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Assumption and Hypothesis in Research: Roles in Scientific Research, Process
of research formulation and influence in decision making and problem
solving
Presentation · December 2024
DOI: 10.13140/RG.2.2.10258.98247
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Assumption and Hypothesis in Research: Roles in Scientific
Research, Process of research formulation and influence in
decision making and problem solving
David Adeyemi Oluyori
SPGS/MTH/PHD/24/0004
Department of Mathematics, Sule Lamido University, Kafin-Hausa, Jigawa State
ICT and Advanced Research Methods Assignment
(MTH 9301)
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Outline
1 Introduction
2 Assumption
3 Identifying Assumption in Research
4 Common Types of Mathematical Assumptions
5 Examples of Assumption
6 Hypothesis
7 Types of Research Hypothesis
8 Working Hypothesis
9 Developing a Working Hypothesis
10 Examples of Working Hypothesis
11 Examples of Mathematical Hypotheses
12 Criteria for determining the type of Hypothesis
13 Differences between Assumption and Hypothesis
14 Conclusion
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Question
Examine the differences between hypotheses and assumptions in great detail,
considering factors such as their role in scientific research, the process of
formulation and their influence on decision making and problem solving?
In this discuss, we will discuss assumption and hypothesis in great detail stating
its definition, types, differences and its place in scientific research process.
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Introduction
To motivate this topic, i start with this quote due to Cresswell & Poth (2018)
[p. 15]
”Whether we are aware of it or not, we always bring certain beliefs
and philosophical assumptions to our research... These (beliefs)
influence how a researcher seeks information to answer the questions
and serve as a basis of evaluation of a study .... and the importance
of these assumptions (in turn) shapes the direction of the research.”
If we have an assumption, we accept the risk that the assumption is
false and move on. If we have a hypothesis, we attempt to falsify it.
Assumption
Assumption is a axiomatic system of enquiry which help in understanding the
problems, thinking of possible dimensions within the problem to achieve the
desired conclusion.
An axiom is any statement that is accepted to be true without a proof.
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Assumption (Definition)
The followings are other key notes on assumption
1) Assumption help create a premise for research and forms a core part in the
research question formulation.
2) Assumption are self evident conditions that are inherent in the study
scenario and would be difficult to achieve without them.
3) In mathematics, assumption play role in proving or disproving results. as it
is fondly said: ”If you don’t LET, you cannot GET.”
4) From [1] and [3], we see that Assumption help create an abstract scenario
under which a condition holds or does not hold in order to evaluate its
implication in both cases.
5) To assume in mathematics, we use phrase like Let, Suppose, Assuming
this is true or there exist.....
6) Assumptions are beliefs that are taken for granted to be true.
7) Assumptions are often Implicit. By Implicit we mean, often times we are
not consciously aware of them.
8) Assumptions are statements believed to be true based on existing theories
or research findings.
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Philosophical Assumption
Philosophical Assumptions are based on the following premise:
1) Ontology: study of the nature of reality concerned with the assumptions
made by the researcher to believe the study is worthwhile.
2) Epistemology: is concerned with the nature and scope of knowledge. It is
concerned with how people comes to know something and how people
know (perceive) the truth.
3) Methodology: concerns the philosophies that guide data gathering and
determine the appropriate method to be used. In statistics or Operations
research, the researcher seek to develop generalizable explanation about
the subject using statistical tools or models.
4) Axiology: Opines that Facts are objective truth whereas values are
subjective truth. It emphasizes the role of values in research.
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Identifying Assumption in Research
Identifying assumptions in research is a critical step in ensuring the validity and
reliability of findings. Here are some common methods used to identify
assumptions:
Literature Review: Researchers often begin by reviewing existing
literatures as this helps them understand the foundational assumptions
made by previous studies and identify gaps or areas where assumptions
may need to be revised or clarified.
Hypothesis Formulation: When formulating hypotheses, the researcher
state their assumption by considering what has been taken for granted
(things that have not been considered) or the condition which the research
has not been conducted.
Peer Review and Feedback: Engaging with peers and experts in the field
can help researchers identify assumptions that they may have overlooked.
Feedback from others can provide new perspectives and highlight potential
weaknesses in the assumptions made.
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Identifying Assumptions in Research (Cont’d)
Critical Analysis: Researchers should critically analyze their own work,
questioning the validity of their assumptions. This involves examining
whether the assumptions are justified and whether they align with the
research objectives.
Modelling and Simulations: In applied mathematics, assumptions are often
identified through the modeling process. Researchers must specify the
assumptions underlying their models, such as linearity or homogeneity, and
assess their impact on the results.
Documentation and Transparency: Documenting assumptions helps you to
get ideas out of the cold warmth of your head to the light of day for
development while Transparency allows others to evaluate the validity of
the assumptions and their implications to your research.
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Most Common Types of Mathematical Assumptions
In mathematics, assumptions are essential for developing theories, proofs, and
models. Here are some common types of assumptions used in mathematical
research:
Axiomatic Assumptions: These are fundamental statements accepted as
true without proof within a particular mathematical framework. For
example, the axioms of set theory or the axioms of Euclidean geometry
serve as the foundation for further reasoning and theorems.
Conditional Assumptions: These assumptions depend on specific
conditions being met. For instance, a theorem may assume that a function
is continuous or differentiable over a certain interval. Such conditions are
crucial for the validity of the results derived from the theorem.
Existential Assumptions: These assumptions assert the existence of certain
mathematical objects or solutions. For example, a researcher might
assume that there exists a solution to a particular equation or that a
certain type of function can be constructed.
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Most Common Mathematical Assumptions (Cont’d)
Universality Assumptions: These are broad statements that apply to all
elements within a certain set or category. For example, a theorem might
assume that a property holds for all integers or all real numbers.
Approximation Assumptions: In applied mathematics, researchers often
make assumptions that simplify complex problems. For instance, they
might assume that a function can be approximated by a polynomial or
that a physical system behaves linearly under certain conditions.
Independence Assumptions: These assumptions are made when researchers
consider variables or events to be independent of one another. For
example, in probability theory, one might assume that the occurrence of
one event does not affect the probability of another.
Symmetry Assumptions: In many mathematical models, researchers
assume symmetry in order to simplify analysis. For instance, in physics,
one might assume that a system behaves the same way regardless of the
direction of observation.
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Examples of Assumption
Common Assumptions in Life and Research
1) ”This research study assumes that respondents will honestly answer
questionnaires, providing valid and reliable data for analysis” [The
respondent’s answer may turn out to be false.]
2) I know i am a true son of my father [you cannot be so sure till have taken
a DNA test - which is the proof.]
3) When assessing the impact of Computer-assisted instruction on
fourth-grade students’ progress, you assume that the students in question
can read and write otherwise there is no research.
4) Every graduate from every Nigerian Universities must be able to speak
good English [Recent statistics shows as sharp contrast as graduates
measure below par as touching their command of English].
5) A researcher trying to discover the relationship between two variables must
believe that the relationship between the two variables exists and can be
discovered.
6) The most basic assumption in research is that every thing in this world
works under a certain system.
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Hypothesis
Hypothesis is a Latin word which means ”to put under”. In general, hypo
means below or sub and thesis is research work. Hypothesis can be perceived
in the following sense:
It is a tentative statement/educational guess made to assist in the search
for facts. It remain valid until facts are available and analyzed.
A tentative prediction about the relationship that exist between two or
more variables which fuel the drive for testing and validation.
A temporal answer to a specific question(s) raised at the beginning of a
research process.
Presumptive statement of a proposition based on available evidence.
Hypothesis is what you are testing explicitly by an experiment.
Hypothesis is a theory that seeks to explain a phenomenon or set of
phenomena.
While assumption is tested implicitly, hypothesis is tested explicitly.
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Types of Research Hypothesis
That system can be predicted in advance based on theory or logical common
sense can be referred to as research hypothesis.
qquad
Research hypothesis is of at least three kinds namely.
Types of Research Hypothesis
1) Theoretical Hypothesis: A prediction of the relationship between research
variables based on theory or logical common sense.
2) Statistical Hypothesis: In testing hypothesis quantitatively, the theoretical
hypothesis should be transformed into statistical hypothesis, which takes
the form of Null hypothesis and its alternatives. It is the Null hypothesis
that is to be tested to justify its rejection or otherwise its acceptance.
3) Empirical Hypothesis: In qualitative study, the result of first data analysis
is called temporal empirical hypothesis that should be validated with more
data. This cycle of rechecking the result with more data is done again and
again until the hypothesis becomes the final conclusion.
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Working Hypothesis
Remark
Aside from the aforementioned, in research we have another type called the
Working Hypothesis.
Working Hypothesis
Working Hypothesis is a tentative assumption made in order to draw out or
test the logical or empirical consequences of a given data or result. They
provide a focal point for research which determines the manner in which the
test is conducted in the derivation and analysis of data. It is an outcome of a
priori thinking on the subject matter, examination of the available data and
materials which includes all related studies. Experienced researcher don’t start
research with a topic they often start with a question - That is the Working
Hypothesis.
Characteristics of Working Hypothesis
It should be clear, precise and limited to the current study.
It must be testable (having the capability of being tested or verified).
It should state the relationship between two or more variable.
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Working Hypothesis (Cont’d)
Developing a Working Hypothesis
Discussion with experts and colleagues about the problem, origin and the
objectives of the research in proffering solution.
Examination of available data/result for possible trend analysis and
peculiarities.
Review of relevant literatures or studies of similar problems and their
solutions.
Exploratory personal investigation with the original field interviewer with a
view to get more insight into the practicality of the problem.
Importance of Working Hypothesis
It guides the researcher in terms of scope to help in delimitating the area
of research and narrow down the research.
It sharpens the thinking capacity of the researcher and increase focus on
the key elements of the research.
It indicates the type of method(s) to be deployed to proffer solution to the
research problem.
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Examples of Working Hypothesis
Working hypotheses are preliminary statements that researchers formulate early
in the research process. They are often broad and subject to revision as more
data is collected and analyzed. Here are some examples of working hypotheses:
Education and Performance: ”Students who receive additional tutoring
will perform better on standardized tests than those who do not receive
tutoring.” This hypothesis can be tested by comparing test scores between
the two groups.
Exercise and Mental Health: ”Regular physical exercise leads to improved
mental health outcomes in adults.” This hypothesis can be explored
through surveys and psychological assessments before and after a
structured exercise program.
Diet and Weight Loss: ”Individuals following a low-carb diet will lose more
weight than those following a low-fat diet over a three-month period.”
This can be tested by monitoring weight changes in participants adhering
to each diet.
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Examples of Working Hypothesis (Cont’d)
Social Media and Self-Esteem: ”Frequent use of social media platforms
decreases self-esteem among adolescents.” This hypothesis can be
examined through surveys measuring social media usage and self-esteem
levels.
Sleep and Academic Performance: ”Students who get at least eight hours
of sleep per night will have higher GPAs than those who sleep less.” This
can be tested by correlating sleep patterns with academic performance
data.
Technology Use and Attention Span: ”Increased use of smartphones
negatively affects the attention span of teenagers.” This hypothesis can be
evaluated through observational studies and attention span tests.
Remark
These examples illustrate how working hypotheses can guide research by
providing specific assertions that can be tested and refined as the study
progresses. They are essential for framing research questions and determining
methodologies, allowing researchers to explore their ideas in a structured
manner.
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Examples of Mathematical Hypotheses
In mathematics, hypotheses often serve as foundational statements or
conjectures that can be tested or explored through logical reasoning, proofs, or
computational methods. Here are some examples of mathematical hypotheses:
Goldbach’s Conjecture: This hypothesis posits that every even integer
greater than two can be expressed as the sum of two prime numbers. For
example, 4 = 2 + 2, 6 = 3 + 3, and so on. Despite extensive testing, it
remains unproven.
Fermat’s Last Theorem: This hypothesis claims that there are no three
positive integers, a, b, c that satisfy the equation an + b n = c n for any
integer value of n > 2. This was famously proved by Prof. Andrew Wiles
in 1994.
Riemann Hypothesis: This famous hypothesis suggests that all
non-trivial zeros of the Riemann zeta function have a real part equal to 12 .
It has significant implications for number theory, particularly in the
distribution of prime number.
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Mathematical Hypothesis Examples (Cont’d)
Poincaré Conjecture: This hypothesis states that every simply connected,
closed 3-manifold is homeomorphic to the 3-sphere. It was proven by
Grigori Perelman in 2003, making it one of the most famous results in
topology. It was part of the 10 Millenial Prize problems proposed by Clay
Institute of Mathematics.
Twin Prime Conjecture: This hypothesis suggests that there are
infinitely many pairs of prime numbers that have a difference of two, such
as (3, 5) and (11, 13). While many twin primes have been found, the
conjecture remains unproven.
Collatz Conjecture: This hypothesis proposes that starting with any
positive integer n and applying a specific iterative process (if n is even,
divide it by 2; if odd, multiply by 3 and add 1), will eventually lead to the
number 1. Despite extensive testing, it has not been proven for all integers.
Remark
These examples shows how hypotheses in mathematics varies from simple
conjectures to complex theories, often driving research and exploration within
the field. Most importantly, Hypotheses serve as starting points for
investigation and can lead to significant discoveries when proven or disproven.
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Criteria for determining Hypotheses Type
The classification of hypotheses in research is influenced by several criteria.
Here are the key factors that determine the types of hypotheses used:
Research Stage: The stage of the research process plays a significant role
in determining the type of hypothesis. Early-stage research often involves
high-level or working hypotheses that are broad and subject to revision as
more data is collected. In contrast, later stages may involve detailed
hypotheses that are specific and rigorously tested.
Nature of Inquiry: The type of inquiry-whether exploratory, descriptive,
or explanatory-affects the hypothesis type. Exploratory research may use
open-ended hypotheses, while explanatory research typically employs more
specific, testable hypotheses that predict relationships between variables.
Complexity of the Phenomenon: The complexity of the phenomenon
being studied can dictate the type of hypothesis. Simple phenomena may
be adequately described by straightforward hypotheses, while complex
systems may require multiple, interrelated hypotheses to capture the
nuances of the relationships involved.
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Criteria for Hypotheses Type (Cont’d)
Data Availability: The availability and type of data can influence
hypothesis formulation. If data is limited or qualitative, researchers may
lean towards broader, more general hypotheses. Conversely, with rich
quantitative data, more specific and detailed hypotheses can be developed.
Theoretical framework: The theoretical background guiding the research
also shapes hypothesis types. Researchers often formulate hypotheses
based on existing theories, which can dictate whether they are testing a
new theory, confirming an existing one, or exploring a new avenue of
inquiry.
Research Objectives: The specific objectives of the research will
determine the hypothesis type. Most often, hypotheses reflects the focus
of the research.
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Differences between Assumption and Hypothesis
As a recap, we state some differences between assumption and hypothesis as
follows:
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Word of Caution
Real World Advice
1) Assumptions can be dangerous because they can lead us to make
mistakes. For example, if we assume that everyone is honest, we may be
more likely to be taken advantage of.
2) Its good to keep academic research strictly academic and the real world in
their place.
3) Hypotheses are important because they help us to advance knowledge. By
testing hypotheses, we can learn more about the world around us.
4) Assumptions can be helpful because they allow us to make quick decisions
without having to think through everything carefully. However, they can
also be dangerous because they can lead us to make mistakes.
5) Over assumption in the real world can be costly. You may even assume a
dead person is alive while his obituary is right before your face. You tend
to lose touch with reality.
6) You may assume T-Pain is the President of Nigeria but in the real sense,
T-Pain is an American Music Artist.
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Conclusion
This presentation is primarily centered on Assumption and Hypothesis. The
followings resonates throughout this presentation: While assumption creates a
premise for research, hypothesis creates a tentative guess which drive the
research process our search for answer(s). So far, we have seen that these duo
terms forms a core part of the research questions we seek to answer.
In addition, we made some striking notes on working hypotheses, its
importance and examples in the problem formulation and validation process.
Finally, we highlight some differences between Assumption and Hypotheses
based on their definition, status, purpose and testability.
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References
Cresswell, J. and Poth, C. (2018),Qualitative Inquiry and Research Design,
Fourth Edition, Sage Publications Limited, London.
Ranjit, Kumar (2011),Research Methodology, Sage Publications Limited,
London.
Shraddha, Bhome. et’al (2013), Research Methodology, First Edition,
Himalaya Publishing House & New Delhi, India.
Estelle M. Phillips and Derek Pugh (2005), How to get a PhD: A
handbook for Students and Supervisors, Fourth Edition, Open University
Press, McGraw-Hill Education, New York, USA.
Joseph E. Hermon and Alan G. Gross, (2010), The Craft of Scientific
Communication, University of Chicago Press, Chicago, London.
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