The study of conducting research is Research Methodology.
Research: The word research is composed of two syllables “Re” and
“Re” is the prefix meaning ‘Again or over again or a new’ and
“Search” is the latter meaning ‘to examine closely and carefully’ or ‘to test
Together they form, a careful, systematic, patient study and
investigation in some field of knowledge undertaken to establish principles
Research can also be defined as
1. Search for knowledge
2. Systematic and scientific search for getting relevant answers on any
taken up specific topic.
3. Scientific enquiry into a subject.
4. Research is a movement from the unknown to the known.
5. It is the voyage of discovery
Acc to Bulmer,
Research is primarily committed to establishing systematic, reliable
and valid knowledge about the social world.
Acc. To Clifford Woody,
Research comprises of
• Defining and redefining problems.
• Formulating hypothesis (basic idea)
• Evaluating datas
• Making decisions
• Suggesting solutions
• Reaching conclusions
• Finally, carefully testing the conclusions
To determine whether they fit the formulated Hypothesis.
Research Methods: May be understood as all those methods or
techniques that are used by a researcher for conducting a Research
depending upon the methods.
(1) Library Research: analysis of historical records and documents.
- Statistical compilation, references, abstracts, guides
manipulation (handle with skill)
(2) Field Research: Observation, questionnaires, personal, Group
or telephonic interviews, case study.
(3) Laboratory Research:
Group (team) study, use of audio visual tools.
Research Methodology: is the way do systematically solve the research
In it we study the various steps that are generally adopted by a
researcher in studying his research problem logically.
When we talk of Research Methodology, we not only talk of
research methods but also consider the logic behind the methods we use
in the context of our research study and explain why we are using a
particular method or we are not using a particular method or technique so
that research results are capable of being evaluated either by the
researcher or others.
1) Why a particular research study has been undertaken?
2) How the Research problem has been defined?
3) What way and why the hypothesis (basic idea) has been
4) Why a particular technique of analyzing data is used? (or) How the
data were collected?
5) How the collected data were interpreted?
6) What deletion was made?
7) What was the conclusion?
Finally what was the solution for the Research problem?
Importance of knowing the subject – research Methodology:
1) A student preparing himself for a career of carrying out research as
his profession –
- Will be trained better to do research
- Will help him develop disciplined thinking
- Will help him observe the field objectively.
- Will enable thoroughly to understand the logic behind the
- Will increase the ability to evaluate the results.
- Face the evaluated results with confidence.
- Useful in various fields such as Govt. Business, administration,
community development & social work.
To qualify a Research or study:
To be a Good or perfect one,
The Research adapted should process certain characteristics,
It must as far as possible be 1) Controlled
1. Controlled: The research problem should not be affected or
influenced by external factors (i.e. variables other than the participating
2. Rigorous: The procedures followed to find answers to questions should
be relevant, appropriate & justified. But the degree of rigiour may vary
from one problem to another problem.
3. Systematic: The investigation should follow a certain logical
sequence (Not in a haphazard manner)
4. Valid & Verifiable: The findings should be valid & can be verified
by you or others at any time.
5. Empirical: The conclusions drawn should be based on hard evidence,
gathered from real life experiences or observations.
6. Critical: The process of investigation must be foolproof and free from
drawbacks. The process adapted and the procedures used must be able to
withstand any critical scrutiny.
Types of Research
Research can be classified from the view point or perspectives as,
From the view point
Application objective Inquiry mode
1) Pure Research 1) Descriptive 1) Quantitative Research
2) Applied Research 2) Correlative 2) Qualitative Research
1) Pure Research: (Basic or Fundamental Research)
Gathering, knowledge is termed as ‘pure’ or ‘basic’ research. Just to
gather knowledge in order to formulate or generalize theories or policies.
Eg) Research on mathematics.
This types of research adds knowledge to the already existing
Applied Research: To find an immediate solution for a pressing practical
Eg: Social, economical and political trends prevailing in a country.
Applied Vs Fundamental Based on the objectives of Research:
1) Descriptive Research:
• Survey or fact finding enquires of different kinds. It
describes the actual prevailing state of affairs, existing
• Otherwise known as ex post facts means existing
position of facts / issues.
• Here the variable influencing the research has no
control or the researcher has no control over the
Eg: Frequency of shopping, customer preference etc.
2) Correlative Research:
• Goes on to discover the existing relationship or
interdependence between two or more aspects /
• Otherwise known as comparative study.
• Investigates association between variables.
Eg: Sum of humour and job satisfaction, (related
Research problem is workers turnover
The researcher has to use facts / information already existing and
analyze these data to make a critical evaluation.
Eg: document study / historical evidence.
Descriptive Vs Analytical Research:
Attempts to clarify or explain why and how, any particular research
problem arises and can be solved.
4. Exploratory Research: Study undertake to explore a new area or an
III. Based on the Inquiry Mode:
1) Quantitative Research:
• Relates to aspects that can be quantified and expressed in
terms of quantity.
• Otherwise known as structured Research.
• In this type of Research, the objectives, design, sample and
all the other factors influencing the research is pre
The research problem and its solution will be expressed in terms of
quantity and hence statistical and economic analysis is adapted in this type
• Otherwise known as unstructured research.
• The aspects related to quality / kind or texture.
Eg: Behaviour science
Apart from the above, other types of Research are,
Conceptual Research: Research related to some abstract idea or theory
• Used by philosophers or thinkers for developing new concepts.
(based on experiments or experience)
• Otherwise known as experimental type of Research.
• The result obtained by adapting Empirical Research is considered to
be most powerful (evidence enclosed)
Based on the time consumed to complete a particular research,
a) one time Research: restricted to a single time period.
b) Longitudinal Research: Conducted over several time period.
Qualities of a Researcher
Top 10 qualities of a Researcher
1) Ananalytical mind: Constant analysis on a variety of factors.
2) A people person : For respondents to get the best out of
interviews / focus groups.
3) The ability to stay calm: especially when you have pressing
deadlines. Keep well focused and think logically there will always be
an end point.
4) Intelligence : Researcher requires critical analysis, but most
of all common sense.
5) Curiosity: Have curiosity and be passionate about developing
deeper to unearth more insight.
6) Quick thinker: Things don’t always go as you plan, so you need
to be able to think fast.
7) Commitment: Research is a tough job, the hours may be long,
the deadlines short. ‘
8) Excellent written and verbal communication skills: So that
different audience can clearly understand the findings.
9) Sympathetic: Having a sympathetic ear when listening to
some respondents (cry etc) is a good skill, to have.
10)Systematic: Check, check and check again. Spending a proper
amount of time for checking always pays.
According to Micheal Foster,
1) Truthful data / facts – desire for accuracy of observation.
2) No expressions like approximately, almost or nearly.
3) Should poccess alert mind. Nature is constantly changing, be keen
and watchful to notice such changes, no matter how small or
insignificant they may.
4) Scientific inquiry – desire for knowledge – it requires moral courage,
Steadfast (constant / not changing) endurance (to tolerate the
difficulty, suffer patiently)
- When a research scientist feel defeated or completely lost, he
needs immense courage and the sense of conviction (found
Significance or Importance of Search
1) Doubt is better than over confidence for it leads to inquiry, inquiry
leads to invention. Process or the three stages of research to bring
out economic policies.
1) Investigation of prevailing economic structure with the available
2) Analyse or diagnose the data.
3) Prediction for future developments.
2) Research encourages scientific and inductive thinking.
Eg:- Role of Research in :
1) Econ omics:
Researches done on applied (production and sales of goods in a
profitable manner) economics is increasing in modern days.
Govt. & business sectors have become more complex, they face
several operational problems to solve this problems, Research is
To frame Govt. economic policies.
Govt. budget a formulation depends on the analysis of
needs & desires of the people, available of revenues
Decision making – requires proper research.
Allocation of a countries scarce resource – also needs
2) Business Decisions:
In business sectors there are both planning and
a) Problems Research: Investigation of the
present structure and development of the market –
relating to purchase, production, promotion and sales.
b) Operational Research: Relates to application of
logical, mathematical and analytical techniques – to
solve market problems – there by minimize cost and
c) Motivational Research: Helps to determine people
behavior or consumer response.
All the above three are responsible for business decision making.
3) Social sectors: To gain knowledge on unknown aspects and do
something better and more efficiently.
Social scientist gain their knowledge for their own sake and for the
development of the society.
1. Formulating the Research problem:-
a) The formulation of a general topic into a specific Research
problem thus constitutes the first step in a scientific inquiry.
Two steps are involved in formulating the Research problem,
a) Understanding the problem thoroughly.
b) Rephrasing the same into meaningful terms from an analytical
point of view.
1. Identify a broad field or subject area of interest to you.
2. Dissect the broad area into small area.
3. Select what is of most interest to you.
4. Raise Research questions.
5. Formulate objectives
6. Assess your objectives
7. Double check
The best way to understand the problem is to discuss
with his own colleague or guide.
Examine all available literatures to get himself acquainted
(get used to ) with the selected problem.
Review two types of literature
Conceptual literature :
Concerning concepts & theories
Empirical Literature : Concerning studies made earlier which are
similar to the one proposed.
Outcome of the review will be the knowledge so as to pre
determine what data or materials are available for operational
Next step – the Researcher rephrases the problem into Analytical or
PUT THE PROBLEM INTO SPECIFIC TERMS
This step is of greatest importance in the entire research process.
The problem to be investigated must be defined unambiguously or
Prof W.A. Neiswanger States,
The statement of the objective of the Research problem is of basic
(i) It determines the data which are to be collected
(ii) Characteristics of the relevant data
(iii) Choice of techniques to be used in these explorations
(iv) Frame a Final report
Extensive Literature Survey:
A brief summary of the problem should be written down.
Make extensive literature survey
Sources of survey can be, journals, bio-graphics, Govt. reports,
books, conference proceedings etc.
Based on the nature of the problem.
Earlier study if any which is similar to the study in hand should be
A good library will be a great help to the researcher at this stage.
Developing Hypothesis : (Development of working Hypothesis)
State in clear terms the working hypothesis (Basic Idea of the
It is a tentative assumption in order to test to logical or empirical
Provide the focal point for research.
Hypothesis should be very specific and very well limited to the place
of research in hand because it has to be tested.
Hypothesis guides the researched by limiting the area of Research
and keep him on the right track.
It sharpens his thinking and focuses attention on important facets
of the problem.
It indicates the type of data required for the study.
Type of methods of data analysis done.
How to develop working Hypothesis?
1) Discuss with collogues / experts, about the problems, its origin, its
objectives and solutions.
2) Examination of data/ records if available.
3) Review similar studies / similar problems.
4) To secure greater insight into the practical aspects of the problem –
conduct personnel investigation or field interviews.
Preparing the Research Design:
Research design is the conceptual structure within which research is
conduction. It constitutes the blue print for the collection, measurement
and analysis of data.
The function of the Research design is to provide relevant evidence
with minimal expenditure of effort, time and money. It provides an outline
of what the researcher is going to do in terms of 1) Framing the
hypothesis, 2) its operational implications and 3) finally data analysis
The Research design highlights certain decision,
1) The nature of the study
2) Purpose of the study
3) Location where the study would be conducted
4) The nature of data required
5) From where the data would be collected
6) The techniques of data collection that would be used
7) What time period the study would cover
8) The type of sample design that would be used
9) The method of data analysis that would be adapted
10)The manner in which the report would be prepared
Type of Research Design : 4 types
1) Sampling Research Design : Deal with selection of relevant
2) Observational Research Design: Deals with the observations (field
observations) that is to be made.
3) Statistical Research design: Deals with the information on the
data collected & analysed.
4) Operational Research Design: How the above three are carried
Determining sample Design:
All the items considered in any field of inquiry constitutes a
“universe” or population. Study of the entire population without
leaving out a single item is known as “Census Study”
This type of census study is practically not possible.
So we select few items from the entire population for our study
purpose. The items so selected constitutes what is technically called
The way of selecting such a “sample” is known as the “Sample
These samples can be either probability samples or non probability
Probability: Each item in the population has on equal chance of
being selected for the study.
1) Simple random sampling
2) Systematic random sampling
3) Stratified random sampling
4) Cluster / area random sampling.
Non Probability sampling: All the items do not have an equal chance of
being selected for the study.
The selection depends upon the convenience & judgment of the
Mixed sampling: When more than one type of sampling
technique is used for a study, it is mixed sampling.
The sample design to be used in a Research study must be decided
by the researcher considering the nature of the study.
6. Collecting the Data:
“Gathering appropriate data” which are made use in Research
Data can be collected in several ways either through (1) Experiment
(or) (2) through surveys.
In experimental means, when a researcher conducts a
research, some quantitative measurements are observed,
based on which, he examines the truth of the underlying
In case of surveys, data are collected by
1) By observations
2) Through personnel interview
3) Through telephone interviews
4) By mailing of questionnaires
5) Through schedules / enumerators
The Researcher should select one of these methods of collecting the
data taking in account the
1) Nature of investigation
2) Objective & scope of Inquiry
3) Financial Resources
4) Time frame
5) Desired degree of Accuracy.
6) Execution of the Project: (Putting a plan)
Important step in Research study.
See that the project is executed in a systematic manner and
Eg) If the survey done in a project is via Questionnaire the
answers can be machine coded / processed
If interview were conducted, make sure that the interviewers is
well trained – to keep the survey as much as realistic as possible.
8. Analysis of Data :
After the data are collected the researcher turns to the task of
analyzing the data the analysis of data require closely related
operations, like ‘coding, Editing & Tabulation’.
The wide data collected should be condensed into small
manageable groups, for easy analysis.
Coding: The collected data are transformed into symbols that
may be tabulated or counted.
Editing: Unwanted & irrelevant data will be removed.
Tabulation: Technical procedure where the data are put in
the form of tables.
The most important step after defining the ‘Research problem’ is
preparing the Research Design
Research design is the conceptual structure within which the
research is conducted.
It constitutes the ‘BLUE PRINT” for collection, measurement and
analysis of data.
Research design provides an answer to the question, what the
Researcher is going to do with regards to framing hypothesis, its
operational implications and how to analyse the data?
Research Design: - Decisions
Highlights certain decisions,
1) Nature of the study
2) Purpose of the study
3) Location where the study would be conducted
4) Nature of “DATA” required
5) From where the “DATA” can be collected
6) Time period of the study
7) Type of sample design to be used
8) Techniques of data collection
9) Methods of Data Analysis
10)Preparation of Report.
May be sub divided into,
1) Sampling design: Deals with, the method of ‘selecting items’ for the
2) Observational design: Relates to the condition under which the
observations are to be made.
3) Statistical Design: Deals with the “no of items” selected or the
study and how the selected data will be analysed.
4) Operation design: The technique by which the sampling,
observational and statistical designs can be carried out.
Research Design – Features :
1) Helps to identify the type and source of information needed for the
2) Specifies the methods to be adopted in collecting & analyzing data.
3) Specifies the time schedule of the research and the monetary budget
Concepts Relating to Research Design
1) Dependent and Independent variables :
Variables : A magnitude that varies is known as “variable”
Continuous variable : Values that can be expressed even in decimal
poins are known as continuous variables
Eg: age (4 years 3 months)
Height (5.2 cm)
Weight (45.3 kg)
Non continuous Variables:Value that can be expressed only in integer
values are called Non continuous variables
Eg: No. of students in a class ( 45)
No. of children in a family (3)
Statistically known as “discrete variables”
Dependent or Endogenous variables :
When the change in one variable depends on the change in other
variable, it is known as dependent or Endogenous variable.
Demand ----- Price (independent)
Independent or Exogenous variable
The variable that causes the change in the dependent variable is
known as independent or exogenous variable.
Demand (Dependent) ------- Price ,Income
Here demand is a dependent variable while price / income is an
Extraneous variable :
The independent variable which is not directly related to the
purpose of the study but affects the dependent variable is know as
The influence caused by the extraneous variable on the dependent
value is technically known as “Experimental Error”
A research study or a Research design should always be framed in
such a manner that the influence of ‘Extraneous variables’ on the
dependent variable is completely controlled and the influence of
the independent variable is clearly evident.
Good Research design should minimize the effect for Extraneous
The relationship between dependent and independent variable is
said to be confounded by an extraneous variables.
When the formulated hypothesis is tested by adopting scientific
methods, it is known as Research Hypothesis.
Experimental & Non Experimental Hypothesis testing:
When the objective of the Research is to test the hypothesis, it is
Research in which the independent variable are (handled with skill)
manipulated, it is experimental hypothesis testing.
When the variables are not manipulated, it is non experimental
Experimental & Control Groups:
When a group is exposed to usual conditions in an experimental
hypothesis, research it is control Groups.
When the group is exposed to special or certain new conditions, it is
The different conditions to which the experimental & control
groups are subject to is known as treatments.
9. Experiment: Fertilizers and crops)
Process of verifying the truth.
Determine the fact
Determine the impact in comparison with another fact.
10. Experimental units
Pre-determined block to which different treatments are
Eg : animal testing
Types of Research Design
There are three different types of Research design,
1) Exploratory Research Design:
Is a “Formulative Research design”
Main purpose is the discovery of ideas & insights
Should be flexible enough considering different dimensions
of the problem under study.
2) Descriptive and Diagnostic Research Design:
Descriptive Research Design is concerned with describing the
characteristics of a particular individual or a group.
Study concerned with narration of facts or characters related
to an individual, group or institution are descriptive research
Diagnostic Research design determines the frequency with
which a variable occurs or its relationship with another
Both the Research designs should be planned carefully.
Research design should be Rigid (No flexibility)
3) Hypothesis testing Research Design:
Test the hypothesis of causal relationship between two or
Adopt procedure that not only reduce bias but enhance
reliability – and facilitates deriving Inferences (results) about
the Research problem.
Importance of Research Design:
Facilitates the smooth flow of the various stages of Research.
Helps yield maximum information with minimum effort, time and
Helps to plan in advance data collecting and analysis techniques.
Prepare with utmost care to avoid errors.
Characteristics of a Good Research Design
Posses the qualities of being flexible, suitable efficient &
Should minimize ‘bias’ and maximize reliability of data collection &
No experimental error should be allowed
Should yield maximum information
Research problem should be viewed from different angles or
The choice of Research design depends on,
Nature of the Research problem
Objectives of the Research problem
Skills / ability of the Researcher
Methods of gathering information
Availability of monetary support
A Research hypothesis is a predictive statement, which is capable of
being ‘tested’ using scientific methods, which involves independent and
dependent valuables. (eg) the female students perform as well as the male
This statement is a hypothesis that can be objectively tested and
It is a proposition that can be put to test in order to examine its
Characteristics of Hypothesis
1) A hypothesis should be precise and clear. If not clear, the inferences
will not be reliable.
2) It must be capable of being put to test.
3) It should state the relationship between the variables, in case
4) It should be stated in a simple language.
5) It should be consistant and derived from all known facts.
6) Hypothesis must be amenable to testing within a reasonable period
7) Hypothesis should explain what it actually to explain. (the solution
for the Research problem). The explanation should be on empirical
Concepts Relating to Testing of Hypothesis
1) Null Hypothesis & Alternative
Hypothesis (Statistical Analysis)
Null Hypothesis: Denoted by H0. If both the variables (say male or
female) or (Head or Tail) are equally good, it is Null Hypothesis.
Alternative Hypothesis: Denoted by Ha or H1. If one variable is
considered superior to other or vice versa or if there is a difference, it is
Mean Population (u) or (p)
Total / No. of variables
Ho : u = 100
Ha : u = 100
Ha : u > 100
Ha : u < 100
Aspects to be considered while formulating Null Hypothesis
1) The researcher always tries to reject Null hypothesis since
Alternative Hypothesis should be proved.
2) Null hypothesis when it is actually true, when rejected involves
great risk, the level of significance should be considered.
3) Null hypothesis should be very specific (No approximation)
The level of significance:
• Important concept of hypothesis testing.
• It is a certain percentage chosen with great ‘care, reason and
(eg) let us consider the level of significance to be 5%. It means the
Researcher takes a risk of rejecting Null hypothesis (Ho) by 5%
when Ho is actually true.
3. Decision Rule
• The researcher should make a decision, if to accept or Reject Ho.
• The decision rule should be decided on the number of items to be
tested and the basic of which to accept or reject.
4. Type I and Type II Errors
(i) Researcher may reject Ho, when it is true – Type I Error (which must
have been accepted).
(ii) Researcher may accept Ho, when it is false – Type II Error (which
must have been rejected)
5. One tailed and Two tailed Tests:
(i) One tailed test rejects the Null hypothesis when the sample mean is
either greater or lower than the hypothesized value of the
Two tailed Test: When the sample mean is both greater and
lower than the hypothesized value of the population mean.
Procedure for Hypothesis Testing:
1. Testing hypothesis refers whether the formulated hypothesis is
valid or not
2. Whether to Accept or Reject Null Hypothesis.
(i) Making a formal statement:
• Making a formal statement of the null hypothesis and
(ii) Selecting a significant level of testing
• A pre-determined level of significance should be specified.
• Either 5% or 1% level can be considered for the purpose.
(iii) Deciding the Distribution to use:
• Choice should be made generally relates to Normal distribution
(iv) Selection of random sample & computing an Appropriate value
• Selection of Random sample
• Computing suitable value
• Drawing a sample for furnishing Empirical data.
(v) Calculation of Probability:
• The diverged results from the expected results, when Ho is true.
(vi) Comparing the probability:
• By making a comparison with the assumed significance level.
• If the value is less than or equal to Ho, in case of one-tailed test,
Ho is rejected. Here type I error is committed.
• If the value is greater than the mean, Ho is accepted. Were
type-I error is committed.
• compile, compare & compute the data and come out with the
Null Hypothesis: The null hypothesis is the proposition or proposal that
implies no effect on the phenomena.
Alternative Hypothesis: is the one predictive statement that implies
some effect on the phenomena.
Concepts Relating to Testing of Hypothesis:
An art of obtaining a sample from a given population. The
technique or procedure the researcher adopts for selecting items for the
sample from the population or universe.
Steps in sampling Design
Type of Universe:
1) The first step in sampling design, is to clearly define the total
number of items / cases to be studied, which is technically known
Finite Universe: The number of items is certain.
Eg: No. of students in a class.
No. of workers in a factory.
Infinite Universe: The number of items is infinite. (No idea about the
number of items)
Eg: Chennai population, No. of stars
2) Sampling Unit:
• A geographical area like a state, district or village.
• Family, religious community or a school.
• Individual (Researcher can select one or two such units).
3) Source List: Otherwise known as “Sampling Frame”
• Consists of names of all items of a universe.
• If not available the researcher has to prepare a “Source list”.
• It must be reliable, comprehensive, correct and appropriate.
• It should be the representative of the population / universe.
4) Size of sample:
• Refers to the “number of items” to be chosen from the
• Size of sample must be optimum. An optimum sample may
defined as the one that satisfies.
• The requirements of representatives.
• Costs or budget should be considered.
Factors Influencing size of sample :
Parameters of Interest:
The items or parameters are selected based on the researchers own
Budgetary constraint :
Cost consideration exercises a major influence.
a) Sampling Procedure:
The type or technique used by the researcher to select the items.
The technique should be selected so that for a given sample size &
budget, the sampling error must be very small or negligible.
Sampling Error: may be caused (In case of Non probability sampling)
(1) Interviewer Bias
(3) Non response problems
(4) Questionnaire design flaws
(5) Data processing & analysis errors
In case of probability sampling, (homogenous items ) the sampling
error is negligible since the sample is more accurate.
Characteristics of a Good sample :
Should bind a truly representative sample.
Small sampling error
Should fit into the budgetary constraints.
Result should be applicable in general.
Characteristics of sample techniques :
1) Much cheaper
2) Saves time
3) Much reliable
4) Suitable for carrying out different surveys
5) Scientific in Nature
Advantages of sampling:
1) Very accurate
2) Economical in Nature
3) Very reliable
4) Suitable for different surveys
5) Less time consumption
6) In case of large universe, sampling method is the only practical
method for collecting the data.
Different types of sample Design:
Classified under two general categories.
1) Probability sampling
2) Non – Probability sampling.
Otherwise known as ‘choice sampling’ or ‘random sampling’.
Every item has an equal chance of being included in the sample.
Eg: Lotteries (or) subscribers
When done property, probability sampling ensures that the sample
has a similar composition and profile as that of the entire
7 different types of probability sampling,
1) Simple Random sampling
2) Stratified Random sampling
3) Cluster sampling
4) Systematic sampling
5) Area sampling
6) Multi stage sampling
7) Sampling with probability propotional to size
(1) Sample Random Sampling
The sample is drawn so that each person or item has an equal
chance of being drawn during the selection.
Eg: Lotteries (in a ball box)
(2) Stratified Random sampling: (strata – layers)
- Stratified sampling technique is generally used when the
population is heterogeneous.
- The entire population is divided into sub population (sub groups)
(i.e. the sub population being homogenous).
- Items are selected from each stratum.
- This method is more reliable & accurate.
- Eg: 50 students of a school having 1000 students on a total were
selected & interviewed on the interest in music.
The students were grouped based on their age, 7 years, 8 years, 9
years, 10 years & 11 years.
From each age group, 5 students were chosen and totally 50
students were interviewed.
(3) Cluster sampling:
• The entire population is sub divided into mutually exclusive groups
• Simple Random sampling is applied and the need clusters are
selected for the study.
• If all the elements found in the selected cluster is taken for the
study, then it is one stage cluster sampling.
• If random sampling is applied in selecting elements found within
the clusters, it is two stage cluster sampling.
(4) Systematic sampling:
- Selecting every nth element for the study.
(5) Area sampling: when the clusters are in the form of some
geographical sub divisions.
(6) Multi stage sampling:
- If the researcher selects elements or items at different stages, it is
multi stage sampling.
- Eg: Survey of work efficiency in nationalized baulks
- Stage level
- District level
Items are selected at four stages / levels.
(7) Sampling with probability proportional to size:
- The probability of inclusion into the study is directly proportional to
the size of the clusters.
- This technique is used when the no. of elements present in each
- Depending on requirement of the researcher the cluster which is
more appropriate can be selected for the study.
II. Non Probability sampling:
- Each item does not have an equal chance of being included in the
- 3 types of non probability samplings are,
1) Convenience sampling
2) Quota sampling
3) Judgmental sampling
1) Convenience sampling:
- Choosing items at the convenience of the Researcher.
Eg: Street interviews (sampling of people who are at easy
Drawback: Lack of accuracy
2. Quota sampling
The researcher simply assume quotas, with certain restrictions
imposed on how they should be selected.
Eg: Caste basic
Benefits: less expensive, very convenient
3. Judgment sampling : (otherwise known as purposive sampling)
Researcher employs his own “Expert” judgment about who to
include in the sample frame.
Disadvantages of sampling:
1) Inadequacy of samples
2) Chances of bias
3) Problems of accuracy
4) Difficulty of getting the representative sample.
5) Untrained Manpower.
6) Absence of Informants
7) Chances of committing errors.
Sampling Error: Sampling error is the deviation of the selected sample
from the true characteristics, traits, behavior, qualities or figures of the
Data Collection is the systematic gathering of information (data) for
a particular purpose from various sources. (Various sources can be
questionnaires, interviews, observations existing records and electronic
Two Important sources of Information are,
(i) Primary Data
(ii) Secondary Data
Refers to the data collected for the first time (Original data)
Example: Proceedings from conferences meetings, Students records.
Refers to the data that have already been collected and used earlier
by somebody or some agency.
Example: Online database, Historical books etc.
Example: Taking census (total population) of Government of India –
When research is done by some other scientist on the basis of this
data, it is secondary data.
Selecting A particular source of Data depends on,
(1) Purpose & Scope of the study.
(2) Availability of time.
(3) Availability of Resources.
(4) The degree of Accuracy desired.
(5) Statistical tools to be used.
(6) Sources of Information (data).
1. Purpose & Scope of Data Collection:
Should be clearly stated at the very beginning of the study.
A statement indicating the Research problem and the type of
information needed for the study in order to solve the Research
Problem, is needed.
Its purpose is to establish a factual information for making
Scope of the enquiry means the coverage with regard to the type of
information, the subject matter and geographical area.
(b) Availability of Time:-
The investigation should be done within a reasonable period of
Taking which the information collected may become outdated.
Example: Demand of a new product launched is studied, if the
result comes out after 2 years, by the time the producer may attain
So, make sure the investigation is carried out within a reasonable
period of time.
(c) Availability of Resources:
Investigation or data collection greatly depends, on resources
1. No. of skilled personnel
2. The Financial Position.
If the no.of skilled personnel to carry our the enquiry is sufficient
and the availability of funds is not a problem, the datas can be
collected from a big area covering a good number of samples.
(d) The desired/expected Degree of Accuracy:-
Deciding the degree of accuracy is a must for the investigator.
Because “Absolute Accuracy” is not possible in statistical works.
Since “Statistics” is based on estimates, tools used for
measurements in not always perfect & there may be unintentional
bias on the part of the investigator, enumerator or informant.
Generally the degree of accuracy depends upon the objections of
Example: During purchase of Gold, even 1/10th
gram in its weight is
But it is not the same in case of purchasing rice or wheat.
(e) Statistical Tools to be used:
Well defined or identifiable object or group of objects that can be
measured or counted in a statistical investigation is called statistical
In the absence of a clear and precise “Statistical Unit” Serious errors
may be committed by collecting irrelevant data. This will ultimately
lead to fallacious (Wrong) conclusions.
(f) Sources of Information:
The researcher has to decide about the source from which the
information can be obtained or collected.
1. First hand data.
2. The data from other published sources. (Publications, Journal,
(g) Method of Data Collection:-
1. Primary Data.
2. Secondary Data.
First hand data.
Either ‘Census’ or ‘Sample’ technique is to be used.
Census: Total no.of items have to be investigated.
Sample: Selected representatives from the total population have to be
Total No. of items, 100% Accuracy
attained, Time consuming, Expensive
Selected Representations, 100%
Accuracy cannot be attained, Less
time taken, Less expensive, Less
Should be very cautious and careful while choosing a particular
Methods of Collecting Primary Data:
May be obtained by applying any of the following methods,
1. Direct Personal Interviews.
2. Indirect Oral Interviews.
3. Information from Correspondents.
4. Mailed questionnaire methods,
5. Schedule sent through Enumerators.
1. Direct Personal Interviews:
A face to face contact is made with the informants.
Interviewer asks them questions regarding the study and tries to
get the desired information.
The information thus collected is first hand and original.
(i) Response is encouraging when personally contacted.
(ii) Information are more accurate (if not found accurate, he can be
reexamined or Cross-examined, there by try to obtain the
(iii) Provides hope for getting supplementary information, which
may be of greater use latter.
(iv) A delicate situation (Some Personnel Questions) can usually be
handled more effectively by a personnel interview than other
(v) The interviewer can adjust the language according to the status
and educational level of the person interviewed, thereby can
avoid inconvenience and misinterpretation.
(i) Expensive – when the no. of informants is large.
(ii) Greater chance of personnel bias and prejudice. (taking a
decision before finding the full facts).
(iii) Interviewer should be thoroughly trained & experienced.
(untrained personal will spoil the work)
(iv) Time consuming (Interviewers can be contacted only at the
convenience of the informants)
Direct personal Interviews can be used in Intensive Field Survey
rather than Extensive Field Survey.
The present day of extreme advancement in communication
system, a good number of survey, can be conducted by News
papers & television channels by replying through e.mails & SMS.
They are less expensive & extremely quick.
Defects – No Phone or Television, delicate & sensitive Questions
cannot be asked, value answers.
2. Indirect Oral Interviews:
The investigator contact a third party called “Witnesses” who is
capable of supplying necessary information.
Generally adopted when the information to be obtained is complex
or the informer is not willing to reveal the answers.
Example: When a drug addicted person is interviewed, he will not be
willing to response directly, so the information are gathered via agents
(may be relatives).
The accuracy of this method depends on,
(i) The proven integrity of the Agency/Person.
(ii) Ability of the interviewer to act the right information from the
(iii) Bribery or other reasons may twist the witness to give false
information there by bringing a wrong conclusion.
(i) Let more care should be taken in the selection of ‘Witness’ because it is
on their views, the final conclusion is reached.
3. Information From Correspondents:
The investigator appoints local agents or correspondents in
different places to collect information under this method.
These correspondents collect the information and transfer or
transmit the information to the central office where the data are
Example: News paper Agencies.
Generally these Agencies are paid staff, sometimes honorary.
2. Can be used to get regular information at regular intervals (daily,
weekly or monthly).
(i) Lacks Accuracy.
4. Mailed Questionnaire Method:
A list of questions pertaining to the survey is known as
“Questionnaire”. It is prepared and sent to various informants by
The questionnaire contains questions and provides space for
A request is made to the informants through a covering letter to fill
up the questionnaire and sent it back within a specified time.
The questionnaire studied can be classified as,
1) The degree to which the questionnaire is formalized or structure.
2) The disguise/lack of disguise of the questionnaire.
3) The communication method used.
4) When no formal questionnaire is used, interviewers adopt other
tactics like showing pictures on which respondents comments.
When a research follows a prescribed sequence of Questions it is
When no prescribed sequence of Question exists, the study is Non-
When the questionnaire is constructed in such a way that the
“Objective is clear” (the questionnaire) it is known as Non-
When the objective is not clear, the questionnaire is a “Disguised”
On this basis, 4 types of studies can be distinguished,
(i) Non-disguised Structured.
(ii) Non-disguised Non-structured.
(iii) Disguised Structured.
(iv) Disguised Non-Structured.
Merits: Questionnaire Methods,
(1) Easily adopted in large populations and when the informants are
wide spread over a large geographical area.
(2) Relatively cheap & timely.
(3) Information pertaining to personnel life or family or confidential
matters will be revealed in written rather than personal interviews
(1) Applicable only among literate people.
(2) Uncertainty of the Respondents lacks co-operation.
(3) Lacks Accuracy because the information may not be correct.
Guideline to make this method more Effective:
(i) Prepaid postage stamp should be affixed.
(ii) Sample should be large.
(iii) Questionnaire should be interesting.
(iv) Legal Compulsion should be made to provide in formations.
5. Schedules sent through Enumerators:-
Sending Schedules through enumerators or interviewers.
The enumerators contacts the informants, gets replied to the
questions contained in the schedule and fill them in their own
Here the questions are asked face to face and the response is
(1) Applicable among illiterates.
(2) Very little scope for Non-response, as the enumerators go
(3) Information are more Reliable & Accurate.
(1) Expensive – Since enumerators are paid personals.
(2) Success – depends on the efficiency of the enumerators.
(3) Interviewer requires training and experience.
(4) Variations in answers must be removed to avoid variations.
Are those data which have already been collected and analyzed by
some earlier agency for its own use and later the same data is used by a
Sources of Secondary Data:
(1) Published Sources.
(2) Unpublished Sources.
1. Published Sources:
The Government, Inter National and local agencies publish
Chief Among them,
(i) Inter National Publications:-
Inter National Institutions & bodies like I.M.J.(International
Monetary Fund), I.B.R.D. (International Bank of Reconstruction and
Development), I.C.A.F.E. (International Conference on Agriculture & Food
Engineering) and U.N.O. United Nations Organization publish regular &
occasional reports on Economics & Statistical matters.
(ii) Official Publications of Central & State Governments:
Several departments of the Central and State Governments publish
reports on different subjects.
Example:- Publications are,
(a) Reserve Bank of India Bulletin.
(b) Census of India.
(c) Statistical Abstract of the states.
(d) Agricultural Statistics of India.
(e) Indian Trade Journal.
(iii) Semi Official Publications:
(a) Indian Statistical Institute (I.S.I)
(b) Indian Council of Agricultural Research (I.C.A.R.)
(c) Indian Agricultural Statistics Research Institute (I.A.S.R.I.)
Publish the findings of their research programs.
(iv) Publications of various commercial and financial institutions.
(v) Reports of various committees & commissions appointed by the
(a) Raj Committee’s Report on Agricultural Taxation.
(b) Wanchoo Committee’s Report on Taxation & Black Money.
(vi) Journals & News Papers:-
Powerful source of secondary data.
Current & important matter can be obtained.
From Journals & News papers like Economic Times, Commerce
Capital, Indian Finance, etc.,
Records maintained by Government & Private Offices.
Theses of Research Scholars from universities & institutions.
Precautions in the use of secondary Data:
Proper scrutiny is made before they are used by investigator.
Be Extra-Cautious while using secondary data.
Should not be accepted as such because the secondary data may
(Bias, Inadequate Size, Substitution, errors of definition or
Factors to be Considered before using the secondary Data:
(i) Suitability of Data:
make sure that the data available is suitable for the purpose of
(ii) Adequacy of Data:
Make sure that the data are sufficient or adequate for the present
(iii) Reliability of Data:
The reliability of data is must, without which there is no meaning in
The reliability of data can be tested by finding the agency that has
collected the data, if the agency has used proper methods for
collection the data.
Once data have been obtained from primary or secondary sources
the next step in a statistical investigation is to edit the data. (to Scrutinize).
Objective, editing is to detect possible errors and irregulations.
Editing needs great care and attention.
Editing Secondary data is simple but the data collected from survey
(Primary Data) need excessive editing.
Editing Primary Data,
(i) The data should be complete in every respect.
(ii) The data should be accurate.
(iii) The data should be consistant.
(iv) The data should be homogenous
1. Editing For Completeness:
The editor should see that each schedule or questionnaire is
complete in all respects.
Answers to every questions is furnished.
If not answered, try to meet them in person to get the answers.
If not just mark “No Answer”.
2. Editing For Accuracy:
The reliability of conclusions depends on the correctness of in
If the information is wrong, the conclusion can never be valid.
Editor should see that the in formations are accurate in all respects.
Arithmetic errors can be detected easily & corrected.
If the error is due to fault information supplied, it may be difficult
3. Editing For Consistency:
Editor should see that the answer to questions are not
contradictory in nature.
Example: Are you a student? No which class do you study? X
The answers are contradictory and such answers should be
4. Editing For Homogeneity:
Understand the questions in the same sense.
Check uniform interpretation and make sure the information
supplied by the various informants are homogenous & uniform.
Example: Income (Yearly, Monthly, Weekly, Daily)
Choice Between Primary & Secondary Data:
A proper choice between the type of data (Primary or Secondary)
needed for a particular statistical investigations is to be made by
considering the nature, objective, scope of the study, time frame &
finances and the degree of precision aimed at, and the status of the
Now, Secondary data are generally used from fairly reliable
published data by Government, Private organizations and research
agencies, periodicals magazines etc.,
In fact, primary data are collected only if there do not exist any
In some cases both Primary & Secondary data may be used.
Questionnaire can be defined as a group of questions designed to
collect information from a specific subject.
List of questions sent to a number of persons for getting answers
and which obtains standardized results that can be tabulated and treated
Media of communication between the investigator and the
Generally used in social research when the population is varied,
large, diverse & Scattered.
Should be designed with utmost care & caution so that all the
needed information are collected without any difficulty.
Drafting a Good questionnaire Requires – Care, Skill, Wisdom,
efficiency and experience.
Points to Remember: While Drafting A Questionnaire
(1) Size of the Questionnaire:
(a) No. of questions should be as small as possible depending on the
nature, objectives & scope of the study.
(b) Large no.of questions may irritate the informants and may be difficult
to Edit or Scrutinize by the investigator.
(c) Avoid irrelevant and unimportant questions.
(d) Average No. of questions should be 15 to 25 (at the most).
(e) If it is more than 25, divide it into various sections.
2. The Questions should be Clear:
Should be Easy, Brief, Unambiguous(Clear in meaning), Non
offending, courteous in tone, corroborative (Supportive) in nature &
to the point.
3. The Questions should be arranged in a Logical Sequence:
When arranged Logically, the answers can be easily tabulated or
coded – and does not leave any chance of omissions.
Example: To find if a person owns a television.
4. Questions should be simple to understand:
Vague & Double meaning words should be avoided.
Example: Price/Cost/Rate/ Capital Income/Salary.
5. Questions should be Comprehensive(Includes Everything) and Easily
Questions should be comprehensive (i.e.) it should include all the
needed in formations.
Easy to be answered. Avoid mathematical calculations like Ratios,
6. Questions of Personal And Sensitive Nature Should Not Be Asked:
Avoid personal questions which the respondent may feel shy or
irritated to answer.
Example: Do do drink ?
If such questions are unavoidable, a highest amount of politeness
should be used.
7. Types of Questionnaire:
(a) Shut Questions:
Where possible answers are suggested by the frames & the
respondents are requested to the tick one of them.
Two types of shut Questions.
(i) Simple Alternative Questions:
(Otherwise known as Dichotomous questions) Choose from two
clear cut alternatives Yes or No/ Right or Wrong.
(ii) Multiple Choice Questions:
When it is difficult to define a clear cut alternative, additional
Questions between Yes & No is inserted,
Example: To find if a person smokes? Do you smoke?
(a) Yes, Regularly ( )
(b) No, Never ( )
(c) Occasionally ( )
(d) Seldom (rarely) ( )
Easy & Convenient to answer.
Easy to tabulate.
8. Leading Questions should be Avoided:
Long Questions leading to several answers should be avoided. It
should be framed into short questions.
Example: Why do you use a particular type of car, say Maruti Car, Avoid
this continuous questions.
Which car do you use ?
Why do you prefer it ?
9. Cross Checks:
Should be designed to provide internal checks on the accuracy of
the in formations given by the respondents.
10. Pre-Testing the Questionnaire:
Try out the Questionnaire on a small scale before using in a large
The drawbacks, short comings and problems faced in the small scale
informants can be improved or modified when used in large scale.
11. A Covering Letter:
A Covering Letter should be enclosed for the purpose regarding
definitions, concepts & purpose.
Attach a self addressed envelope in case of mailed questionnaire.
Mentions about Awards or incentives for quick reply.
Promise to send a survey copy of the report.
A carefully designed sample may actually be better than a poorly
planned and executed census.
1. It saves time:
Saves time because fewer items are collected and processed.
2. It Reduces Cost:
Since only few items are studied, there is reduction in cost &
reduction in man power.
3. More Reliable Results can be Obtained:
Sampling is more Reliable because
(i) fewer chance of sampling error.
(ii) Experience, Trained & Technical people can be employed to process &
analyze the data.
4. It provides more detailed in formations:-
More detailed information can be obtained by sample survey.
5. Only Sampling Method to depend upon:
When the population is large and finite, the only method applicable
6. Administration Convenience:
The organization and administration is easy in sample survey.
7. More Scientific:
Results can be tested since more scientific.
Shortcomings (or) Demerits
1. Illusory (False) Conclusion:
If sampling is not carefully planned & executed, the conclusions
may be false.
2. Sample Not Representative:
If the sample taken from the population is not the right
representative, the result may be false or misleading.
3. Lack of Experts:
If there is a lack of experts to plan, execute and analyze the
samples, the result would be unsatisfactory.
4. Personal Bias:
There may be personal bias & prejudice in choosing the sampling
5. Size of Sample:
If the size of the sample is not appropriate, it leads to untrue
Essentials of Sampling:
1. It must be the right representative:
The Sample selected should process the similar characteristics of
the original universe.
Selected samples should be homogenous with the samples & the
3. Adequate Samples:
A good number of items should be included for the study.
A proper size of sample should be maintained to have optimized
results in terms of cost & efficiency.
The logical process of drawing a general conclusion from the study
of representative items is called Induction.
Sampling is based on two fundamental principles of Statistics theory
(i) Law of Statistical Regularity
(ii) The Law of Inertia of Large Numbers.
The Law of Statistical:
Regularity: (Mathematical Theory of Probability), States,
“ A moderately large number of items chosen at random from a
very large group are almost sure to have the characteristics of the large
1. Average income of 1,000 people is to be found out,
2. We take a sample of 100 people & find the average.
3. Another person takes 100 people & find the average.
The Average income found by both the persons will have least
If the average income of the same 1000 people is found out by
census, the result will be more or less the same.
2. Law of Inertia of Large Numbers:
It States, Other Using being equal, as the sample size increases, the
results tend to be more accurate & reliable.
The deviations or difference between the actual population and the
Reasons For Sampling Error:
1. Faulty Selection of Sample
3. Faulty Demarcation (Demographic limit) of sampling Unit:
In case of Area sampling the sampling units at the borders should
be decided if to take it or reject it.
4. Faulty estimation techniques:
Wrong selection of sampling techniques.
Types of Sampling Errors:
(i) Bias Error:
Caused due to bias or prejudice on the part of the informant.
(ii) Unbias Error:
Error caused due to the Normal Course of investigation.
Reducing Sampling Error:
Sampling Error can be reduced by increasing the size of the sample.
Experiment is the process of examining the truth of a statistical
Hypothesis related to some research problem.
Experiments are of two types,
1. Absolute Experiment.
2. Comparative Experiment.
When a researcher wants to determine the impact of a fertilizer on
the yield of a crop, it is a case of Absolute Experiment.
When a researcher wants to determine the impact of one fertilizer
as compared to the impact of some other fertilizer, it will be called as
Research Design are of three types,
1. Research design in case of descriptive & diagnostic studies.
2. Research design in case of exploratory Research studies.
3. Research design in case of Hypothesis Testing Research Studies.
Research Design In case of Hypothesis Testing Research Studies:
Hypothesis testing research studies are generally known as
The researcher test the casual relationship between the variables.
Professor Fisher is considered as the pioneer of this type of studies.
He performed this study when he was working at a Agricultural
Research Station in London.
“His found out that, by dividing plots into different blocks and then
by conducting experiments in each of these blocks, whatever in
formations is collected and inference drawn from them can be
more reliable Professor Fisher laid three principles of Experimental
1. The Principal of Replication
2. The Principal of Randomization.
3. The Principal of Local Control.
The Principal of Replication :
“The Experiment should be repeated more than once”.
The treatment is applied to many experimental units.
The information collected and the inference drawn from these
experimental units will be more reliable and statistically accruable.
Aim: To examine the effect of two varieties of paddy.
Example: A paddy field is divided into 2 parts. Grow one variety in one
part and the other variety in the other. Then we compare the yield of the
Draw conclusion on that basis.
No Principle of Replication is
Part I Part I
Treatment Compare the yield of the two parts.
One variety Another
of Paddy Variety of Paddy.
When Principle of Replication is used:
First divide the field into several parts.
Grow one variety in half of the parts and the other variety in the
Collect the information of the two varieties and draw the conclusion
by comparing both.
The Results so obtained will be more reliable and accurate compared
to the results drawn without using the principle of Replication.
The Experiment can be repeated several times.
2. The Principle of Randomization:
“Principle of Randomization “Provides us a protection against the
effects of “Extraneous Variables.”
The variations or effects caused by these extraneous variables can
be combined under the heading “Chance”.
Example: When the researcher grows one variety of paddy in the first half
of the field and the other variety in the next half of the field, there may be
a possibility or chance that the soil fertility of the first half of the field may
be different in comparison to the next half.
rr rr R r r
rr rr R r r
rr rr R r r
rr rr R r r
rr rr R r r
In this case, he may go on to cultivate the two varieties of paddy in
different parts of the field on the basis of some random sampling
(i.e.) He may apply Randomization principle and protect himself from
the effects of the Extraneous Factors.
By using Randomization Principle a better estimate can be drawn.
Conclusion drawn is more
(Can protect Effects of Extraneous Variables)
rr rr r r r
rr rr r r r
rr rr r r r
rr rr r r r
rr rr r r r
3. The Principle of Local Control:
The extraneous variable which is a known source of variability can
be made to vary extensively or deliberately over a wide range.
Now the variability it causes can be measured and eliminated.
In short, through the principle of Local Control, we can eliminate
the variability due to extraneous factors from the experimental
The extraneous variable is brought to a control.
Kinds of Experimental Design:
Experimental Design refers to the framework of the structure of an
Classified into 2 Broad Categories,
1. Informal Experimental designs.
2. Formal Experimental designs,
Informal Experimental Designs:
Designed based only on the difference between the magnitudes or
1. Before and after without control design.
2. After Only with Control design.
3. Before and after with control design.
Before and after without control design:
Consider a test group,
Step.1: The dependent variable is measured before introduction of the
Step.2: The treatment is introduced.
Step.3: The dependent variable is measured after the treatment has been
The effect of the Treatment : The level o the phenomenon after the
The level of the phenomenon before the treatment.
Test Area Level of Phenomenon Treatment Level of Phenomenon
Before Treatment (X) After Treatment (Y)
þ Effect of the Treatment = (Y) – (X)
With the passage of time, several extraneous variable may be there
in the treatment effect.
(2) After only with control Design:
Step.1: Two Areas are selected, the control Area & the test area.
Step.2: The treatment is introduced in the test area alone.
Step.3: The dependent variable in both the areas are measured, at the
Step.4: Treatment Effect is calculated by subtracting the value of the
dependent variable in the control area from its value in the test area.
Effect = Value of dependent variable in the
control Area – Value of Dependent Variable in the test area.
Test Area Treatment Introduced Level of Phenomenon (Y)
Control Area No Level of Phenomenon (Z)
(3) Before And After with Control Design:
Step.1: In this design, two areas are selected and the dependent variables
in both the areas are measured for an identical time period before
Step.2: Treatment is introduced only in the test area.
Step 3 : The dependent valuable is measured on both the areas (control
area & test area) for an identical time period.
Setp4 : The effect of the treatment is determined by subtracting the
change in the dependent valuable in the control area with the charge in
the dependent valuable of the test area.
Effect = ((Y) – (X)) – ((Z)-(A))
Merits: Avoids Extraneous variables resulting from passage of time and non
comparability of control and test areas.
II Formal Experimental Design:
Offer relatively more control and use specific statistical procedures for
1) Complete Randomized design (Generally called C.R. Design)
2) Randomized Block Design (R.B. Design)
3) Latin Square Design (L.S. Design)
4) Factorial Designs .
(1) Completely Randomized Design :-
Involves two principals, the principle of replication and the principle of
Randomized of the experimental designs.
The items are randomly assigned do experimental treatments.
This design is simpler and easier.
Example: It the research has 2 items of 20 parts and if he wishes to test to
under treatment B, this completely randomized design gives every possible
group of 10 items selected from a set of 20, an equal chance of being
assigned to treatment A & treatment B.
One way analysis of variance (one way ANOVA) is used to analyze such a
2. Randomizes Block Design:-
The subjects or items are first divided into groups, known as “Blocks”
See that, the items in each group or black is homogenous.
Randomly select items from each given block and assign treatment.
Extraneous variables can be fixed and can be measured.
The main feature of this study is, each treatment appears the same no of
times in each block.
This design is analyzed two way analyses of variance (two way ANOVA)
3. Latin Square Design:-
Used in Agricultural Research.
L.S Design is used when two or more extraneous variables is found.
Example: Effect of fertilizer on the field of wheat is do be determined.
Here along with the effect of fertilizer, the fertility of the soil must be
If the facility of the soil is not considered along with the fertilizer the
result obtained may be dependable.
Similarly the impact of the various seeds used many also vary the yield.
To over come this difficulty L.S design is used.
Each fertilizer (X1, X2, X3, X4, X5) will appear 5 items but will be used
only once in each row and in each coloumn.
Example: No treatment occurs more than once.
I II III IV V
X1 A B C D E
X2 B C D E A
X3 C D E A B
X4 D E A B C
X5 E A B C D
The field is divided into several blocks (I, II, III, IV & V) and there are variety
of fertilizer (X1, X2, X3, X4, X5).
But each fertilizer is used in each block only once.
a two way ANOVA technique.
4. Factorial Design :
Are used in experiments where the effect of the depended variable, when
affected by more than one variable is to be determined.
Used in social & economic studies where usually large no of factors affect
a particular problem.
Factorial design are of two types:
I . Simple Factorial design
II. Complex Factorial designs.
Simple Factorial Design :
When the effect of the dependent variable is affect by only two factors, it
is simple factorial designs.
Otherwise known as “ TWO factors Factorial Design”.
Complex Factorial Design :
This design is used when more than two factors at a time affects the
Or the design considers three or more independent variable.
The greater the no of independent variable, the higher the order of
interaction, analysis possible.
Can determine the effects of more variable in a single experiment.
Observation is defined as a planned method of watching that involves
constraints (steps) to improve accuracy.
Characteristics of Observation :
i. Observation are direct
ii. takes place in natural situations
iii. Less Structured.
iv. Makes only quantitative study.
Applicable in :
1. Life styles
2. Encounters / Settlement.
4. Groups / Organization.
Acc. to Block & Camion :
1. Observed in natural surroundings
2. Understands events affecting social relations.
3. Identifies regulatives in social life.
4. Hypothesis free enquiry.
5. Avoids manipulations of independent variable.
6. Recording is not selective.
Differentiate Experimental Technique & Observation Technique :
Experimental Technique Observation Technique
No such controls
Conducted in smaller units
No so. Study is towards sharpening the
Observation is natural conducted in
large unit. Fewer subjects are watched
for long period .Study is directed
towards sensitizing the observer /
Behavior observed is more different.
Probability: IS a measure of the expectation that an certain event will occur.
Probability value ranges from 0-1.
The Main terms pertaining to probability theory:-
1.Random Experiment: An experiment which can be repeated under the same
conditions and the outcome cannot be prod iced is known as Random
Example:- When a coin is tossed, we cannot predict whether head or tail is going
2.Sample Space:- A set of possible outcomes of a random experiment is know as
Example: When a coin is tossed twice the possible outcomes are HH, HT, TH & TT,
IT is represented,
S = (HH, HT, TH, TT)
3.An Event: Any possible outcome of an experiment is know as an event.
Example: When a coin is tossed twice, HH is an event.
An event can be classified as,
a. Simple Event: Which has only one sample point
Example: HH, TT.
b. Compound Event: Which has more than one sample point.
Example : TH.
d. Complimentary Event : A and A’ are complementary events, if A’ consists of all
the sample point which is not included in A’ than the sum of the probability of
the sample space is equal to 1.Hence P(A’)-P(A’) P(A’)+P(A’) = 1 P(A’) = 1 – P(A’).
Example: When a dice is thrown, the probability of odd Numbers turn up are
complimentary to even number turn up.
A = 1,3,5
A1 = 2,4,6
e. Mutually Exclusive Event: A and B two mutually exclusive event, if A prevents
the occurrence of B.
Example: When a coin is tossed once the occurrence of Head prevents the
occurrence of Tail.
If A and B are mutually exclusive events than the probability of occurrence of A or
B is the sum of their individuals probability.
P(AUB) = P(A) + P(B).
If A and B is joint sets, than the addition theorem of probability can be stated as.
P(AUB) = P(A) + P(B) – P(AB)
f. Independent Event: A and B are in dependant event, if the occurrence of A
does not influence the occurrence of B these two events are called independents
Example: When a coin is tossed twice the occurrence of head in the first toss
dose not influence the toss in the second coin.
Product of A and B is the product of their individuals probability P(AB) = P(A) X
Probability Distribution: IF ‘X’ is total no of success discrete Random variables
which takes the value of X1,X2, X3........... Xn, P1,P2,Pn then follows the
Properties of probability Distribution / 2 Main properties:
1. P(X1) is greater than or equal Zero and less than or equal / one (Expressed
2. The sum of all be probability distribution will be equal to one.
Example: When a coin is tossed Twice the probability distribution is,
X( probability of obtaining hed) = 0,1,2 P(X1) = ¼, ½, ¼ = ¼.
Expectation of Probability: Let ‘X’ be the discrete Random Variable, which takes
the value X1, X2, X3..........Xn
Respective probability is P1, P2, P3 ............ Pn
Expectation of Probability distribution: P1X1 + P2X2............PnXn.
Probability Distribution = (0 x 1/4) + (1 x 1/2) + (2 x ¼) = 1.
Binomial Distribution: A Binomial experiment is a statistical experiment. It has the
(i) The experiment consists of ‘n’ repeated trials.
(ii) Each trail can result in just two possible outcomes. We call one of this
outcomes as “Success” and the other “Failure” .
(iii) The probability of success is denoted by ‘P’, in every trail and the
probability of failure is denoted by l – p or ‘q’.
(iv) The trials are independent.
(v) The outcome on one trail dose not affect the outcome of other trials.
Notations: X – The number of successes that result from the Binomial
n - The no of trail in the binomial experiment.
P – The probability of success on an individual trial.
C - No of coefficient .
Binomial Formula : Suppose a Binomial experiment consists of ‘n’ ------- and result
in ‘X’ successes & if the probability of success on an individuals trial is P, then the
Binomial probability is B (x, n, p) = nCx X Px X (1 – P)
Coefficient of Binomial Distribution: The binomial coefficients are the coefficients
in the expansion of two terms (x + 1)n.
The coefficient of xr in (x+1)n is denoted by nCr or (n/r).
Example: The coefficient of (x+1)2 = (x+1) (x+1)
= 1x2 + x +x+1
= 1x2 + 2x +1
The Confidents are = 1+2+1
The coefficient of (x+1)3 = (x+1) (x+1) (x+1)
= (x2+2x+1) (x+1)
= x3 + x2 +2x2 +2x +x+1
= x3 + 3x2 +3x +1
The Coefficient is = 1. 3 .3 1
The “Pascal triangle” lists out all the Binomial Coefficient.
1 2 1 (x+1)2
1 3 3 1 (x+1)3
1 4 6 4 1 (x+1)4
1 5 10 10 5 1 (x+1) 5
1 6 15 20 15 6 1 (x+1)6
1 7 21 35 35 21 7 1 (x+1)7
Example: A coin is tossed Four Times what is the probability of obtaining two or
more heads? .
Step –I : When a coin is tossed One time, the probability of ‘Head’ of tail is equal,
(ie) P = q =1/2.
Step – II : The various possibilities of Head and tail events will be,
(p+q)4 = 1p4 + 4p3q +6p3q + 6p2q2 + 4pq3 +1q4
1p4 = (1/2) where P = 1/2) (q = 1/2.)
= ½ x ½ x ½ x 1/2
4p3q = 4x(1/2)3 x ½ = 4 x ½ x ½ x ½ x ½
6p2q2 = 6 x(1/2 x ½ x ½ x1/2 = 3/8
Therefore, the probability of obtaining 2 or more heads is,
3/8 + ¼ + 1/16 = 11/16
2. POSSION DISTRIBUTION:
When ‘P’ is very small (Success rate is extremely small) and ‘n’ is very large
(total no of trail items of events is large) then “POISSON distribution” is used.
P – O (Successes approach zero) (np = m is finite)
The experimental result in outcomes that can be classified as “Successes”
X – The Actual Number of successes that occurs in a specific region.
P (x, u) = (eu) (ux)
This is Poisson formula here we conduct a Poisson experiment in which the
average number of successes within a given region is ‘U’. Then the Poisson
probability is as above .
Where x is the Actual number of successes.
‘e’ is equal to 2.71828.
‘u’ is the mean of the distribution.
The average number of successes (u) that occurs in a specified region is
The probability of success is proportional to the size of the region.
The probability of successes occurring in an extremely small region
‘e’ = A constant equal to approximately 2.71828.
u = The mean (average) no of success that occurs in a specific region.
Example: The average no of homes sold by A really company is 2 Homes per day.
What is the probability that exactly 3 homes will be sold tomorrow?.
u = 2 (Average of 2 homes sold per day)
x = 3 (3 homes will be sold tomorrow)
e = 2.71828 (Constant)
P (x, u) = (eu) (ux)
P(3, 2) = (2.72828²) (2³)
1 x 2 x 3
= (0.13534) (8)/6
Normal Distribution and its properties:
Normal distribution refers do a family of continuous probability
distribution described by the normal equation.
The value of the random variable ‘Y’ is - (x –u) ²/2²
Y = — x C (Coefficient)
Where ‘ X’ is a normal Random variable.
‘u’ is the mean
‘ ’ is the standard deviation
‘π ‘ is constant (3.14159)
‘e’ is constant (2.71828)
Represented by ‘ ’ it means how much variance (difference) or dispersion
exist from the average.
Example: = Variance (Root of its variance let us consider a population has eight
= 40/8 = 5 1) difference between the mean & the mean & the valiance value is
Standard Deviation 25 square the value.
(2 - 5) ² = (-3) ² = 9 ( 4 – 5) ² = (-1) ² =1 (5 – 5) ² = 0² = 0
(4 – 5) ² = -1² = 1 ( 4 – 5) ² = (-1) ² =1 (7 – 5) ² = 2² = 4
(5 – 5) ² = (0) ² = 0
Rate of √ 9+1+1+1+0+0+4+16 38
---------------------------- = — = 4/-
Example: An average light bulb manufactured by Acme Corporation lasts 300days
with a standard deviation of 50 days. Assuming that the bull life is normally
distributed what is the probability that an Acme light bulb will last at most 365
Answer: The value of the normal Random valuable (X) = 365 days.
The mean (u) = 300 days standard deviation = 50 days.
Normal Distribution Y = 1 x e(xu) ²
50√2 x 3.14159 x 2.71828 – (365 – 300) ²/2 x 50
50 x 6013 x 2.71828/100 = 1/306.5 x 271 = 884//
Y = .88 or 88%
Hence there is an 88% chance that the bulb will last most 365 days.