Quantitative research

‫الرحیم‬ ‫الرحمان‬ ‫اللہ‬ ‫بسم‬‫۔‬
Quantitative Research Methods
Resource Person
Dr. FAISAL ANIS
Assistant Professor
Chairman, Department of Special Needs Education School of Social
Sciences and Humanities, University of Management and
Technology

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Department of Special education, UMT
Contents
Introduction to Educational Research ......................................................................................................3
Ways of Knowing:- ....................................................................................................................................3
The Scientific Method...............................................................................................................................3
What is Quantitative Research? ...............................................................................................................4
Foundations of Quantitative Research Methods......................................................................................5
Realism..................................................................................................................................................5
Positivism..............................................................................................................................................5
Positivism..............................................................................................................................................5
Subjectivism..........................................................................................................................................5
Post-positivism......................................................................................................................................6
Experiential Realism..............................................................................................................................6
Pragmatism ...........................................................................................................................................7
When we don’t use quantitative methods:-.............................................................................................7
Quantitative Methods...............................................................................................................................8
Selection and definition of a Problem (Research Topic):- ........................................................................8
Selection and Statement of Problem........................................................................................................8
Selection of Research Problem.................................................................................................................9
Sources of Research Topic ........................................................................................................................9
Originality of the Research Problem.........................................................................................................9
Statement of Problem.............................................................................................................................10
Literature Review....................................................................................................................................10
Purpose of Literature Review .................................................................................................................10
Sources of Literature...............................................................................................................................10
Abstracting of References.......................................................................................................................10
Guidelines for Analyzing, Organizing, and Reporting Literature Review:-..............................................11
Sequence of Writing Literature Review..................................................................................................11
Introduction ........................................................................................................................................11
The Body .............................................................................................................................................11
Conclusion...........................................................................................................................................12
Research Goal & Objectives....................................................................................................................12
Goal.....................................................................................................................................................12
Objective.............................................................................................................................................12
Considerations for Research Objectives .................................................................................................12

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SMART Objectives:-.....................................................................................................................................13
Formulation and Statement of Hypothesis.................................................................................................13
Hypothesis:- ............................................................................................................................................13
Characteristics of Good Hypothesis:-......................................................................................................13
Types of Hypothesis:-..............................................................................................................................13
Research Hypothesis:-.............................................................................................................................14
Null Hypothesis:-.....................................................................................................................................14
Null Hypothesis vs. Alternative Hypothesis:-..........................................................................................14
Type I and Type II Errors:-.......................................................................................................................14
Type I Error..........................................................................................................................................14
Type II Error.........................................................................................................................................15
Alpha vs. Beta, Part II:-............................................................................................................................15
Type I and Type II Errors:-.......................................................................................................................15
Forming Conclusions:-.............................................................................................................................15
Seven Steps to Hypothesis Testing Happiness (Traditional or Classical Method):-................................15

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Introduction to Educational Research
• Research or Re-Search?
• Why Research?
• How to Research?
Research or Re-Search?
• Research is an important means of creating new knowledge by investigating a new problem or
phenomenon
• Re-search: subject matter is already known but, for one reason or another, needs to be
studied again and validating it.
Why Research?
• Answer question
• Solve problems
• Develop new insights
• Explore a wide array of possibilities.
Ways of Knowing:-
• Five ways we can know something
– Personal experience
– Tradition
– Experts and authorities
– Logic
• Inductive
• Deductive
– The scientific method
The Scientific Method
• A systematic approach which enables us to explain, predict and/or control phenomenon-The
Scientific Method
• This involves the acquisition of knowledge and the development and testing of theory
• The use of the scientific method is more efficient and reliable than any other source of
knowledge

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• The scientific method is a body of techniques for investigating phenomena, acquiring new
knowledge, or correcting and integrating previous knowledge.
• Application of Scientific methods and techniques to understand and enhance the teaching and
learning process.
• To be termed scientific, a method of inquiry is commonly based on empirical or measurable
evidence subject to specific principles of reasoning.
• A cyclic process comprising of sequential steps
• Recognition and definition of problem
• Formulation of hypothesis
• Collection of data
• Analysis of data
• Drawing and stating conclusion
• Limitations of the scientific method
• Inability to answer value-based questions involving “should”
• Inability to capture the full richness and complexities of the participants
• Limitations of our measurement instruments
• Ethical and legal responsibilities
What is Quantitative Research?
• Aliaga and Gunderson (2000) describe quantitative research methods as, “Explaining
phenomena by collecting numerical data that are analyzed using mathematically based
methods (in particular statistics)”.
• The specificity of quantitative research lies in collecting numerical data and then analyzing
using mathematically based methods.
• In order to be able to use mathematically based methods, our data have to be in numerical
form
• But this characteristic severely limit the usefulness of quantitative research as there are many
phenomena we might want to look at, but which don’t seem to produce any quantitative
data.
• In fact, relatively few phenomena in education actually occur in the form of ‘naturally’
quantitative data.
• However, research does provide us this flexibility to collect data that do not naturally appear
in quantitative form can be collected in a quantitative way.
• We do this by designing research instruments aimed specifically at converting phenomena
that don’t naturally exist in quantitative form into quantitative data, which we can analyze
statistically

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• Using the right data analysis tools is based on using the right research design and data
collection instruments
Foundations of Quantitative Research Methods
Realism
• Realists take the view that what research does is to uncover an existing reality. ‘The truth is
out there’ and it is the job of the researcher to use objective research methods to uncover
that truth.
• This means that the researcher needs to be as detached from the research as possible, and
use methods that maximize objectivity and minimize the involvement of the researcher in the
research.
Positivism
• Positivism is the most extreme form of this world view.
• According to positivism, the world works according to fixed laws of cause and effect.
• Scientific thinking is used to test theories about these laws, and either reject or provisionally
accept them.
• In this way, we will finally get to understand the truth about how the world works.
• By developing reliable measurement instruments, we can objectively study the physical
world.
Positivism
• However, this view that there is a true reality out there that we can measure completely
objectively is problematic.
• We are all part of the world we are observing, and cannot completely detach ourselves from
what we are researching.
• What is being studied, and what findings are produced, are influenced by the beliefs of the
people doing the research and the political/social climate at the time the research is done.
• In contrast to the realist view that the truth is out there and can be objectively measured and
found through research,
Subjectivism
• Subjectivists point to the role of human subjectivity in the process of research.
• According to Subjectivism, reality is not ‘out there’ to be objectively and dispassionately
observed, but is at least, in part, constructed by the observer
• The process of our observing reality changes and transforms it according to the context, and
therefore subjectivists may also be called are relativistic.
• All truth can only be relative, and is never definitive, as the positivist claims.

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• The extreme relativist position is obviously as problematic as the extreme positivistic one, as
it would in theory deny every reality which is beyond the social consensus.
• Very few people following either of the paradigms hold the extreme views.
Post-positivism
• Post-positivists accept the critique of traditional positivism that has been presented by the
subjectivists, without going so far as to reject any notion of realism.
• Post-positivists accept that reality cannot be observed as totally objective and disinterested
outsiders, and accept that the natural sciences do not provide the model for all social
research.
• However, they do believe in the possibility of there being an objective reality considering that
they will never be able to totally uncover that reality through research
• They believe that they should try to approximate that reality as best as they can, all the while
realizing that their own subjectivity is shaping that reality.
• Rather than finding the truth, post-positivists will try to represent reality as best they can.
• In contrast to positivists, post-positivists believe that research can never be certain. Rather
than focusing on certainty and absolute truth, post-positivist social science focuses on
confidence – how much can we rely on our findings?
Experiential Realism
• A second world view or epistemology that underlies the work of some quantitative
researchers is called experiential realism.
• Experiential realism claims that reality cannot be observed in a purely objective way, as
observer’s perception itself influences what is being observed and measured.
• However, experiential realists believe that there is a limit to subjectivity by the fact that
limited numbers of schemas are used to formulate views of the world.
• This is because perception is ‘embodied’ and observation cannot be passive, but actively
interacted with the world through mind and body.
• Experiential realists see the use of metaphor as crucial to make sense of the world around
them.
• One of the main metaphors is the subject–object schema, which divides the world into objects
(things) and subjects (people).
• This metaphor has its origins in the fact that while dealings with the world it is observed that
there is a distinction between an external world consisting of edges, surfaces and textures
that do not belong to the researcher, and there are those things that belong to the researcher.
• As we move around our world, the objects remain invariant.
• Science, according to this view, is an activity that is based on this subject–object schema
(Mulaik, 1995).

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Pragmatism
• Many researchers, both quantitative and qualitative take a pragmatist approach to research,
using different methods depending on the research question they are trying to answer.
• In some cases, this will lead them to quantitative research e.g to give a quantitative answer to
a question, need to generalize findings to a population, or are looking to test a theory
mathematically
• In other cases, they will employ qualitative methods and in many cases, a mixed-methods
approach combining quantitative and qualitative methods will be the most appropriate.
• One of the main contentions of this school of philosophy is that the meaning and the truth of
any idea are a function of its practical outcome(s).
• Pragmatists strongly oppose the absolutism they see as a key part of most other philosophical
beliefs.
• They feel that too often a chosen philosophy is put in opposition to other philosophies (think
of the positivist/subjectivist debate), which are totally rejected.
• As for the subjectivists, there is no definite truth in pragmatic philosophy. Truth is constantly
changing and being updated through the process of human problem solving. The key question
for pragmatists is not ‘is it true?’, or ‘is it right?’, but ‘does it work?’
• The first type of research question is that demanding a quantitative answer. Examples are:
‘How many students choose to study education?’ or ‘How many maths teachers do we need?
• Numerical change can likewise accurately be studied only by using quantitative methods. Are
the numbers of students in our university rising or falling? Is sale going up or down?
• We often want to explain phenomena. What factors predict the recruitment of maths
teachers? What factors are related to changes in student achievement over time?
• The testing of hypotheses. We might want to explain something – for example, whether there
is a relationship between pupil’s achievement and their self-esteem and social background.
• Problems one and two above are called ‘descriptive’. We are merely trying to describe
a situation.
• Three and four are ‘inferential’. We are trying to explain something rather than just
describe it.
When we don’t use quantitative methods:-
• When we want to explore a problem in depth.
• To develop hypotheses and theories
• If the issues to be studied are particularly complex, an in-depth qualitative study (a case study,
for example) is more likely to pick up on this than a quantitative study.
• To look at the meaning/context of particular events or circumstances.

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Quantitative Methods
General purpose
• Collect and analyze data to explain, predict, or control phenomena of interest
– Describe current conditions
– Investigate relationships
– Study causes and effects
Assumptions of the researcher
• We live in a stable, uniform, and coherent world
• We can measure, understand, and generalize about our world
Characteristics
• Numerical data
• Use of formally stated hypotheses and procedures
• Use of controls to minimize the effects of factors that could interfere with the outcome of the
research
• Large numbers of participating subjects
• An objective, detached researcher
• Use of pencil and paper tests, questionnaires, etc.
Basic designs
• Historical
• Descriptive
• Correlational
• Causal-comparative
• Experimental
• Single subject
Selection and definition of a Problem (Research Topic):-
• Selection and statement of Problem
• Review of related literature
• Formulation and statement of Hypothesis
Selection and Statement of Problem
• Selection of Problem

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• Statement of Problem
Selection of Research Problem
• Identify a general problem area
– Expertise of Researcher
– Interest of Researcher
• Narrow Down the General Problem Area
– Theory
– Literature
Characteristics of a Good Problem
• Researchable
• Significant
• Suitable
– Skill
– Resources
Sources of Research Topic
Some major sources of choosing a research topic include:
• Existing support literature.
• Literature from other disciplines.
• Social concerns.
• Popular issues.
• Your own history and personal characteristics.
• Your tutors.
Originality of the Research Problem
To ensure the originality of the research, a research problem may be considered :
• Geographically
• Socially
• Temporal
• Contextually
• Methodologically (Veal 2006)

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• Geographically. Certain theories may have been tested in one area but have not received the
same attention elsewhere.
• Socially. You may find that certain social groups have not received as much attention as
others.
• Methodologically. You could collect different data to explore a phenomenon.
• Temporally. A theory may have been developed a number of years ago, thus its relevance in
contemporary society could be investigated.
• Contextually. You may find existing theories from outside the field of one discipline.
Alternatively, you could revisit existing research using new theories and assess whether such
theories have greater explanatory power.
Statement of Problem
• Defines relevant variables
• Relationship among variables
Literature Review
• Process of systematically identifying, locating and analyzing of documents
Purpose of Literature Review
• What has already been done relating to your topic
• What research strategy and procedures have been adopted
• Facilitation in interpretation of results
Sources of Literature
• Books
• Educational Indexes
• Periodicals
• Dissertations
• Abstracts
• Internet
Abstracting of References
• The process of locating, reviewing, summarizing, and classifying the literature references
• Sort out the references according to the sources
• Make a list of references in each source in chronological order, starting with most recent one
• Read the summary of abstract of the reference

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• Scan through the complete article noting down main idea
• Develop an index card with complete bibliographic reference and catalogue number as well
• Classify and code the article according to some system and mark each card with its relevant
code
• Summarize the reference and put the summary on the index card
• Mark each index card with your degree of understanding of it
• Mark the direct quotations of the reference on the index card
• Photocopying may be an alternate strategy
Guidelines for Analyzing, Organizing, and Reporting Literature
Review:-
• Make an outline of headings and subheadings
• Study and fit each reference according to your outline
• Analyze the relationship or difference between different references sorted under one
subheading
• Succession of the literature should be from least relevant to most relevant
• Conclude the literature review with a brief summary and its implications
Sequence of Writing Literature Review
– The introduction
– The body
– The conclusion
Introduction
• Define or identify the general topic, issue, or area of concern, thus providing an appropriate
context for reviewing the literature.
• Point out overall trends in what has been published about the topic; or conflicts in theory,
methodology, evidence, and conclusions; or gaps in research
• Establish the writer's reason (point of view) for reviewing the literature; explain the criteria to
be used in analyzing and comparing literature
The Body
• Group research studies and other types of literature (reviews, theoretical articles, case
studies, etc.) according to common denominators such as qualitative versus quantitative
approaches, conclusions of authors, specific purpose or objective, etc.
• Summarize individual studies

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• Make comparisons and analyses.
Conclusion
• Summarize major contributions of significant studies and articles to the body of knowledge
under review, maintaining the focus established in the introduction.
• Evaluate the current "state of the art" pointing out major methodological flaws or gaps in
research, inconsistencies in theory and findings, and areas or issues pertinent to future study.
• Conclude by providing some insight into the relationship between the central topic of the
literature review and a larger area of study (rationale)
Research Goal & Objectives
Goal
• It describes the aim of the work in broad terms
Objective
• These are more specific and relate directly to research question. They may be divided into two
types:
– Primary objectives  (bound to be achieved)
– Secondary objectives  (by the way)
• The goal (aim) and objectives must be stated at the very beginning of the study, since they will
guide the investigator during the process of formulating research questions and hypothesis.
• They will also help in the prioritization process.
• They will enable the reader or consumer of the work to judge whether the investigator had
achieved these objectives or not.
Considerations for Research Objectives
• Properly formulated, specific objectives will facilitate the development of your research
methodology and will help to orient the collection, analysis, interpretation and utilization of
data.
The research objectives should be:
– Closely related to the research question
– Covering all aspects of the problem
– Very specific
– Ordered in a logical sequence
– Stated in action verbs that could be evaluated e.g. to describe, to identify, to measure,
to compare, etc.
– Achievable, taking into consideration the available resources and time

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– Mutually exclusive, with no repetitions or overlaps
SMART Objectives:-
 S Specific.
 M Measurable.
 A Achievable.
 R Relevant
 T Time-bound.
Formulation and Statement of Hypothesis
Hypothesis:-
• Tentative statement concerning the relationship between the variables concerned is called
Hypothesis
• It is the most specific statement of a problem
• It determines the outcome of the research implied through literature review
• Whole research process revolves around hypothesis
Characteristics of Good Hypothesis:-
• It should be testable within some reasonable period of time
• It should be based on a sound rationale
• It should follow from previous research
• It should lead to future research
• It should be consistent with previous researches
• It should provide a reasonable explanation of relationship between variables
• It should clearly and concisely state the expected relationship between variable
• It should define the variable in operational and measureable term
Types of Hypothesis:-
Hypothesis is classified as:-
• Research Hypothesis
• Statistical Hypothesis

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Research Hypothesis:-
• Stated in declarative form
• Describes the expected relationship or difference between variables
• In general, it is denoted by H1
• May be non-directional or directional
• Non-directional hypothesis simply describes relationship
• Directional hypothesis indicates the nature of relationship or difference
Null Hypothesis:-
• Stated in null form
• Defies any sort of expected relationship or difference between variables
• In general, it is denoted by H0
• Used because they suit statistical techniques to determine whether expected relationship is just
a probability or a true one
• They rarely express the researchers expectation regarding result of study
Null Hypothesis vs. Alternative Hypothesis:-
Null Hypothesis Alternative Hypothesis
• Statement about the value of a population
parameter
• Represented by H0
• Always stated as an Equality
• Statement about the value of a population
parameter that must be true if the null
hypothesis is false
• Represented by H1
• Stated in on of three forms
• >
• <
• 
Type I and Type II Errors:-
Type I Error
• Also known as a “false positive”
• It is the error of rejecting a null hypothesis when it is actually true.
• It occurs when we are observing a difference when in truth there is none (or more specifically -
no statistically significant difference).

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Type II Error
• Also known as a "false negative":
• It is the error of accepting a null hypothesis when it is actually false.
• It occurs when we are failing to observe a difference when in truth there is one.
Alpha vs. Beta, Part II:-
• It would be wonderful if we could force both  and  to equal zero. Unfortunately, these
quantities have an inverse relationship. As  increases,  decreases and vice versa.
• The only way to decrease both  and  is to increase the sample size. To make both quantities
equal zero, the sample size would have to be infinite—you would have to sample the entire
population.
Type I and Type II Errors:-
Table
Forming Conclusions:-
• Every hypothesis test ends with the experimenters (you and I) either
• Rejecting the Null Hypothesis, or
• Failing to Reject the Null Hypothesis
• As strange as it may seem, you never accept the Null Hypothesis. The best you can ever say
about the Null Hypothesis is that you don’t have enough evidence, based on a sample, to reject
it!
Seven Steps to Hypothesis Testing Happiness (Traditional or
Classical Method):-
1) Describe in words the population characteristic about which hypotheses are to be tested
2) State the null hypothesis, Ho
3) State the alternative hypothesis, H1 or Ha
4) Display the test statistic to be used
5) Identify the rejection region
1) Is it an upper, lower, or two-tailed test?
2) Determine the critical value associated with , the level of significance of the test
6) Compute all the quantities in the test statistic, and compute the test statistic itself

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7) State the conclusion. That is, decide whether to reject the null hypothesis, Ho, or fail to reject
the null hypothesis. The conclusion depends on the level of significance of the test. Also,
remember to state your result in the context of the specific problem.

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