by collec ng data regarding
all the four [A,x,y and z]. The researcher is able to state what percentage
change in the final food (A) is explained by x,y and z. The effect of x on A, y on A
and z on A is also studied. In this manner the researcher is able to successfully
indicate to what extent various factors included in the study are important.
Merits of Experimental Approach (Research)
This approach provides the social scien sts a reliable method it observe under given
condi ons to evaluate various social programmes.
This is one of the best methods of measuring the rela onship between variables.‟ This
approach is more logical and consistent that the conclusions drawn but of research
based on this approach is well received.
It helps to determine the cause – effect rela onship very precisely and clearly.
Following this approach researchers could indicate clearly the areas of future research
Limita ons of Experimental Approach (Research)
Unless a researcher is well experienced and trained in model building this approach
can not be easily followed.
By relying more on models this approach may not add anything significant to
knowledge
A serious limita on of this approach is that it relies on sampling and collec on
of data. Unless these are properly planned and executed. the outcome of
analysis will not be accurate
DIAGNOSTIC STUDY;
This is similar to descrip ve study but with a different focus. It is directed
towards discovering what is happening, why it is happening and what can be
done about. It aims at iden fying the causes of a problem and the possible
solu ons for it.
A diagnos c study may also be concerned with discovering and tes ng whether
certain variables are associated. E.g., are persons having from rural areas more
suitable for manning rural branches of banks? (or) Do more villagers than city
voters vote for a par cular party.
Validity and Reliability
Validity: Are You Measuring What You Intend to Measure?
Definition:
Validity refers to the accuracy and truthfulness of a measurement tool—whether the instrument measures
what it is supposed to measure.
Types of Validity:
•Face Validity:
Does the test appear to measure the concept? (Most basic form, subjective.)
•Content Validity:
Does the instrument cover the full range of the concept’s meaning? (Judged by experts.)
•Construct Validity:
Does it truly measure the theoretical construct? (Includes convergent and discriminant validity.) •Criterionrelated Validity:
• Predictive Validity: Can the tool predict future outcomes?
• Concurrent Validity: Does it correlate with existing validated tools?
Reliability: Are Your Results Consistent and Stable?
Definition:
Reliability is about the consistency or stability of measurement—whether you get the
same results if the measurement is repeated under the same conditions.
Types of Reliability:
•Test-Retest Reliability:
The same test is administered at two different times to the same group.
•Inter-Rater Reliability:
Consistency between different observers or raters.
•Parallel-Forms Reliability:
Two different versions of a test yield similar results.
•Internal Consistency Reliability:
Consistency within the test itself.
➔ Measured using Cronbach’s Alpha.
Sampling
INTRODUCTION
Population/Universe: in statistics denotes the
sample (items) is to be taken.
aggregate from which
A population can be defined as including all people or items with the
characteristic one wishes to understand.
Because there is very rarely enough time or money to gather information
from everyone or everything in a population, the goal becomes finding a
representative sample (or subset) of that population.
INTRODUCTION
Sampling frame is the list from which the
potential respondents are drawn .
A sample is “a smaller (but hopefully
representative) collection of units from a
population used to determine truths about that
population” (Field, 2005)
SAMPLING
Sampling: the process of learning about population on the
basis of sample drawn from it.
Three elements in process of sampling:
Selecting the sample
Collecting the information
Making inference about population
Statistics: values obtained from study of a sample.
Parameters: such values from study of population.
SAMPLINGPROCESS
Defining the population of concern.
Specifying a sampling frame, a set of items or events
possible to measure.
Specifying a sampling method for selecting items or events
from the frame.
Determining the sample size.
Implementing the sampling plan.
Sampling and data collection
ESSENTIALS OFSAMPLING
Representativeness- ensure by random selection
Adequacy - sample size
Independence - same chance of selection
Homogeneity - no basic difference in nature of
units.
SAMPLINGMETHODS
NON
PROBABILITY
PROBABILITY
M IXED
JUDGMENT
SIMPLERANDOM
MULTISTAGE
QUOTA
STRATIFIED
RANDOM
MULTIPHASE
CONVENIENC
E
SNOWBALL
SYSTEMATIC
CLUSTER
JUDGMENTSAMPLING
Judgment/Purposive/Deliberate sampling.
Depends exclusively on the judgment of
investigator.
Sample selected which investigator thinks to be
most typical of the universe.
JUDGMENTSAMPLING
Merits
 Small no. of sampling units
 Study unknown traits/case sampling
 Urgent public policy & business decisions
Demerits
 Personal prejudice & bias
 No objective way of evaluating reliability of results
CONVENIENCESAMPLING
Convenient sample units selected.
Selected neither by probability nor by
judgment.
Merit – useful in pilot studies.
Demerit – results usually biased and
unsatisfactory.
CONVENIENCE SAMPLING -EXAMPLE
Class of 100students
20 Students selected asper
convenience
QUOTASAMPLING
Most commonly used in non probability sampling.
Quotas set up according to some specified
characteristic.
Within the quota , selection depends on personal
judgment.
Merit- Used in public opinion studies
Demerit – personal prejudice and bias
SNOWBALLSAMPLING
A special non probability method used when the desired
sample characteristic is rare.
It may be extremely difficult or cost prohibitive to locate
respondents in these situations.
Snowball sampling relies on referrals from initial subjects to
generate additional subjects.
SNOWBALLSAMPLING-STEPS
Make contact with one or two cases in
the population.
Ask these cases to identify further cases.
Ask these new cases to identify further new
cases.
Stop when either no new cases are given or the
sample is as large as is manageable.
SNOWBALLSAMPLING
Merit
access to difficult to reach populations (other
methods may not yield any results).
Demerit

not representative of the population and will result in
a biased sample as it is self-selecting.
SIMPLE RANDOMSAMPLING
Each unit has an equal opportunity of being
selected.
Chance determines which items shall be included.
SIMPLE RANDOMSAMPLING
The sample is a simple random sample if any of
the following is true –
 All items selected independently.
 At each selection , all remaining items have same
chance of being selected.
 All the possible samples of a given size are equally
likely to be selected.
Simple or unrestricted randomsampling
Lotterymethod
Random
numbertables
LOTTERY METHODWith replacement Probability each item: 1/N
Without replacement –
st
 Probability 1 draw: 1/N
Probability 2nddraw: 1/N-1 TABLE OF
RANDOMNUMBERS

SIMPLE RANDOMSAMPLING
Merits

No personal bias.

Sample more representative of population.

Accuracy can be assessed as sampling errors follow principals of chance.
Demerits

Requires completely catalogued universe.
STRATIFIED RANDOM SAMPLING
Universe is sub divided into mutually exclusive
groups.
A simple random sample is then chosen
independently from each group.
STRATIFIED RANDOM SAMPLING
Issues involved in stratification
 Base of stratification
 Number of strata Sample size within strata.
Sample
size
withinstrata
Proportional
(proportion in each stratum)
Disproportional (equal no.
in each stratum)
STRATIFIED RANDOM SAMPLING
Merits
 More representative.
 Greater accuracy.
 Greater geographical concentration.
Demerits
 Utmost care in dividing strata.
 Skilled sampling supervisors.
 Cost per observation may be high.
SYSTEMATICSAMPLING
Selecting first unit at random.
Selecting additional units at evenly spaced intervals.
Complete list of population available.
k=N/n
Classof95students:rollno.1to95
k=sampling interval
N=universe size
Sample of 10students
n=Sample size
1st student random then every10th
k=9.5 or10
SYSTEMATICSAMPLING
Merits
 Simple and convenient.
 Less time consuming.
Demerits
 Population with hidden
periodicities.
CLUSTERSAMPLING
A sampling technique in which the entire population of
interest is divided into groups, or clusters, and a random
sample of these clusters is selected.
Each cluster must be mutually exclusive and together the
clusters must include the entire population .
After clusters are selected, then all units within the clusters are
selected. No units from non-selected clusters are included in
the sample.
CLUSTERSAMPLING
In cluster sampling, the clusters are the primary sampling unit
(PSU’s) and the units within the clusters are the secondary
sampling units (SSU’s)
STRATIFICATION V/S CLUSTERING
Stratification
Clustering
All strata are represented in the
sample.
Only a subset of clusters are in the
sample.
Less error compared to simple
random.
More error compared to simple
random.
More
expensive
to
stratification information
sampling.
obtain Reduces costs to sample only some
before areas or Organizations.
CLUSTERSAMPLING
Merits

Most economical form of sampling.

Larger sample for a similar fixed cost.

Less time for listing and implementation.

Reduce travel and other administrative costs.
Demerits

May not reflect the diversity of thecommunity.

Standard errors of the estimates are high, compared to other sampling designs
with same sample size .
MULTISTAGESAMPLING
Sampling process carried out in various stages.
An effective strategy because it banks on multiple
randomizations.
Used frequently when a complete list of all
members of the population does not exist and is
inappropriate.
MULTISTAGE SAMPLING
MULTISTAGESAMPLING
Merits
 Introduces flexibility in the sampling method.
 Enables existing divisions and sub divisions of population to
be used as units.
 Large area can be covered.
 Valuable in under developed areas.
Demerits
 Less accurate than a sample chosen by a single stage process.
Scaling Technique
The Measurement & Scaling Technique helps us to :
explain the concepts of measurement and scaling,
discuss four levels of measurement scales,
classify and discuss different scaling techniques, and
select an appropriate attitude measurement scale for our research
problem.
As we discussed earlier, the data consists of quantitative
variables, like price, income, sales etc., and qualitative
variables like knowledge, performance , character etc.
The qualitative information must be converted into
numerical form for further analysis. This is possible
through
measurement and scaling techniques. A
common feature of survey based research is to have
respondent’s
feelings, attitudes, opinions, etc. in some measurable form.
Before we proceed further it will be worthwhile to
understand the following two terms: (a) Measurement,
and (b) Scaling.
a)Measurement: Measurement is the process of observing and recording the
observations that are collected as part of research. The recording of the
observations may be in terms of numbers or other symbols to characteristics of
objects according to certain prescribed rules. The respondent’s, characteristics are
feelings, attitudes, opinions etc.
The most important aspect of measurement is the specification of rules for
assigning numbers to characteristics. The rules for assigning numbers should be
standardized and applied uniformly. This must not change over time or objects.
b)Scaling: Scaling is the assignment of objects to numbers or semantics according
to a rule. In scaling, the objects are text statements, usually statements of attitude,
opinion, or feeling.
When a researcher is interested in measuring the
attitudes, feelings or opinions of respondents he/she
should be clear about the following:
a)What is to be measured?
b)Who is to be measured?
c)The choices available in data collection techniques
The level of measurement refers to the relationship among
the values that are assigned to the attributes, feelings or
opinions for a variable.
Typically, there are four levels of measurement scales or
methods of assigning numbers:
(a)Nominal scale, (b)Ordinal scale, (c)Interval scale, and
(d)Ratio scale.
Nominal Scale is the crudest among all measurement scales
but it is also the simplest scale. In this scale the different scores
on a measurement simply indicate different categories. The nominal
scale does not express any values or relationships between variables.
The nominal scale is often referred to as a categorical scale. The
assigned numbers have no arithmetic properties and act only as labels.
The only statistical operation that can be performed on nominal scales
is a frequency count. We cannot determine an average except mode.
For example: labeling men as ‘1’ and women as ‘2’ which is the most
common way of labeling gender for data recording purpose does not
mean women are ‘twice something or other’ than men. Nor it suggests
that men are somehow ‘better’ than women.
Ordinal Scale involves the ranking of items along the continuum of the
characteristic being scaled. In this scale, the items are classified according to
whether they have more or less of a characteristic.
The main characteristic of the ordinal scale is that the categories have a logical or
ordered relationship. This type of scale permits the measurement of degrees of
difference, (i.e. ‘more’ or ‘less’) but not the specific amount of differences (i.e. how
much ‘more’ or ‘less’). This scale is very common in marketing, satisfaction and
attitudinal research.
Using ordinal scale data, we can perform statistical analysis like Median and Mode,
but not the Mean.
For example, a fast food home delivery shop may wish to ask its
customers:
How would you rate the service of our staff?
(1) Excellent • (2) Very Good • (3) Good • (4) Poor • (5) Worst •
Interval Scale is a scale in which the numbers are used to rank
attributes such that numerically equal distances on the scale represent equal
distance in the characteristic being measured. An interval scale contains all the
information of an ordinal scale, but it also one allows to compare the
difference/distance between attributes. Interval scales may be either in numeric
or semantic formats.
The interval scales allow the calculation of averages like
Mean, Median and Mode and dispersion like Range and Standard Deviation.
For example, the difference between ‘1’ and ‘2’ is equal to
the difference between ‘3’ and ‘4’. Further, the difference between ‘2’ and ‘4’ is twice
the difference between ‘1’ and ‘2’.
Measuring temperature is an example of interval scale. But, we cannot
say 40°C is twice as hot as 20°C.
Ratio Scale is the highest level of measurement scales.
This has the properties of an interval scale together with a fixed
(absolute) zero point. The absolute zero point allows us to
construct a meaningful ratio.
Ratio scales permit the researcher to compare both differences in
scores nd relative magnitude of scores. Examples of ratio scales
include weights, lengths and times.
For example, the number of customers of a bank’s ATM in the last
three months is a ratio scale. This is because you can compare
this with previous three months.
For example, the difference between 10 and 15 minutes is the
same as the difference between 25 and 30 minutes and 30
minutes is twice as long as 15 minutes
In comparative scaling, the respondent is asked to
compare one object with another.
The comparative scales can further be divided into the
following four types of scaling techniques:
(a)Paired Comparison Scale,
(b)Rank Order Scale,
(c)Constant Sum Scale, and
Paired ComparisonScale:
This is a comparative scaling technique in which a respondent is
presented with two objects at a time and asked to select one object
according to some criterion. The data obtained are ordinal in nature.
For example, there are four types of cold drinks Coke, Pepsi, Sprite, and Limca. The respondents can prefer Pepsi to
Coke or Coke to Sprite, etc.
RankOrder Scale:
This is another type of comparative scaling technique in
which respondents are presented with several items
simultaneously and asked to rank them in the order of
priority. This is an ordinal scale that describes the favored
and unfavoured objects, but does not reveal the distance
between the objects.
The resultant data in rank order is ordinal data. This yields
better results when direct comparison are required between
the given objects.
The major disadvantage of this technique is that only
ordinal data can be generated.
Constant Sum Scale:
• In this scale, the respondents are asked to allocate a constant sum of units
such as points, rupees, or chips among a set of s mulus objects with respect to
some criterion.
• For example, you may wish to determine how important the a ributes of
price, fragrance, packaging, cleaning power, and lather of a detergent are to
consumers. Respondents might be asked to divide a constant sum to indicate
the rela ve importance of the a ributes.
• The advantage of this technique is saving me. However, main disadvantages
are the respondents may allocate more or fewer points than those specified.
The second problem is respondents might be confused.
In non-comparative scaling respondents need only
evaluate a single object. Their evaluation is
independent of the other object which the
researcher is studying.
The non-comparative scaling techniques can be
further divided into:
(a)Continuous Rating Scale, and
(b)Itemized Rating Scale.
Con nuous Ra ng Scales:
It is very simple and highly useful. In continuous rating scale, the
respondent’s rate the objects by placing a mark at the appropriate position on
a continuous line that runs from one extreme of the criterion variable to the
other.
Example :
Question: How would you rate the TV advertisement as a guide for buying?
Itemized
Ra ng
Scales
:
Itemized rating scale is a scale having numbers or brief descriptions
associated with each category. The categories are ordered in terms
of scale position and the respondents are required to select one of
the limited number of categories that best describes the product,
brand, company, or product attribute being rated. Itemized rating
scales are widely used in marketing research.
Theitemisedratingscalescanbeinthe formof :(a)graphic,(b)
verbal,or(c)numericasshownbelow:
LikertScale:
Likert, is extremely popular for measuring attitudes, because, the method is simple
to administer. With the Likert scale, the respondents indicate their own attitudes by
checking how strongly they agree or disagree with carefully worded statements that
range from very positive to very negative towards the attitudinal object.
Respondents generally choose from five alternatives (say strongly agree, agree,
neither agree nor disagree, disagree, strongly disagree).
A Likert scale may include a number of items or statements. Disadvantage of Likert
Scale is that it takes longer time to complete than other itemised rating scales
because respondents have to read each statement.
Despite the above disadvantages, this scale has several advantages.
It is easy to construct, administer and use.
Seman c Differen alScale:
This is a seven point rating scale with end points associated with
bipolar labels (such as good and bad, complex and simple) that
have semantic meaning. It can be used to find whether a
respondent has a positive or negative attitude towards an object.
It has been widely used in comparing brands, products and
company images. It has also been used to develop advertising
and promotion strategies and in a new product development
study.
StapleScale:
The Stapel scale was originally developed to measure the
direction and intensity of an attitude simultaneously. Modern
versions of the Stapel scale place a single adjective as a
substitute for the Semantic differential when it is difficult to create
pairs of bipolar adjectives. The modified Stapel scale places a
single adjective in the centre of an even number of numerical
Values.
A number of issues decide the choice of scaling technique.
Some
significant issues are:
1)Problem Definition and Statistical Analysis,
2)The Choice between Comparative and Non-comparative
Scales,
3)Type of Category Labels,
4)Number of Categories,
5)Balanced versus Unbalanced Scale, and
6)Forced versus Non-forced Categories
THANK YOU
COLLECTION OF DATA
Data refers to information of facts often researchers understand by data only numerical figure. It also includes
facts non-numerical information qualitative and quantitative information in a research of the data are available the
research is half-complete.
Data could be broadly classified as primary data and secondary data they are also mentioned as sources of data.
Primary Data:
Primary Data is known as the data collected for the first time through field survey. Such data are collected with specific set of objectives
assess the current status of any variable studied. By survey methods the data can be collected by any one (or) more of the following ways.
to
Questionnaire (or) Schedule:
In this method a pre-printed list of questions arranged in sequence is used to elicit response from the respondent
Interview:
This is a method in which the researcher and the respondent meet and questions raised are answered and answered and recorded. This method is
adopted when personal opinion or view point are to be gathered as a part of data.
Observation:
In this method the observer applies his sense organs to note down whatever that he could observe in the field and relate these data to explain
some phenomena.
Feed Back Form:
In the case of the consumer goods the supplier or the manufacturer send the product along with a pre-paid reply cover in which questions on the product and its
usage are raised and the customer is requested to fill it up and send. Based on this first hand information about the product from the consuming public is obtained.
Sales Force opinion:
On several occasions the manufacturers or distributors collect information about the movement of the product or market size, market share etc. through sales force
on the field.
The salesman visit the retailer‟s shop to not down the details of stock movement. Availability of items etc which give valuable information.
Projective techniques:
This technique is adopted to study the consumers though methods like recalling advertisements them story completion tests etc. Through this technique it is possible
to compile information to be used as the basis for projecting the demand for the product at different points of time.
Collection through Mechanical Devices:
There are several shopping establishments where hidden video cameras are positioned at vantage points this are used for observing the public inside the ship. Apart
from helping to eliminate pilferage and theft they provide very useful information on the consumers and their preference of products
1.OBSERVATION;
Observation as a method of data collection ois used very frequently whenever collection of data through other methods is difficult
for example it is not always possible to conduct interviews with every person to collect required information. There are occasion
when no other method can be adopted for data collections. For instance, suppose a scholar wants to study the life style of hill
tribe. It is certainly not possible to use a questionnaire or schedule or interview only alternative available is observation as the
respondents would not rely any question orally or in written.
Observation may be defined as, “sensible application of sense organs in understanding less explained or unexplained
phenomena” Whenever a researcher is unable to compile information through any other method then he has to effectively apply
his sense organs to observe and explain. So it may be said that observation involves recording of information applying visual
understanding backed by alert sense organs.
Types of Observation:
Structured observation:
When observation takes place strictly in accordance with a plan or a design prepared in advance it is called structured observation
in such a type the observer decides what to observe what to focus on what type of activity should be given importance who are
all to be observed etc in advance.
Unstructured Observation:
In this type of observation there is no advance planning of what how when, who etc., of observation. The observer is given the
freedom to decide on the spot to observe everything that is relevant.
Participant Observation:
In this method the observer is very much present in the mindset of what is observed for example, suppose a researcher is studying
the life style of a hill tribe, then he might understand the life style of the tribe better only when the stays with them.
He is a participant in the sense he is physically present on the spot to observe and not influencing the activities.
Non-participant Observation:
This is a method in which the observer remain detached from whatever is happening around and does not involve himself in
any activities tapes place. He is present only to observe and not to take part in the activities. That is the target audience does
not know his presence at all. For example, the police men not in uniform is deputed on observation duty whenever a processing
tapes place.
Controlled Observation:
In this method the observer performs his work in on environment or situation, which is very much planned (or) set. For
example, sometimes to the effectiveness and alertness of airport security system a mock even (like fire accident) is carried out.
Then how the security staff reacts to such mock event is observed. Based on this the weakness on his system are noticed and
steps taken to eliminate them.
Merits of Observation Method of Data Collection: If observation is done
correctly, the scope for bias is very much minimized.

Through observation, the current scenario in which anything is happening noticed and explained there is no interpretation of how
things would be happened in the past or will happen in future etc.
 As there is no need to get any reply or details from the respondents, observation does no require any co-operation of the
respondents. This is fairly reliable method, provided the observer is well experienced trained and sincere.

 Whenever respondents are illiterate and incapable of answering any question (due to language barrier (or) cultural
background etc.,) observation is the only method of data collection available
Limitations of Observation:
This is a relatively costly method of data collection

It could be noticed that what is observed may bring out only part of the facts. While data collected through questionnaire or
interview ensure letter coverage.

There is a lot of scope for the observer to get distracted or influenced by unexpected factors which would affect the accuracy
of information collected
2 .INTERVIEW
One of the very old methods of collecting data is the interview method. Interview method involves direct or indirect meeting of th
respondents by the researcher. The researcher determines the questions to be raised at the time of interview and elicit the respons
for them. The reply given is either written down in a note book or recorded in audio or video cassette. This method has to b
necessarily adopted whenever details regarding any confidential matter are to be collected or the research requires data collectio
directly from the respondents.
Interview may be broadly classified as 1.Direct interview and 2.Indirect interview
Direct Interview:
In this type of interview, the interviewer and the interviewee meet personally either with prior appointment or not. Usually when this technique is adopted the
interviewer may brief the respondent about the purpose of interview and its scope in advance. This enables the respondent to be ready with necessary details (or)
data. This type of interview may be classified as structure a interview un structured interview focused interview clinical interview and non directive interview.
(A)structured Interview:
In this type of interview the person collecting information decides in advance the nature scope questions to be asked, the person to be contacted etc in advance. At
the time of interview no deviation is made from the questions to be asked. For example, it is usual for journalist to interview the Finance Minister after the presentation
of Budget. In such occasions, the journalist should be were prepared and decide in advance the questioned to be asked etc., Sometimes even the questions to be asked
and other details are to be submitted to the authorities concerned, before conducting the interview. The most important advantages of such interview are below.
The interview is well prepared and so the interview is conducted in the focused manner‟
Time of both the interviewer and respondents could be saved.

There is no scope for irrelevant matter to find a place in the course of interview
If the respondent is informed in advance he could prepare necessary details so that the outcome is reliable But this method of interview has the following limitations
Since the subject matter is decided in advance there is no scope for extending the interview even in case of need.
(A)Un Structured Interview:
In this type of interview, interview is conducted on the spot without any preparations (or) advance information oto
the respondent. For example, suppose an organization producing a new health drink wants to know the opinion
of the people directly. Then it might send trained field investigators who meet people directly. Then it might send
trained field investigators who meet people at random and offer them a cp of that new drink. After they drink,
their opinion is asked and the responses are noted down or recorded. Such interviews are also conducted when
opinion poll is conducted. For example during election time, the TV channels would meet people moving around
and ask them about their opinion about different parties and the one to which they would vote.
(C) Focused Interview:
In this type of interview the object of the interviewer is to focus the attention of the respondent ion a specific issue (or)
point /for example suppose a detective is questioning a person regarding a crime committed in an area. The detective has
to be very much experienced to make the person interviewed to answer only about the crime and nothing else.
In this type ,the interviewer encourages the respondents to say whatever he likes and feels on a subject matter. There may
not me much questing taking place. The respondent is free to express his views or opinions without any direction from
the interviewer.. For example suppose in a college strike, an interviewer encourage the students to say whatever they feel
above the reasons for the strike.
(E) Telephone Interview:
This is basically a type of direct interview and but there is no scope for physical presence of both the parties to the
interview. This method will be useful in the following situations. When the informant and interviewer are geographically separated.

When the study requires responses to five (or) six sample questions e.g.

Radio, TV program me survey
Questionnaire Method
A questionnaire is a sheet(s) of paper containing questions relating to certain specific aspect. Regarding which the
researcher collects the data. The questionnaire is given to the informant or respondent to be filled up. Sometimes
questionnaire is also in the form of files generated trough computer. This usually called soft copy of questionnaire.
Generally to test the reliability of the questionnaire, it should be tested on a limited scale and this is technically
known as Pilot Survey. The objective of a pilot survey is to filter unnecessary questions, and the questions which
are difficult to answer.
Open – end questions:
In these questions the respondents are given freedom to express their views as there is wide range of choice. E.g.
“How would you describe the use of this soap”?
Closed questions:
These type of questions do not allow the respondents to given answers freely E.g.
“Would you describe the smell of this soap is attractive”? Yes / No Pictorial
Questions:
In this type of questions picture are drawn, and the respondents indicate the answer by selecting the pictures he prefers.
Dichotomous questions:
In this questions two alternatives are given a positive one and a negative one. E.g.
“Do you own a watch”? Yes --------- No ------
Multiple choice questions:
These questions contains more than two alternatives e.g.
“Why have you preferred this brand of two wheeler?”
-Price
-Fuel – efficient
-comfort
-others (please specify)
Type of questions to be avoided:
(a)Leading questions:
A leading questions is one which makes it easier for the respondent to react in a certain way and is not natural. Examples of leading questions are : “Are
you against giving too much power to the trade unions”? “Don‟t you that yesterday‟s T.V. Drama was thrilling?”
(b)Loaded Questions:
Loading means attaching emotional feelings to particular words of concepts which tends to produce automatic approval or disapproval. Here the respondent would react to the word than the Question.
Example:
“Have you tried to get special favours from a business establishment by pressuring them?” Yes
---------
No----------
(c )Ambiguous questions:
An ambiguous question is one that does not have a clear meaning. It may mean different things to different people example.
Are you interested in a small house?
What does the word “interested” mean to own or hire?
What does the word “small” mean
QUESTIONNAIRE CONSTRUCTION PROCEDURE
Decide what information is needed.
Determine the type of collecting data
Interview
Questionnaire
Determine the content of individual questions.
Is question necessary
Does respondent have the information
Respondent remembers the same
Several questions needed instead of one
Determine the type of questions -open ended
-closed -dichotomous -pictorial -multiple choice

Decide on wordings of questions

Decide question sequence
-Physical appearance -easy to access
-easy to understand -motivate

Preliminary Draft

Revision and final draft
(3) SCHEDULES
Schedules (contains a set of questions) are being filled in by the enumerators who are specially appointed for the purpose.
Enumerators go to respondents, ask them questions from the proforma in the same order in which the questions are listed
and record the replies on the space given.
Enumerators should be trained Example: Population census.
Basis of Difference
Usage
Questionnaire
Respondent himself records the answers
obtained.
Schedule
Researcher/Enumerator records the answers obtained.
Cost
Relatively cheaper as it is sent by mail to the Costlier, as investigators have to be appointed, trained, and meet every informant
targeted respondents.
at their place.
Coverage
Wide coverage possible, as it can be sent to any
place by post.
Relatively limited coverage, as the investigator cannot be sent to every place.
Time Taken to Apply
Cannot be established, as the respondent may
reply at his convenience.
It is possible to plan the enquiry and depute investigators accordingly to collect
information in time.
Degree of Response
Less, as not all respondents reply.
Relatively good, as the investigator is focused and obtains details personally.
Quality of Response
Not very good, as the respondent answers based
on their own understanding.
Pre-condition for Use
The respondent should be literate and
cooperative.
Literacy of the respondent is not a limitation; the investigator explains and
obtains the response.
Sample Coverage
Possible to cover a wide range of sample
elements as questionnaires are sent by post.
Limited, as the investigator has to personally contact each respondent.
Accuracy of Information
Not likely to be high, as it depends on the
structure of the questionnaire.
Relatively better accuracy, as the investigator can verify and ensure accuracy on
the field.
Presentation Requirement
Should be designed properly and made
attractive to encourage respondents to fill it.
No such requirement.
Relatively better, as the investigator guides the respondent for proper
understanding of the questions.
Field Control and Monitoring
Not possible, as there is no direct control once
questionnaires are sent.
Good scope for monitoring and controlling the fieldwork.
SECONDARY DATA
The secondary data, are those which have already been collected some other agency and which have already been processed. Generally speaking secondary data is collected by some organization
to satisfy its own need but it is being used by various departments for different reasons. For example, census figures taken are used by social scientists (economists) for social planning and research.
SOURCES OF SECONDARY DATA:
Doing the research with the secondary data is called as Desk research. The sources for secondary data or the sources for doing desk research will be gathered by the following ways:
Internal Sources: Registers, Documents, Annual Reports, Sales Reports, previous Research papers , Sales records, invoices etc.,
External Sources: Journals on magazines, newspapers, public speeches, state and central govt., departments, reports etc., The information had from any published documents which may documents
the researcher should consider the following points:
Exactly what products are included in the statistical classification

Who originally collected the data for what purpose, and whether three might any motive for misrepresentation‟ 
From whom the data were collected and how reliable the methodology might have been and How
consistent the data are with other local or international statistics.
Pilot Study
It is difficult to plan a major study or project without adequate knowledge of its subject matter, the population it is to cover, their level of knowledge and
understanding and the like. What are the issues involved? What are the concepts associated with the subject matter? How can they be operationalise? What
method of study is appropriate? How much money it will cost? investigation is conducted. This is called pilot study. The size scope and design of the pilot
study is a matter of convenience, time and money. It should be large enough to fulfill the following functions.
Functions of Pilot Study:
It provides a better knowledge about problem.
It helps to identification and operationalization of concepts relating to the study.
It assists in discovering the nature of relationship between variables and in formulating hypothesis.\
It shows the nature of the population to be surveyed and the variability within it
It shows the adequacy of the tool for data collection‟
It provides information for structuring questions with alternative answers.
It helps the researcher to develop an appropriate plan of analysis
It provides information for estimating the probable cost and duration of the main study and of its various stages
TYPE I ERROR AND TYPE II ERROR:
In the process of testing a hypothesis, a researcher may commit two type of errors namely type I error and Type II error.
Type I error: We commit this error when we reject a null hypothesis which is true.
Type II error: This error is committed when we accept the null hypothesis which is false. This could be stated below:
Accept Ho
Reject Ho
H(true)
Type I Error
Type I Error
H(false)
Type II error
Correct Decision
Difference between Descrip ve Analysis and Inferen al Analysis
Basis of Difference
Descriptive Analysis
Inferential Analysis
Definition
Summarizes and describes the main
features of a dataset (e.g., mean, median,
frequency, graphs).
Uses sample data to make generalizations,
predictions, or decisions about a larger
population.
Purpose
To provide a snapshot or summary of the
data collected.
To draw conclusions and test hypotheses
about a population based on sample data.
Focus
Focuses only on the dataset at hand.
Focuses on making predictions
inferences beyond the dataset.
Techniques Used
Measures of central tendency (mean, Hypothesis testing, confidence intervals,
median, mode), dispersion (range, regression analysis, ANOVA, chi-square
standard deviation), tables, charts, graphs. tests.
Population vs. Sample
Describes data from the entire population
or sample without going beyond it.
Makes estimations or conclusions about a
population based on sample data.
Uncertainty
No uncertainty; purely factual about the
given data.
Involves uncertainty and probability
because it deals with generalizations.
or
Example
"The average score of students in Class A
is 75."
"We are 95% confident that the average
score of all students in the school lies
between 72 and 78."
Application
Useful for reporting, summarizing, and
organizing data (e.g., surveys, census
data).
Useful for making decisions, forecasting,
or testing theories (e.g., clinical trials,
market research predictions).
Multiple and Logistics Regression
What is Multiple Regression?
Multiple regression is a statistical technique used to examine the relationship between one dependent variable (DV) and two
or more independent variables (IVs).
It extends simple regression (which uses only one IV) to allow for more complex real-world situations.
The Basic Formula:
Y=a+b1X1+b2X2+...+bnXn+eY = a + b_1X_1 + b_2X_2 + ... + b_nX_n + eY=a+b1X1+b2X2+...+bnXn+e Where:
•Y = Dependent variable (outcome)
•X1, X2, ..., Xn = Independent variables (predictors)
•a = Intercept
•b1, b2, ..., bn = Regression coefficients (effect of each IV)
•e = Error term
Why Do We Use Multiple Regression?
•To predict the value of the dependent variable.
•To understand the impact of each independent variable on the dependent variable while controlling for others.
•To test hypotheses and relationships between variables in business, marketing, HR, finance, etc.
Key Outputs to Know:
•R (Multiple Correlation): How strongly all IVs together relate to DV.
•R² (Coefficient of Determination): % of the DV’s variance explained by IVs.
•Adjusted R²: Adjusts R² for the number of predictors (important when you have many variables).
•Regression Coefficients (b values): Show direction & strength of each IV’s effect.
•Significance (p-value): Tests if each IV’s effect is statistically significant.
Business Uses:
•Predicting sales, profits, market share.
•Analyzing employee performance drivers.
•Estimating customer satisfaction based on service features.
Basic Assump ons of Mul ple Regression (with Examples)
1. Linearity
What it means:
The relationship between the dependent variable (DV) and each independent variable (IV) is linear.
Example:
You study the impact of advertising spend (X1) and sales force size (X2) on sales revenue (Y). The assumption is that
doubling advertising budget will approximately double its effect on sales, not have a curved or unpredictable effect.
2. Independence of Errors (No Autocorrelation)
What it means:
The residuals (errors) are independent of each other. Especially important in time-series data.
Example:
You predict quarterly profits using past sales and marketing spend. If the error in Q1 affects the error in Q2 (like patterns
in time), this violates the assumption.
3. Homoscedasticity (Equal Variance of Errors)
What it means:
The residuals have constant variance at every level of the IVs.
Example:
Imagine you're predicting employee productivity based on hours of training and experience. If the prediction errors are small
for junior employees but large for seniors, it’s a sign of heteroscedasticity (a violation).
4. No Multicollinearity What it means:
The IVs should not be too highly correlated with each other.
Example:
In a model predicting company performance, if you include both total assets and total liabilities, these may be highly
correlated (since both relate to the balance sheet), causing multicollinearity issues.
5. Measurement Level (Interval or Ratio Data)
What it means:
The dependent variable should be continuous (interval or ratio scale).
Example:
Predicting market share % using predictors like ad spend, pricing strategy, etc., is valid because market share is a
continuous variable. But using regression to predict a categorical outcome (e.g., buy/not buy) would require logistic
regression, not multiple regression.
What is Logistic Regression?
Logistic regression is a statistical method used to predict the probability of a binary outcome (yes/no, success/failure,
buy/don’t buy) based on one or more independent variables.
It is used when the dependent variable (DV) is categorical, typically binary (0 or 1). Like True/false, Yes/No
Example:
Objective: Predict if a customer will purchase (1) or not purchase (0)
based on: •X1 = Age
•X2 = Income
The output tells us the probability of purchase, such as:
•"A 30-year-old with $50,000 income has a 72% chance of buying."
When to Use Logistic Regression:
•Customer churn prediction (stay/leave)
•Loan default prediction (default/no default)
•Email classification (spam/not spam)
•Employee attrition (stay/quit)
Assumptions of Logistic Regression:
1.Binary DV: Outcome should be dichotomous.
2.Independent Observations: No repeated measures or time-series unless handled properly.
3.Little or No Multicollinearity: IVs should not be highly correlated.
4.Linearity of Logit: IVs and log odds should have a linear relationship (can check with Box-Tidwell test).
5.Large Sample Size: Logistic regression needs enough cases, especially for rare events.
INTERPRETATIONS
ANOVA
METHODS
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
17.500
25
.700
1.120
.517
Within Groups
2.500
4
.625
Total
20.000
29
1.Null Hypothesis (H₀):
All teaching methods have the same mean score.
2.Alternative Hypothesis (H₁):
At least one teaching method has a different mean score.
3.F-value:
The F-statistic is 1.120, which compares variance between groups to variance within groups.
4.p-value (Sig.):
The significance level is 0.517.
Conclusion:
•Since p = 0.517 > 0.05, we fail to reject the null hypothesis.
•There is no statistically significant difference in test scores among the different teaching methods in this sample.
Correlation Between hour studies and exam score
Correla ons
Pearson Correla on
Hour Studies
Exam Score
Hour Studies
Exam Score
1
.987**
Sig. (2-tailed)
.000
N
10
10
Pearson Correla on
.987**
1
Sig. (2-tailed)
.000
N
10
**. Correla on is significant at the 0.01 level (2-tailed).
10
Correlation
•Correlation coefficient (r) = 0.987, which means a very strong positive relationship.
•Sig. (2-tailed) < 0.01, so the result is statistically significant at the 1% level.
Interpretation:
As the number of hours studied increases, exam scores also increase. The Pearson correlation is
0.987, indicating a very strong, statistically significant positive correlation between the two variables.
Correla ons
Hour Studies
Pearson Correla on
Hour Studies
Exam Score
A endance
1
.987**
.987**
.000
.000
Sig. (2-tailed)
Exam Score
A endance
N
13
13
10
Pearson Correla on
.987**
1
.979**
Sig. (2-tailed)
.000
N
13
13
10
Pearson Correla on
.987**
.979**
1
Sig. (2-tailed)
.000
.000
N
10
10
.000
10
**. Correla on is significant at the 0.01 level (2-tailed).
All correlations are very strong positive, and statistically significant
at 0.01 level.
Interpretation: More study hours and better attendance are both strongly
associated with higher exam scores.
Scenario for Multiple Regression:
A researcher investigates how Hours Studied (X₁) and Class Attendance (X₂) affect Exam Scores (Y) among 100 students.
Sample Mul ple Regression Output:
Variable
Coefficient (B)
Standard Error
t-value
p-value
(Constant)
40.50
5.20
7.79
0.000
Hours Studied (X₁)
2.80
0.45
6.22
0.000
Class A endance
(X₂)
1.50
0.60
2.50
0.014
Model Summary:
•R = 0.75
•R² = 0.56
•Adjusted R² = 0.55
•F(2, 97) = 62.30, p < 0.001
Interpretation:
1.Model Fit:
•The R² = 0.56 means that 56% of the variance in Exam Scores is explained by the two predictors (Hours Studied and
Class Attendance). This suggests a good fit of the model.
•The F-statistic (62.30, p < 0.001) shows the overall model is statistically significant, meaning at least one of the predictors
significantly affects exam scores.
2.Coefficients:
•Intercept (40.50): When both Hours Studied and Class Attendance are zero, the expected exam score is 40.50 marks.
•Hours Studied (2.80, p < 0.001): For every additional hour of study, exam scores increase by 2.8 marks, holding attendance
constant. This effect is highly significant.
•Class Attendance (1.50, p = 0.014): For every additional class attended, exam scores increase by 1.5 marks, holding
study hours constant. This is also statistically significant at the 5% level.
3.Significance:
•Both predictors have p-values < 0.05, so they are significant contributors to predicting exam scores.
•Hours Studied has a stronger effect (higher coefficient and t-value) compared to Class Attendance.
In the simple language:
The study finds that students who study more hours and attend more classes tend to score higher on exams.
Specifically, every extra hour of study increases scores by about 2.8 points, and attending an extra class adds about 1.5 points.
The model explains 56% of the variation in exam scores, making it a reliable prediction tool in this context.
Example
A company wants to study how Adver sement Budget and Brand Name Strength impact Total Sales. They collect the following
data for 10 products:
Interpreta on:
•Model Fit:
The R² value is 0.90, meaning 90% of the variance in Total Sales is explained by Advertisement Budget and Brand
Name Strength.
•Coefficients: • Advertisement (X₁): For every additional $1000 spent on advertising, sales increase by $5000 (B
= 5.00), holding brand strength constant.
• Brand Name Strength (X₂): Each 1-point increase in brand name strength (on a 10-point scale) increases sales
by $8000 (B = 8.00), holding ad budget constant.
•Significance:
• Both independent variables are statistically significant (p < 0.05), indicating they both meaningfully predict
sales.
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