STUDY MATERIAL
BSM 224: RESEARCH TECHNIQUES
BACHELOR OF BUSINESS ADMINISTRATION
AND
BACHELOR OF SCIENCE IN ACCOUNTING AND
FINANCE
@TU
RESEARCH TECHNIQUES (BSM 224)
TABLE OF CONTENTS
COURSE NAME : RESEARCH TECHNIQUES ..................Ошибка! Закладка не определена.
LECTURE ONE ................................................................................................................ 10
INTRODUCTION TO RESEARCH METHODS .............................................................. 10
1.0 Introduction ............................................................................................................... 11
1.1 Role of Research in Business Decision’s ...................................................................... 11
1.2 Research Process........................................................................................................ 12
1.3 Types of Research ...................................................................................................... 12
1.3.1 Exploratory Research: - ............................................................................................... 12
1.3.2....................................................................................................................................... 13
Descriptive Research: - ......................................................................................................... 13
1.3.3 Analytical research: - ................................................................................................... 13
1.3.4 Causal Research: -........................................................................................................ 13
1.3.5 Quantitative Research: - ............................................................................................... 13
1.3.6 Qualitative Research: -................................................................................................. 13
1.3.7....................................................................................................................................... 13
Conceptual Research: - ......................................................................................................... 13
1.3.8 Modelling Research: - .................................................................................................. 14
1.4 Criteria of good research ............................................................................................ 14
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LECTURE TWO ............................................................................................................... 15
RESEARCH PROBLEM ................................................................................................... 15
2.0 Introduction: .............................................................................................................. 15
2.1 What is a Research Problem? ..................................................................................... 15
2.3 Statement of the Problem .......................................................................................... 16
2.3 Steps involved in defining a Problem ......................................................................... 16
LECTURE THREE ........................................................................................................... 18
RESEARCH DESIGN........................................................................................................ 18
3.0 Introduction: .............................................................................................................. 18
3.1 Meaning, Need and Features of a Research Design ..................................................... 18
3.2 Need for Research Design:.......................................................................................... 19
3.4 Elements of a Research Design: .................................................................................. 19
3.5 Different Research Designs: ........................................................................................ 21
3.5.1 Different types of Exploratory Research ..................................................................... 21
3.5.2 Research Design in case of Descriptive Research: - .................................................... 21
LECTURE FOUR .............................................................................................................. 23
METHODS OF DATA COLLECTION ............................................................................. 23
4.0 Introduction: .............................................................................................................. 23
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4.1 Data: Definition.......................................................................................................... 23
4.1.1. Qualitative data: .......................................................................................................... 23
4.1.2 Quantitative data: ......................................................................................................... 23
4.1.3 Primary data: -.............................................................................................................. 24
4.1.4 Secondary data: -.......................................................................................................... 24
4.2 Collection of primary data .......................................................................................... 24
4.2.1 Observation method ..................................................................................................... 24
4.2.2 Interview method ......................................................................................................... 25
4.2.3. Collection of data through questionnaires .................................................................. 26
4.3 Guidelines for constructing questionnaire .................................................................. 26
4.4 Collection of Secondary Data ...................................................................................... 27
LECTURE FIVE................................................................................................................ 28
DATA ANALYSIS ............................................................................................................. 28
5.0 Introduction: .............................................................................................................. 28
5.1 Data Entry .................................................................................................................. 28
5.2 Decision on File Format .............................................................................................. 28
5.3 Devise Code for Analysis ............................................................................................ 28
5.4 Processing of Data...................................................................................................... 29
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5.4.1 Frequency Distribution ................................................................................................ 29
5.4.2 Cumulative Frequency Distribution ............................................................................. 30
5.4.3 Relative Frequency Distribution .................................................................................. 30
5.5 Presenting Data ......................................................................................................... 30
5.3 Measures of Central Tendency ................................................................................... 31
5.3.1 The mode ..................................................................................................................... 31
5.3.2 The median................................................................................................................... 31
5.3.4 Standard deviation ....................................................................................................... 32
LECTURE SIX .................................................................................................................. 33
LEVELS OF MEASUREMENT ........................................................................................ 33
6.0 Introduction ............................................................................................................... 33
6. 1 Types of Measurement Scales ................................................................................... 34
6.1.1 Nominal scale............................................................................................................... 34
6.1.2 Ordinal Scale ................................................................................................................ 34
6.1.3 Interval Scale .............................................................................................................. 35
6.1.4 Ratio Scale ................................................................................................................... 36
6.2 Important Scaling Techniques..................................................................................... 38
6.2.1 Rating Scales:............................................................................................................... 38
6.2.2 Ranking Scales: ............................................................................................................ 38
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6.2.3 Scale construction techniques: .................................................................................... 38
LECTURE SEVEN ............................................................................................................ 42
SAMPLING DESIGN ........................................................................................................ 42
7.0 Introduction: .............................................................................................................. 42
7.1 Need for Sampling...................................................................................................... 42
7.2 Concept of Population and Sample ............................................................................ 42
7.2.1 Descriptive statistics .................................................................................................... 42
7.2.2 Inferential statistics ...................................................................................................... 43
7.3 Population ................................................................................................................. 43
7.4 Sample ....................................................................................................................... 43
7.5 Sampling Frame ........................................................................................................ 43
7.6 Census and Sample Survey ......................................................................................... 43
7.7 Types of Sampling ...................................................................................................... 44
7.7.1 Non-Probability Sampling Methods: ........................................................................... 44
7.7.2 Convenience Sampling ................................................................................................ 44
7.7.3 Judgment Sampling...................................................................................................... 45
7.7.4 Quota Sampling ........................................................................................................... 46
7.7.5 Snowball Sampling ..................................................................................................... 46
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7.8.1 Simple Random Sampling ........................................................................................... 47
7.8.2 Selection of a Simple Random Sample:....................................................................... 47
7.8.3 Lottery Method ............................................................................................................ 47
7.8.4 Stratified Random Sampling ........................................................................................ 48
7.8.5 Systematic Random Sampling .................................................................................... 49
7.8.6 Cluster Sampling.......................................................................................................... 50
7.8.7 Multistage Sampling .................................................................................................... 50
7.9 Sample size and its determination .............................................................................. 51
7.10 Sampling Distributions ............................................................................................. 52
7.11 Central Limit Theorem: ............................................................................................. 53
7.12 The Sample Distribution ........................................................................................... 54
7.12.1 Relationship between Population, Sample and Sampling Distribution ..................... 56
7.12.2 Sampling distribution of mean: ................................................................................. 56
LECTURE EIGHT ............................................................................................................ 58
TESTING OF HYPOTHESES ........................................................................................... 58
8.0 Introduction ............................................................................................................... 58
8.1 What is Hypothesis? ................................................................................................... 59
8.2 Procedure for Hypotheses Testing .............................................................................. 59
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8.3 Type I and Type II Errors ............................................................................................. 61
8.3.1 One-Tailed and Two-Tailed Tests ............................................................................... 63
LECTURE NINE ............................................................................................................... 65
IMPORTANT SAMPLING DISTRIBUTIONS ................................................................. 65
9.0 Introduction ............................................................................................................... 65
9.1 Z TEST: Tests of Hypothesis Concerning Large Samples................................................ 65
9.2 Theory for Small Samples ........................................................................................... 68
9.3.1 Degrees of freedom: ..................................................................................................... 69
9.4. CHI SQUARE TEST ...................................................................................................... 74
9.4.1 Degrees of Freedom ..................................................................................................... 75
9.4.2 Properties of Chi- Square distribution ......................................................................... 76
9.4.5 USES OF ψ2TEST....................................................................................................... 76
9.4.6 Conditions For Applying The Chi-Square Test ........................................................... 77
9.4.7 Working Rule For ψ2 -Test ......................................................................................... 77
9.4.7 Ψ2 Test For Goodness of Fit........................................................................................ 78
9.4.8 Ψ2 Test As A Test Of Independence ........................................................................... 79
LECTURE TEN ................................................................................................................. 80
REPORT WRITING.......................................................................................................... 80
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10.0 Introduction: ............................................................................................................ 80
10.1 Steps in Writing Report ............................................................................................ 81
10.2 Layout of the Research Report: ................................................................................ 82
10.4 Precautions for Writing a Research Report ............................................................... 83
4.
Schutt R. K. (2006) Investigating the social world: the process and practice of
research, 5th edition, Sage Publications Ltd, London ......................................................... 84
PREFACE
Course Description;
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The course provides a critical appreciation of theoretical and practical foundation necessary for
problem identification and investigation in order to come out with answers solving managerial
problems as well as adding to the existing knowledge. The course places the main issues on
problem identification, methods of investigation, analysis and interpretation so as to come up
with solutions that affect society politically, socially, economically, and culturally and other
aspects.
Course Objectives/Learning Outcomes;
1) To engage students in a detailed exposition on research methods used.
2) To equip students with analytical tools to appreciate the multi-disciplinary approach in
research.
3) Provide a firm foundation to students in order to develop research proposals and research
reports
Expected Learning Outcomes;
1) Be able to develop a research proposal and report.
2) Use analytical tools to appreciate the multi-disciplinary approach in research.
3) understand a firm foundation to students in order to develop research proposals and
research reports
COURSE OUTLINE
1. Overview of research
 Types of research
 Preparing for research
 Presenting findings
6hrs
2. The nature of research
 Purposes of research
 Characteristics of scientific inquiry and problems of research
 Challenges in undertaking research
 Qualities of a good research.
5hrs
3. The research problem and research objectives
 Identifying the problem
 Stating the research problems
 Setting research objectives
 Setting research questions
6hrs
4. Literature Review
3hrs
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Sources of literature
Collecting relevant materials
Referencing
5. Theoretical analysis
 Theoretical framework
 Conceptual framework
 Research variables and how they are related to one another
 Causal inferences
 Co-variation.
6hrs
6. Research Methods
 Research designs
 Data collections
 Data sources
 Data sampling
 Data processing
8hrs
7. Data analysis
 Quantitative and Qualitative data analysis
 Scales measurements
6hrs
8.
10hrs
Writing research Proposals and Research Reports
Principles of writing
Research Proposal
Report writing
Total lecture hours= 50
Mode of assessment
Course work
40%
Final exam
60%
Teaching methods
Face to face lectures, hand outs, group and class discussions
References
1. Punch, K. F. (2005) Introduction to Social Research: Quantitative and Qualitative
Approaches, Second Edition, Sage Publications Ltd, London
2. Schutt R. K. (2006) Investigating the social world: the process and practice of research, 5th
edition, Sage Publications Ltd, London
LECTURE ONE
INTRODUCTION TO RESEARCH METHODS
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Lecture outline:
 Introduction
 The role of research in business decisions
 Research process
 Types of research
 Criteria for good research
1.0 Introduction
This lecture introduces you to research methods which are very essential in analyzing problems
often encountered in our environment. We shall look at the research process, types of research
and criteria for a good research.
Research forms a cycle. It starts with a problem and ends with a solution to the problem. The
problem statement is therefore the axis which the whole research revolves around, because it
explains in short the aim of the research.
1.1 Role of Research in Business Decision’s
Research is a process of using the methods of science to the art of management for decisionmaking. Every organization operates under some degree of uncertainty. This uncertainty cannot
be eliminated completely, although it can be minimized with the help of research methods.
Research is particularly important in the decision making process of various business
organizations.
To choose the best line of action (in the light of growing competition and increasing
uncertainty); it is very important that one should be able to gather all the data, analyze it and
reach to the appropriate decisions. Research in common context refers to a search for knowledge.
It can also be defined as scientific and systematic search for gaining information and knowledge
on a specific topic or phenomena. In management research is extensively used in various areas.
Research provides a base for your business sound decision - making. There are three parts
involved in any of your systematic finding: Implicit question posed, explicit answer proposed
and Collection, analysis, and interpretation of the information leading from the question to
answer Illustration. “Research comprises of defining and redefining problems, formulating
hypothesis or suggested solutions; making deductions and reaching conclusions; and at last
carefully testing the conclusions to determine whether they fit the formulating hypothesis”.
Market Research has become an important part in management decision-making. Marketing
research is a critical part of such a Market intelligence system; it helps to improve management
decision making by providing relevant, accurate, & timely information. Every decision poses
unique needs for information gathered through marketing research. Thus, we can say that
marketing research is the function that links the Consumer, Customer, and the public to the
marketer through information used to identify and define marketing opportunities and problems;
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Generate, Refine, and evaluate marketing actions and monitor marketing performance; improve
understanding of marketing as a process.
1.2 Research Process
i. Selecting A Topic: Topic is related to the area of interest.
ii. Literature Search: A researcher should be aware of the current research in the related area
and further scope of expansion.
iii. Discussion with "Informants and Interested Parties"
iv.
Sampling (described in Chapter VI)
v. . Formulating Your Hypothesis (described in Chapter VII)
vi.
Questionnaire Design -Translating the broad objectives of the study into questions that
will obtain the necessary information.
vii.
Fieldwork - Collection of data through questionnaire or interview
viii. Data Processing - coding and inputting the responses
ix. Statistical Analysis (hypotheses testing)
x. . Assembly of Results
xi. Writing up the Results- drawing conclusions / interpretations and relating the findings to
other research. You will have been given separate notes on report writing.
1.3 Types of Research
A research can be classified as follows
o Exploratory Research
o Descriptive Research
o Analytical Research
o Causal Research
o Quantitative Research
o Qualitative Research
o Conceptual Research
o Modeling Research
1.3.1 Exploratory Research: The Exploratory Research structures and identifies new problems; it is an initial research which
is commonly unstructured, “informal” research that is undertaken to gain background
information about the general nature of the research problem, without having any specific endobjective. It is usually conducted when the researcher does not know much about the problem
and needs additional information or desires new or more recent information. A research that
analyzes the data and explores the possibility of obtaining as many as relationships as possible
between different variables of the study.
Ex: - Literature Survey, Experience survey.
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1.3.2 Descriptive Research: Descriptive research is more rigid than exploratory research, this research carries out specific
objectives and hence it results to a definite conclusion. Descriptive research is undertaken to
provide answers to questions of who, what, where, when, and how – but not why. For example, it
describes users of a product, determines the proportion of the population that uses a product, or
predicts future demand for a product or describes the happening of a certain phenomenon. As
opposed to exploratory research, if you are doing descriptive research you should define
questions, people surveyed, and the method of analysis prior to beginning data collection.
1.3.3 Analytical research: This type of research is used where information is already available, and analyzes these to make
a critical evaluation of the material.
Analytical research takes descriptive research one stage further by seeking to explain the reasons
behind a particular occurrence by discovering causal relationships. Once causal relationships
have been discovered, the search then shifts to factors that can be changed (variables) in order to
influence the chain of causality. Typical questions in analytical research are: What factors
might account for the high drop-out rate on a particular degree programme?
Typical methods used in analytical research include:
 Case studies
 Observation
 Historical analysis
 Attitude surveys
 Statistical surveys
1.3.4 Causal Research: Casual Research seeks to find cause and affect relationships between variables. It accomplishes
this goal through laboratory and field experiments.
1.3.5 Quantitative Research: This research answers the questions about data that can be measured in terms of quantity or
amount. It is applicable to phenomena that can be expressed in terms of quantity.
1.3.6 Qualitative Research: This research involves analysis of data such as words (e.g., from interviews), pictures (e.g.,
video), or objects (e.g., an artifact). Answer questions about nature of phenomena in order to
describe phenomena and understand it from the participant’s point of view.
1.3.7 Conceptual Research: This type of research is related to some ideas or theory and generally used by philosopher.
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1.3.8 Modelling Research: This type of research is related to business situation where business situation is formulated into
different types of model. Ex:-Mathematical model, simulation models
1.4 Criteria of good research
One thing that is important is the research work and the studies meet on the common ground of
the scientific method. One expects scientific research to satisfy the following criteria.
1. The purpose of research should be clearly defined and common concepts be used.
2. The research procedure used should be described in sufficient detail to permit another
researcher to repeat the research for further advancement.
3. The procedural design of the research should be carefully planned to yield results that are
as objective as possible.
4. The researcher should report with complete frankness, flaws in procedural designs and
estimate their effects upon the findings.
5. The analysis of data should be sufficiently adequate to reveal its significance and the
methods of analysis used should be appropriate.
6. Conclusion should be considered to those justified by the data of the research and limited
to those for which the data provide an adequate basis.
7. Greater confidence in research is warranted if the researcher is experienced, has a good
reputation in research.
In other words we can state the qualities of a good research as under:
1. Good research is systematic: it means that research is structured with specified steps
to be taken in a specific sequence in accordance with well defined set of rules.
2. Good research is logical: this implies that research is guided by the rules of logical
reasoning and logical process of induction and deduction are of great value in
carrying out research.
3. Good research is empirical: it implies that research is related basically to one or more
aspects of real situation and deals with concrete data that provides a basis for external
validity to research results.
4. Good research is replicable: this characteristic allows research results to be verified
by replicating the study and thereby building a sound basis for decisions.
Review Questions:
1. Describe the steps that should be followed when carrying out research.
2. Explain the different types of research
3. State the qualities of a good research.
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LECTURE TWO
RESEARCH PROBLEM
Lecture Outline:
 Introduction
 Definition of a research problem
 Sub problem
 Statement of the problem
 Steps in defining a problem
 Testing feasibility of the research problem
2.0 Introduction:
In our first lecture we saw that we need to carry out research because of a problem that exists and
needing a solution. So in this lecture we shall find out how a problem can be identified and
defined. We also highlight tests that are carried out to find out if the problem to be investigated is
feasible.
Lecture objectives:
By the end of this lecture, you should be able to;
 Easily identify a research problem in any given scenario
 Write the statement of the problem for the identified research problem
2.1 What is a Research Problem?
A research problem is the situation that causes the researcher to feel apprehensive, confused and
ill at ease. In other words, it refers to some difficulty which a researcher experiences in context
of a situation and wants to obtain the solution for the same. It is the demarcation of a problem
area within a certain context involving the WHO or WHAT, the WHERE, the WHEN and the
WHY of the problem situation. There are many problem situations that may give rise to research.
Three sources usually contribute to problem identification.
 Own experience or the experience of others may be a source of problem supply.
 A second source could be scientific literature. You may read about certain findings and
notice that a certain field was not covered. This could lead to a research problem.
 Theories could be a third source. Shortcomings in theories could be researched.
The research problem should be stated in such a way that it would lead to analytical thinking on
the part of the researcher with the aim of possible concluding solutions to the stated problem.
Research problems can be stated in the form of either questions or statements.
 The research problem should always be formulated grammatically correct and as
completely as possible. You should bear in mind the wording (expressions) you use.
Avoid meaningless words. There should be no doubt in the mind of the reader what your
intentions are.
 Demarcating the research field into manageable parts by dividing the main problem into
sub-problems is of the utmost importance.

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2.2. Sub-problem(S)
Sub-problems are problems related to the main problem identified. Sub problems flow from the
main problem and make up the main problem. It is the means to reach the set goal in a
manageable way and contribute to solving the problem.
2.3 Statement of the Problem
The statement of the problem involves the demarcation and formulation of the problem, i.e., the
WHO/ WHAT, WHERE, WHEN, WHY. It usually includes the statement of the hypothesis.
2.3 Steps involved in defining a Problem
1) Statement of a problem should be given in broad general way: For example in case of a
social research it is advisable to perform some field operations, collect the survey, study it,
and then phrase the problem in operational terms.
2) Understanding the origin and the nature of the problem clearly: It is essential to know the
point of origin of the problem and discuss the problem with those who has a better
knowledge of the concerned area.
3) Survey all the literature available and examine them before defining a research problem.
4) Finally rephrase the research problem in to a walking proposition.
2.4 Checklist for Testing the Feasibility of the Research Problem
YES NO
1
Is the problem of current interest? Will the research results have social,
educational or scientific value?
2
Will it be possible to apply the results in practice?
3
Does the research contribute to the science of education?
4
Will the research opt new problems and lead to further research?
5
Is the research problem important? Will you be proud of the result?
6
Is there enough scope left within the area of research (field of research)?
7
Can you find an answer to the problem through research? Will you be able to
handle the research problem?
8
Will it be practically possible to undertake the research?
9
Is the research free of any ethical problems and limitations?
10 Will it have any value?
11 Do you have the necessary knowledge and skills to do the research? Are you
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qualified to undertake the research?
12
Is the problem important to you and are you motivated to undertake the
research?
13
Is the research viable in your situation? Do you have enough time and energy to
complete the project?
14 Do you have the necessary funds for the research?
15 Will you be able to complete the project within the time available?
16
Do you have access to the administrative, statistic and computer facilities the
research necessitates?
TOTAL:
Review Questions
1. Review the prevailing circumstances in your environment and identify any problem that needs
a solution. Transform that problem into a problem statement which is researchable.
2. Explain how you can evaluate the feasibility of the statement of proble.
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LECTURE THREE
RESEARCH DESIGN
Lecture Outline:
 Introduction
 Meaning, need and features of a research design
 Elements of a research design
 Types of research designs
3.0 Introduction:
This lecture introduces you to a plan for a researcher and looks at the techniques for data
collection and analysis. It also looks at the population to be surveyed.
Lecture Objectives:
By the end of this lecture, you should be able to;
 Describe the different parts of a research design
 State the features of a good research design
 Identify a research design suitable for investigating a specific problem.
3.1 Meaning, Need and Features of a Research Design
A research design is the plan or strategy, which helps in arranging the resources required for
research purpose. It acts as a path or blueprint for the researcher. In other words, it is the
advanced planning of the steps to be adapted for collection of relevant data and techniques to be
used in their analysis keeping different time and budget constraint in mind. Along with the
population to be surveyed, size of sample, tools for analyzing data, interpretation of data, it also
includes the budget and the time constraints too.
The Design decision is in respect to following terms:
 What is the study about?
 Why to study a particular topic?
 Where the study will be conducted?
 Techniques to collect the relevant data?
 What will be the sample design?
 How will the data be analyzed?
 What is the time required?
 What is the allocated Budget?
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3.2 Need for Research Design:
It helps for a smooth running of various research operations thereby making the research
efficient, gaining maximum information with the minimum expenditure of time, effort, and
money. The Research Design is divided into following parts:-
Research Design
Operational Design
Sampling Design
Observational Design
Statistical Design
(Sub-divisions of a Research Design)
Sampling Design: It deals with method of selection of samples to be collected /observed for a
given study.
Observational Design: It deals with the constraints and exceptions under which the observations
are to be made.
Statistical Design: It deals with the editing, coding and analysis of the data gathered.
Operational Design: It deals with the techniques by which the procedures specified in the
above designs can be carried out.
3.3 Features of a Good Design
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It should define the objective of problem to be studied
It should minimize the biasness and maximize the reliability of data
It should give smallest experimental error
It should be flexible enough to permit the consideration of many different aspects of a
phenomenon.
3.4 Elements of a Research Design:
The important elements of a research design are:
 Introduction: The Research proposal should define the research problem and the
researcher’s precise interest in studying it. In other words it deals with the scope of study.
 Statement of the problem: It includes the formulation of problem which actually explains
the objective of research.
 Literature Review: It includes a review of different literatures and articles related to
objective of study. It is performed to get all the information’s and researches done on the
topic earlier.
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Scope of Study: A complete study of any problem is difficult to study as it would entail
an overwhelming amount of data. Therefore, the scope and dimensions of the study
should be delimited with reference to its depth, length, and geographical area to be
covered, reference period, respondents to be studied and many other different issues. We
should consider the time frames decided for the study and should finish it within the same
tome slot.
Objective of Study: The questions to which the researcher proposes to seek answers
through the study, comes under objectives. It should be stated clearly. For example:
I. To study the nature of …………………
II. To investigate the impact of ……………………..
III. To examine the nature of relation between ………… and …………………
IV. To identify the causes of ………………………
The objective statements should not be vague like “to explore unemployment in India”
Conceptual Model: After completing the above steps the researcher formulates and
develops the structure of relationships among the variables under investigation.
Hypotheses: A hypothesis is a specific statement of prediction. They refer to different
possible outcomes.
Operational definition of concepts: It involves the different techniques used in
exploratory and descriptive research in operational terms.
Significance of study: It is a careful statement of the value of the study and the possible
applications of its findings which helps to justify purpose of study, its importance and
social relevance.
Geographical area to be covered: The territorial area to be covered depends on the
purpose, nature of study and availability of resources. It should be decided and specified
in the research plan.
Reference Period: This refers to the time period of which the data is analyzed. Also it
depends on the availability of data.
Sampling Plan: It is the study that requires collection of data from the fields, then we
should decide the population to be selected for study and the sampling design.
Tools for Gathering data: Personal and Telephonic Interviews, Questionnaire, checklist
are different tools for data collection.
Plan of Analysis: This includes the statistical techniques used for editing, coding and
analysis of data.
Chapter Scheme: The chapter scheme of report or dissertation should be prepared to give
the outlines and the studies of the research conducted.
Time Budget: The time period of research should be decided in advance and the research
work should not exceed the time limits. This leads to loss of resources and extra cost is
involved.
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
Financial Budget: The cost of the project includes major categories like salary, printing,
stationery, postage, travel expenses etc.
3.5 Different Research Designs:
Research Design in case of Exploratory Research: -It is also termed as Formulative Research
Studies. In this case we do not have enough understanding of the problem. Its main purpose is
more precise investigation about the objective of study. It is particularly useful when researchers
lack a clear idea of the problems they will meet during the study. Through this the researcher
develops more clear concepts, establishes priorities, develop operational definitions also. This
means that a general study will be conducted without having any end-objective except to
establish as many relationships as possible between the variables of study. The Research Design
in such studies must have inbuilt flexibility because the research problem broadly defined
initially, is transformed into one with more precise meaning. This type of research lay the
foundation for formulation of different hypotheses of research problems. It involves the study of
secondary data. It rarely involves structured questionnaire, large samples and probability
sampling plans.
3.5.1 Different types of Exploratory Research
 Literature Survey: It is a study involving a collection of literatures in the selected area in
which the researcher has limited experience, and critical examination and comparison of
them to have better understanding. It helps in updating the past data related to the topic of
research. It also helps in formulation of relevant hypothesis if it is not formed.
 Experience Survey: It is a survey of experiences of experts/specialists related to the field
of research which acts as a database for future research. This helps in generating ideas
with minimum data collection. The decision making in the probabilistic situations is a
complex process therefore the study of the experiences of the executives/researchers can
be carried out using experience survey. Bidding of Tenders, Technology forecasting,
Manpower and Materials planning, Production Scheduling, Portfolio Decisions etc. are
examples of experience survey.
3.5.2 Research Design in case of Descriptive Research: It is carried out with specific objectives and hence a definite end-result. It is structured research
with clearly stated hypothesis or investigative questions. It deals with describing the
characteristics associated with the population chosen for research, Estimates of the proportions
of a population that have these characteristics and discovery of relationship among several
variables. It is based on large representative samples. The design in such studies must be rigid
and focus attention on the following:
 What is the study about and why is it done?
 Designing methods of data collection.
 Selecting the sample.
 Processing and analysis of data.
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

Interpretations of Results.
Budget and Time Constraints.
For example: to describe characteristics of consumers, sales people, market areas or
organizations.
Longitudinal Studies
Longitudinal studies are time series analyses that make repeated measurements of the same
individuals, thus allowing you to monitor behavior such as brand switching. However,
longitudinal studies are not necessarily representative since many people may refuse to
participate because of the commitment required.
Cross-sectional Studies
Cross-sectional studies sample the population to make measurements at a specific point in time.
A special type of cross-sectional analysis is a cohort analysis, which tracks an aggregate of
individuals who experience the same event within the same time interval over time. You can use
Cohort analyses for long forecasting of product demand.
Research Design in case of Causal Research: -When it is necessary to determine that one
variable determines values of other variables, causal research design is used. Thus the
relationship between different variables is established. It is a research design in which the major
emphasis is on determining a cause-and-effect relationship. When we start the research work it is
not necessary that only one type of research is used, we can use a combination of two or all the
three types of research. Also research is an unending process, so there may be a clue left, which
can initiate a research objective for other researchers.
Review Questions
1. Explain why we need a research design.
2. Describe the elements of a research design.
3. When are the different research designs suitable?
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LECTURE FOUR
METHODS OF DATA COLLECTION
Lecture outline:
 Introduction
 Collection of primary data
 Collection of data through questionnaires
 Guidelines for construction of a questionnaire
 Collection of secondary data.
4.0 Introduction:
In this lecture we shall look at the different methods that are used to collect data. We start by
defining data and explore the primary and secondary methods of data collection. We shall go
ahead and look at guidelines for constructing a questionnaire.
4.1 Data: Definition
Data: collection of any number of related observations.
Statistical data are basic material needed to make an effective decision in a particular situation. It
is a continuous process of measuring, counting and observing. It is necessary because
 It provides important inputs of the topic under study.
 Measure of performance of an ongoing process and situations under study.
 The hidden facts can also be discovered.
 To help in decision making and estimating the cost.
The work of data collection starts when the research problem and research design has been
planned. The data can be classified into
(i)
Qualitative data
(ii)
Quantitative data
4.1.1. Qualitative data:
The data which can’t be expressed numerically i.e. it can be only expressed in terms of its
attributes
4.1.2 Quantitative data:
The data which can be expressed numerically i.e. its characteristics is expressed in terms of
numbers.
Example:
When the people are grouped according to their heights, we can find their average height. But if
they are classified according to their occupation it is not possible to find anything like average
occupation. Thus height is quantitative data and occupation is qualitative data. Also religion,
language, beauty, behavior belongs to qualitative data.
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4.1.3 Primary data: It is the data gathered by the researcher for the purpose of the project/research at hand. It is the
data collected by the researcher for the first time in respect to specific purpose.
Advantages: original in character, reliable information
4.1.4 Secondary data: The data which is already been collected by someone else and which have already been passed
through the statistical process.
Advantages: easy to collect, involves less time and cost, deficiencies can be identified easily.
4.2 Collection of primary data
4.2.1 Observation method
It is a common method used for data collection primarily used in the fields of behavioral
sciences. It becomes a scientific tool when it becomes a formulated research purpose; it is
systematically planned and recorded and is subjected to checks and controls on validity and
reliability. Here the information is sought by way of the investigator’s own direct observation
and without asking the respondent. We should keep in mind the following points:
I. What should be observed?
II. How the observations should be recorded?
I. How to ensure the accuracy of observations?
Structured observation:
Here the observation is characterized by definition of units to be observed, steps of
recording the observed information, standardized conditions to be observed. It is
appropriate in descriptive studies.
Unstructured observation:
Here the observation takes place without taking the specific characteristics into
consideration. It is appropriate in exploratory studies.
Participant observation:
Here the observer observes the situation by making himself the member of the group he
is observing. It helps to record the natural behavior of the group. The observer can verify
the truth of the statements with respect to the contents of a questionnaire. But if the
observer extends his participation emotionally, he may narrow-down the researcher’s
range of experience.
Non-participant observation:
Here the observer observes as a detached emissary. He does not experience what the
respondents feel.
Controlled observation:
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Here the observation takes place according to definite pre-arranged plan, involving
experimental procedure. It usually takes place in laboratories.
Uncontrolled observation:
Here the observations take place according to natural settings. The main aim here is to
get spontaneous picture of the real life situations. It is resorted to in case of exploratory
studies.
Advantages of observation method:
I. If the observation is done accurately, it helps to eliminate subjective bias.
II. The current information is neither affected by past information’s nor by future
intensions.
III. It is independent of willingness of the respondent to respond and hence it is
suitable for the situations when the verbal report of the respondent is not
required.
Limitations of observation method
I. Expensive method.
II. We get very limited information.
III. Since we don’t talk to people hence it may happen that some unforeseen factors
may interfere with the observational task.
4.2.2 Interview method
Interview is a type of discussion between two or more people for a definite purpose. It is
the most powerful method of data collection. It helps us to gather valid and reliable data
related to the research objective. It is divided into two parts: personal interview and
telephonic interview.
Personal interviews:
This method requires two persons sitting in front of each other, the one who initiates and
asks the question is called the interviewer and the respondent is called as the interviewee.
I.
Structured interviews:
It is a rigid way which involves set of predetermined questions and highly
standardized techniques of recordings. It is used in case of descriptive studies. We
often use this method because of ease of generalization of the responses given by
several interviewee’s and requiring lesser skill on the part of interviewer. For
example: if a company is conducting a survey before launching a product, then
their questionnaire consists of a set of pre-defined questions.
II.
Unstructured interviews:
It is characterized by a flexibility of approach to questioning. Here the interviewer
may ask the questions in any order, he may also ask some extra questions or drop
some questions. It requires the interviewer to be highly skilled and he should have
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III.
IV.
deep knowledge of the subject. It helps us in collecting information in case of
exploratory research studies. But this flexibility results in lack of comparability of
one interview with other. It is time consuming. For example: the faculty interview
for a specific subject, the corporate interviews for a domain.
Focused interviews:
It is meant to focus attention on the given experience of the respondent. Here the
interviewer decides the sequence of the questions and also has the freedom to
explore the reasons and motives. The respondent is given sufficient time to
express their thoughts and observation’s. It deals with the situations that have
been analyzed prior to the interview. It takes place with the persons known to
have been in a particular situation. For example: if a person has witnessed a live
incident , then the reporters would talk to that person about that incident and
allow his to express his thoughts. Also an attempt to interview well-known
persons like sports person on issues related to sports and its areas of development
can be cited as a good example of focused interview.
Non-directive interviews:
In these interviews, the interviewer allows the respondent to speak on a particular
topic, relate their concrete experiences with no or little direction from the
interviewer.
4.2.3. Collection of data through questionnaires
A questionnaire is a research instrument consisting of a series of questions and other prompts
for the purpose of gathering information from respondents. Questionnaire-based surveys are
one of the most common tools used by market researchers to establish consumer preferences.
Bad questionnaires are misleading and likely to yield meaningless data, so an awareness of the
techniques of questionnaire design is essential to any student or researcher wanting to establish
opinions on their subject of specialization.
There are two main objectives in designing a questionnaire:
 To maximize the proportion of subjects answering our questionnaire - that is, the
response rate. Response error should be avoided and try to obtain accurate relevant
information for our survey.
 To develop the question’s which the respondent can and will answer. Two apparently
similar ways of posing a question may yield different information.

4.3 Guidelines for constructing questionnaire
The researcher must pay attention to the following points in constructing an appropriate and
effective questionnaire:
1. The researcher must keep in view the problem he is to study for it provides the starting
point for developing the questionnaire. He must be clear about the various aspects of case
research problem to be dealt with in the course of his research project.
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2. Appropriate form of questions depends on the nature of information sought, the sampled
respondents & the kind of analysis intended. The researcher must decide whether to use
closed or open ended questions. Questions should be simple & must be constructed with
a view to there forming a logical path of a well through out tabulation plan. The unit of
enumeration should also be defined precisely so that they can ensure accurate & full
information.
3. Rough draft of the questionnaire should be prepared, giving due through the appropriate
sequence by putting questions. Questionnaires previously drafted may as well be looked
into at this stage.
4. Researcher must invariably re-examine, and in case of need may revise the rough draft
for a better one. Technical must be minutely scrutinized & removed.
5. Pilot study should be undertaken for pre testing the questionnaire. The questionnaire may
be edited in the light of the results of the pilot study.
6. Questionnaire must contain simple but straight forward direction for the respondent so
that they may not feel any difficult in answering the questions.
4.4 Collection of Secondary Data
The data that are already available is called Secondary data. It has already been collected and
analysed by someone else. Secondary data may be published data or unpublished data. The
published data are usually available in books, magazines, reports and publications of various
associations, reports prepared by research scholars, economists, universities etc. The unpublished
data may be found in diaries, letters, unpublished biographies and also may be available with the
research scholars, trade associations and other public / private individuals and organizations. The
researcher must do the minute scrutiny because it may be possible that the secondary data may
be unsuitable or may be inadequate in the context of the problem the researcher wants to study.
Review Questions:
1. Describe the different types of observations that can be used to collect data.
2. What are the merits and demerits of observation as methods of data collection?
3. When is it suitable to use a questionnaire in collecting data?
4. Explain the guidelines that have to be followed in constructing a questionnaire.
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LECTURE FIVE
DATA ANALYSIS
Lecture Outline:
 Introduction
 Data entry
 Decision of file format
 Code for analysis
 Processing data
 Presenting data
5.0 Introduction:
In this lecture we look at ways of analyzing the data collected so as to come up with meaningful
information. It looks at ways of presenting and processing data. It also looks at measures of
central tendency and dispersion as some of the ways of analyzing data and different graphs that
can be used to present data.
After collecting data, they must be classified and presented in meaningful forms to have better
insight of a research problem. Once the information is tabulated, it is easy to perform various
statistical tests for their validity, accuracy and significance. Gathered information should be
presented in such a manner that even a layman understands what, why, when and how of
information.
5.1 Data Entry
It is the process of taking completed questionnaires\surveys and putting them into a form that can
readily be analyzed. A series of options need to consider when you enter the information you
have gathered. You will first have to decide on a file format and then devise a code for analysis.
5.2 Decision on File Format
It comprises of decisions regarding:
1 The way the data will be organized in a file
1. Order of information collected
2. How subject is referenced
3. Constructing individual records
4. Application to statistics programs
5.3 Devise Code for Analysis
The main points you need to remember while devising the code for analysis are:
1. Set of rules that translates answers into discrete values
2. Alphabetical or Numerical depending on measurement scale
3. Preserve level of measurement for each item
4. General Considerations (closed questions)
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5.4 Processing of Data
5.4.1 Frequency Distribution
If the data are of repeating nature, then they should be presented in forms of the number of
occurrences of each value of the data of particular type. The following are the steps of
constructing a frequency distribution:
1. Specify the number of class intervals. A class is a group (category) of interest. No
totally accepted rule tells us how many intervals are to be used. Between 5 and 15 class intervals
are generally recommended. Note that the classes must be both mutually exclusive and allinclusive. Mutually exclusive means that classes must be selected such that an item can’t fall into
two classes and all-inclusive classes are classes that together contain all the data.
2. When all intervals are to be the same width, the following rule may be used to find
the required class interval width:
W = (L - S) / K where: W= class width, L= the largest data,
S= the smallest data, K= number of classes
The frequency distribution can be classified into discrete frequency distribution and continuous
frequency distribution which are demonstrated in Table 1 and 2, respectively.
Table 1 Discrete Frequency Distribution
Income Category
Low Income
Medium Income
High Income
Number of Respondents (frequency)
300
200
100
Table 2 Continuous Frequency Distribution
Monthly income (in rupees) (class
Number of Respondents
interval)
(frequency)
0-5000
20
5000-10000
30
10000-15000
40
15000-20000
60
20000-25000
30
25000-30000
20
The Frequency Distribution: 1. Shows how the observations cluster around a central value.
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1. Shows the degree of difference between observations. For example, in the above problem
we know that none of the person has monthly income greater than 30,000, and the
maximum number of people has monthly income between 15000 and 20000. This
descriptive analysis provides us with an image of the monthly income of the population,
which is not available from raw data.
5.4.2 Cumulative Frequency Distribution
The cumulative frequency distribution is a modified form of frequency distribution, as shown in
Table 3. In a given row, the value in the last column is the cumulative value of the frequencies
shown in its last but one column up to that value.
Table 3 Cumulative Frequency Distribution
Number of
Monthly income (in
Respondents
rupees) (class interval)
(frequency)
Cumulative frequency
0-5000
20
20
5000-10000
30
50
10000-15000
40
90
15000-20000
60
150
20000-25000
30
180
25000-30000
20
200
5.4.3 Relative Frequency Distribution
The relative frequency distribution is a modified form of frequency distribution, as shown in
Table 4. In a given row, the value in the last column is the ratio between the frequency of that
row and the total frequency.
Monthly income (in rupees)
(class interval)
0-5000
5000-10000
10000-15000
15000-20000
20000-25000
25000-30000
Number of Respondents
(frequency)
20
30
40
60
30
20
Relative
frequency
20/200=0.10
30/200=0.15
40/200=0.20
60/200=0.30
30/200=0.15
20/200=0.10
5.5 Presenting Data
Graphs, curves, and charts are used to present data. Bar charts are used to graph the
qualitative data. The bars do not touch, indicating that the attributes are qualitative categories;
variables are discrete and not continuous.
o Histograms are used to graph absolute, relative, and cumulative frequencies.
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o Ogive is a cumulative frequency curve. This can be classified into less-than-ogive and
more-than-ogive. An ogive is constructed by placing a point corresponding to the upper
end of each class at a height equal to the cumulative frequency of the class. These points
then are connected. An ogive also shows the relative cumulative frequency distribution
on the right side axis.
o A less-than ogive shows how many items in the distribution have a value less than the
upper limit of each class.
o A more-than ogive shows how many items in the distribution have a value greater than or
equal to the lower limit of each class.
o A less-than cumulative frequency polygon is constructed by using the upper true limits
and the cumulative frequencies.
o A more-than cumulative frequency polygon is constructed by using the lower true limits
and the cumulative frequencies.
o Pie chart is often used in newspapers and magazines to depict budgets and other
economic information. A complete circle (the pie) represents the total number of
measurements. The size of a slice is proportional to the relative frequency of a particular
category.
o For example, since a complete circle is equal to 360 degrees, if the relative frequency for
a category is 0.40, the slice assigned to that category is 40% of 360 or (0.40)(360)= 144
degrees.
o Pareto chart is a special case of bar chart and often used in quality control. The purpose
of this chart is to show the key causes of unacceptable quality. Each bar in the chart
shows the degree of quality problem for each variable measured.
o Time series graph is a graph in which the X axis shows time periods and the Y axis
shows the values related to these time periods.
5.3 Measures of Central Tendency
Central tendency is defined as the central point around which data revolve. The following
techniques can be employed:
5.3.1 The mode
The mode is defined as the score (value or category) of the variable which is observed most
frequently. For example: 3 7 5 8 6 4 5 9 5.From the above mentioned, the mode equals 5 because 5
appears to be the most frequent score amongst all the numbers (occurred 3 times).
5.3.2 The median
The median indicates the middle value of a series of sequentially ordered scores. Because the
median divides frequencies into two equal parts, it can also be described as being the fiftieth
percentile:
10 13 14 15 18
19 22 25
25
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The median in the above-mentioned is the fifth score, which is 18. There are 4 counts on both sides
of the numerical value 18. In cases where you have, for instance:
10 13 14 15 18 19 22 25
26 29
There are 2 numerical values indicating the median. By dividing the result by 2, the median can be
determined. The fifth score with a numerical value of 18 and the sixth score with the numerical
value of 19 are in the middle of the sequentially ordered scores. The median for the above
mentioned scores is therefore (18 + 19)/ 2 = 18.5.
Note: Mode=3*median – 2* mean
Arithmetic mean
The arithmetic mean refers to a measure of central tendencies found by adding all scores and
dividing them by the number of scores. The following is an example:
5, 2, 6, 1, 6 = (Sum total of scores)/N
Thus 5 + 2 + 6 + 1 + 6 = 20, because there are 5 scores, N = 5, and the sum total of the scores (20)
is divided by 5.
m= (∑fx)/ ∑f; ∑f=n
f= frequency; x= mid value of class interval; n= total frequency
5.3.4 Standard deviation
The standard deviation is a measure of the spread of dispersion of a distribution of scores. The
deviation of each score from the mean is squared; the squared deviations are then summed, the
result divided by n, and the square root taken. It is denoted by σ
σ = √ {∑(x-m) 2/ n}
(Note: In case of Ungrouped Data)
Where m= (∑fx)/ ∑f; ∑f=n
f= frequency; x= mid value of class interval; n= total frequency
Calculation of Standard Deviation – Grouped Data.
σ = √ [{∑f(x-m) 2}/ n]
Where m= (∑fx)/ ∑f; ∑f=n
f= frequency; x= mid value of class interval; n= total frequency
Review Questions:
1. Describe different ways in which raw data can be analyzed to come up with a information
about the problem to be solved.
2. When should the following be used to analyse data
a) Frequency distribution
b) Cumulative frequency distribution
c) Relative frequency distribution
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LECTURE SIX
LEVELS OF MEASUREMENT
Lecture Outline:
 Introduction
 Types of measurement scales
 Scale and technique of construction
 Procedure for development of Likert scale
 Cumulative scales
6.0 Introduction
In this lecture we shall look at scales that can be used to measure different variables so as to
determine the precision of the responses to different questions.
The level of measurement is a scale by which a variable is measured. For 50 years, with few
detractors, science has used the Stevens (1951) typology of measurement levels (scales). There
are three things, which you need to remember about this typology: Any thing that can be
measured falls into one of the four types:
The higher the level of measurement, the more precision in measurement and every level up
contains all the properties of the previous level. The four levels of measurement, from lowest to
highest, are as follows:
1. Nominal
2. Ordinal
2. Interval
3. Ratio
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Fig. 4 levels of measurement
6. 1 Types of Measurement Scales
Ordinal and nominal data are always discrete. Continuous data has to be at either ratio or interval
level of measure.
6.1.1 Nominal scale
It is a system of assigning number symbols to events in order to label the data. It includes
demographic characteristics like sex, race, and religion and therefore performs a major role in
surveys and other ex-post-facto research where we classify the data by major sub-groups of
population. Thus nominal level of measurement describes variables that are categorical in
nature. The characteristics of the data you’re collecting fall into distinct categories:
1. If there are a limited number of distinct categories (usually only two), then you’re dealing with
a dichotomous variable.
2. If there are an unlimited or infinite number of distinct categories, then you’re dealing with a
continuous variable.
Nominal Scale is the least powerful level of measurement. It indicates no order, no relationship
and has no arithmetic origin.
For example:
Which of the following food items do you tend to buy at least once per month? (Please
tick)
Okra
Palm Oil
Milled Rice
Peppers
Prawns
Pasteurized milk
The numbers have no arithmetic properties and act only as labels. The only measure of average
that can be used is the mode because this is simply a set of frequency counts.
6.1.2 Ordinal Scale
It is the lowest level of Ordered Scale.
1The ordinal level of measurement describes variables that can be ordered or ranked in some
order of importance.
It describes most judgments about things, such as big or little, strong or weak.
Most opinion and attitude scales or indexes in the social sciences are ordinal in nature.
The Ordinal Scale determines the students Rank in his class. Thus its use implies a statement of
“greater than” or “lesser than” without being able to state how much great or less. An example of
an ordinal scale used to determine farmers' preferences among 5 brands of pesticide.
Order of preference Brand
1
Rambo
2
R.I.P.
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3
Killalot
4
D.O.A.
5
Bugdeath
From such a table the researcher knows the order of preference but nothing about how much
more one brand is preferred to another, which is there is no information about the interval
between any two brands. All of the information a nominal scale would have given is available
from an ordinal scale. In addition, positional statistics such as the median, quartile and percentile
can be determined.
6.1.3 Interval Scale
The interval scales have more or less equal intervals, or meaningful distances between their
ranks. For example, if you were to ask somebody if they were first, second, or third generation
immigrant, the assumption is that the distance or number of years, between each generation is the
same.
Interval Scales may have arbitrary zero, but it is not possible for them to determine what may be
called as “absolute zero” or “a unique origin”.
Fahrenheit Scale is an example of Interval scale.
Figure 3.3 Examples of interval scales in numeric and semantic formats
Please indicate your views on Balkan Olives by scoring them on a scale of 5 down to 1
(i.e. 5 = Excellent; = Poor) on each of the criteria listed
Balkan Olives are:
Circle the appropriate score on each line
Succulence
5 4 3 2 1
Fresh tasting
5 4 3 2 1
Free of skin blemish
5 4 3 2 1
Good value
5 4 3 2 1
Attractively packaged
5 4 3 2 1
(a)
Please indicate your views on Balkan Olives by ticking the appropriate responses below:
Excellent
Very Good
Good
Fair Poor
Succulent
Freshness
Freedom from skin blemish
Value for money
Attractiveness of packaging
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(b)
Most of the common statistical methods of analysis require only interval scales in order that they
might be used.
6.1.4 Ratio Scale
The ratio level of measurement describes variables that have equal intervals and a fixed zero (or
reference) point. It is possible to have zero income, zero education, and no involvement in crime,
but rarely do we see ratio level variables in social science since it’s almost impossible to have
zero attitudes on things, although “not at all”, “often”, and “twice as often” might qualify as ratio
level measurement. It helps in measurement of physical dimensions such as weight, height
distance etc. It allows to compare both differences in scores and the relative magnitude of scores,
multiplication, division and all the Statistical Techniques are generally usable with ratio scales.
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6.2 Important Scaling Techniques
We now take up some scaling techniques that are often used in context of social or business
research.
6.2.1 Rating Scales:
The Rating Scales involves qualitative description of a limited number of aspects of a thing or of
traits of a person. In this we judge the properties of objects against the specified criteria, without
reference to other similar object. In practice, three to seven-point scale are generally used for the
reason that more points on a scale provide an opportunity for greater sensitivity of measurement.
Rating Scale may be either a graphic rating scale or an itemized rating scale.
Graphic rating scale is quite simple and is commonly used in practice. The various points are
usually put along the line to form a continuum and the rater indicates his rating by simply
making a mark at the appropriate point on a line that runs from one extreme to the other.
Itemized rating scale presents a series of statements from which a respondent selects one as best
reflecting his evaluation. These statements are ordered progressively in terms of more or less of
some property.
6.2.2 Ranking Scales:
In this we make relative judgments against other similar objects. The respondents under this
method directly compare two or more objects and make choices among them.
How do you like the product?
(Please check)
Like very
Like some
Neutral Dislike Some Dislike very
much
what
what
much
6.2.3 Scale construction techniques:
In social science studies, while measuring attitudes of the people we generally follow the
technique of preparing the opinionnaire (or attitude scale) in such a way that the score of the
individual responses assigns him a place on a scale. Under this approach, the respondent
expresses his agreement or disagreement with a number of statements relevant to the issue.
While developing such statements, the researcher must note the following two points:
1. That the statements must elicit responses which are psychologically related to the
attitude being measured;
2. That the statements need to be such that they discriminate not merely between extremes
of attitude but also among individuals who differ slightly.
a) Arbitrary scales:
These scales are developed on ad hoc bases and are designed largely through the researchers own
subjective selection of items. The researcher first collects few statements or items which he
believes are unambiguous and appropriate to a given topic. Some of these are selected for
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inclusion in the measuring instrument and then people are asked to check in a list the statement
with which they agree.
The chief merit of such scales is that they can be developed very easily, quickly and with
relatively less expense. They can also be designed to be highly specific and adequate. Because of
these benefits, such scales are widely used in practice.
At the same time there are some limitations to these scales. The most important one is that we
do not have objective evidence that such scale measure the concepts for which they have been
developed. We have simply to rely on researcher’s insight and competence.
b) Likert scales:
A Likert scale is what is termed a summated instrument scale. This means that the items making
up a Likert scale are summed to produce a total score. In fact, a Likert scale is a composite of
itemized scales. Typically, each scale item will have 5 categories, with scale values ranging from
-2 to +2 with 0 as neutral response. This explanation may be clearer from the example in figure
3.12.
Figure 3.12 The Likert scale
Strongly
Agree
If the price of raw materials fell firms 1
would reduce the price of their food
products.
Agree Neither Disagree Strongly
Disagree
2
3
4
5
Without government regulation
firms would exploit the consumer.
the 1
2
3
4
5
Most food companies are so concerned 1
about making profits they do not care
about quality.
2
3
4
5
The food industry spends a great deal of 1
money
making
sure
that
its
manufacturing is hygienic.
2
3
4
5
Food companies should charge the same 1
2
3
4
5
price for their products throughout the
country
Likert scales are treated as yielding Interval data by the majority of marketing researchers.
The scales which have been described in this chapter are among the most commonly used in
marketing research. Whilst there are a great many more forms which scales can take, if students
are familiar with those described in this chapter they will be well equipped to deal with most
types of survey problem.
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Strongly agree agree
undecided disagree strongly disagree
Procedure for developing a likert- type scale:
1. The researcher collects large number of statements which are relevant to the attitude
being studied and each of the statements expresses definite favorableness or unfavorableness to a particular point of view.
2. After the statements have been gathered, a trial test should be -administered to a number
of subjects.
3. the response to various statements are scored in such a way that the response indicative
of most favorable attitude is given the highest score of five and that with the most
unfavorable attitude is given lowest score one.
4. Then the total score of each respondent is obtained by adding his scores that he receives
for separate statements.
5. The next step is to array these total scores and find out those statements which have a
high discriminatory power. For this purpose, the researcher may select some part of the
highest and the lowest total scores say the top 25% and the bottom 25%.
6. Only those statements that correlate with the total test should be retained in the final
instrument and al others must be discarded from it.
Advantages of Likert scales:
1. Likert type scale is considered more reliable because under it respondents answer each
statement included the instrument. As such it also provides more information.
2. Likert type scale can easily be used in respondent centered and stimulus centered studies.
Limitations of Likert scale:
There are several limitations to the likert type scale, one important limitation is that, with this
scale, we can simply examine weather respondents are more or less favorable to topic, but we
can not tell how much more or less they are. There is no basis for belief that the five positions
indicated on the scale are equally spaced.
c) Cumulative scale:
Cumulative scale like other scales consists of series of statements to which a respondent
expresses his agreement or disagreement. The special feature of this type of is that statements in
it form a cumulative series. In other words the statements are related to one another in such a
way that an individual, who replies favorably to item no 3 also replies favorably to items 2 and
1and 1 who replier favorably to item 4 also replies favorably to item no 3, 2 and 1 and so on.
Procedure for cumulative scales:
1. We must lay down in clear terms the issue we want to deal with in our study.
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2. The next step is to develop a number of items relating the issue and to eliminate by
inspection the items that are ambiguous, irrelevant or those that happen to be too extreme
items.
3. This step consists in pre-testing the items to determine whether the issue at hand is
scalable. In a pre- test the respondents are ask to record the opinions on all selected items
using the likert type 5 point scale, ranging from ‘strongly agree’ to strongly ‘disagree’.
The strongest favorable response is scored as 5, where as the strongest unfavorable
response as 1. the total score can thus range , if there are 15 items in all from 75 for most
favorable to 15 for the least favorable.
4. The next step is to total the scores for various opinions and to rearray them to reflect any
shift in order, resulting from reducing the items, say, from 15 in pretest, say, 5 for the
final scale.
Advantages of cumulative scale:
It assures that only a single dimension of attitude is being measured. Researcher’s subjective
judgment is not allowed to creep in the development of scale since the scale is determined by the
replies of respondents.
Disadvantage of cumulative scale:
The main difficulty in using the scaling technique is that in practice perfect cumulative or
unidirectional scales are very rarely found and we have only to use its approximation testing
through coefficient of reproducibility or examining on the bases of some other criteria. This
method is not frequently used for simple reason that its development procedure is tedious and
complex.
Review Questions
1. Describe the different scales of measurement and outline scenarios where each scale can be
suitably used.
2. What are the merits and demerits of each of the different scales of measurement.
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LECTURE SEVEN
SAMPLING DESIGN
Lecture Outline
 Introduction
 Need for sampling
 Concept of population and sample
 Types of sampling
 Sampling distribution
 Central limit theorem
 Relationship between population and sample
7.0 Introduction:
In this lecture, we shall describe the basic thing, how to collect data. We shall also discuss a
variety of methods of selecting the sample called Sampling Designs, which can be used to
generate our sample data sets.
Lecture objectives:
By the end of this lecture, you should be able to;
 Describe the different sampling methods and when it is suitable to use each of them.
 Describe the different sampling designs.
 Generate data from the different sampling designs.
7.1 Need for Sampling
Sampling is used in practice for a variety of reasons such as:
1. Sampling can save time and money. A sample study is usually less expensive than a
census study and produces results at a relatively faster speed.
2. Sampling may enable more accurate measurements for a sample study is generally
conducted by trained and experienced investigators.
3. Sampling remains the only way when population contains infinitely many members.
4. Sampling remains the only choice when a test involves the destruction of the items under
study.
5. Sampling usually enables to estimate the sampling errors and, thus, assists in obtaining
information concerning some characteristic of the population.
7.2 Concept of Population and Sample
Statisticians commonly separate the statistical techniques into two broad categories7.2.1 Descriptive statistics
This deals with collecting, summarizing and simplifying the complicated data. It also helps in
understanding the data and report making.
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7.2.2 Inferential statistics
This deals with methods used for drawing inferences about the totality of observations on the
basis of knowledge gained.
7.3 Population
This is roughly defined as collection of all elements taken into consideration and about which
conclusion have to be drawn. For example: If the study is been conducted to determine average
salary of the workers of a factory, then the population will consists workers in the factory.
Similarly, if we investigate about fertility of land in a region, then the population will consists of
all lands under cultivation. Thus population refers to all items under investigation.
7.4 Sample
This can be defined as collection of some elements of population. In other words, a part of
totality on which information is generally collected and analyzed for the purpose of
understanding any aspect of the population. The part of population taken into consideration is
called Sampling Unit. For example: A doctor examines a few drops of blood to draw conclusions
about the nature of disease or blood constitution of the whole body.
If the sampling unit comprises of all units of all elements of population may be viewed as
Elementary Sampling Unit
For example: In textile industry, the workers of a department whose wages may be a sample and
all the workers of the company will be considered as population.
The total number of units in the population is known as population size.
The total number of units in the sample is known as sample size.
Any characteristic of population is called parameter and that of sample is called statistic.
7.5 Sampling Frame
To select a random sample of sampling units, we need a list of all sampling units contained in the
population. Such a list is called a Sampling Frame
7.6 Census and Sample Survey
It is possible to examine every person of the population if we want to calculate average wage of a
person working in a factory, then all the elements of population will be called as primary
sampling unit. Also we call this a complete enumeration or CENSUS.
The census method is not very popularly used in practice. Since the effort, money & time
required for carrying out complete enumeration will generally be extremely large and in many
cases, it involves huge cost.
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The standard deviation of sampling distribution is called standard error, larger the sample size
lower will be the standard error. We have also studied various sources of sampling and nonsampling error along with principles of sampling.
For the process of statistical inference to be valid we must ensure that we take a representative
sample of our population. Whatever method of sample selection we use, it is vital that the
method is described. How do we know if the characteristics of a sample we take match the
characteristics of the population we are sampling? The short answer is we don’t. We can,
however, take steps that make it as likely as possible that the sample will be representative of the
population. Two simple and effective methods of doing this are making sure that the sample size
is large and making sure it is randomly selected. A large sample size is more likely to be
representative of a population than a small one.
Think of extreme cases. If we want to know the average height of the population and we select
just one person and measure their height it is unlikely to be close the population average. If we
took 1,000,000 people, measured their heights and took the average, this figure would be likely
to be close to the population average.
7.7 Types of Sampling
The type of enquiry you want to have and the nature of data that you want to collect
fundamentally determines the technique or method of selecting a sample.
The procedure of selecting a sample may be broadly classified under the following three heads:
· Non-Probability Sampling Methods
· Probability Sampling
· Mixed Sampling
Now let us discuss these in detail. We will start with the non-probability sampling then we will
move on to probability sampling.
7.7.1 Non-Probability Sampling Methods:
The common feature in non probability sampling methods is that subjective judgments are used
to determine the population that are contained in the sample .We classify non-probability
sampling into four groups:
1. Convenience Sampling
2. Judgement Sampling
3. Quota Sampling
4. Snowball sampling
7.7.2 Convenience Sampling
 These types of sampling are used primarily for reasons of convenience.
 It is used for exploratory research and speedy situations.
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
It is often used for new product formulations or to provide gross-sensory evaluations by
using employees, students, peers, etc.
 Convenience sampling is extensively used in marketing studies
This would be clear from the following examples:
1. Suppose a marketing research study aims at estimating the proportion of Pan (Beetle leaf)
shops in Delhi, which store a particular drink Maaza. It is decided to take a sample of size 150.
What the investigator does is to visit 150 Pan shops near his place of office as it is very
convenient to him and observe whether a Pan shop stores Maaza or not. This is definitely not a
representative sample, as most Pan shops in Delhi had no chance of being selected. It is only
those Pan shops which were near the office of the investigator has a chance of being selected
2. A ball pen manufacturing company is interested in knowing the opinions about the ball pen
(like smooth flow of ink, resistance to’ breakage of the cover etc.) it is presently manufacturing
with a view to modify it to suit customers
need. The job is given to a marketing researcher who visits a college near his place of residence
and asks a few students (a convenient sample) their opinion about the ‘ball pen” in question.
7.7.3 Judgment Sampling
 It is that sample in which the selection criteria are based upon the researcher’s personal
judgment that the members of the sample are representative of the population under
study.
 It is used for most test markets and many product tests conducted in shopping malls. If
personal biases are avoided, then the relevant experience and the acquaintance of the
investigator with the population may help to choose a relatively representative sample
from the population. It is not possible to make an estimate of sampling error as we cannot
determine how precise our sample estimates are.
Judgment sampling is used in a number of cases, some of which are:
1. Suppose we have a panel of experts to decide about the launching of a new product in the next
year. If for some reason or the other, a member drops out, from the panel, the chairman of the
panel may suggest the name of another person whom he thinks has the same expertise and
experience to be a member of the said panel. This new member was chosen deliberately - a case
of Judgment sampling.
2. The method could be used in a study involving the performance of salesmen. The salesmen
could be grouped into top-grade and low-grade performer according to certain specified
qualities. Having done so, the sales manager may indicate who in his opinion, would fall into
which category. Needless to mention this is a biased method. However in the absence of any
objective data, one might have to resort to this type of sampling.
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7.7.4 Quota Sampling
This is a very commonly used sampling method in marketing research studies. Here the sample
is selected on the basis of certain basic parameters such as age, sex, income and occupation that
describe the nature a population so as to make it representative of the population. The
Investigators or field workers are instructed to choose a sample that conforms to these
parameters. The field workers are assigned quotas of the number of units satisfying the required
characteristics on which data should be collected. However, before collecting data on these units,
the investigators are supposed to verify that the units qualify these characteristics. Suppose we
are conducting a survey to study the buying behavior of a product and it is believed that the
buying behavior is greatly influenced by the income level of the consumers. We assume that it is
possible to divide our population into three income strata such as high-income group, middleincome group and low-income group. Further it is known that 20% of the population is in high
income group, 35% in the middle-income group and 45% in the low-income group. Suppose it is
decided to select a sample of size 200 from the population. Therefore, samples of size 40, 70
and90 should come from high income, middle income and low income groups respectively. Now
the various field workers are assigned quotas to select the sample from each group in such a way
that a total sample of 200 is selected in the same proportion as mentioned above.
7.7.5 Snowball Sampling
· The sampling in which the selection of additional respondents (after the first small group of
respondents is selected) is based upon referrals from the initial set of respondents.
· It is used to sample low incidence or rare populations
· It is done for the efficiency of finding the additional, hard-to-find members of the sample.
Advantages of Non-probability Sampling
· It is much cheaper to probability sampling.
· It is acceptable when the level of accuracy of the research results is not of utmost importance.
· Less research time is required than probability samples.
· It often produces samples quite similar to the population of interest when conducted properly.
Disadvantages of Non-probability Sampling
· You cannot calculate Sampling error. Thus, the minimum required sample size cannot be
calculated which suggests that you (researcher) may sample too few or too many members of the
population of interest.
· You do not know the degree to which the sample is representative of the population from which
it was drawn.
· The research results cannot be projected (generalized) to the total population of interest with
any degree of confidence.
7.8 Probability Sampling Methods
Probability sampling is the scientific method of selecting samples according to some laws of
chance in which each unit in the population has some definite pre-assigned probability of being
selected in the sample. The different types of probability sampling are:
1. Where each unit has an equal chance of being selected.
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2. Sampling units have different probabilities of being selected
3. Probability of selection of a unit is proportional to the sample size.
7.8.1 Simple Random Sampling
It is the technique of drawing a sample in such a way that each unit of the population has an
equal and independent chance of being included in the sample.
In this method an equal probability of selection is assigned to each unit of population at the first
draw. It also implies an equal probability of selecting in the subsequent draws.
Thus in simple random sample from a population of size N, the probability of drawing any unit
in the first draw is 1/N.The probability of drawing a second unit in the second draw is (1/N)-1.
The probability of selecting a specified unit of population at any given draw is equal to the
probability of its being selected at the first draw.
7.8.2 Selection of a Simple Random Sample:
As we all know Simple Random Sample refers to that method of selecting a sample in which
each and every unit of population is given independent and equal chance to be included in the
sample. But, Random Sample does not depend only upon selection of units, but also on the size
and nature of the population. One procedure may be good and simple for a small sample but it
may not be good for the large population.
Generally, the method of selecting a sample must be independent of the properties of sampled
population. Proper precautions should be taken to ensure that your selected sample is random.
Although human bias is inherent in any sampling scheme administered by human beings.
Random selection is best for two reasons - it eliminates bias and statistical theory is based on the
idea of random sampling. We can select a simple random sample through use of tables of
random numbers, computerized random number generator or lottery method. Thus, the three
methods of drawing simple random sample are mechanical method and using tables of random
numbers and sealed envelopes (lottery system) etc.
7.8.3 Lottery Method
This is the simplest method of selecting a random sample. We will illustrate it by means of
example for better understanding. Suppose, we want to select “r” candidates out of “n”. We
assign the numbers from 1 to n i.e. to each and every candidate we assign only one exclusive
number. These numbers are then written on n slips which are made as homogeneous as possible
in shape, size, colour, etc. These slips are then put in a bag and thoroughly shuffled and then “r”
slips are drawn one by one. The “r” candidates corresponding to numbers on the slips drawn will
constitute a random sample.
This method of selecting a simple random sample is independent of the properties of population.
Generally in place of slips you can use cards also. We make one card corresponding to one unit
of population by writing on it the number assigned to that particular unit of population. The pack
of cards is a miniature of population for sampling purposes. The cards are shuffled a number of
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times and then a card is drawn at random from them. This is one of the most reliable methods of
selecting a random sample.
Merits and Limitations of Simple Random Sampling
Merits
1. Since sample units are selected at random providing equal chance to each and every unit of
population to be selected, the element of subjectivity or personal bias is completely eliminated.
Therefore, we can say that simple random sample is more representative of population than
purposive or judgment sampling.
2. You can ascertain the efficiency of the estimates of the parameters by considering the
sampling distribution of the statistic (estimates)
For example: One measure of calculating precision is sample size. Sample mean becomes an
unbiased mean of population mean or a more efficient estimate of population mean as sample
size increases.
Limitations
1. The selection of simple random sample requires an up-to-date frame of population from which
samples are to be drawn. Although it is impossible to have knowledge about each and every unit
of population if population happens to be very large. This restricts the use of simple random
sample.
2. A simple random sample may result in the selection of the sampling units, which are widely
spread geographically and in such a case the administrative cost of collecting the data may be
high in terms of time and money.
3. For a given precision, simple random sample usually requires larger sample size as compared
to stratified random sampling which we will be studying next.
The limitations of simple random sample will be clear from the example.
Therefore, some of the randomly allocated samples prove very non-random. This type of
problem can be eliminated by use of Stratified Random Sampling, in which the population is
divided into different strata. Now, we will move into details of stratified random sampling.
7.8.4 Stratified Random Sampling
We have understood that in simple random sampling, the variance of the sample estimate of the
population is a. inversely proportional to the sample size, and
b. directly proportional to the variability of the sampling units in the population.
We also know that the precision is defined as reciprocal of its sampling variance. Therefore as
sample size increases precision increases. Apart from increasing the sample size or sampling
fraction n/N, the only way of increasing the precision of sample mean is to devise a sampling
technique which will effectively reduce variance, the population heterogeneity. One such
technique is Stratified Sampling.
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Stratification Means Division into Layers
Past data or some other information related to the character under study may be used to divide
the population into various groups such that
i. units within each group are as homogeneous as possible and
ii. the group means are as widely different as possible.
Thus, if we have a population consisting of N sampling units, it is divided into k relatively
homogeneous mutually disjoint (non overlapping) sub-groups, termed as strata, of sizes N1,
N2,……,.., Nk , such that N = “Ni for i =1 to k .
Now you draw a simple random sample of size ni (i=1, 2, 3,... k) from each stratum. This type of
technique of drawing a sample is called stratified random sampling and the sample is called
stratified random sample.
There are two points which you have to keep in mind while drawing a stratified random sample.
· Proper classification of the population into various strata, and
· A suitable sample size from each stratum.
Both these points are important to be considered because if your stratification is faulty, it cannot
be compensated by taking large samples.
Advantages of Stratified Random Sampling
1. More representative
In non-stratified random sample some strata may be over represented, others may be underrepresented while some may be excluded altogether. Stratified sampling ensures any desired
representation in the sample of the various strata in the population. It over-rules the possibility of
any essential group of the population being completely excluded in the sample. Stratified
sampling thus provides a more representative cross section of the population and is frequently
regarded as the most efficient system of sampling.
2. Greater Accuracy
Stratified sampling provides estimates with increased precision. Moreover, stratified sampling
enables us to obtain the results of known precision for each stratum.
3. Administrative Convenience
As compared with simple random sample, the stratified random samples are more concentrated
geographically. Accordingly, the time and money involved in collecting the data and
interviewing the individuals may be considerably reduced and the supervision of the field work
could be allocated with greater ease and convenience.
7.8.5 Systematic Random Sampling
If you have the complete and up-to-date list of sampling units is available you can also employ a
common technique of selection of sample, which is known as systematic sampling.
In systematic sampling you select the first unit at random, the rest being automatically selected
according to some predetermined pattern involving regular spacing of units.
Now let us assume that the population size is N. We number all the sampling units from 1 to N in
some order and a sample of size n is drawn in such a way that
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N = nk i.e. k = N/n , where k, usually called the sampling interval, is an integer. In systematic
random sampling we draw a number randomly, let us suppose that the number drawn is i and
selecting the unit corresponding to this number and every kth unit subsequently. Thus the
systematic sample of size n will consist of the units
i, i+k, i+2k, - - - - - - - - - - - - , i+ (n-1)k.
The random number i is called the random start and its value determines the whole sample.
Merits and Demerits of Systematic Random Sampling
Merits
I. .Systematic sampling is operationally more convenient than simple random sampling or
stratified random sampling. It saves your time and work involved.
II. This sampling is more efficient to simple random sample, provided the frame (the list from
which you have drawn the sample units ) is arranged wholly at random
Demerits
I. The main disadvantage of systematic sampling is that systematic sampling is that systematic
samples are not in general random samples since the requirement in merit two
is rarely fulfilled.
II. If N is not a multiple of n, then the actual sample size is different from that required, and
sample mean is not an unbiased estimate of the population mean.
7.8.6 Cluster Sampling
In this type of sampling you divide the total population, depending upon the problem under
study, into some recognizable sub-divisions which are termed as clusters and a simple random
sample of n blocks is drawn. The individuals whom you have selected from the blocks constitute
the sample.
Notes
· Clusters should be as small as possible consistent with the cost and limitations of the survey.
· The number of sampling units in each cluster should be approximately same.
Thus cluster sampling is not to be recommended if we have sampling areas in the cities where
there are private residential houses, business and industrial complexes, apartment buildings, etc.,
with widely varying number of persons or households.
7.8.7 Multistage Sampling
One better way of selecting a sample is to resort to sub-sampling within the clusters, instead of
enumerating all the sampling units in the selected cluster. This technique is called two-stage
sampling, clusters being termed as primary units and the units within the clusters being termed as
secondary units. This technique can be generalized to multistage sampling. We regard population
as a number of primary units each of which is further composed of secondary stage units and so
on, till we ultimately reach a stage where desired sampling units are obtained. In multi-stage
sampling each stage reduces the sample size.
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Merits and Limitations
Merits:
i. Multistage sampling is more flexible as compared to other methods .It is simple to carry out
and results in administrative convenience by permitting the field work to be concentrated and yet
covering large area.
ii. It saves a lot of operational cost as we need the second stage frame only for those units which
are selected in the first stage sample.
iii. It is generally less efficient than a suitable single- stage sampling of the same size.This brings
an end on today’s discussion on sampling techniques.
Thus in the nutshell we can say that Non probabilistic sampling such as Convenience sampling,
Judgments Sampling and Quota sampling are sometimes used although representative ness of
such a sample cannot be ensured. Whereas a probabilistic sampling to each unit of the population
to be included in the sample and in this sense it is a representative sample of the population.
Points to Ponder
· Sampling is based on two premises. One is that there is enough similarity among the elements
in a population that a few of these elements will adequately represent the characteristic of the
total population.
· The second premises is that while some elements in a sample underestimate the population
value, others overestimate the value.
· The results of these tendencies are that a sample mean is generally a good estimate of
population mean.
· A good sample has both accuracy & precision. An accurate sample is one which there is little
or no bias or systematic variance. A sample with adequate precision is one that has a sampling
error that is within acceptable limits.
· A variety of sampling technique is available, of which probability sampling is based on random
selection – a controlled procedure that ensures that each population element is given a known
nonzero chance of selection.
· In contrast non-probability selection is not random. When each sample element is drawn
individually from the population at large, it is unrestricted sampling.
7.9 Sample size and its determination
In sample analysis the most ticklish question is: What should be the size of the sample or how
large pr small should be ‘n’? If the sample size (‘n’) is too small, it may not serve to achieve the
objectives and if it is too large, we may incur huge cost and waste resources. As a general rule,
one can say that the sample must be of an optimum size i.e., it should neither be excessively
large nor too small. Technically the sample size should be large enough to give a confidence
interval of desired width and as such the size of the sample must be chosen by some logical
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process before sample is taken from the universe. Size of the sample should be determined by
researcher keeping in view the following points:
1. Nature of Universe: Universe may be either homogenous or heterogeneous in nature. If
the items of the universe are homogenous, a small sample can serve the purpose. But if
the sample is heterogeneous, a large sample would be required. Technically, this can be
termed as the dispersion factor.
2. Number of classes proposed: If many class – groups (groups and sub – groups) are to be
formed, a large sample would be required because a small sample might not be able to
give a reasonable number of items in each class – groups.
3. Nature of Study: If items are to be intensively and continuously studied, the sample
should be small. For general survey the size of the sample should be large, but a small
sample is considered appropriate in technical surveys.
4. Type of Sampling: Sampling technique plays an important part in determining the size of
the sample. A small random sample is apt to be much superior to a larger but badly
selected sample.
5. Standard of accuracy and acceptable confidence level: If the standard of accuracy or the
level of precision is to be kept high, we shall require relatively larger sample. For
doubling the accuracy for a fixed significance level, the sample size has to be increased
fourfold.
6. Availability of finance: In practice, size of the sample depends upon the amount of
money available for the study purposes. This factor should be kept in view while
determining the size of the sample for large samples result in increasing the cost of
sampling estimates.
Other considerations: Nature of units, size of the population, size of questionnaire, availability of
trained investigators, the conditions under which the sample is being conducted, the time
available for completion of the study are a few other considerations to which a researcher must
pay attention while selecting the size of the sample
7.10 Sampling Distributions
The process of generalizing the sample results of the population is referred to as statistical
inference. Here, we shall use certain sample statistics (such as the sample mean, the sample
proportion, etc.) in order to estimate and draw inferences about the true population parameters.
For example, in order to be able to use the sample mean to estimate the population mean, we
should examine every possible sample (and its mean) that could have occurred in the process of
selecting one sample of a certain size. If this selection of all possible samples actually were to be
done, the distribution of the results would be referred to as a sampling distribution. Although, in
practice, only one such sample is actually selected, the concept of sampling distributions must be
examined so that probability theory and its distribution can be used in making inferences about
the population parameter values.
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Sampling theory has made it possible to deal effectively with these problems. However, before
we discuss in detail about them from the standpoint of sampling theory, it is necessary to
understand the central limit theorem and the following three probability distributions, their
characteristics and relations:
(1) The population (universe) distribution,
(2) The sample distribution, and
(3) The sampling distribution.
7.11 Central Limit Theorem:
The Central Limit Theorem, first introduced by De Moivre during the early eighteenth century,
happens to be the most important theorem in statistics. According to this theorem, if we select a
large number of simple random samples, say, from any population distribution and determine the
mean of each sample, the distribution of these sample means will tend to be described by the
normal probability distribution with a mean μ and variance σ2/n. This is true even if the
population distribution itself is not normal. Or, in other words, we say that the sampling
distribution of sample means approaches to a normal distribution, irrespective of the distribution
of population from where sample is taken and approximation to the normal distribution becomes
increasingly close with increase in sample size. Symbolically, the theorem can be explained as
follows:
When given n independent random variables X1, X2,X3……Xn, which have the same
distribution (no matter what the distribution), then:
X= X1+X2+X3+…….Xn
is a normal variate. The mean μ and variance σ2 of X are
μ = μ1+ μ2+ μ3+…+ μn = n μi
σ2 = σ21+ σ22+ σ23 +…+ σ2n= n σ2i
where μi and σ2i are the mean of Xi.
The utility of this theorem is that it requires virtually no conditions on distribution patterns of the
individual random variable being summed. As a result, it furnishes a practical method of
computing approximate probability values associated with sums of arbitrarily distributed
independent random variables. This theorem helps to explain why a vast number of phenomena
show approximately a normal distribution. Let’s consider a case when the population is skewed,
skewness of the sampling distribution of means is inversely proportional to the square root of the
sample size. Consider the case when n=16 that means is inversely proportional to the square root
of the sample size. Consider the case when n=16 that means the sampling distribution of means
will exhibit only one-fourth as much skewness as the population has. Consider the case when
n=100, skewness becomes one-tenth as much, ie., as the sample size increases, the skewness will
decrease. As a practical consequence, the normal curve will serve as a satisfactory model when
samples are small and population is close to a normal distribution, or when samples are large and
population is markedly skewed. Because of its theoretical and practical significance, this theorem
is considered as most remarkable theoretical formulation of all probability laws.
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The Population (Universe) Distribution
When we talk of population distribution, we assume that we have investigated the population and
have full knowledge of its mean and standard deviation. For example, a company might have
manufactured 1, 00,000 tyres of cars in the year 2004. Suppose, it contacts all those who had
bought these tyres and gathers information about the life of these tyres. On the basis of the
information obtained, the mean of the population which is also called true mean symbolized by μ
and its standard deviation symbolized by σ can be worked out. These Greek letters μ and σ are
used for these measures to emphasise their difference from corresponding measure taken from a
sample. It may be noted such measures characterizing a population care called population
parameters.
The shape of the distribution of the life of tyres may be as follows:
Distribution of the Life of Tyres
It is clear from above that, though, the distribution shows slight skewness,
it does not depart radically from a normal distribution. However, this should not lead one to the
conclusion that for sampling theory to apply, it is necessary that the distribution must be
normally distributed.
7.12 The Sample Distribution
When we talk of a sample distribution, we take a sample from the population. A sample
distribution may take any shape. The mean and standard deviation of the sample distribution are
symbolized by x and s respectively. A measure characterizing a sample such as x or s is called a
sample statistic. It may be noted that several sample distributions are possible from a given
population.
Suppose, in the above illustration, the manufacturer takes a s sample of 500 tyres. He contacts
the buyers and enquiries about he life of tyres. The shape of the distribution of these tyres may
be as follows:
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Sample distribution of 500 tyres
The mean values of these tyres can be expected to differ somewhat from one sample to another.
The sample means constitute the raw material out of which a sampling distribution is
constructed.
Sampling distributions constitute the theoretical basis of statistical inference and are of
considerable importance in business decision making. If we take numerous different samples of
equal size from the same population, the probability distribution of all the possible values of a
given statistic from all the distinct possible samples of equal size is called a sampling
distribution. It is interesting to note that sampling distributions closely approximate a normal
distribution. It can be see that the mean of a sampling distribution of sample means is the same
as the mean of the population distribution from which the sample are taken.
The mean of the sampling distribution is designated by the same symbol as the mean of the
population, namely μ. However, the standard deviation of the sampling distribution of means
given a special name, standard error of mean, and is symbolized by σxˉ. The subscript indicates
that in this case, we are dealing with a sampling distribution of means.
The greatest importance of sampling distributions is the assistance that they give us in
revealing the patterns of sampling errors and their magnitude in terms of standard error. In
sampling with replacement, we can observe a good deal of fluctuations in the sample mean as
compared to fluctuations in the actual population. The fact that the sample means are less
variable than the population data follows logically from an understanding of the averaging
process. A particular sample mean averages together all the values in the sample. A population
(universe) may consist of individual outcomes that can take on a wide range of values from
extremely small to extremely large. However, if an extreme value falls into the sample, although
it will have an effect on the mean, the effect will be reduced since it is being averaged in with all
the other values in the sample. Moreover, as the sample size increases, the effect of a single
extreme value gets even smaller, since it is being averaged with more observations. This is a
single extreme value gets even smaller, since it is being averaged with more observations. This
phenomenon is expressed statistically in the value of the standard deviation of the sample mean.
This is the measure of variability of the mean from sample to sample and is referred to as the
standard deviation of the sampling distribution of sample mean or the standard error of the mean
denoted as σxˉ and is calculated by
σxˉ = σ/ √n
This formula holds only when population is infinite or sample are from finite population with
replacement.
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It may be noted that in deducing a sampling distribution, we must first make an assumption
about the appropriate parameter. In as much as any value can be assumed for a parameter. In as
much as any value can be assumed for a parameter, depending upon our knowledge or a guess of
the population, there is no theoretical limit to the number of sampling distribution of the same
sample size that can be taken from the population. There is a sampling distribution for each
assumed value of a parameter. Also, given the assumed value of a parameter, there is a different
sampling distribution of statistics for each specific sample size. Further, under the same
assumptions about a population and the same sample size, the distribution of one statistic differs
from that of another statistic. For example, the pattern of the distribution of Xˉ (x bar) will differ
from that of s2, even though both measures are computed from the same sample.
7.12.1 Relationship between Population, Sample and Sampling Distribution
It will be interesting to note that the mean of the sampling distribution is the same as the mean of
the population. It is possible that many sample means may differ from the population mean.
However, the sample information can be used as an estimate of population values.
It has also been established that the observed standard deviation of a sample is close to the
standard deviation of the population values.
In fact, the standard deviation of the sample is usually so good an approximation that it can
safely be used as an estimate of the corresponding population measure. In order to use s of the
sample to estimate σ of the population, we make a slight adjustment which has been found to
contribute to greater accuracy of the estimate. The adjustment consists of using (n-1) instead of n
in the formula for the standard deviation of a sample, i.e., we use
s =√{ ∑(x-xˉ)/n-1}
The adjustment decreases the denominator and, therefore, gives a larger result. Thus, the
estimated standard deviation of the population is slightly larger than the observed standard
deviation of the sample
Important sampling distributions
Some important sampling distribution, which are commonly used are: (1) sampling distribution
of mean; (2) sampling distribution of proportion; (3) student’s,‘t’ distribution; (4) F distribution;
and (5) Chi-square distribution. A brief mention of sampling distribution of mean is described
below:
7.12.2 Sampling distribution of mean:
Sampling distribution of mean refers to the probability distribution of all the possible means of
random samples if a given size that we take from a population. If samples are taken from a
normal population, N(µ, σxˉ), the sampling distribution of mean would also be normal with mean
µx¯ = µ and standard deviation σxˉ=σ/√n where µ is the mean of the population, σxˉ is the
standard deviation of the population and n means the number of items in a sample. But when
sampling is from a population which is not normal (may be positively or negatively skewed),
even then, as per the central limit theorem, the sampling distribution of mean tends quite closer
to the normal distribution, provided the number of sample items is large i.e., more than 30. In
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case we want to reduce the sampling distribution of mean to unit normal distribution i.e., N(0,1),
we can write the normal variable
z = (x¯-µ)/( σ/√n)
for the sampling distribution of mean. This characteristic of the sampling distribution of mean is
very useful in several decision situations for accepting or rejection of hypothesis
Review Questions
1. Describe the different sampling techniques.
2. Discuss when it is suitable to use each of the sampling techniques above.
3. Discuss the merits and demerits of different sampling techniques
4. Differentiate between a sample and a population.
5. Discuss the points you should consider in determining the sample size.
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LECTURE EIGHT
TESTING OF HYPOTHESES
Lecture. Outline
 Introduction
 Testing hypotheses
 Definition hypothesis
 Procedure for hypothesis testing
 Type I and Type II errors
 One tailed and 2 tailed tests
8.0 Introduction
This lecture introduces you to different methods of testing hypotheses and analyzing data to
come up with useful information. It defines a hypothesis and names the different types of
hypotheses. It also defines the different errors that are often encountered when carrying out
research.
A hypothesis is an assumption about the population parameter to be tested based on sample
information. The statistical testing of hypothesis is the most important technique in statistical
inference. Hypothesis tests are widely used in business and industry for making decisions. It is
here that probability and sampling theory plays an ever-increasing role in constructing the
criteria on which business decisions are made. Very often in practice we are called upon to
make decisions about population on the basis of sample information. For example, we may wish
to decide on the basis of sample data whether a new medicine is really effective in curing a
disease, whether one training procedure is better than another, etc. Such decisions are called
statistical decisions. In other words, a hypothesis is the assumption that we make about the
population parameter. This can be any assumption about a population parameter not necessarily
based on statistical data. For example it can also be based on the gut feel of a manager.
Managerial hypotheses are based on intuition; the market place decides whether the manager’s
intuitions were in fact correct.
In fact managers propose and test hypotheses all the time. For example:
1. If a manager says ‘if we drop the price of this car model by Rs15000, we’ll increase sales by
25000 units’ is a hypothesis. To test it in reality we have to wait to the end of the year to and
count sales.
2. A manager estimates that sales per territory will grow on average by 30% in the next quarter is
also an assumption or hypotheses. How would the manager go about testing this assumption?
Suppose he has 70 territories under him.
One option for him is to audit the results of all 70 territories and determine whether the average
growth is greater than or less than 30%. This is a time consuming and expensive procedure.
Another way is to take a sample of territories and audit sales results for them. Once we have our
sales growth figure, it is likely that it will differ somewhat from our assumed rate. For example
we may get a sample rate of 27%. The manager is then faced with the problem of determining
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whether his assumption or hypothesized rate of growth of sales is correct or the sample rate of
growth is more representative.
To test the validity of our assumption about the population we collect sample data and determine
the sample value of the statistic. We then determine whether the sample data supports our
hypotheses assumption regarding the average sales growth.
8.1 What is Hypothesis?
In attempting to reach decisions, it is useful to make assumptions or guesses about the
populations involved. Such assumptions, which may or may not be true, are called statistical
hypothesis and in general are statements about the probability distributions of the population.
The hypothesis is made about the value of some parameter, but the only facts available to
estimate the true parameter are those provided by a sample. If the sample statistic differs from
the hypothesis made about the population parameter, a decision must be made as to whether or
not this difference is significant. If it is, the hypothesis is rejected. If not, it must be accepted.
Hence, the term "tests of hypothesis".
Now, if Ө be the parameter of the population and is the estimate of Өˆ in the random sample
drawn from the population, then the difference between Ө and Өˆ should be small. In fact, there
will be some difference between Ө and Өˆ because Өˆ is based on sample observations and is
different for different samples. Such a difference is known as difference due to sampling
fluctuations. If the difference between Ө and Өˆ is large, then the probability that it is
exclusively due to sampling fluctuations is small. Difference which is caused because of
sampling fluctuations is called insignificant difference and the difference due to some other
reasons is known as significant difference. A significant difference arises due to the fact that
either the sampling procedure is not purely random or sample is not from the given population.
8.2 Procedure for Hypotheses Testing
The general procedure followed in testing hypothesis comprises the following steps:
Set up a hypothesis. The first step in hypothesis testing is to establish the hypothesis to be
tested. Since statistical hypothesis are usually assumptions about the value of some unknown
parameter, the hypothesis specifies a numerical value or range of values for the parameter. The
conventional approach to hypothesis testing is not to construct single hypothesis about the
population parameter, but rather to set up two different hypothesis. These hypothesis are
normally referred to as (i) null hypothesis denoted by Ho and (ii) alternative hypothesis denoted
by H1. The null hypothesis asserts that there is no true difference in the sample statistic and
population parameter under consideration (hence the word "null" which means invalid, void or
amounting to nothing and that the difference found is accidental arising out of fluctuations of
sampling. A hypothesis which states that there is no difference between assumed and actual
value of the parameter is the null hypothesis and the hypothesis that is different from the null
hypothesis is the alternative hypothesis. If the sample information leads us to reject Ho then we
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will accept the alternative hypothesis H1 Thus, the two hypothesis are constructed so that if one
is true, the other is false and vice versa.
The rejection of the null hypothesis indicates that the differences have statistical significance
and the acceptance of the null hypothesis indicates that the differences are due to chance. As
against the null hypothesis, the alternative hypothesis specifies those values that the researcher
believes to hold true. The alternative hypothesis may embrace the whole range of values rather
than single point.
o Set up a suitable significance level. Having set up a hypothesis, the next step is to select
a suitable level of significance. The confidence with which an experimenter rejects or
retains null hypothesis depends on the significance level adopted. The level of
significance, usually denoted by "α", is generally specified before any samples are
drawn, so that results obtained will not influence our choice. Though any level of
significance can be adopted, in practice, we either take 5 per cent or 1 per cent level of
significance. When we take 5 per cent level of significance then there are about 5
chances out of 100 that we would reject the null hypothesis when it should be accepted,
i.e., we are about 95% confident that we have made the right decision. When we test a
hypothesis at a 1 per cent level of significance, there is only one chance out of 100 that
we would reject the null hypothesis when it should be accepted, i.e., we, are about 99%
confident that we have made the right decision. When the null hypothesis is rejected at α
= 0.5, the test result is said to be "significant". When the null hypothesis is rejected at α
= 0.01, the test result is said to be "highly significant".
o Determination of a suitable test statistic. The third step is to determine a suitable test
statistic and its distribution. Many of the test statistics that we shall encounter will be of
the following form:
o D
e
t
ermine the critical region. It is important to specify, before the sample is taken, which
values of the test statistic will lead to a rejection of Ho and which lead to acceptance of
Ho. The former is called the critical region. The value of α, the level of significance,
indicates the importance that one attaches to the consequences associated with
incorrectly rejecting Ho. It can be shown that when the level of significance is α, the
optimal critical region for a two-sided test consists of that α/2 per cent of the area in the
right-hand tail of the distribution plus that α/2 percent in the left hand tail. Thus,
establishing a critical region is similar to determining a 100(I - α)% confidence interval.
In general, one uses a level of significance of α = 0.05, indicating that one willing to
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accept a 5 per cent chance of being wrong to reject Ho.
o Doing computations. The fifth step in testing hypothesis is the performance of various
computations from a random sample of size n, necessary for the test statistic obtained in
step 7.3.3. Then, we need to see whether sample result falls in the critical region or in
the acceptance regions.
o Making decisions. Finally, we may draw statistical conclusions and the management
may take decisions. A statistical decision or conclusion comprises either accepting the
null hypothesis or rejecting it. The decision will depend on whether the computed value
of the test criterion falls in the region of rejection or the region of acceptance. If the
hypothesis is being tested at 5 per cent level of significance and the observed set of
results has a probability less than 5 per cent, we reject the null hypothesis and the
difference between the sample statistic and the hypothetical population parameter is
considered to be significant. On the other hand, if the testing statistic falls in the region
of non-rejection, the null hypothesis is accepted and the difference between the sample
statistic and the hypothetical population parameter is not regarded as significant, i. e., it
can be explained by chance variations.
8.3 Type I and Type II Errors
When a statistical hypothesis is tested, there are four possible results:
(I) the hypothesis is true but our test rejects it.
(2) The hypothesis is false but our test accepts it.
(3) The hypothesis is true and our test accepts it.
(4) The hypothesis is false and our test rejects it.
Obviously, the first two possibilities lead to errors. If we reject a hypothesis when it should be
accepted (possibility No.1), we say that a Type I error has been made. On the other hand, if we
accept a hypothesis when it should be rejected (possibility No.2), we say that a Type II error has
been made. In either case a wrong decision or error in judgment has occurred.
The probability of committing a type I error is designated as "α." and is called the level of
significance. Therefore,
α = P r [Type I error]
= Pr [Rejecting Ho| Ho is true]
must be the complement of
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(I - α) = Pr [Accepting Ho| Ho is true].
This probability (I - α) corresponds to the concept of 100(1- α) % confidence interval. Our
efforts would obviously be to have a small probability of making a type I error. Hence the
objective is to construct the test to minimize α.
Similarly, the probability of committing a type II error is designated by β. Thus
β = P r [Type II error]
= Pr [Accepting HoI Ho is false]
and
(1 - β) = Pr [Rejecting HolHo is false].
This probability (1 - β) is known as the power of a statistical test.
The following table gives the probabilities associated with each of the four cells shown in the
previous table:
The decision is :
Accept Ho
Reject Ho
Sum
The null hypothesis is
True
False
(1 -α)
Confidence level
β
(1- β)
α
Power of the test
1.00
1.00
Note that the probability of each decision outcome is a conditional probability and the
elements in the same column sum to 1.0, since the events with which they are associated are
complement. However, α and β are not independent of each other, nor are they independent of
the sample size n. When n is fixed, if α is lowered then β normally rises and vice versa. If n is
increased, it is possible for both α and β to decrease. Since, increasing the sample size involves
money and time, therefore, one should decide how much additional money and time, he is
willing to spare on increasing the sample size in order to reduce the size of α and β.
In order for any tests of hypothesis or rules of decisions to be good, they must be designed so as
to minimise errors of decision. However, this is not a simple matter, since for a given sample
size, an attempt to decrease one type of error is accompanied in general by an increase in other
type of error. The probability of making type I error is fixed in advance by the choice of level of
significance employed in the test. We can make the type I error as small as we please, by
lowering the level of significance. But by doing so, we increase the chance of accepting a false
hypothesis, i. e., of making a type II error. It follows that it is impossible to minimize both
errors simultaneously. In the long run, errors of type I are perhaps more likely to prove serious
in research programmes in social sciences than are errors of type II. In practice, one type of
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error may be more serious than the other and so a compromise should be reached in favour of
limitations of the more serious error. The only way to reduce both types of error is to increase
the sample size that may or may not be possible.
8.3.1 One-Tailed and Two-Tailed Tests
Basically, there are three kinds of problems of tests of hypothesis. They include:
(i) two-tailed tests, (ii) right-tailed test, and (iii) left-tailed test.
Two-tailed test is that where the hypothesis about the population mean is rejected for value of
falling into either tail of the sampling distribution. When the hypothesis about population mean
is rejected only for value of falling into one of the tails of the sampling distribution, then it is
known as one-tailed test. If, it is right tail then it is called right-tailed test or one-sided alternative
to the right and if it is on the left tail, then, it is one-sided alternative to the left and called lefttailed test.
For example, Ho: μ = 100 tested against H1: μ > 100 or < 100 is one-tailed test since HI specifies
that μ lies on particular side of 100. The same null hypothesis tested against H1: μ ≠ 100 is a twotailed test since μ can be on either side of 100. The following diagrams would make it clearer:
The following table gives critical values of Z for both one-tailed and two-tailed tests at
various levels of significance. Critical values of Z for other levels of significance are found by
use of the table of normal curve areas:
Level of Significance
Critical value of z for one-
0.10
-1.28
0.05
-1.645
tailed tests
or 1.28
or 1.645
Critical value of z for two-
- 1.645
and
1.645
- 1. 96
tailed tests
STUDY MATERIAL FOR TEAM UNIVERSITY
and I. 96
0.01
-2.33
or
2.33
- 2.58
and
2.58
0.005
-2.58
0.0002
-2.88
or 2.58
or 2.88
-2.81
-3.08
and 2.81 and 3.08
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and
the
that
and
be
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Review
Questions:
1. Define a
hypothesis.
2.
Differentiate
between a null
an
alternative
hypothesis
3. Describe
procedure to be
followed when
testing
a
hypotheisis.
4. State the
different errors
may
occur
during research
explain
how
such errors can
corrected
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LECTURE NINE
IMPORTANT SAMPLING DISTRIBUTIONS
Lecture Outline:
 Introduction
 Z test
 CHI square test
 T- test
9.0 Introduction
This lecture looks at different sampling distributions and how they can be used to analyse data.
We shall look at the Z test, T- test and Chi square test.
Lecture Objectives:
By the end of this lecture, you should be able to
 Use the different sampling distributions to analyse data.
 Evaluate the suitability of each sampling technique to data analysis.
 Interpret the results got from the use of the above sampling distributions.
9.1 Z TEST: Tests of Hypothesis Concerning Large Samples
Though, it is difficult to draw a clear-cut line of demarcation between large and small samples,
it is generally agreed that if the size of sample exceeds 30, it should be regarded as a large
sample. The tests of significance used for large samples are different from the ones used for
small samples for the reason that the assumptions we make in case of large samples do not hold
for small samples. Tests of hypothesis involving large samples are based on the following
assumptions:
(1) The sampling distribution of a sample statistic is approximately normal.
(2) Values given by the samples are sufficiently close to the population value and can be
used in its place for the standard error of the estimate.
Thus, we have seen that the normal distribution plays a vital role in tests of hypothesis based
on large samples (central limit theorem).
Suppose Өˆis an unbiased estimate of Өˆ, the population parameter. On the basis of Өˆ ,
taken from sample observations, it is to test the hypothesis whether the sample is drawn from a
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population whose parameter value is Ө, i. e., we have to test the hypothesis
Ho: Ө= Өˆ
If the Sampling distribution of Ө is normal, then
Let us test the hypothesis at 100 α% level of significance. From tables of area under the standard
normal curve corresponding to given α, we can find an ordinate z α such that
Pr[IzαI>zα]=α
P r [ - z α ≤ Z ≤ z α] = 1 – α
If α = .01, then z α = 2.58 and if α = 0.05, then z α = 1.96, and so on.
If the difference between Ө and Өˆ is more than z α times, the standard error of Өˆ , the
difference is regarded significant and Ho is rejected at 100 α % level of significance and if the
difference between Ө and Өˆ is less than or equal to z α times the standard error of Өˆ , the
difference is insignificant and Ho is accepted at 100 α % level of significance.
Testing Hypothesis about the Difference between Two Means:
a) For the hypothesis testing concerning the population parameter μ by considering the two-tailed
test.
Ho: μ= μo
Since the best unbiased estimator of μ is the simple mean x` (x bar), therefore, we shall focus our
attention on the sampling distribution of x`(x bar). From Central Limit theorem, we know that
x` (x bar) ~ N(μ,σx)
z = (x`- μ)/σx
where
σx = σ/ √ N = s/ √ N
( if s is unknown for large samples)
If the calculated value of z<-z α/2 or z>z α/2 , the null hypothesis is rejected.
a) If the hypothesis involves a right-tailed test. For example,
Ho: μ ≤ μo and H1: μ > μo
For the calculated values z> z α , the null hypothesis is rejected.
b) If the hypothesis involves a left-tailed test. For example,
Ho: μ ≥ μo and H1: μ < μo
For the calculated values z<-z α, the null hypothesis is rejected.
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Testing Hypothesis about the Difference between two Means
The test statistic for testing the difference between two population means, when the populations
are normally distributed, is based on the general form of the standard normal statistic as given
below:
Z= (Өˆ- Ө) / σ Өˆ
where θ= μ1-μ2
Therefore the z statistic is given by
The null hypothesis is Ho: μ1-μ2 =0
Then, the z statistic is reduced to
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At 5% level of significance, the critical value of z for two-tailed test = ± 1.96. If the computed
value of z is greater than +1.96 or less than –1.96, then reject Ho, otherwise accept Ho.
S12 and S22 can be used if the values of σ12 and σ22 are unknown.
Illustration2: You are working as a purchase manager for a company. Two manufacturers of
electric bulbs have supplied the following information to you
Mean Life(in hours)
Standard Deviation
hours)
Sample Size
(in
Company A
1300
Company B
1288
82
93
100
100
Which brand of bulb are you going to purchase if you desire to take a risk of 5%?
9.2 Theory for Small Samples
If the original population is normally distributed, all sampling distributions of the mean shall be
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normally distributed regardless of the sample size (central limit theorem). If the original
population is normally distributed and the standard deviation of the population is unknown (and
therefore, has to be estimated from a sample), the sampling distribution of the mean derived
from large samples will also be normally distributed, but if the sample size is small (say 30, or
less) then the sample statistic will follow a t-distribution.
The Student's t-distribution obtained by W.S. Gosset was published under the pen name of
"Student" in the year 1908. It is reported that Gosset was a statistician for a brewery, and that
the management did not want him to publish his scholarly theoretical work under his real name
and bring shame to his employer. Consequently, he selected the pen name of Student.
The study of statistical inference with the small samples is called small sampling theory or
exact sampling theory. We shall discuss in detail the "t" and "F' distributions. These two
distributions are defined in terms of number of degrees of freedom. It is appropriate at this
stage to clarify this concept.
9.3.1 Degrees of freedom:
The number of degrees of freedom can be interpreted as the number of useful items of
information generated by a sample of given size with respect to the estimation of a given
population parameter. Thus, a sample of size 1 generates one piece of useful information if one
is estimating the population mean, but none, if one is estimating the population variance. In
order to know about the variance, one need at least a sample of size n≥ 2. The number of
degrees of freedom, in general, is the total number of observations minus the number of
independent constraints imposed on the observations.
Suppose the expression ∑X = X1 + X2 + X3 has four terms. We can arbitrarily assign values to
any three of these four values (for example, 15 = X1 + 2 + 8) but the value of the fourth is
automatically determined (for example, X1 = 5).
In this example, there are 3 degrees of freedom. If n is the number of observations and k is the
number of independent constants (the number of constants that have to be estimated from the
original data) then n - k is the number of degrees of freedom.
If we consider sample of size n drawn from a normal (or approximately normal) population with
mean μ and if for each sample we compute t, using the sample mean x` and sample standard
deviation s, the distribution for t can be obtained. The probability density function of the tdistribution is given by
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(1) The t-distribution ranges from -∞ to ∞ just as does a normal distribution.
(2) The t-distribution like the standard normal distribution is bell-shaped and symmetrical around
mean zero.
(3) The shapes of the t-distribution changes as the number of degrees of freedom changes.
Therefore, for different degrees of freedom, the t-distribution has a family of t-distributions.
Hence, the degrees of freedom v is a parameter of the t distribution.
(4) The variance of the t-distribution is always greater than one and is defined only when v≥ and is
given as:
(5) The t-distribution is more of platykurtic (less peaked at the centre and higher in tails) than the
normal distribution.
(6) The t-distribution has a greater dispersion than the standard normal distribution. As n gets
larger, the t-distribution approaches the normal form. When n is as large as 30, the difference is
very small. Relation between the t-distribution and standard normal distribution is shown in the
diagram.
Properties of t-Distribution
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The t-distribution has different shapes depending on the size of the sample. When the sample is
quite small, for example, if n equals five, the height of the t-distribution is shorter than the
normal distribution and the tails are wider. As n nears 30, however, the I-distribution approaches
the normal distribution in shape.
The t-table: The t-table given is the probability integral of t-distribution. It gives over a range of
values of v at different levels of significance. By selecting particular degrees of freedom and
level of significance, we determine the tabular value of t. We establish a null hypothesis, and if
our computed t is greater than the tabular t, we reject the null hypothesis; if our computed t is
smaller than the tabular t, we accept the null hypothesis.
Applications of t-distribution. The following are some important applications of the tdistribution:
(I) Test of Hypothesis about the population mean.
(2) Test of Hypothesis about the difference between two means.
(3) Test of hypothesis about the difference between two means with dependent samples.
(4) Test of hypothesis about coefficient of correlation.
We would consider application (1) and (2) for our study
(I) Test of Hypothesis about the Population Mean (0" unknown and sample size is small).
When the population distribution is normal and standard deviation 0" is unknown then the "t"
statistic is defined as :
follows the Student’s t-distributions with (n-1) degree of freedom.
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Illustration 3. Prices of shares in Rs. of a company on the different days in a month were found
The null hypothesis to be tested is whether there is a significant difference between x`(x
bar) and μ.
If the calculated value of t exceeds the table value of t at a specified level of significance,
the null hypotheses is rejected and the difference between x`(x bar) and μ is regarded
significant.
If the calculated value of t is less than the table value of t at a specified level of
significance, the null hypotheses is rejected and the difference between x`(x bar) and μ is
not considered significant. This test is based on n-1 degrees of freedom.
to be:
66 ,65 , 69, 70, 69, 71, 70, 63, 64 and 68
Test Whether the mean price of the shares in the month is 65
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(2) Test of Hypothesis about the Difference between Two Means
In testing a hypothesis concerning the difference between the means of two normally distributed
populations when the population variances are unknown, the t-test can be used in two types of
cases:
(a) the case in which variances are equal, i.e., σ12=σ22, (b) the case in which variances are not
equal, i.e σ12≠σ22,
(b) Case of equal variances. Let the null hypothesis be that there is no significant difference between the means of the two populations, i.e., Ho:μ1=μ2 When the population variances (though
unknown) are equal then the appropriate test statistic to be used is
will follow t-distribution with (n1+n2-2) degree of freedom, where x1ˉ and x2ˉ are sample means
of size n1 and sample 2 of size n2 respectively; μ1 and μ2 are the population means, and s is
"pooled" estimate of the common population standard deviation obtained by pooling the data
nom both the samples as given below:
If the computed value of t is less than the table value of t at a specified level of significance, the
null hypothesis is accepted and the difference between the two means is regarded as
insignificant. If the computed value of t is more than the table value of t, the null hypothesis is
rejected and the difference between the sample means is regarded as significant.
9.4. CHI SQUARE TEST
The chi-square test, written as ψ2 - test, is a useful measure of comparing experimentally
obtained results with those expected theoretically and based on the hypothesis. It is used as a test
statistic in testing a hypothesis that provides a set of theoretical frequencies with which observed
frequencies are compared. In general Chi-square test is applied to those problems in which we
study whether the frequency with which a given event has occurred is significantly different
from the one as expected theoretically. The measure of Chi-square enables us to find out the
degree of discrepancy between observed frequencies and theoretical frequencies and thus to
determine whether the discrepancy so obtained between observed frequencies and theoretical
frequencies is due to error of sampling or due to a chance.
The Chi-square is computed on the basis of frequencies in a sample and thus the value of Chisquare so obtained is a statistic. Chi-square is not a parameter as its value is not derived from the
observations in a population. Hence Chi-square test is a Non-Parametric test. Chi-square test is
not concerned with any population distribution and its observations.
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The Χ2 test was first used in testing statistical hypothesis by Karl Pearson in the year 1900. It is
defined as
where Oi = observed frequency of ith event,
Ei = Expected frequency of ith event.
We require the following steps to calculate ψ2.
Step 1. Calculate all the expected frequencies, i.e., Ei for all values of i = 1,2, ..n.
Step 2. Take the difference between each observed frequency Oi and the corresponding expected
frequency Ei for each value of i, i.e., find (Oi - Ej)
Step 3. Square the difference for each value of i, i.e., calculate (Oi – Ei)2 for all values of i = I, 2,
3,
, n.
Step 4. Divide each square difference by the corresponding expected frequency, i.e.,
Calculate
for all the values of I=1,2,….,n.
Step 5 Compute
It should be noted that
(a) The value of ψ2 is always positive as each pair is a squared one.
(b) ψ2 will be zero if each pair is zero and it may assume any value extending to infinity, when
the difference between the observed frequency and expected frequency in each pair is unequal.
Thus ψ2 lies between 0 and ∞
(c ) The significance test on ψ2 is always based on One Tailed test of the right hand side of the
standard curve ψ2 is always non-negative.
9.4.1 Degrees of Freedom
The number of data that are given in the form of a series of variables in a row or column or the
number of frequencies that are put in cells in a contingency table, which can be calculated
independently is called the degrees of freedom and is denoted by v.
Case I If the data is given in the form of a series of variables in a row or column, then the
Degrees of freedom = (number of items in the series) - 1, i.e.,
V = n -1, where n is the number of variables in the series in a row or column.
Case II When the number of frequencies are put in cells in a contingency table, the degrees of
freedom will be the product of (number of rows less one) and the (number of columns less one),
i.e., V = (R -1) (C -1), where R is the number of rows and C is the number of columns.
Chi-Square distribution is a continuous distribution whose probability density function is given
by:
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9.4.2 Properties of Chi- Square distribution
1. Chi-square curve is always positively skewed.
2. The mean of chi-square distribution is the number of degrees of freedom.
3. The standard deviation of chi-square distribution =√2v; where v is the degrees of
freedom.
4. Chi-square values increases with the increase in degrees of freedom.
The value of chi-square lies between zero and infinity.
5. The sum of two chi-square distributions is again a chi-square distribution.
6. For different degrees of freedom, the shape of the curve will be different. 7. Its shape
depends on the degree of freedom but it is not a symmetrical distribution.
9.4.5 USES OF ψ2TEST
The ψ2 test is a very powerful test for testing the hypothesis of a number of statistical
problems. The important uses of ψ2 test are:
1.Test of Goodness of Fit. If the two curves, viz, (i) Observed frequency curve and (ii) the
expected frequency curve, .are drawn, then the Chi-square statistic may be used to determine
whether the two curves so drawn are fitted good or not. Thus, the term goodness of fit is used to
test the concordance of the fitness of these two curves. Under this test there is only one variable,
i.e., the degrees of freedom v = n -1.
2.Test of Independence of Attributes. The Chi-square test is used to see that the principles of
classification of attributes are independent. In this test the attributes are classified into a twoway table or a contingency table as the case may be. The observed frequency in each cell
(square) is known as
Cell frequency. The total frequencies in each row or column of the two way contingency table is
known as Marginal frequency.
The degrees of freedom are v = (R -1) (C -1),
where R = number of rows, C = number of columns in the two way contingency table. This
test discloses whether there is any association or relationship between two or more attributes.
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9.4.6 Conditions For Applying The Chi-Square Test
1. Each of the observations constituting the sample for this test should be independent of
each other.
2. The expected frequency of any item or cell should not be less than 5. If it is less than 5,
then frequencies from the adjacent items or cells are pooled together in order to make it 5 or
more than 5.
3. The total number of observations used in this test must be large,i.e., n > 30.
4. This test is used only for drawing inferences by testing hypothesis. It cannot be used for
estimation of parameter or any other value.
5. It is wholly dependent on the degrees of freedom.
6. The frequencies used in ψ2-test should be absolute and not relative in terms.
7. The observations collected for ψ2-test should be on random basis of sampling.
9.4.7 Working Rule For ψ2 -Test
The Chi-square test is widely used to test the independence of attributes. It is applied to test
the association between the attributes when the sample data is presented in the form of a
contingency table with any number of rows or columns.
Step 1. Set up the Null Hypothesis Ho : No Association exists between the attributes.
Alternative Hypothesis HI: An association exists between the attributes
Step 2. Calculate the expected frequency E corresponding to each cell by the formula
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Step 3. Calculate ψ2 -statistic by the fonnula
The characteristics of this distribution are completely defined by the number of degrees of freedom v
which is given by v = (R - 1) (C - 1),
where R = number of rows. and C = number of columns in the contingency table
Step 4. Find from the table the value of ψ2 for a given value of the level of significance α and for
the degrees of freedom v, calculated in STEP 2. If no value for α is mentioned, then take α =
0.05.
Step 5. Compare the computed value of ψ2, with the tabled value of ψ2 found in
(a) If calculated value of ψ2 < tabulated value of ψ2, then accept the null
hypotheses Ho
(b) If calculated value of ψ2 > tabulated value of ψ2 , then reject the null
hypotheses Ho and accept the alternative hypothesis H1
9.4.7 Ψ2 Test For Goodness of Fit
ψ2 -test is a measure of probabilities of association between the attributes. It gives us an idea
about the divergence between the observed and expected frequencies. Thus the test is also
described as the test of "Goodness of Fit". If the curves of these two distributions, when
superimposed do not coincide or appear to diverge much we say that the fit is poor. On the other
hand if they don't diverge much, then the fit is less poor.
Illustration 4. A survey of 320 families with 5 children each revealed the
No. of boys:
5
4
5
2
1
0
No. of girls:
0
1
2
3
4
5
No. of families:
14
56
110
88
40
12.
Is this result consistent with the hypothesis that the male and female births are equally
probable?
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9.4.8 Ψ2 Test As A Test Of Independence
Ψ2 -test can also be applied to test, the independence between various attributes when the sample
data is presented in the form of a contingency table with any number of rows 'R' and columns
'C'. The null hypothesis and alternative hypothesis are set as follows:
Null Hypothesis Ho: The attributes are independent.
Alternative Hypothesis H1: The attributes are not independent.
We then calculate Ψ2 If the calculated value of Ψ2 is less than the tabled value of Ψ2α,v at a
given level of significance α and degrees of freedom v, the hypothesis is accepted and viceversa.
Illustration 5. 50 students selected at random from 500 students enrolled in a computer crash
programme were classified according to age and grade points giving the following data.
Grade Points
Age (in years)
20 and under
21 - 30
Above 30
Upto 5.0
3
5
2
5.1 to 7.5
8
7
5
7.6 to 10.0
4
8
8
Test at 5% level of significance the hypothesis that age and grade point are independent.
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Report Writing
Contents:
Significance of Report Writing
Steps in Writing Report
Layout of Research Report
Precautions for Writing a Research Report
Significance of Report Writing
Review Questions:
1. Describe the different tests that can be used when the population is small or when the
population is large.
2. Discuss the suitability of each test statistic in analyzing research data.
LECTURE TEN
REPORT WRITING
Lecture Outline:
 Introduction
 Contents of a report
 Significance of report writing
 Steps in report writing
 Lay out of research report
10.0 Introduction:
This is the last lecture of this paper and it looks at how to write a research report.The task of
research remains incomplete until the report has been presented and/or written. The results of
research must invariably enter the general store of knowledge. Presenting the results of research
study, generally involves a formal written report as well as an oral presentation. The report and
presentation are extremely important as the results of research are often intangible the written
report is usually the only documentation of the project. The written report and the oral
presentation are typically the only aspect of the study that the examining committee is exposed
to, and consequently the overall evaluation of the research project rests on how well this
information is communicated. Every person has a different style of writing. There is not really
one right style for a report, but there are some basic principles for writing a research report
clearly.
Lecture Objectives:
By the end of this lecture, you should be able to;
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 Write a research report.
 Describe the contents of a research report
10.1 Steps in Writing Report
Preparing a research report involves other activities besides writing; in fact, writing is actually
the last step in the preparation process. Before writing can take place, the results of the research
project must be fully understood and thought must be given to what the report will say. Thus,
preparing a research report involves three steps: understanding, organizing and writing. The
general guidelines that should be followed for any report or research paper are as follows:
Logical analysis of the subject matter: It is the first step. The two ways, which develop a subject:
logical and chronological. When we understand the subject, analyze it and associate one thing
with another, it is logical development. It often consists of arranging the simplest content to the
complex one. Chronological development is based on a connection or a sequence in time or
occurrence.
Preparation of the final outline: Outlines are the framework upon which long written works are
constructed. They are an aid to the logical organization of the material and a remainder of the
points to be stressed in the report.
Preparation of the rough draft: This follows the logical analysis of the subject and the preparation
of the final outline. In this step the researcher writes his work performed, procedure, results
obtained in context of his research study.
Rewriting and polishing the rough draft: It is the most difficult part of all formal writing. It
usually requires much more time than it required for preparation of rough draft. The careful
revision helps to identify the weaknesses in terms of logical development or presentation. While
preparing the final content, one should also check the mechanics of writing –grammar, spelling
and usage.
Preparation of final bibliography: The bibliography, which is generally appended to the research
report, is a list of books, magazines, and all the work that the researcher has consulted. The
bibliography should be arranged alphabetically and may be divided into two pars; the first part
may contain the names of books and pamphlets, and the second part may contain the names of
magazine and newspaper articles.
For books and pamphlets, the order may be as under: 1. Name of the author, last name, first
name 2. Title, underlined to indicate italics. 3. Place, publisher and date of publication. 4.
Number of volumes.
For Example:
Kothari, C.R., Quantitative Techniques, New Delhi, Vikas Publishing House Pvt.Ltd.,
1978.
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For the magazines and newspapers the order may be as under: 1. Name of the author, last name
first 2.Title of article, in quotation marks. 3. Name of the periodical, underlined to indicate
italics. 4. The volume or volume and number. 5. The date of the issue. 6. The pagination.
For Example:
Robert V. Roosa, “Coping with Short-term International Money Flows”, The
Banker,London,September,1971,p.995.
Writing the final draft: This constitutes the last step. The final draft should be written in a
concise and objective style and in simple language, avoiding vague expressions. While writing
the final draft, the researcher must avoid abstract terminology and technical jargon. A research
report must not be dull rather it should maintain interest of the people and show originality.
10.2 Layout of the Research Report:
The research report must necessarily convey enough about the study so that the researcher can
place it in its general scientific context, judge the adequacy of its methods and thus form an
opinion of how seriously the findings are to be taken. For this purpose there is the need of proper
layout of the report. The layout of the report means as to what the research report should contain.
A comprehensive layout of the research report should comprise of:
(a) preliminary pages;
(b) the main text and;
(c) The end matter.
(a) Preliminary pages:
In this the repot should carry a title and date, followed by acknowledgments in the form of ‘
pre-phase ’ or ‘forward’. Then there should be a table of contents followed by list of tables
and illustrations so that the decision –maker or anybody interested in reading the report can
easily locate the required information in the report
(b)Main text:
The main text provides the complete outline of the research report along with all details. Title
of the research study is repeated at the top of the first page of the main text and then follows
the other details on pages numbered consecutively, beginning with the second page. Each
main section of the report should begin on a new page .the main text of the report should
have the following section:
1. introduction
2. statement of findings and recommendations
3. the results
4. the implications drawn from the results and
5. the summary.
1. Introduction:
The purpose of introduction is to introduce the research project to the readers. It should
contain a clear statement of the objectives of research i.e. enough background should be
given to make clear to the reader why the problem was considered worth investigating.
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A brief summary of other relevant research may also be stated so that the present study can
be seen in that context. The hypothesis of study, if any, and the definitions of the major
concepts employed in the study should be explicitly stated in the introduction of your report.
2. statement of findings and recommendations:
after introduction, the research report must contain a statement of findings and
recommendations in non-technical language so that it can be easily understood by all
concerned. If the findings happen to be extensive, at this pont they should be pu in
summarized form.
3. Results:
a detailed presentation of the findings of the study , with supporting data in the form of tables
and charts together with a validation of results, is the next step in writing the main text of the
report. This generally comprises the main body of the report.
The result section of the report should contain statistical summaries and reductions of the data
rather than the raw data. All the results should be presented in logical sequence and spitted into
readily identifiable sections. All relevant results must find a place in the report.
4. implementations of the results:
Towards the end of the main text the researcher should again put down the results of his
research clearly and precisely. He should, state the implications and that flow from the results
of the study for understanding the human behavior. Such implications must have three
aspects as stated belowa) a statement of the inferences drawn from the present study which may be expected to
apply in similar circumstances
b) the conditions of the present study which may limit the extent of legitimate
generalization o the inferences drown from the study
c) The relevant questions that still remain unanswered or to new questions rose by the study
along with suggestions for the kind to research and would provide answers for them.
5. Summary: it has become customary to conclude the research report with a very brief
summary, resting in brief the research problem, the methodology, the major findings and
the major conclusions drawn from the research results.
(c) End Matter:
At the end of the report appendices should be enlisted in respect of all technical data such as
questionnaire, sample information, mathematical derivation and the like ones. Bibliography of
sources consulted should also be given. Index( an alphabetical listing of names, places and topics
along with the no of the pages in a book or repot in on which they are mentioned or disused)
should invariably given at the end of the report. The value of index lies in the fact that it works
as a guide to the reader for the contents in the report
10.4 Precautions for Writing a Research Report
The Report must be prepared keeping the following precautions in view:
1. Abstract terminology and jargon should be avoided in a research report.
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2. Readers are often interested in acquiring a quick knowledge of the main findings
and for this purpose charts, graphs and the statistical tables must be used for
various results in the main report in addition to summary of important findings.
3. The report must present logical analysis of the subject matter.
4. A research report should show originality and should necessarily be an attempt to
solve some intellectual problem.
Review Questions:
1. Describe the contents of a research report.
2. What precautions must be taken when writing a research report?
3. Describe the different formats of writing references.
REFERENCES
3. Punch, K. F. (2005) Introduction to Social Research: Quantitative and Qualitative
Approaches, Second Edition, Sage Publications Ltd, London
4. Schutt R. K. (2006) Investigating the social world: the process and practice of research, 5th
edition, Sage Publications Ltd, London
APPENDIX
Question 1
Uganda as a country has taken strides in developing the education sector compared to its
neighbours in East Africa, Uganda boosts of a strong establishment in higher education, as a
matter of fact, Uganda has over thirty four universities spread across the country. Although
the Universities are mushrooming, management of these Universities have experienced
problems in assuring quality and this has consequentlycompromised the standard of
graduates. Some stake holders blame the Management styles used to run the Ugandan
Universities.
In view of the above case, you have been tasked by National Council for Higher
Education(NCHE) to undertake research.
Task;
a) Give a suitable title for the study.
(02 Marks)
b) Identify two study variables in your study.
(01 Marks)
c) State three research objectives of the above study.
(03 Marks)
d) State three research questions of the above study.
(03 Marks)
e) Determine a suitable research design for the above Study and explain why.
(04 Marks)
f) Describe at least two methods of data collection you would use.
(04 Marks)
g) Indicate the significance of the study.
(04 Marks)
h) Give the possible limitation to the study.
(04 Marks)
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Question 2
a) Describe the steps taken in the literature review process.
(10 Marks)
b) Elucidate the importance of chapter 2 of a dissertation to the research process. (15 Marks)
Question 3
a) Collecting the necessary data (data gathering) for the relevant information is perhaps
the step in scientific Research that requires real expertise. As a research expert, describe
any four data collection techniques.
(12 Marks)
b) Illustrate the steps of the sampling process.
(12 Marks)
c) What is meant by stratified random sampling?
(01 Mark)
Question 4
a) Researchers often communicate their findings in a prescribed report of five chapters.
Identify the chapters and describe at least three components in each of the five chapters.
(15 Marks)
b) As a researcher, what ethical principles should be of concern to you when conducting
research?
(10 Marks)
Question 5
a) Write precise notes on the following concepts and phrases related to research:
i.
Descriptive research.
ii. Analytical research.
iii. Probability sampling.
iv.
Research design.
v. population for a study
b) Describe the purpose of data interpretation in research.
(04 Marks)
(04 Marks)
(04 Marks)
(04 Marks)
(04 Marks)
(05 Marks)
Question 6
a) What is meant by the term data analysis?
b) Why is it important to carryout data analysis?
c) Describe the operations under taken in data processing.
(03 Marks)
(12 Marks)
(10 Marks)
Question 7
a) Describe the following used as in presentation of findings.
i.
Tables
ii.
Histogram
iii. Bar Charts
iv.
Pie or Circle Charts
(03 Marks)
(03 Marks)
(03 Marks)
(03 Marks)
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v.
Frequency Polygons
b) Explain the steps involved in preparing a research report.
(03 Marks)
(10 Marks)
Question
8
The Managing Director (MD) of Mpaka Events Management Ltd, a company establishedTen
(10) years ago, is facing a problem. The company which was initially profitable and attracted
very many graduates to work with is currently unprofitable and can hardly attract any competent
personnel. It is operating, in the MD’s opinion, inefficiently. The company offers a wide range of
events management services in the country, region and worldwide. Initially, the company had a
wide market share but with the changing world market trends and globalization; survival will be
more difficult in the future. In particular, many events management companies
are by passing its services by not only offering multiple services but also offering the services at
affordable rates. In addition, many of the companies that have joined events management have
strategically positioned themselves in the market. As a research consultant, the MD has
commissioned you to undertake a comprehensive study on the firm as a whole to determine
possible strategies the company can undertake to face the existing problem.
a) Give an appropriate research title for the study.
(02 Marks)
b) What are the independent and the dependent variables from your proposed topic in 1 a)
above.
(02Marks)
c) Draw a Conceptual frame work for identified variables in b) above.
(06Marks)
d) In view of your proposed topic in a) above;
i). Precisely state a possible research problem.
(04 Marks)
ii). Formulate three possible research objectives
(03 Marks)
iii). Formulate three possible research questions for the proposed study.
(03 Marks)
e) What are the possible limitations to your proposed study?
(05 Marks)
Question 9
a) What are five critical conditions that must be considered in selecting aresearch topic or
research problem for your study?
(15 Marks)
b) Explain any five ethical considerations that you would bear in mind while conducting
yourresearch.
(10 Marks)
Question 10
a) Explain the benefits of empirical literature review to a researcher.
(15Marks)
b) Describe the steps of empirical literature review process.
(10 Marks)
Question 11
a) Discuss the merits of the interview method of data collection for research. (13 Marks)
b) Describe the following sampling techniques used in data collection.
i). Stratified sampling
( 03 Marks)
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ii). Multistage sampling
iii). Cluster sampling
iv). Quota sampling
( 03 Marks)
( 03 Marks)
( 03 Marks)
Question 12
a) Differentiate between the following terms as used in research.
i). Reliability and Validity.
(03 Marks)
ii). Experimental Research and Applied Research.
(02 Marks)
b) Precisely explain five characteristics of scientific research.
(10 Marks)
c) Research design can be thought of as the structure of research. It is the “glue” that holds all
of the elements in a research project together. Explain any five types of research designs.
(10 Marks)
Question 13
The text below is part of a statement of a problem in a study… Education is considered the
foundation for socio-economic development in Uganda. The government promotes quality and
equitable education for all citizens. In 1997 the government of Uganda introduced free primary
education in order to increase access to basic education to its citizens. The government also
supports the training of teachers, curriculum development and revision. Despite the above
efforts, there is a wide gap in educational coverage between different counties as well as between
boys and girls…
a) Give the significance of the study in the case above.
(10 Marks)
b) What arethe possible sources of literature for the study in the case above? (10 Marks)
c) As a university student carrying out such a study as a programme requirement,
i). State the research design you would adopt for such a study.
ii). Explain the appropriateness of the research design mention in Qn 6 c) i) above.
(05 Marks)
Question 14
The objective of a good research report is to communicate the research findings to readers
efficiently and effectively. A research report has five major components, describe the five major
components of a research report.
(25 Marks)
Question 15
The Head Teacher of Kapeka Secondary School is vehemently concerned about the students
complaints regarding the learning conditions in which lessons are conducted. A number of
students have claimed that they would learn better if lessons were conducted in a more
conducive atmosphere. Students attribute their general decline in academic performance to poor
class room facilities including old furniture, black boards, dirty floors etc. They also claim that
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the class rooms are very congested and the student teacher contact is very low as well as the
student teacher relationships. Students claim to lack learning materials like text books, computers
and science laboratories. Students argue that such conditions have consequently led to poor
performance including failure to complete class assignment, absenteeism, late coming and poor
grades. The Head Teacher presented the matter to the Board of Directors (BOT) that has
commission a research to confirm these claims. The Head Teacher has identified you as a
Principal Investigator (PI).
Task
Basing on the case above
a) Explain the factors you are likely to consider in accepting to undertake the research task.
(03 Marks)
b) Propose a title for your research.
(02 Marks)
c) Identify the key variables in your title.
(02 Marks)
d) Using the identified variables in (b) above, draw a conceptual framework for you
research.
(06 Marks)
e) Give three research objectives and three research questions for your study.
(06 Marks)
f) Highlight the significance of your research.
(03 Marks)
g) Explain the likely limitations to your study.
(03 Marks)
Question 16
a) Define the term "research".
b) Give reasons why it is important for you to carry out research.
c) Give attributes of a good survey investigator.
(03 Marks)
(12 Marks)
(10 Marks)
Question 17
a) Explain the source of research problem/questions.
(05 Marks)
b) Give cardinal reasons why it is important to conduct a literature review in the preliminary
stages of conducting research.
(08 Marks)
c) Highlight the main preparation stages a researcher should take before getting started.
(06 Marks)
d) Enumerate ethical issues that should be observed when conducting research.
(06 Marks)
Question 18
a) The quality of data collected will heavily depend on the quality of the questionnaire used.
Mention the aspects that must be considered in order to have a good questionnaire.
(15 Marks)
b) Give 5 advantages of using interviews as a method of data collection.
(10 Marks)
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Question 19
a) Present and explain the various sampling techniques.
b) Explain the advantages of sampling.
(19 Marks)
(06 Marks)
Question 20
Describe the important statistical measures that summarise research data.
(25 Marks)
Question 21
The presentation of final research findings is fundamental in every study as it highlights whether
the study was able to achieve all the intended areas of coverage. The format adopted in reporting
findings will be indicated by the rules and research manuals of the relevant institutions.
Task
Basing on the research format of your University, describe the contents of a research report.
(25 Marks)
Question 22
The electoral commission of Uganda has of recent been experiencing diverse challenges in
preparation for the Feb 2016 Elections. Suppose you were conducting research on service
delivery within the Electoral Commission:
a) Identify a suitable topic for your research.
(03 Marks)
b) Formulate a statement of the problem to suite the scenario above.
(05 Marks)
c) Identify three objectives that your research will focus on.
(03 Marks)
d) Formulate three research questions.
(03 Marks)
e) Give the significance of such a study.
(03 Marks)
f) Explain the characteristics such research would possess to qualify as good research.
(08 Marks)
Section B (attempt any three (3) questions from this section)
Question 23
Mr. Mbaga, a prominent business practitioner intends to carry out a study on the topic: Effective
Communication and Employee Performance in Organizations.
In view of the above topic,
a) Give an appropriate case study to the topic above.
(01 Marks)
b) Develop a suitable conceptual framework for the study above.
(04 Marks)
c) Describe the steps Mr. Mbaga would follow in writing a research proposal for the topic
above.
(10 Marks)
d) Explain the significance of research to Mr. Mbaga, a prominent business practitioner.
(10 Marks)
Question 24
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RESEARCH TECHNIQUES BSM 224
a) Giving an example of a problem in each case, give at least five (5) sources of research
problems.
(15 Marks)
b) With examples describe the three broad categories of research variables.
(09 Marks)
Question 25
Mr. Tutu is to undertake research on: Employee’s Training and Quality Service Delivery in
Tourism Sector in Uganda.
a) Explain the possible sources of literature review applicable to Mr.Tutu’s study.
(09 Marks)
b) Describe the qualities Mr. Tutu would require as a researcher to carry out successful
research.
(10 Marks)
c) What are the problems Mr.Tutu is likely to encounter?
(06 Marks)
Question 26
a) Distinguish between population and a sample.
(03 Marks)
b) Illustrate the advantages of sampling.
(12 Marks)
d) Explain any five (5) probability sampling techniques used in research.
(10 Marks)
Question 27
a) By giving a likely topic in each case, explain at least five types of research. (15 Marks)
b) Describe the various ethical issues in research.
(10 Marks)
Question 28
a) Write precise notes on the following;
(i) A sampling frame.
(02 Marks)
(ii) Hypothesis.
(02 Marks)
(iii)Judgmental (purposive) sampling.
(02 Marks)
(iv) Plagiarism.
(03 Marks)
b) Explain at least three (3) types of questionnaires.
(06 Marks)
c) What are the key considerations to take into account while designing a research questionnaire?
(10 Marks)
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