operational form of hypothesis

Operational Hypothesis

An Operational Hypothesis is a testable statement or prediction made in research that not only proposes a relationship between two or more variables but also clearly defines those variables in operational terms, meaning how they will be measured or manipulated within the study. It forms the basis of an experiment that seeks to prove or disprove the assumed relationship, thus helping to drive scientific research.

The Core Components of an Operational Hypothesis

Understanding an operational hypothesis involves identifying its key components and how they interact.

The Variables

An operational hypothesis must contain two or more variables — factors that can be manipulated, controlled, or measured in an experiment.

The Proposed Relationship

Beyond identifying the variables, an operational hypothesis specifies the type of relationship expected between them. This could be a correlation, a cause-and-effect relationship, or another type of association.

The Importance of Operationalizing Variables

Operationalizing variables — defining them in measurable terms — is a critical step in forming an operational hypothesis. This process ensures the variables are quantifiable, enhancing the reliability and validity of the research.

Constructing an Operational Hypothesis

Creating an operational hypothesis is a fundamental step in the scientific method and research process. It involves generating a precise, testable statement that predicts the outcome of a study based on the research question. An operational hypothesis must clearly identify and define the variables under study and describe the expected relationship between them. The process of creating an operational hypothesis involves several key steps:

Steps to Construct an Operational Hypothesis

• Define the Research Question : Start by clearly identifying the research question. This question should highlight the key aspect or phenomenon that the study aims to investigate.
• Identify the Variables : Next, identify the key variables in your study. Variables are elements that you will measure, control, or manipulate in your research. There are typically two types of variables in a hypothesis: the independent variable (the cause) and the dependent variable (the effect).
• Operationalize the Variables : Once you’ve identified the variables, you must operationalize them. This involves defining your variables in such a way that they can be easily measured, manipulated, or controlled during the experiment.
• Predict the Relationship : The final step involves predicting the relationship between the variables. This could be an increase, decrease, or any other type of correlation between the independent and dependent variables.

By following these steps, you will create an operational hypothesis that provides a clear direction for your research, ensuring that your study is grounded in a testable prediction.

Evaluating the Strength of an Operational Hypothesis

Not all operational hypotheses are created equal. The strength of an operational hypothesis can significantly influence the validity of a study. There are several key factors that contribute to the strength of an operational hypothesis:

• Clarity : A strong operational hypothesis is clear and unambiguous. It precisely defines all variables and the expected relationship between them.
• Testability : A key feature of an operational hypothesis is that it must be testable. That is, it should predict an outcome that can be observed and measured.
• Operationalization of Variables : The operationalization of variables contributes to the strength of an operational hypothesis. When variables are clearly defined in measurable terms, it enhances the reliability of the study.
• Alignment with Research : Finally, a strong operational hypothesis aligns closely with the research question and the overall goals of the study.

By carefully crafting and evaluating an operational hypothesis, researchers can ensure that their work provides valuable, valid, and actionable insights.

Examples of Operational Hypotheses

To illustrate the concept further, this section will provide examples of well-constructed operational hypotheses in various research fields.

The operational hypothesis is a fundamental component of scientific inquiry, guiding the research design and providing a clear framework for testing assumptions. By understanding how to construct and evaluate an operational hypothesis, we can ensure our research is both rigorous and meaningful.

Examples of Operational Hypothesis:

• In Education : An operational hypothesis in an educational study might be: “Students who receive tutoring (Independent Variable) will show a 20% improvement in standardized test scores (Dependent Variable) compared to students who did not receive tutoring.”
• In Psychology : In a psychological study, an operational hypothesis could be: “Individuals who meditate for 20 minutes each day (Independent Variable) will report a 15% decrease in self-reported stress levels (Dependent Variable) after eight weeks compared to those who do not meditate.”
• In Health Science : An operational hypothesis in a health science study might be: “Participants who drink eight glasses of water daily (Independent Variable) will show a 10% decrease in reported fatigue levels (Dependent Variable) after three weeks compared to those who drink four glasses of water daily.”
• In Environmental Science : In an environmental study, an operational hypothesis could be: “Cities that implement recycling programs (Independent Variable) will see a 25% reduction in landfill waste (Dependent Variable) after one year compared to cities without recycling programs.”

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2023 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

• Collecting Data

Frequently Asked Questions

A hypothesis is a tentative statement about the relationship between two or more  variables. It is a specific, testable prediction about what you expect to happen in a study.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. It is only at this point that researchers begin to develop a testable hypothesis. Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk wisdom that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis.   In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in a number of different ways. One of the basic principles of any type of scientific research is that the results must be replicable.   By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. How would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests that there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative sample of the population and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
• "There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

• "Children who receive a new reading intervention will perform better than students who did not receive the intervention."
• "Adults will perform better on a memory task than children." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when it would be impossible or difficult to  conduct an experiment . These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can then be used to look at how the variables are related. This type of research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

A Word From Verywell

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Some examples of how to write a hypothesis include:

• "Staying up late will lead to worse test performance the next day."
• "People who consume one apple each day will visit the doctor fewer times each year."
• "Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

• The research question
• The independent variable (IV)
• The dependent variable (DV)
• The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

• cognitive sophistication
• tolerance of diversity
• exposure to higher levels of math or science
• age (which is currently related to educational level in many countries)
• social class and other variables.
• For example, suppose you designed a treatment to help people stop smoking. Because you are really dedicated, you assigned the same individuals simultaneously to (1) a "stop smoking" nicotine patch; (2) a "quit buddy"; and (3) a discussion support group. Compared with a group in which no intervention at all occurred, your experimental group now smokes 10 fewer cigarettes per day.
• There is no relationship among two or more variables (EXAMPLE: the correlation between educational level and income is zero)
• Or that two or more populations or subpopulations are essentially the same (EXAMPLE: women and men have the same average science knowledge scores.)
• the difference between two and three children = one child.
• the difference between eight and nine children also = one child.
• the difference between completing ninth grade and tenth grade is  one year of school
• the difference between completing junior and senior year of college is one year of school
• In addition to all the properties of nominal, ordinal, and interval variables, ratio variables also have a fixed/non-arbitrary zero point. Non arbitrary means that it is impossible to go below a score of zero for that variable. For example, any bottom score on IQ or aptitude tests is created by human beings and not nature. On the other hand, scientists believe they have isolated an "absolute zero." You can't get colder than that.

Principles of Research Methodology pp 31–53 Cite as

The Research Hypothesis: Role and Construction

• Phyllis G. Supino EdD 3  
• First Online: 01 January 2012

5961 Accesses

A hypothesis is a logical construct, interposed between a problem and its solution, which represents a proposed answer to a research question. It gives direction to the investigator’s thinking about the problem and, therefore, facilitates a solution. There are three primary modes of inference by which hypotheses are developed: deduction (reasoning from a general propositions to specific instances), induction (reasoning from specific instances to a general proposition), and abduction (formulation/acceptance on probation of a hypothesis to explain a surprising observation).

A research hypothesis should reflect an inference about variables; be stated as a grammatically complete, declarative sentence; be expressed simply and unambiguously; provide an adequate answer to the research problem; and be testable. Hypotheses can be classified as conceptual versus operational, single versus bi- or multivariable, causal or not causal, mechanistic versus nonmechanistic, and null or alternative. Hypotheses most commonly entail statements about “variables” which, in turn, can be classified according to their level of measurement (scaling characteristics) or according to their role in the hypothesis (independent, dependent, moderator, control, or intervening).

A hypothesis is rendered operational when its broadly (conceptually) stated variables are replaced by operational definitions of those variables. Hypotheses stated in this manner are called operational hypotheses, specific hypotheses, or predictions and facilitate testing.

• Attention Deficit Hyperactivity Disorder
• Operational Definition
• Moderator Variable
• Ventricular Performance
• Attention Deficit Hyperactivity Disorder Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Wrong hypotheses, rightly worked from, have produced more results than unguided observation

—Augustus De Morgan, 1872[ 1 ]—

This is a preview of subscription content, log in via an institution .

Buying options

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

De Morgan A, De Morgan S. A budget of paradoxes. London: Longmans Green; 1872.

Google Scholar  

Leedy Paul D. Practical research. Planning and design. 2nd ed. New York: Macmillan; 1960.

Bernard C. Introduction to the study of experimental medicine. New York: Dover; 1957.

Erren TC. The quest for questions—on the logical force of science. Med Hypotheses. 2004;62:635–40.

Article   PubMed   Google Scholar  

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 7. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1966.

Aristotle. The complete works of Aristotle: the revised Oxford Translation. In: Barnes J, editor. vol. 2. Princeton/New Jersey: Princeton University Press; 1984.

Polit D, Beck CT. Conceptualizing a study to generate evidence for nursing. In: Polit D, Beck CT, editors. Nursing research: generating and assessing evidence for nursing practice. 8th ed. Philadelphia: Wolters Kluwer/Lippincott Williams and Wilkins; 2008. Chapter 4.

Jenicek M, Hitchcock DL. Evidence-based practice. Logic and critical thinking in medicine. Chicago: AMA Press; 2005.

Bacon F. The novum organon or a true guide to the interpretation of nature. A new translation by the Rev G.W. Kitchin. Oxford: The University Press; 1855.

Popper KR. Objective knowledge: an evolutionary approach (revised edition). New York: Oxford University Press; 1979.

Morgan AJ, Parker S. Translational mini-review series on vaccines: the Edward Jenner Museum and the history of vaccination. Clin Exp Immunol. 2007;147:389–94.

Article   PubMed   CAS   Google Scholar  

Pead PJ. Benjamin Jesty: new light in the dawn of vaccination. Lancet. 2003;362:2104–9.

Lee JA. The scientific endeavor: a primer on scientific principles and practice. San Francisco: Addison-Wesley Longman; 2000.

Allchin D. Lawson’s shoehorn, or should the philosophy of science be rated, ‘X’? Science and Education. 2003;12:315–29.

Article   Google Scholar  

Lawson AE. What is the role of induction and deduction in reasoning and scientific inquiry? J Res Sci Teach. 2005;42:716–40.

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 2. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1965.

Bonfantini MA, Proni G. To guess or not to guess? In: Eco U, Sebeok T, editors. The sign of three: Dupin, Holmes, Peirce. Bloomington: Indiana University Press; 1983. Chapter 5.

Peirce CS. Collected papers of Charles Sanders Peirce, vol. 5. In: Hartshorne C, Weiss P, editors. Boston: The Belknap Press of Harvard University Press; 1965.

Flach PA, Kakas AC. Abductive and inductive reasoning: background issues. In: Flach PA, Kakas AC, ­editors. Abduction and induction. Essays on their relation and integration. The Netherlands: Klewer; 2000. Chapter 1.

Murray JF. Voltaire, Walpole and Pasteur: variations on the theme of discovery. Am J Respir Crit Care Med. 2005;172:423–6.

Danemark B, Ekstrom M, Jakobsen L, Karlsson JC. Methodological implications, generalization, scientific inference, models (Part II) In: explaining society. Critical realism in the social sciences. New York: Routledge; 2002.

Pasteur L. Inaugural lecture as professor and dean of the faculty of sciences. In: Peterson H, editor. A treasury of the world’s greatest speeches. Douai, France: University of Lille 7 Dec 1954.

Swineburne R. Simplicity as evidence for truth. Milwaukee: Marquette University Press; 1997.

Sakar S, editor. Logical empiricism at its peak: Schlick, Carnap and Neurath. New York: Garland; 1996.

Popper K. The logic of scientific discovery. New York: Basic Books; 1959. 1934, trans. 1959.

Caws P. The philosophy of science. Princeton: D. Van Nostrand Company; 1965.

Popper K. Conjectures and refutations. The growth of scientific knowledge. 4th ed. London: Routledge and Keegan Paul; 1972.

Feyerabend PK. Against method, outline of an anarchistic theory of knowledge. London, UK: Verso; 1978.

Smith PG. Popper: conjectures and refutations (Chapter IV). In: Theory and reality: an introduction to the philosophy of science. Chicago: University of Chicago Press; 2003.

Blystone RV, Blodgett K. WWW: the scientific method. CBE Life Sci Educ. 2006;5:7–11.

Kleinbaum DG, Kupper LL, Morgenstern H. Epidemiological research. Principles and quantitative methods. New York: Van Nostrand Reinhold; 1982.

Fortune AE, Reid WJ. Research in social work. 3rd ed. New York: Columbia University Press; 1999.

Kerlinger FN. Foundations of behavioral research. 1st ed. New York: Hold, Reinhart and Winston; 1970.

Hoskins CN, Mariano C. Research in nursing and health. Understanding and using quantitative and qualitative methods. New York: Springer; 2004.

Tuckman BW. Conducting educational research. New York: Harcourt, Brace, Jovanovich; 1972.

Wang C, Chiari PC, Weihrauch D, Krolikowski JG, Warltier DC, Kersten JR, Pratt Jr PF, Pagel PS. Gender-specificity of delayed preconditioning by isoflurane in rabbits: potential role of endothelial nitric oxide synthase. Anesth Analg. 2006;103:274–80.

Beyer ME, Slesak G, Nerz S, Kazmaier S, Hoffmeister HM. Effects of endothelin-1 and IRL 1620 on myocardial contractility and myocardial energy metabolism. J Cardiovasc Pharmacol. 1995;26(Suppl 3):S150–2.

PubMed   CAS   Google Scholar  

Stone J, Sharpe M. Amnesia for childhood in patients with unexplained neurological symptoms. J Neurol Neurosurg Psychiatry. 2002;72:416–7.

Naughton BJ, Moran M, Ghaly Y, Michalakes C. Computer tomography scanning and delirium in elder patients. Acad Emerg Med. 1997;4:1107–10.

Easterbrook PJ, Berlin JA, Gopalan R, Matthews DR. Publication bias in clinical research. Lancet. 1991;337:867–72.

Stern JM, Simes RJ. Publication bias: evidence of delayed publication in a cohort study of clinical research projects. BMJ. 1997;315:640–5.

Stevens SS. On the theory of scales and measurement. Science. 1946;103:677–80.

Knapp TR. Treating ordinal scales as interval scales: an attempt to resolve the controversy. Nurs Res. 1990;39:121–3.

The Cochrane Collaboration. Open Learning Material. www.cochrane-net.org/openlearning/html/mod14-3.htm . Accessed 12 Oct 2009.

MacCorquodale K, Meehl PE. On a distinction between hypothetical constructs and intervening ­variables. Psychol Rev. 1948;55:95–107.

Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: ­conceptual, strategic and statistical considerations. J Pers Soc Psychol. 1986;51:1173–82.

Williamson GM, Schultz R. Activity restriction mediates the association between pain and depressed affect: a study of younger and older adult cancer patients. Psychol Aging. 1995;10:369–78.

Song M, Lee EO. Development of a functional capacity model for the elderly. Res Nurs Health. 1998;21:189–98.

MacKinnon DP. Introduction to statistical mediation analysis. New York: Routledge; 2008.

Download references

Author information

Authors and affiliations.

Department of Medicine, College of Medicine, SUNY Downstate Medical Center, 450 Clarkson Avenue, 1199, Brooklyn, NY, 11203, USA

Phyllis G. Supino EdD

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Phyllis G. Supino EdD .

Editor information

Editors and affiliations.

, Cardiovascular Medicine, SUNY Downstate Medical Center, Clarkson Avenue, box 1199 450, Brooklyn, 11203, USA

Phyllis G. Supino

, Cardiovascualr Medicine, SUNY Downstate Medical Center, Clarkson Avenue 450, Brooklyn, 11203, USA

Jeffrey S. Borer

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter.

Supino, P.G. (2012). The Research Hypothesis: Role and Construction. In: Supino, P., Borer, J. (eds) Principles of Research Methodology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3360-6_3

Download citation

DOI : https://doi.org/10.1007/978-1-4614-3360-6_3

Published : 18 April 2012

Publisher Name : Springer, New York, NY

Print ISBN : 978-1-4614-3359-0

Online ISBN : 978-1-4614-3360-6

eBook Packages : Medicine Medicine (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 2 April 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

Is this article helpful?

Shona McCombes

Other students also liked, operationalisation | a guide with examples, pros & cons, what is a conceptual framework | tips & examples, a quick guide to experimental design | 5 steps & examples.

Theory, hypothesis, and operationalization

Approach, theory, model.

First, you have to determine the general state of knowledge (or state of the art) as regards a certain objective. Are there already relevant attempts of explanation (models, theories, approaches, debates)? Many times there are theories already existing that provide a basis for discussing or looking at a certain problem.

When choosing a certain approach to explain complex circumstances, specific aspects of your problem area will be highlighted more prominently. Deciding on an approach means considering which questions can then be answered best. After choosing an approach it is necessary to use its related methods consequently.

Examples for approaches: «Education is an important prerequisite for a society's economic development» or «Earnings from tourism support national economy.»

Hypotheses and presumptions

Hypotheses are assumptions that could explain reality or - in other words - that could be the answer to your question. Such an assumption is based on the current state of research; it therefore delivers an answer that is theoretically possible («proposed solution») and applies at least to some extent to the question posed. When dealing with complex topics it is sometimes easier to develop a number of subordinate working hypotheses from just a few main hypotheses.

Example for a hypothesis: «Tourism offers children the possibility to earn money instead of going to school» or «The more tourists the fewer the children are going to school.»

Not all research projects are conducted by means of methods to test hypotheses. In social research, for example, there are reconstructive or interpretive methods as well. Here you try to explain and understand people's actions based on their interpretation of certain issues ( Bohnsack 2000: 12–13). However, also with such an approach researchers use hypotheses or presumptions to structure their work. The point is not to finally acknowledge or reject those hypotheses. You rather search for explanations that are plausible and comprehensible.

Example for a presumption: «In developing countries parents are skeptical about their children working for the tourism industry.»

However, most of the time one again acts on theses or presumptions. The point is not to finally acknowledge or reject those assumptions. One rather searches for explanations that are plausible and comprehensible.

Example for an explanation: «Parents don't worry about their children not going to school; they are afraid of losing their status when earning less than their children.»

Operationalization

It is necessary to operationalize the terms used in scientific research (that means particularly the central terms of a hypothesis). In order to guarantee the viability of a research method you have to define first which data will be collected by means of which methods. Research operations have to be specified to comprehend a subject matter in the first place ( Bopp 2000: 21). In order to turn the operationalized term into something manageable you determine its exact meaning during a research process.

Example for an operationalization: «When compared to other areas, tourist destinations are areas where children are less likely to go to school.»

Online Guidelines for Academic Research and Writing : The academic research process : Theory, hypothesis, and operationalization

Update: 28.10.2021 ( eLML ) - Contact - Print (PDF) - © OLwA 2011 (Creative Commons)

Piaget’s Formal Operational Stage: Definition & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

The formal operational stage begins at approximately age twelve and lasts into adulthood. As adolescents enter this stage, they can think abstractly by manipulating ideas in their head, without any dependence on concrete manipulation (Inhelder & Piaget, 1958).

In the formal operational stage, children tend to reason more abstractly, systematically, and reflectively. They are more likely to use logic to reason out the possible consequences of each action before carrying it out.

He/she can do mathematical calculations, think creatively, use abstract reasoning, and imagine the outcome of particular actions.

An example of the distinction between concrete and formal operational stages is the answer to the question, “If Kelly is taller than Ali and Ali is taller than Jo, who is tallest?”

This is an example of inferential reasoning, which is the ability to think about things which the child has not actually experienced and to draw conclusions from its thinking.

The child who needs to draw a picture or use objects is still in the concrete operational stage , whereas children who can reason the answer in their heads are using formal operational thinking.

Formal Operational Thought

Hypothetico-deductive reasoning.

Hypothetico-deductive reasoning is the ability to think scientifically through generating predictions, or hypotheses, about the world to answer questions.

The individual will approach problems in a systematic and organized manner rather than through trial-and-error.

A teenager can consider “what if” scenarios, like imagining the future consequences of climate change based on current trends.

Abstract Thought

Concrete operations are carried out on things, whereas formal operations are carried out on ideas. Individuals can think about hypothetical and abstract concepts they have yet to experience. Abstract thought is important for planning the future.

A student understands and manipulates concepts like justice, love, and freedom without needing concrete examples or experiences. For instance, they can comprehend and discuss a statement such as “Justice is not always fair.”

Scientific Reasoning

An example of formal operational thought could be the cognitive ability to plan and test different solutions to a problem systematically, a process often referred to as “scientific thinking.”

The ability to form hypotheses, conduct experiments, analyze results, and use deductive reasoning is an example of formal operational thought.

A student forms a hypothesis about a science experiment, predicts potential outcomes, systematically tests the hypothesis, and then analyzes the results.

For example, they could hypothesize that increasing sunlight exposure will increase a plant’s rate of growth, design an experiment to test this, and then understand and explain the results.

Metacognition

Adolescents can think about their own thought processes, reflecting on how they learn best or understanding why they might have made a mistake in judgment.

For example, they might realize that they rush decisions when they’re feeling stressed and plan to use stress-reducing techniques before making important decisions in the future.

Testing Formal Operations

Piaget (1970) devised several tests of formal operational thought. One of the simplest was the “third eye problem”.  Children were asked where they would put an extra eye, if they could have a third one, and why.

Schaffer (1988) reported that when asked this question, 9-year-olds all suggested that the third eye should be on the forehead.  However, 11-year-olds were more inventive, suggesting that a third eye placed on the hand would be useful for seeing round corners.

Formal operational thinking has also been tested experimentally using the pendulum task (Inhelder & Piaget, 1958). The method involved a length of string and a set of weights. Participants had to consider three factors (variables) the length of the string, the heaviness of the weight, and the strength of the push.

The task was to work out which factor was most important in determining the speed of swing of the pendulum.

Participants can vary the length of the pendulum string, and vary the weight. They can measure the pendulum speed by counting the number of swings per minute.

To find the correct answer, the participant has to grasp the idea of the experimental method -that is to vary one variable at a time (e.g., trying different lengths with the same weight). A participant who tries different lengths with different weights will likely end up with the wrong answer.

Children in the formal operational stage approached the task systematically, testing one variable (such as varying the string length) at a time to see its effect. However, younger children typically tried out these variations randomly or changed two things simultaneously.

Piaget concluded that the systematic approach indicated that children were thinking logically, in the abstract, and could see the relationships between things. These are the characteristics of the formal operational stage.

Critical Evaluation

Psychologists who have replicated this research, or used a similar problem, have generally found that children cannot complete the task successfully until they are older.

Robert Siegler (1979) gave children a balance beam task in which some discs were placed on either side of the center of balance. The researcher changed the number of discs or moved them along the beam, each time asking the child to predict which way the balance would go.

He studied the answers given by children from five years upwards, concluding that they apply rules which develop in the same sequence as, and thus reflect, Piaget’s findings.

Like Piaget, he found that eventually, the children were able to take into account the interaction between the weight of the discs and the distance from the center, and so successfully predict balance. However, this did not happen until participants were between 13 and 17 years of age.

He concluded that children’s cognitive development is based on acquiring and using rules in increasingly more complex situations, rather than in stages.

Learning Check

Which of the following is/are not an indication of an individual being in the formal operational stage?

Mark often struggles with planning for the future. He can’t envision different possible outcomes based on his actions. Which of the following is true about Mark? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

Which of the following actions does NOT indicate that Lucy is in the Formal Operational stage? a. Lucy can think about abstract concepts like justice and fairness. b. Lucy enjoys debates and discussions where she can express her thoughts. c. Lucy can only solve problems that are concrete and immediately present. d. Lucy enjoys conducting experiments to test her hypotheses.

Sam can play with his friends and imagine what they think about him. However, he can’t conceptualize different outcomes of a hypothetical situation. What stage is Sam likely in? a. He is in the Formal Operational stage. b. He is in the Preoperational stage. c. He is in the Concrete Operational stage. d. He is in the Sensorimotor stage.

• (b) He is in the Preoperational stage.
• (c) Lucy can only solve problems that are concrete and immediately present.
• (c) He is in the Concrete Operational stage.

According to Jean Piaget, in what stage do children begin to use abstract thinking processes?

According to Jean Piaget, children begin to use abstract thinking processes in the Formal Operational stage, which typically develops between 12 and adulthood.

In this stage, children develop the capacity for abstract thinking and hypothetical reasoning. They no longer rely solely on concrete experiences or objects in their immediate environment for understanding. Instead, they can imagine realities outside their own and consider various possibilities and perspectives.

They can formulate hypotheses, consider potential outcomes, and plan systematic approaches for problem-solving. Additionally, they can understand and manipulate abstract ideas such as moral reasoning, logic, and theoretical concepts in mathematics or science.

Based on Piaget’s theory, what should a teacher provide in the formal operational stage?

Based on Piaget’s theory, a teacher should provide the following for students in the Formal Operational stage:

Abstract Problems and Hypothetical Tasks : Encourage students to think abstractly and solve complex problems. Provide tasks that require logical reasoning, hypothesizing, and the consideration of multiple variables.

Opportunities for Debate and Discussion : Encourage students to express their thoughts and challenge the views of others. This can help them learn to view problems from multiple perspectives.

Experiments : Design lessons to allow students to develop hypotheses and conduct experiments. The scientific method is a valuable tool at this stage.

Real-world Applications : Connect classroom learning to real-world scenarios. This can help students understand the relevance and application of abstract ideas.

Higher-order Questions : Use questions involving analysis, synthesis, and evaluation to improve students’ critical thinking skills.

Guidance in Self-reflection : Encourage students to reflect on their thoughts, emotions, and behavior, which can help them understand their own cognitive processes better.

Moral and Ethical Discussions : As students in this stage begin to think more about abstract concepts such as justice, fairness, and rights, engage them in discussions around moral and ethical issues.

Piaget’s formal operational stage begins around age 11 or 12 and continues throughout adulthood. Does this suggest that once one reaches this level of cognitive development, they plateau? or are there different levels of formal operations?

According to Piaget’s theory, once individuals reach the Formal Operational stage, they have attained the highest level of cognitive development, as defined by his model. However, this does not suggest a cognitive plateau.

Cognitive development is individual and influenced by a range of factors beyond mere biological maturation.

The nature of human cognition is such that there’s always room for refinement, growth, and development throughout adulthood.

Furthermore, individual competence can vary greatly within the Formal Operational stage. For instance, a person might employ formal operational thinking in one area of life (such as their professional specialization) but not others.

Similarly, skills like problem-solving, logical reasoning, and handling abstract concepts can continue to improve with practice and experience.

Inhelder, B., & Piaget, J. (1958). Adolescent thinking.

Piaget, J. (1970). Science of education and the psychology of the child . Trans. D. Coltman.

Schaffer, H. R. (1988). Child Psychology: the future. In S. Chess & A. Thomas (eds), Annual Progress in Child Psychiatry and Child Development . NY: Brunner/Mazel.

Siegler, R. S. & Richards, D. (1979). Development of time, speed and distance concepts. Developmental Psychology, 15 , 288-298.

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

2.3: Propositions and Hypotheses

• Last updated
• Save as PDF
• Page ID 26213

• Anol Bhattacherjee
• University of South Florida via Global Text Project

Figure 2.2 shows how theoretical constructs such as intelligence, effort, academic achievement, and earning potential are related to each other in a nomological network. Each of these relationships is called a proposition. In seeking explanations to a given phenomenon or behavior, it is not adequate just to identify key concepts and constructs underlying the target phenomenon or behavior. We must also identify and state patterns of relationships between these constructs. Such patterns of relationships are called propositions. A proposition is a tentative and conjectural relationship between constructs that is stated in a declarative form. An example of a proposition is: “An increase in student intelligence causes an increase in their academic achievement.” This declarative statement does not have to be true, but must be empirically testable using data, so that we can judge whether it is true or false. Propositions are generally derived based on logic (deduction) or empirical observations (induction).

Because propositions are associations between abstract constructs, they cannot be tested directly. Instead, they are tested indirectly by examining the relationship between corresponding measures (variables) of those constructs. The empirical formulation of propositions, stated as relationships between variables, is called hypotheses (see Figure 2.1). Since IQ scores and grade point average are operational measures of intelligence and academic achievement respectively, the above proposition can be specified in form of the hypothesis: “An increase in students’ IQ score causes an increase in their grade point average.” Propositions are specified in the theoretical plane, while hypotheses are specified in the empirical plane. Hence, hypotheses are empirically testable using observed data, and may be rejected if not supported by empirical observations. Of course, the goal of hypothesis testing is to infer whether the corresponding proposition is valid.

Hypotheses can be strong or weak. “Students’ IQ scores are related to their academic achievement” is an example of a weak hypothesis, since it indicates neither the directionality of the hypothesis (i.e., whether the relationship is positive or negative), nor its causality (i.e., whether intelligence causes academic achievement or academic achievement causes intelligence). A stronger hypothesis is “students’ IQ scores are positively related to their academic achievement”, which indicates the directionality but not the causality. A still better hypothesis is “students’ IQ scores have positive effects on their academic achievement”, which specifies both the directionality and the causality (i.e., intelligence causes academic achievement, and not the reverse). The signs in Figure 2.2 indicate the directionality of the respective hypotheses.

Also note that scientific hypotheses should clearly specify independent and dependent variables. In the hypothesis, “students’ IQ scores have positive effects on their academic achievement,” it is clear that intelligence is the independent variable (the “cause”) and academic achievement is the dependent variable (the “effect”). Further, it is also clear that this hypothesis can be evaluated as either true (if higher intelligence leads to higher academic achievement) or false (if higher intelligence has no effect on or leads to lower academic achievement). Later on in this book, we will examine how to empirically test such cause-effect relationships. Statements such as “students are generally intelligent” or “all students can achieve academic success” are not scientific hypotheses because they do not specify independent and dependent variables, nor do they specify a directional relationship that can be evaluated as true or false.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base
• Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis ( H 0 ): There’s no effect in the population .
• Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:

• The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
• The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question.
• They both make claims about the population.
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

Prevent plagiarism. Run a free check.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
• Alternative hypothesis ( H a ): Independent variable affects dependent variable.

Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved April 4, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

Is this article helpful?

Shaun Turney

Other students also liked, inferential statistics | an easy introduction & examples, hypothesis testing | a step-by-step guide with easy examples, type i & type ii errors | differences, examples, visualizations, what is your plagiarism score.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Korean Med Sci
• v.36(50); 2021 Dec 27

Formulating Hypotheses for Different Study Designs

Durga prasanna misra.

1 Department of Clinical Immunology and Rheumatology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, India.

Armen Yuri Gasparyan

2 Departments of Rheumatology and Research and Development, Dudley Group NHS Foundation Trust (Teaching Trust of the University of Birmingham, UK), Russells Hall Hospital, Dudley, UK.

Olena Zimba

3 Department of Internal Medicine #2, Danylo Halytsky Lviv National Medical University, Lviv, Ukraine.

Marlen Yessirkepov

4 Department of Biology and Biochemistry, South Kazakhstan Medical Academy, Shymkent, Kazakhstan.

Vikas Agarwal

George d. kitas.

5 Centre for Epidemiology versus Arthritis, University of Manchester, Manchester, UK.

Generating a testable working hypothesis is the first step towards conducting original research. Such research may prove or disprove the proposed hypothesis. Case reports, case series, online surveys and other observational studies, clinical trials, and narrative reviews help to generate hypotheses. Observational and interventional studies help to test hypotheses. A good hypothesis is usually based on previous evidence-based reports. Hypotheses without evidence-based justification and a priori ideas are not received favourably by the scientific community. Original research to test a hypothesis should be carefully planned to ensure appropriate methodology and adequate statistical power. While hypotheses can challenge conventional thinking and may be controversial, they should not be destructive. A hypothesis should be tested by ethically sound experiments with meaningful ethical and clinical implications. The coronavirus disease 2019 pandemic has brought into sharp focus numerous hypotheses, some of which were proven (e.g. effectiveness of corticosteroids in those with hypoxia) while others were disproven (e.g. ineffectiveness of hydroxychloroquine and ivermectin).

Graphical Abstract

DEFINING WORKING AND STANDALONE SCIENTIFIC HYPOTHESES

Science is the systematized description of natural truths and facts. Routine observations of existing life phenomena lead to the creative thinking and generation of ideas about mechanisms of such phenomena and related human interventions. Such ideas presented in a structured format can be viewed as hypotheses. After generating a hypothesis, it is necessary to test it to prove its validity. Thus, hypothesis can be defined as a proposed mechanism of a naturally occurring event or a proposed outcome of an intervention. 1 , 2

Hypothesis testing requires choosing the most appropriate methodology and adequately powering statistically the study to be able to “prove” or “disprove” it within predetermined and widely accepted levels of certainty. This entails sample size calculation that often takes into account previously published observations and pilot studies. 2 , 3 In the era of digitization, hypothesis generation and testing may benefit from the availability of numerous platforms for data dissemination, social networking, and expert validation. Related expert evaluations may reveal strengths and limitations of proposed ideas at early stages of post-publication promotion, preventing the implementation of unsupported controversial points. 4

Thus, hypothesis generation is an important initial step in the research workflow, reflecting accumulating evidence and experts' stance. In this article, we overview the genesis and importance of scientific hypotheses and their relevance in the era of the coronavirus disease 2019 (COVID-19) pandemic.

DO WE NEED HYPOTHESES FOR ALL STUDY DESIGNS?

Broadly, research can be categorized as primary or secondary. In the context of medicine, primary research may include real-life observations of disease presentations and outcomes. Single case descriptions, which often lead to new ideas and hypotheses, serve as important starting points or justifications for case series and cohort studies. The importance of case descriptions is particularly evident in the context of the COVID-19 pandemic when unique, educational case reports have heralded a new era in clinical medicine. 5

Case series serve similar purpose to single case reports, but are based on a slightly larger quantum of information. Observational studies, including online surveys, describe the existing phenomena at a larger scale, often involving various control groups. Observational studies include variable-scale epidemiological investigations at different time points. Interventional studies detail the results of therapeutic interventions.

Secondary research is based on already published literature and does not directly involve human or animal subjects. Review articles are generated by secondary research. These could be systematic reviews which follow methods akin to primary research but with the unit of study being published papers rather than humans or animals. Systematic reviews have a rigid structure with a mandatory search strategy encompassing multiple databases, systematic screening of search results against pre-defined inclusion and exclusion criteria, critical appraisal of study quality and an optional component of collating results across studies quantitatively to derive summary estimates (meta-analysis). 6 Narrative reviews, on the other hand, have a more flexible structure. Systematic literature searches to minimise bias in selection of articles are highly recommended but not mandatory. 7 Narrative reviews are influenced by the authors' viewpoint who may preferentially analyse selected sets of articles. 8

In relation to primary research, case studies and case series are generally not driven by a working hypothesis. Rather, they serve as a basis to generate a hypothesis. Observational or interventional studies should have a hypothesis for choosing research design and sample size. The results of observational and interventional studies further lead to the generation of new hypotheses, testing of which forms the basis of future studies. Review articles, on the other hand, may not be hypothesis-driven, but form fertile ground to generate future hypotheses for evaluation. Fig. 1 summarizes which type of studies are hypothesis-driven and which lead on to hypothesis generation.

STANDARDS OF WORKING AND SCIENTIFIC HYPOTHESES

A review of the published literature did not enable the identification of clearly defined standards for working and scientific hypotheses. It is essential to distinguish influential versus not influential hypotheses, evidence-based hypotheses versus a priori statements and ideas, ethical versus unethical, or potentially harmful ideas. The following points are proposed for consideration while generating working and scientific hypotheses. 1 , 2 Table 1 summarizes these points.

Evidence-based data

A scientific hypothesis should have a sound basis on previously published literature as well as the scientist's observations. Randomly generated (a priori) hypotheses are unlikely to be proven. A thorough literature search should form the basis of a hypothesis based on published evidence. 7

Unless a scientific hypothesis can be tested, it can neither be proven nor be disproven. Therefore, a scientific hypothesis should be amenable to testing with the available technologies and the present understanding of science.

Supported by pilot studies

If a hypothesis is based purely on a novel observation by the scientist in question, it should be grounded on some preliminary studies to support it. For example, if a drug that targets a specific cell population is hypothesized to be useful in a particular disease setting, then there must be some preliminary evidence that the specific cell population plays a role in driving that disease process.

Testable by ethical studies

The hypothesis should be testable by experiments that are ethically acceptable. 9 For example, a hypothesis that parachutes reduce mortality from falls from an airplane cannot be tested using a randomized controlled trial. 10 This is because it is obvious that all those jumping from a flying plane without a parachute would likely die. Similarly, the hypothesis that smoking tobacco causes lung cancer cannot be tested by a clinical trial that makes people take up smoking (since there is considerable evidence for the health hazards associated with smoking). Instead, long-term observational studies comparing outcomes in those who smoke and those who do not, as was performed in the landmark epidemiological case control study by Doll and Hill, 11 are more ethical and practical.

Balance between scientific temper and controversy

Novel findings, including novel hypotheses, particularly those that challenge established norms, are bound to face resistance for their wider acceptance. Such resistance is inevitable until the time such findings are proven with appropriate scientific rigor. However, hypotheses that generate controversy are generally unwelcome. For example, at the time the pandemic of human immunodeficiency virus (HIV) and AIDS was taking foot, there were numerous deniers that refused to believe that HIV caused AIDS. 12 , 13 Similarly, at a time when climate change is causing catastrophic changes to weather patterns worldwide, denial that climate change is occurring and consequent attempts to block climate change are certainly unwelcome. 14 The denialism and misinformation during the COVID-19 pandemic, including unfortunate examples of vaccine hesitancy, are more recent examples of controversial hypotheses not backed by science. 15 , 16 An example of a controversial hypothesis that was a revolutionary scientific breakthrough was the hypothesis put forth by Warren and Marshall that Helicobacter pylori causes peptic ulcers. Initially, the hypothesis that a microorganism could cause gastritis and gastric ulcers faced immense resistance. When the scientists that proposed the hypothesis themselves ingested H. pylori to induce gastritis in themselves, only then could they convince the wider world about their hypothesis. Such was the impact of the hypothesis was that Barry Marshall and Robin Warren were awarded the Nobel Prize in Physiology or Medicine in 2005 for this discovery. 17 , 18

DISTINGUISHING THE MOST INFLUENTIAL HYPOTHESES

Influential hypotheses are those that have stood the test of time. An archetype of an influential hypothesis is that proposed by Edward Jenner in the eighteenth century that cowpox infection protects against smallpox. While this observation had been reported for nearly a century before this time, it had not been suitably tested and publicised until Jenner conducted his experiments on a young boy by demonstrating protection against smallpox after inoculation with cowpox. 19 These experiments were the basis for widespread smallpox immunization strategies worldwide in the 20th century which resulted in the elimination of smallpox as a human disease today. 20

Other influential hypotheses are those which have been read and cited widely. An example of this is the hygiene hypothesis proposing an inverse relationship between infections in early life and allergies or autoimmunity in adulthood. An analysis reported that this hypothesis had been cited more than 3,000 times on Scopus. 1

LESSONS LEARNED FROM HYPOTHESES AMIDST THE COVID-19 PANDEMIC

The COVID-19 pandemic devastated the world like no other in recent memory. During this period, various hypotheses emerged, understandably so considering the public health emergency situation with innumerable deaths and suffering for humanity. Within weeks of the first reports of COVID-19, aberrant immune system activation was identified as a key driver of organ dysfunction and mortality in this disease. 21 Consequently, numerous drugs that suppress the immune system or abrogate the activation of the immune system were hypothesized to have a role in COVID-19. 22 One of the earliest drugs hypothesized to have a benefit was hydroxychloroquine. Hydroxychloroquine was proposed to interfere with Toll-like receptor activation and consequently ameliorate the aberrant immune system activation leading to pathology in COVID-19. 22 The drug was also hypothesized to have a prophylactic role in preventing infection or disease severity in COVID-19. It was also touted as a wonder drug for the disease by many prominent international figures. However, later studies which were well-designed randomized controlled trials failed to demonstrate any benefit of hydroxychloroquine in COVID-19. 23 , 24 , 25 , 26 Subsequently, azithromycin 27 , 28 and ivermectin 29 were hypothesized as potential therapies for COVID-19, but were not supported by evidence from randomized controlled trials. The role of vitamin D in preventing disease severity was also proposed, but has not been proven definitively until now. 30 , 31 On the other hand, randomized controlled trials identified the evidence supporting dexamethasone 32 and interleukin-6 pathway blockade with tocilizumab as effective therapies for COVID-19 in specific situations such as at the onset of hypoxia. 33 , 34 Clues towards the apparent effectiveness of various drugs against severe acute respiratory syndrome coronavirus 2 in vitro but their ineffectiveness in vivo have recently been identified. Many of these drugs are weak, lipophilic bases and some others induce phospholipidosis which results in apparent in vitro effectiveness due to non-specific off-target effects that are not replicated inside living systems. 35 , 36

Another hypothesis proposed was the association of the routine policy of vaccination with Bacillus Calmette-Guerin (BCG) with lower deaths due to COVID-19. This hypothesis emerged in the middle of 2020 when COVID-19 was still taking foot in many parts of the world. 37 , 38 Subsequently, many countries which had lower deaths at that time point went on to have higher numbers of mortality, comparable to other areas of the world. Furthermore, the hypothesis that BCG vaccination reduced COVID-19 mortality was a classic example of ecological fallacy. Associations between population level events (ecological studies; in this case, BCG vaccination and COVID-19 mortality) cannot be directly extrapolated to the individual level. Furthermore, such associations cannot per se be attributed as causal in nature, and can only serve to generate hypotheses that need to be tested at the individual level. 39

IS TRADITIONAL PEER REVIEW EFFICIENT FOR EVALUATION OF WORKING AND SCIENTIFIC HYPOTHESES?

Traditionally, publication after peer review has been considered the gold standard before any new idea finds acceptability amongst the scientific community. Getting a work (including a working or scientific hypothesis) reviewed by experts in the field before experiments are conducted to prove or disprove it helps to refine the idea further as well as improve the experiments planned to test the hypothesis. 40 A route towards this has been the emergence of journals dedicated to publishing hypotheses such as the Central Asian Journal of Medical Hypotheses and Ethics. 41 Another means of publishing hypotheses is through registered research protocols detailing the background, hypothesis, and methodology of a particular study. If such protocols are published after peer review, then the journal commits to publishing the completed study irrespective of whether the study hypothesis is proven or disproven. 42 In the post-pandemic world, online research methods such as online surveys powered via social media channels such as Twitter and Instagram might serve as critical tools to generate as well as to preliminarily test the appropriateness of hypotheses for further evaluation. 43 , 44

Some radical hypotheses might be difficult to publish after traditional peer review. These hypotheses might only be acceptable by the scientific community after they are tested in research studies. Preprints might be a way to disseminate such controversial and ground-breaking hypotheses. 45 However, scientists might prefer to keep their hypotheses confidential for the fear of plagiarism of ideas, avoiding online posting and publishing until they have tested the hypotheses.

SUGGESTIONS ON GENERATING AND PUBLISHING HYPOTHESES

Publication of hypotheses is important, however, a balance is required between scientific temper and controversy. Journal editors and reviewers might keep in mind these specific points, summarized in Table 2 and detailed hereafter, while judging the merit of hypotheses for publication. Keeping in mind the ethical principle of primum non nocere, a hypothesis should be published only if it is testable in a manner that is ethically appropriate. 46 Such hypotheses should be grounded in reality and lend themselves to further testing to either prove or disprove them. It must be considered that subsequent experiments to prove or disprove a hypothesis have an equal chance of failing or succeeding, akin to tossing a coin. A pre-conceived belief that a hypothesis is unlikely to be proven correct should not form the basis of rejection of such a hypothesis for publication. In this context, hypotheses generated after a thorough literature search to identify knowledge gaps or based on concrete clinical observations on a considerable number of patients (as opposed to random observations on a few patients) are more likely to be acceptable for publication by peer-reviewed journals. Also, hypotheses should be considered for publication or rejection based on their implications for science at large rather than whether the subsequent experiments to test them end up with results in favour of or against the original hypothesis.

Hypotheses form an important part of the scientific literature. The COVID-19 pandemic has reiterated the importance and relevance of hypotheses for dealing with public health emergencies and highlighted the need for evidence-based and ethical hypotheses. A good hypothesis is testable in a relevant study design, backed by preliminary evidence, and has positive ethical and clinical implications. General medical journals might consider publishing hypotheses as a specific article type to enable more rapid advancement of science.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Data curation: Gasparyan AY, Misra DP, Zimba O, Yessirkepov M, Agarwal V, Kitas GD.

Philosophia Scientiæ

Travaux d'histoire et de philosophie des sciences

Accueil Numéros 15-2 Varia The operationalization of general...

The operationalization of general hypotheses versus the discovery of empirical laws in Psychology

L’enseignement de la méthodologie scientifique en Psychologie confère un rôle paradigmatique à l’opérationnalisation des « hypothèses générales » : une idée sans rapport précis à l’observation concrète se traduit par la tentative de rejeter une hypothèse statistique nulle au profit d’une hypothèse alternative, dite de recherche, qui opérationnalise l’idée générale. Cette démarche s’avère particulièrement inadaptée à la découverte de lois empiriques. Une loi empirique est définie comme un trou nomothétique émergeant d’un référentiel de la forme Ω x  M ( X ) x  M ( Y ), où Ω est un ensemble d’événements ou d’objets datés dont certains états dans l’ensemble M ( Y ) sont par hypothèse impossibles étant données certaines conditions initiales décrites dans l’ensemble M ( X ) . Cette approche permet de préciser le regard que l’historien des connaissances peut porter sur les avancées descriptives et nomothétiques de la Psychologie empirique contemporaine.

Psychology students learn to operationalise ’general hypotheses’ as a paradigm of scientific Psychology : relatively vague ideas result in an attempt to reject the null hypothesis in favour of an alternative hypothesis, a so-called research hypothesis, which operationalises the general idea. Such a practice turns out to be particularly at odds with the discovery of empirical laws. An empirical law is defined as a nomothetic gap emerging from a reference system of the form Ω x  M ( X ) x  M ( Y ), where Ω is a set of events or dated objects for which some states in the set M ( Y ) are hypothetically impossible given some initial conditions depicted in the set M ( X ). This approach allows the knowledge historian to carefully scrutinise descriptive and nomothetic advances in contemporary empirical Psychology.

Texte intégral

I wish to express my thanks to Nadine Matton and Éric Raufaste for their helpful comments on a previous version of this article. This work was funded in part by the ANR-07-JCJC-0065-01 programme.

1 This article is the result of the author’s need to elaborate on the persistent dissatisfaction he feels with the methodology of scientific research in Psychology, and more precisely with his perception of the way in which it is taught. It would indeed be presumptuous to present the following criticism as being a criticism of the methodology of scientific research in Psychology as a whole, since the latter is a notion which is too all-encompassing in its scope to serve as a precise description of the diversity of research practice in this vast field. The source of this dissatisfaction is to be found in what [Reuchlin 1992, 32] calls the ‘distance’ between ‘general theory’ and a ‘specific, falsifiable hypothesis’. A certain form of academism shapes the approach to scientific research in Psychology according to a three-stage process for the formulation of hypotheses e.g., [Charbonneau 1988]. When they write the report of an empirical study, researchers in Psychology must supply the grounds for their research by introducing a so-called general (or theoretical) hypothesis, then show how they have tested this hypothesis by restating it as a so-called operational (or research) hypothesis. In principle, this restatement should involve data analysis, finalised by testing at least one inferential statistical hypothesis, the so-called null hypothesis.

2 As a socially regulated procedure, the sequencing of theoretical, operational and null hypotheses—which we refer to here as operationaliza-tion —may not pose scientific problems to researchers who are mainly concerned with adhering to a socio-technical norm. The sense of dissatisfaction arises when this desire for socio-technical compliance is considered in the light of the hope (albeit an admittedly pretentious or naïve hope) of discovering one or more empirical laws, i.e. demonstrating at least one, corroborated general empirical statement, [Vautier 2011].

3 With respect to the discovery of empirical laws, operationalization may be characterised as a paradigm, based on a ‘sandwich’ system, whose workings prove to be strikingly ineffective. The ‘general hypothesis’ (the uppermost layer of the ‘sandwich’ system) is not the statement of an empirical law, but a pre-referential statement, i.e. a statement whose empirical significance has not (yet) been determined. The null hypothesis test (the lower layer of the ‘sandwich’) binds the research procedure to a narrow, pragmatic decision-making approach amid uncertainty— rejection or acceptance of the null hypothesis—which is not germane to the search for empirical laws if the null hypothesis is not a general statement in the strict sense of the term, i.e. held to be true for all the elements in a given set. Between the external layers of the ’sandwich’ system lies the psychotechnical and statistical core of the operationalization paradigm, i.e. the production of psychological measurements to which the variables required for the formulation of the operational hypothesis are linked. Again, the claim here is not that this characterization of research procedure in Psychology applies absolutely universally ; however, operationalization as outlined above does appear to be sufficiently typical of a certain orthodoxy to warrant a thorough critical analysis.

4 This paradigm governs an approach which is destined to establish a favourable view of ‘general hypotheses’ inasmuch as they have psy-chotechnical and inferential support. However, the ideological interest of these statements does not automatically confer them with nomothetic import. Consequently, one cannot help wondering whether the rule of operationalization does not in fact serve to prevent those who practise it from ever discerning a possible historical failure of orthodox Psychology to discover its own empirical laws, by training the honest researcher not to hope for the impossible. After all, we are unlikely to worry about failing to obtain something which we were not looking for in the first place. We shall see that an empirical law consists precisely of stating an empirical impossibility, i.e. a partially deterministic falsifiable statement. As a result, we have inevitably come to question psychological thought as regards the reasons and consequences of an apodictic approach to probabilistic treatment of the empirical phenomena which it is investigating.

5 This article comprises four major parts. First of all, we shall illustrate operationalization on the basis of an example put forward by [Fernandez & Catteeuw 2001]. Next, we shall identify two logical and empirical difficulties which arise from this paradigm and demonstrate that they render it unsuitable for the discovery of empirical laws, then detail the logical structure of these laws. Lastly, we shall identify some methodological guidelines which are compatible with an inductive search for partial determinisms.

1 An example of operationalization : smoking cessation and anxiety

6 [Fernandez & Catteeuw 2001, 125] put forward the following sequence :

General hypothesis : undergoing smoking cessation tends to increase anxiety in smokers rather than reduce it.

Operational hypothesis : smokers undergoing smoking cessation are more prone to anxiety than non-cessation smokers.

Null hypothesis : there is no difference between anxiety scores for smokers undergoing smoking cessation and non-cessation smokers.

7 This example can be expanded so as to offer more opportunities to engage with the critical exercise. There is no difficulty in taking [Fernandez & Catteeuw 2001] operational hypothesis as a ‘general hypothesis’. Their formulation specifies neither the empirical (nominal) meaning of the notion of smoking cessation, nor the empirical (ordinal or quantitative) significance of the notion of anxiety, even though it makes reference to the ordinal operator more prone to anxiety than  ; lastly, the noun smokers signifies only an indefinite number of people who smoke.

8 The researcher may have given themselves a set of criteria which is sufficient to decide whether, at the moment when they examine an individual, the person is a smoker or not, and if they are a smoker, another set of criteria sufficient to decide whether or not they are undergoing smoking cessation. These sets of criteria allow the values for two nominal variables to be defined, the first attributing the value of smoker or non-smoker, and the second, which is conditional on the status of ‘smoker’, attributing the value of undergoing cessation or non-cessation. However, the statistical definition of the ’undergoing cessation’ variable requires a domain, i.e. elements assigned a value according to its codomain, the (descriptive) reference system of the variable : {undergoing cessation, non-cessation}. The researcher may circumscribe the domain to pairs (smoker, examination date) which they already have obtain or will obtain during the course of their study, and thus define a so-called independent nominal variable.

9 They then need to specify the function which assigns an anxiety score for each (smoker, examination date) pair, in order to define the ’anxiety score’ statistical variable, taken as the dependent variable. The usual solution for specifying such a function consists in using the answers to an anxiety questionnaire to determine this score, according to a numerical coding rule for the responses to the items on the questionnaire. Such procedures, in which standardised observation of a verbal behaviour is associated with the numerical coding of responses, constitute one of the fundamental contributions of psychotechnics (or psychological testing) to Psychology ; it enables anxiety means conditional on the values of the independent variable to be calculated, whence the operational hypothesis : smokers undergoing smoking cessation are more anxious than non-cessation smokers.

10 The operational hypothesis constitutes a descriptive proposition whose validity can easily be examined. However, to the extent that they consider their sample of observations to be a means of testing a general hypothesis, the researcher must also demonstrate that the mean difference observed is significant, i.e. rejects the null hypothesis of the equality of the means for the statistical populations composed of the two types of smokers, using a probabilistic procedure selected from the available range of inferential techniques, for instance Student’s t -test for independent samples. Only then can the operational hypothesis, considered in the light of the two statistical populations, acquire the status of an alternative hypothesis with respect to the null hypothesis.

11 Now, let us restate the sequence of hypotheses put forward by [Fernandez & Catteeuw 2001] thus :

General hypothesis : smokers undergoing smoking cessation are more anxious than non-cessation smokers

Operational hypothesis : given a pair of variables (‘undergoing cessation’, ‘anxiety score’), mean anxiety conditional on the undergoing cessation value is greater than mean anxiety conditional on the non-cessation value.

Null hypothesis : the two conditional means are equal.

2 Operationalization criticised

12 The example which we have just developed is typical of operational-ization in Psychology, irrespective of the experimental or correlational nature [Cronbach 1957, 1975] of the study. In this section, we make two assertions by dealing with the operationalization approach in reverse : (i) the empirical relevance of the test of the null hypothesis is indeterminate (ii) the statistical fact of a mean difference has no general empirical import.

2.1 The myth of the statistical population

13 To simplify the discussion, let us suppose that the researcher tests the null hypothesis of the equality of two means using Student’s t procedure. The issue at stake in the test from a socio-technical point of view is that by qualifying the difference observed as a significant difference, the cherished notation “p < .05” or “p < .01” may be included in a research paper. The null hypothesis test has been the subject of purely statistical criticisms e.g., [Krueger 2001], [Nickerson 2000] and it is not within the scope of this paper to draw up an inventory of these criticisms. In the empirical perspective under examination here, the problem is that this type of procedure is nothing more than a rhetorical device, insofar as the populations to which the test procedure is applied remain virtual in nature.

14 In practice, the researcher knows how to define their conditional variables on the basis of pairs : (smoker undergoing cessation, examination date) and (non-cessation smoker, examination date), assembled by them through observation. But what is the significance of the statistical population to which the inferential exercise makes reference ? If we consider the undergoing cessation value, for example, how should the statistical population of the (smoker undergoing cessation, examination date) pairs be defined ? Let us imagine a survey which would enable the anxiety score for all the human beings on the planet with the status of ‘smoker undergoing smoking cessation’ to be known on a certain date each month in the interval of time under consideration. We would then have as many populations as we have monthly surveys ; we could then consider grouping together all of these monthly populations to define the population of observations relating to the ‘cessation’ status. There is not one single population, but rather a number of virtual populations. The null hypothesis is therefore based on a mental construct. As soon as this is defined more precisely, questions arise as to its plausibility and the interest of the test. Indeed, why should a survey supply an anxiety variable whose conditional means, subject to change, are identical ?

15 Ultimately, it appears that the null hypothesis test constitutes a decision-making procedure with respect to the plausibility of a hypothesis devoid of any determined empirical meaning. The statistical inference used in the operationalization system is an odd way of settling the issue of generality : it involves deciding whether the difference between observed means may be generalised, even if the empirical meaning of this generality has not been established.

2.2 The myth of the average smoker

16 The difference between the two anxiety means may be interpreted as the difference between the degree of anxiety of the average smoker undergoing cessation and the degree of anxiety of the average non-cessation smoker, which poses two problems. Firstly, the discrete nature of the anxiety score contains a logical dead-end, i.e. the use of an impossibility to describe something which is possible. Let us assume an anxiety questionnaire comprising five items with answers scored 0, 1, 2 or 3, such that the score attributed to any group of 5 responses will fall within the sequence of natural numbers (0, 1, 15). A mean score of 8.2 may indeed ‘summarise’ a set of scores, but cannot exist as an individual score. Consequently, should we wish to use a mean score to describe a typical smoker, it must be recognised that such a smoker is not possible and therefore not plausible. As a result, the difference between the two means cannot be used to describe the difference in degrees of anxiety of the typical smokers, unless it is admitted that a typical smoker is in fact a myth.

17 Let us now assume that the numerical coding technique enables a continuous variable to be defined by the use of so-called analogue response scales. The score of any smoker is by definition composed of the sum of two quantities, the mean score plus the deviation from the mean, the latter expressing the fact that the typical smoker is replaced in practice by a particular specimen of the statistical population, whose variable nature is assumed to be random—without it appearing necessary to have empirical grounds for the probability space on which this notion is based. In these conditions, the mean score constitutes a parameter, whose specification is an empirical matter inasmuch as the statistical population is actually defined. An empirical parameter is not, however, the same thing as an empirical law.

3 Formalization of an empirical law

• 2  This is a more general and radical restatement of the definition given by [Piaget 1970, 17] of the (...)

18 According to the nomothetic perspective, scientific ambition consists in discovering laws, i.e. general implications 2 A general implication is a statement in the following form :

which reads thus “for any x of A , if p ( x ) then q ( x )”, where x is any component of a given set A , and p (•) and q (•) are singular statements. This formalization applies without any difficulty to any situation in which the researcher has a pair of variables ( X , Y ), from a domain Ω n  = { ω i , i  =   1, …, n }, whose elements w are pairs (person, observation date). The codomain of the independent variable X is a descriptive reference system of initial conditions M ( X ) = ( x i , i  = 1, …, k }, whilst the dependent variable, Y , specifies a value reference system, M ( Y ) = ( y i , i  = 1, …, l }, the effective observation of which depends, by hypothesis, on the independent conditions. Thus, the onto-logical substrate of an empirical law is the observation reference system Ω x  M ( X ) x  M ( Y ), where Ω ⊃ Ω is an extrapolation of Ω n  : any element of Ω is, as a matter of principle, assigned a unique value in M ( X ) x  M ( Y ) by means of the function ( X , Y ).

19 Two comments arise from this definition. Firstly, as noted by [Popper 1959, 48], “[natural laws] do not assert that something exists or is the case ; they deny it”. In other words, they state a general ontological impossibility in terms of Ω x  M ( X ) x  M ( Y ) : a law may indeed by formulated by identifying the initial conditions α ( X ) ⊂  M ( X ) for which a non-empty subset β ( Y ) ⊂  M ( Y ) exists such that,

This formulation excludes the possibility of X ( ω ) ∈  α ( Y ) and Y ( ω ) ∈ ∁ β ( Y ) being observed, where ∁ β ( Y ) designates the complementary set β ( Y ) with respect to M ( Y ). Making a statement in the form of (2) amounts to stating a general empirical fact in terms of Ω n , and an empirical law in terms of Ω, by inductive generalisation. This law can be falsified, simply by exhibiting an example of what is said to be impossible in order to falsify it. The general nature of the statement stems from the quantifier ∀ and its empirical limit is found in the extension of Ω. The law may then be corroborated or falsified. If it is corroborated, it is possible to measure its degree of corroboration by the number of observations applying to it, i.e. by the cardinality of the equivalence class formed by the antecedents of α ( X )—the class is noted Cl Ω n/X [ α ( X )].

20 The second comment relates to the notion of partial determinism. The mathematical culture passed on through secondary school teaching familiarises honest researchers with the notion of numerical functions y  =  f ( x ), which express a deterministic law, i.e. that x being given, y necessarily has a point value. If the informative nature of the law is envisaged in negative terms [Dubois & Prade 2003], the necessity of the point is defined as the impossibility of its complement. In the field of humanities [Granger 1995], seeking total determinisms appears futile, but this does not imply that there is no general impossibility in Ω x  M ( X ) x  M ( Y ) and therefore no partial determinism. The fact that partial determinism may not have a utility value from the point of view of social or medical decision-making engineering has nothing to do with its fundamental scientific value. The subject of nomothetic research therefore appears in the form of a ‘gap’ in a descriptive reference system, this gap being theoretically interpreted as the effect of a general ontological impossibility. This is why in teaching, a methodology to support the nomothetic goal of training student researchers to ’search for the impossible’ is called for.

4 How to seek the impossible

21 Discovery of a gap in the descriptive reference system involves the discovery of a general empirical fact, from which an empirical law is inferred by extending the set of observations Ω n to an unknown phe-nomenological field Ω ⊃ Ω n (e.g. future events). A general empirical fact makes sense only with reference to the descriptive reference system M ( X ) x  M ( Y ). Practically speaking, dependent and independent variables are multivariate. Let X  = ( X 1 , X 2 , ..., X p ) be a series of p independent variables and M ( X ) the reference system of X  ; M ( X ) is the Cartesian product of the p  reference systems M ( X i ), i  = 1, …, p . Similarly, let Y  = ( Y 1 , ..., Y q ) be a series of q  dependent variables and M ( Y ) the reference system of Y . The descriptive reference system of the study is therefore :

Thus the contingency table (the rows of which represent the multivari-ate values of X , and the columns the multivariate values of Y ) can be defined. Observation readings are then carried out so that the cells in the contingency table are gradually filled in... or remain empty.

22 Two cases must be distinguished here. The first corresponds to the situation in which the researcher is completely ignorant of what is happening in their observation reference system, in other words, they do not have any prior observations. They therefore have to carry out some kind of survey in order to learn more. Knowing what is happening in the reference system means knowing the frequency of each possible state. It does not involve calling on the notion of probability (the latter being firmly in the realm of mathematical mythology) since it would involve knowing the limit of the frequency of each cell in the contingency table as the number of observations ( n ) tends towards infinity.

• 3  “But in terms of truth, scientific psychology does not deal with natural objects. It deals with te (...)

23 A nomothetic gap arises when there is at least one empty cell in at least one row of the contingency table, when the margin of the row (or rows) is well above the cardinality of M (Y ). It is possible to identify all the gaps in the reference system only if its cardinality is well below the cardinality of lln, n. This empirical consideration sheds light on a specific epistemological drawback in Psychology : not only are its descriptive reference systems not given naturally, as emphasised by [Danziger 1990, 2], 3 but in addition the depth of constructible reality is such that its cardinality may be gigantic—so much so that discussing what is happening in an observation reference system cannot be achieved in terms of sensible intuition. The fact is that the socio-technical norms which shape the presentation of the observation techniques used in empirical studies do not refer either to the notion of descriptive reference system or the necessity of plotting the cardinality card[ M ( X ) x  M ( Y )] against the cardinality of the set of observations, card(Ω n ) =  n . If the quotient card[ M ( X ) x  M ( Y )]/ n is not much lower than 1, planning to carry out an exhaustive examination of the nomothetic gaps in the descriptive reference system is unfeasible. This does not prevent the researcher from working on certain initial conditions α ( X ), but in such cases it must nonetheless be established that dividing the number of values of M ( Y ) by the cardinality of the class Cl Ω n/ X [ α ( X )] of antecedents of α ( X ) in Ω n gives a result which is far less than 1.

24 Let us now present the second case, for which it is assumed that the researcher has been lucky enough to observe the phenomenon of a gap, whose ’coordinates’ in the descriptive reference system of the study are [ α ( X ), ∁ β ( Y )]. The permanent nature of this gap constitutes a proper general hypothesis. This hypothesis should be tested using a targeted observation strategy. Indeed, accumulating observations in l is of interest from the point of view of the hypothesis if these observations are such that : —  X ( ω ) ∈  α ( X ), in which case we seek to verify that Y ( ω ) ∈  β ( Y ), —  Y ( ω ) ∈ ∁ β ( Y ), in which case we seek to verify that X ( ω ) ∈ ∁ α ( X ).

This approach to observation is targeted, and indeed makes sense, in that it focuses on a limited number of states : the researcher knows exactly what they are looking for. It is the very opposite of blindly reproducing an experimental plan or survey plan.

25 When a counterexample is discovered, i.e. ω e exists such that X ( ω e ) ∈  α ( X ) and Y ( ω e ) ∈ ∁ β ( Y ), this observation falsifies the general hypothesis. The researcher can then decide either to reject the hypothesis or to defend it. If they decide to defend it, they may restrict the set of conditions α ( X ), or try to find a variable X p +1 which modulates verification of the rule. Formally speaking, this modulating variable is such that there is a strict non-empty subset of M ( X p +1 )—let this be γ ( X p +1 )—such that :

Irrespective of how they revise the original hypothesis, they will have to restrict its domain of validity with respect to the—implicit—set of possible descriptive reference systems. A major consequence of revising the law by expanding the descriptive reference system of initial conditions is resetting the corroboration counter, since the world being explored has been given an additional descriptive dimension : this is the reference system Ω x  M ( X 1 ) x  M ( Y ), where X 1  = ( X , X p +1 ).

4.1 Example

26 Without it being necessary to develop the procedure presented here in its entirety, we can illustrate it using the example of smokers’ anxiety. The problem consists of restating the ’general hypothesis’ as a statement which is (i) general, properly speaking, as understood in (1) –, and (ii) falsifiable. We may proceed in two stages. Firstly, it is not necessary to talk in terms of reference systems to produce a general statement. Expressing the problem in terms of the difference between two means is not relevant to what is being sought ; however, the idea according to which any smoker undergoing cessation becomes more anxious may be examined, along the lines of the ’general hypothesis’ described by [Fernandez & Catteeuw 2001]. This idea is pre-referential inasmuch as we are unable to define a smoker, a smoker undergoing cessation, or a person who is becoming more anxious.

27 Since we cannot claim to be able to actually settle these issues of definition, we shall use certain definitions for the purposes of convenience. Let U be a population of people and T a population of dates on which they were observed. Let Ω n be a subset of U  x  T  x  T such that, for any triplet ω  = ( u , t 1 , t 2 ), u is known on dates t 1 and t 2 in terms of their status as : — a non-smoker, a smoker undergoing cessation or a non-cessation smoker — and their state of anxiety, for instance with reference to a set of clinical signs, of which the person is asked to evaluate the intensity on date t , using a standard ‘state-anxiety’ questionnaire.

28 It can be noted that the set Ω n is a finite, non-virtual set, in that a person u whose smoker status is not known on date t 1 or t 2 for example, constitutes a triplet which does not belong to this set. According to our approach to the statistical population, it is not necessary for the observations to be the result of applying a specific random sampling technique. Since Ω n constitutes a set of known observations from the point of view of the descriptive reference system, it is a numbered set, to which new observations can be added over time ; whence the notation Ω nj (read “j-mat”), where n j stands for the cardinality of the most recent update to the set of observations.

• 4  It may be noted that an observation p such that X j ( p ) = ( n f, f 2 ) is not plausible ; this relates t (...)

29 We can then define the following variables X j and Y j , from the subset P j of Ω nj , which includes the triplets ( u , t 1 , t 2 ) such that t 2  –  t 1  =  d , where d is a transition time (e.g. 2 days). The variable X j matches any component of P j with an image in M ( X j ) = { n f, f 1 , f 2 } x { n f, f 1 , f 2 } where n f, f 1 and f 2 signify ‘non-smoker’, ‘non-cessation smoker’ and ‘smoker undergoing cessation’ respectively. Let us call α ( X j ) the subset of M ( X j ) including all the pairs of values ending in f 2 which do not begin with f 2 and take an element p  ∈  P j , : the proposition ‘ X j ( p ) ∈  α ( X j )’ means that in the period during which they were observed, person u had been undergoing smoking cessation for two days whereas they have not been before. 4

30 The dependent variable Y j must now be defined. Let us assume that for any sign of anxiety, we have a description on an ordinal scale (i.e., a Likert scale). Anxiety can then be described as a multivariate state varying within a descriptive reference system A . Consider A  x  A  ; in this set a subset β ( Y j ) can be defined which includes changes in states defined as a worsening of the state of anxiety. The variable Y j can then be defined, which, for each p  ∈  P j , corresponds to a state in M ( Y j ). The proposition ‘ Y j ( p ) ∈  β ( Y j )’ signifies that in the period during which they were observed, person u became more anxious. Lastly, the general hypothesis can be formulated in terms which ensure that it may be falsified :

31 We have just illustrated an apparently hypothetical-deductive approach ; but in fact it is an exploratory procedure if the community is not aware of any database enabling a nomothetic gap to be identified. Let us assume that the work of the researcher leads to the provision of a database Ω 236 for the community and that sets α ( X j ) and β ( Y j ) are defined after the fact, such that at least one general fact may be stated. The community with an interest in the general fact revealed by this data may seek new supporting or falsifying observations in order to help update the database.

32 If a researcher finds an individual v , with q  = ( v , t v 1 , t v 2 ) and t v 2  –  t v 1  =  d , such that X j ( q ) ∈  α ( X j ) and Y j ( q ) ∈ ∁ β ( Y j ), this means that there is a smoker who has been undergoing cessation for two days, whose anxiety has not worsened. Let us assume that the researcher investigates whether the person was already ‘very anxious’ ; they may suggest that rule (5) should be revised so as to exclude people whose initial clinical state corresponds to certain values in the reference system A . This procedure usually consists in restricting the scope of validity of the general hypotheses.

5 Discussion

• 5  [Meehl 1967] noted several decades ago that the greater the ‘experimental precision’, i.e. sample (...)

33 Operationalization in Psychology consists in restating a pre-referential proposition in order to enable the researcher to test a statistical null hypothesis, the rejection of which enables the ‘general hypothesis’ to be credited with a certain degree of acceptability. 5 Using an example taken from [Fernandez & Catteeuw 2001], we have shown that the aim of such a procedure is not the discovery of empirical laws, i.e. the discovery of nomothetic gaps in a reference system. We shall discuss two consequences of our radical approach to seeking empirical laws in an observation reference system Ω x  M ( X ) x  M ( Y ). The first relates to the methodology for updating the state of knowledge in a field of research, the second to the probabilistic interpretation of accumulated observations.

34 The state of knowledge in a given field of research can be apprehended in practical terms by means of a list of m so-called scientific publications. Let us call this set composed of specialist literature Lm and let Zj be an element in this list. The knowledge historian can then ask the following question : does text Zj allow an observation reference system of the type Ω n  x  M ( X ) x  M ( Y ) to be defined ? Such a question can only be answered in the affirmative if it is possible to specify the following :

n   >  0 pairs ( u , t ),

p  > 0 reference systems enabling the description of the initial conditions affecting the n pairs ( u , t ),

q   >  0 reference systems enabling the description of states affecting the n pairs ( u , t ) according to the initial conditions in which they are found.

35 Specifying a descriptive reference system consists in identifying a finite set of mutually exclusive values. Not all the description methods used in Psychology allow such a set to be defined ; for example, a close examination of the so-called Exner scoring system [Exner 1995] for verbatims which may be collected for any [Rorschach 1921] test card did not enable us to determine the Cartesian product of the possible values. And yet, to find a gap in a reference system, this reference system must be constituted, so as to form a stabilised and objective descriptive framework. Faced with such a situation, a knowledge historian would be justified in describing a scientific era in which research is based on such a form of descriptive methodology as being a pre-referential age.

• 6  We cannot simply classify the sources of score-subjectivity as measurement errors in the quantitat (...)

36 With regard to the matter of the objectivity of a descriptive reference system, we shall confine ourselves to introducing the notion of score-objectivity. Let P   =  ( p i , i   =  1, …, z } be a set of Psychologists and ω j  ∈ Ω. ( X , Y ) i ( ω j ) is the value of ( ω j ) in M ( X ) x  M ( Y ) as determined by the Psychologist p i . We may say that M ( X ) x  M ( Y ) is score-objective relative to P if ( X , Y ) i ( ω j ) depends only on j for all values of j . If a descriptive reference system is not score-objective, an event in Ω x  M ( X ) x  M ( Y ) which occurs in a gap cannot categorically be interpreted as a falsifying observation, since it may depend on a particular feature of the way the reporting Psychologist views it. Unless and until the descriptive definition of an event is regulated in a score-objective manner, the nomothetic aspiration appears to be premature, since it requires the objective world to be singular in nature. 6 Only once a descriptive reference system has been identified may the knowledge historian test its score-objectivity experimentally.

• 7  This type of database, established by merging several databases, has nothing to do with the aggreg (...)

37 The historian might well discover that a field of research is in fact associated with the use of divergent description reference systems. Their task would then be to connect these different fields of reality by attempting to define the problem of the correspondence between the impossibilities identified in the field R a and the impossibilities identified in the field R b —which assumes such identification is possible. Given a certain descriptive reference system of cardinality c, the historian may evaluate its explorability and perhaps note that certain description reference systems are inexplorable. Concerning explorable reference systems, they could perhaps try to retrieve data collected during the course of empirical studies, constitute an updated database, and seek nomothetic gaps in it. 7

38 Let us now move on to the second point of this discussion. If the reference system is explorable and assumed to be score-objective, it may be that each of its possible states has been observed at least once. In this case, the descriptive reference system is sterile from the nomothetic point of view and this constitutes a singular observation fact : everything is possible therein. In other words, given an object in a certain initial state, nothing can be asserted regarding its Y -state. This does not prevent the decision-making engineer from wagering on the object’s Y -state based on the distribution of Y -states, conditioned by the initial conditions in which the object is found. These frequencies may be used to measure ’expectancies’, but they do not form a basis on which to deduce the existence of a probability function for these states. Indeed, defining a random variable Y or Y | X requires the definition of a probability space on the basis of the possible states M ( X ) x  M ( Y ). In order to be probabilistic, such a space requires a probability space established on the basis of Ω e.g. [Renyi 1966]. Since Ω is a virtual set, adding objective probabilities to it is wishful thinking : seeing ( X , Y ) as a pair of random variables constitutes an unfalsifiable interpretation. Since such an interpretation is nonetheless of interest for making decisions, the existence of a related law of probability being postulated, the probability of a given state may be estimated on the basis of its frequency. The higher the total number of observations, the more accurate this estimation will be, which is why a database established by bringing together the existing databases is of interest. With the advent of the internet, recourse to probabilistic mythology no longer requires the inferential machinery of null-hypotheses testers to be deployed ; it rather requires the empirical stabilization of the parameters of the mythical law.

39 We conclude this critical analysis with a reminder that scientific research in Psychology is also aimed at the discovery of empirical laws. This requires two types of objectives to be distinguished with care : practical objectives, which focus on decision amid uncertainty, and nomoth-etic objectives, which focus on the detection of empirical impossibilities. Has so-called scientific Psychology been able to discover any empirical laws, and if so, what are they ? From our contemporary standpoint, this question is easy to answer in principle—if not in practice.

Bibliographie

charbonneau, c. — 1988, Problématique et hypothèses d’une recherche, in Fondements et étapes de la recherche scientifique en psychologie, edited by Robert, m., Edisem, 3rd ed., 59-77.

Cronbach, l. j. — 1957, The two disciplines of scientific psychology, American Psychologist, 12, 671-684. — 1975, Beyond the two disciplines of scientific psychology, American Psychologist, 30, 116-127.

Danziger, k. — 1990, Constructing the subject : Historical origins of psychological research , New York : Cambridge University Press.

Dubois, D. & Prade, H. — 2003, Informations bipolaires : une introduction, Information Interaction Intelligence , 3, 89-106.

Exner, J. E. Jr — 1995, Le Rorschach : un système intégré, Paris : Éditions Frison-Roche (A. Andronikof, traduction).

Fernandez, L. & Catteeuw, M. — 2001, La recherche en psychologie clinique , Paris : Nathan Université.

Granger, G.-G. — 1995, La science et les sciences, Paris : Presses Universitaires de France, 2nd ed.

Krueger, J. — 2001, Null hypothesis significance testing, American Psychologist, 56, 16-26.

Meehl, P. H. — 1967, Theory-testing in psychology and physics : A methodological paradox, Philosophy of Science, 34, 103-115.

Nickerson, R. S. — 2000, Null hypothesis significance testing : A review of an old and continuing controversy, Psychological Methods, 5, 241-301.

Piaget, J. — 1970, Epistémologie des sciences de l’homme, Paris : Gallimard.

Popper, K. R. — 1959, The logic of scientific discovery, Oxford England : Basic Books.

Renyi, A. — 1966, Calcul des probabilités, Paris : Dunod (C. Bloch, trad.).

Reuchlin, M. — 1992, Introduction à la recherche en psychologie, Paris : Nathan Université.

Rorschach, H. — 1921, Psychodiagnostik, Bern : Bircher (Hans Huber Verlag, 1942).

Rosenthal, R. & DiMatteo, M. R. — 2001, Meta-analysis : Recent developments in quantitative methods for literature reviews, Annual Review of Psychology, 52, 59-82.

Stigler, S. M. — 1986, The history of statistics : The measurement of uncertainty before 1900 , Cambridge, MA : The Belknap Press of Harvard University Press.

Vautier, S. — 2011, How to state general qualitative facts in psychology ?, Quality & Quantity, 1-8. URL http ://dx.doi.org/10.1007/s11135-011-9502-5 .

2  This is a more general and radical restatement of the definition given by [Piaget 1970, 17] of the notion of laws. For him laws designate “relatively constant quantitative relations which may be expressed in the form of mathematical functions”, “general fact” or “ordinal relationships, [...] structural analyses, etc. which are expressed in ordinary language or in more or less formalized language (logic, etc.)”.

3  “But in terms of truth, scientific psychology does not deal with natural objects. It deals with test scores, evaluation scales, response distributions, series lists, and countless other items which the researcher does not discover but rather constructs with great care. Conjectures about the world, whatever they may be, cannot escape from this universe of artefacts.”

4  It may be noted that an observation p such that X j ( p ) = ( n f, f 2 ) is not plausible ; this relates to the question of the definition of the state of cessation and does not affect the structure of the logic.

5  [Meehl 1967] noted several decades ago that the greater the ‘experimental precision’, i.e. sample size, the easier it is to corroborate the alternative hypothesis.

6  We cannot simply classify the sources of score-subjectivity as measurement errors in the quantitative domain [Stigler 1986], since most descriptive reference systems in Psychology are qualitative ; diverging viewpoints for the same event described in a certain descriptive reference system represent an error, not of measurement, but of definition.

7  This type of database, established by merging several databases, has nothing to do with the aggregation methodology of ‘meta-analyses’ based on the use of statistical summaries e.g., [Rosenthal & DiMatteo 2001].

Pour citer cet article

Référence papier.

Stéphane Vautier , «  The operationalization of general hypotheses versus the discovery of empirical laws in Psychology  » ,  Philosophia Scientiæ , 15-2 | 2011, 105-122.

Référence électronique

Stéphane Vautier , «  The operationalization of general hypotheses versus the discovery of empirical laws in Psychology  » ,  Philosophia Scientiæ [En ligne], 15-2 | 2011, mis en ligne le 01 septembre 2014 , consulté le 08 avril 2024 . URL  : http://journals.openedition.org/philosophiascientiae/656 ; DOI  : https://doi.org/10.4000/philosophiascientiae.656

Stéphane Vautier

OCTOGONE-CERPP, Université de Toulouse (France)

Droits d’auteur

Le texte et les autres éléments (illustrations, fichiers annexes importés), sont « Tous droits réservés », sauf mention contraire.

Numéros en texte intégral

• 28-1 | 2024 Richesse et variété du néokantisme : Helmholtz, Cassirer, Vaihinger
• 27-3 | 2023 Études poincaréiennes (II)
• 27-2 | 2023 Études poincaréiennes (I)
• 27-1 | 2023 La « parenthèse Vichy » ?
• 26-3 | 2022 Gestalts praxéologiques. Quand la philosophie, les sciences cognitives et la sociologie rencontrent la psychologie de la forme
• 26-2 | 2022 Patrimonialisation des mathématiques (XVIIIe-XXe siècles)
• 26-1 | 2022 La désuétude conceptuelle : abandon ou transformation ?
• 25-3 | 2021 L’analyse dans les mathématiques grecques
• 25-2 | 2021 Mathématique et philosophie leibniziennes à la lumière des manuscrits inédits
• 25-1 | 2021 The Peano School: Logic, Epistemology and Didactics
• 24-3 | 2020 Lectures et postérités de La Philosophie de l’algèbre de Jules Vuillemin
• 24-2 | 2020 Philosophies de la ressemblance
• 24-1 | 2020 Les mathématiques dans les écoles militaires (XVIIIe-XIXe siècles)
• 23-3 | 2019 Les circulations scientifiques internationales depuis le début du XX e siècle
• 23-2 | 2019 Expérimentation dans les sciences de la nature Expérimentation dans les sciences humaines et sociales
• 23-1 | 2019 Y a-t-il encore de la place en bas ?
• 22-3 | 2018 Sur la philosophie scientifique et l’unité de la science
• 22-2 | 2018 Études de cas en épistémologie sociale
• 22-1 | 2018 Science(s) et édition(s) des années 1780 à l'entre-deux-guerres
• 21-3 | 2017 N'allez pas croire !
• 21-2 | 2017 Raymond Ruyer
• 21-1 | 2017 Homage to Galileo Galilei 1564-2014
• 20-3 | 2016 Le scepticisme selon Jules Vuillemin
• 20-2 | 2016 Circulations et échanges dans l'espace euro-méditerranéen (XVIIIe-XXIe siècles)
• 20-1 | 2016 Le kantisme hors des écoles kantiennes
• 19-3 | 2015 The Bounds of Naturalism
• 19-2 | 2015 Circulations et échanges mathématiques
• 19-1 | 2015 Logic and Philosophy of Science in Nancy (II)
• 18-3 | 2014 Logic and Philosophy of Science in Nancy (I)
• 18-2 | 2014 Hugo Dingler et l’épistémologie pragmatiste en Allemagne
• 18-1 | 2014 Standards of Rigor in Mathematical Practice
• 17-3 | 2013 Tacit and Explicit Knowledge: Harry Collins’s Framework
• 17-2 | 2013 The Mind–Brain Problem in Cognitive Neuroscience
• 17-1 | 2013 The Epistemological Thought of Otto Hölder
• 16-3 | 2012 Alan Turing
• 16-2 | 2012 Modal Matters
• 16-1 | 2012 From Practice to Results in Logic and Mathematics
• 15-3 | 2011 L'espace et le temps
• 15-2 | 2011 La syllogistique de Łukasiewicz
• 15-1 | 2011 Hugh MacColl after One Hundred Years
• 14-2 | 2010 Louis Rougier, De Torricelli à Pascal
• 14-1 | 2010
• 13-2 | 2009
• 13-1 | 2009
• 12-2 | 2008 Normes et santé
• 12-1 | 2008 (Anti-)Realisms: The Metaphysical Issue
• 11-2 | 2007
• 11-1 | 2007 Karl Popper : un philosophe dans le siècle
• 10-2 | 2006 Louis Rougier : vie et œuvre d'un philosophe engagé
• 10-1 | 2006 Jerzy Kalinowski : logique et normativité
• 9-2 | 2005 Aperçus philosophiques en logique et en mathématiques
• 9-1 | 2005
• 8-2 | 2004 Logique & théorie des jeux
• 8-1 | 2004 Le problème de l’incommensurabilité, un demi-siècle après

Cahiers spéciaux

• CS 7 | 2007 Louis Rougier : vie et œuvre d'un philosophe engagé
• CS 6 | 2006 Constructivism: Mathematics, Logic, Philosophy and Linguistics
• CS 5 | 2005 Fonder autrement les mathématiques

Tous les numéros

Collection numérisée, présentation.

• Les comités
• Instructions aux auteurs
• Indications techniques

Informations

• Mentions légales et crédits
• Politiques de publication

Appels à contributions

• Appels en cours
• Appels clos

Suivez-nous

Lettres d’information

• La Lettre d’OpenEdition

Affiliations/partenaires

• Revue soutenue par l’Institut des sciences humaines et sociales (InSHS) du CNRS, 2023-2024

ISSN électronique 1775-4283

Voir la notice dans le catalogue OpenEdition  

Plan du site  – Mentions légales et crédits  – Flux de syndication

Politique de confidentialité  – Gestion des cookies  – Signaler un problème

Nous adhérons à OpenEdition  – Édité avec Lodel  – Accès réservé

Vous allez être redirigé vers OpenEdition Search

Hypothesis: Forms and Samples

Hypothesis is a wise guess prepared and temporarily adopted to explain the observed factors covered by the study.  It is a tentative conclusion or answer to a specific question raised at the beginning of the investigation.

Hypothesis helps the researcher in designing the study such as the methods, research instruments, and sampling design to be used as well as the data to be gathered. It also use as bases for determining assumptions and for the explanation about the data gathered.

Forms of Hypothesis

• Operational Form – It is stated in the affirmative.  It states that there is a difference between two phenomena
• Null Form – It is stated in the negative. It states that there is no difference between the two phenomena. It is more commonly used.

Question: Is there any significant difference between the perceptions of the teachers and those of the students concerning the different aspects in the teaching of science?

Operational hypothesis There is a significant difference between the perceptions of the teachers and those of the students concerning the different aspects in the teaching of science.

Null hypothesis There is no significant difference between the perceptions of the teachers and those of the students concerning the different aspects in the teaching of science.

3 thoughts to “Hypothesis: Forms and Samples”

hey how we do this hypothesis…………………………….

You know so many interesting infomation. You might be very wise. I like such people. Don’t top writing.

Thate is fine. You shoud proud of youer worke.

Comments are closed.

share this!

April 2, 2024

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

fact-checked

peer-reviewed publication

trusted source

Botanists analyze the role of pollinators in the evolution of flowers with various sexual forms

by University of Seville

Researchers Violeta Simón, Marcial Escudero and Juan Arroyo, from the Department of Botany at the Faculty of Biology of the University of Seville, in collaboration with researchers from four other countries, led a study in which they demonstrate Darwin's hypothesis of precise pollination across all angiosperms (flowering plants). The research is published in the journal Nature Communications .

In heterostylous species, there are two (sometimes three) types of flowers, called morphs, which differ according to the location of their sexual organs. The L-morph has the stigma (female sex organs) higher and the anthers (male sex organs) below. And in the S-morph they are the other way around. Darwin proposed that this system evolved to promote cross-pollination (between different individuals, to increase the vigor of their progeny) through a mechanism of precise pollination between the male and female sex organs of each morph, on different parts of the pollinator's body.

This hypothesis of precise pollination hinges on the presence of floral traits and pollinators that fit together like a jigsaw puzzle , so that pollen is accurately deposited and transferred.

"We conducted a comprehensive review of the presence of heterostyly in all angiosperm genera and found many more cases than had been reported in recent literature reviews on the subject. We then collected more than 10,000 data about floral morphology and pollinators across many heterostylous and non-heterostylous species, and placed these data into a mega-phylogeny of all angiosperms to find whether the evolution of heterostyly is associated with floral traits and pollinators that promote precise pollination ," explains researcher Violeta Simón.

By looking at the correlations between heterostyly, floral traits and pollinators, the researchers found that heterostyly does indeed evolve in flower lineages with a narrow floral tube and long proboscis pollinators such as butterflies and moths. These pieces fit together to allow pollen to be transferred precisely from one morph to another, as Darwin predicted.

"Heterostyly has been used as a model for studies of floral evolution since Darwin's time, but such an ambitious study on a macroevolutionary scale has never before been undertaken. We believe it will be a seminal work for many researchers in this field," says the researcher Simón. It is worth stressing that this research group has been studying this plant reproductive mechanism for almost 30 years, and is a leader in the role of ecology in its evolution.

Journal information: Nature Communications

Provided by University of Seville

Explore further

Feedback to editors

What do scientists hope to learn from total solar eclipse in US?

15 hours ago

Rare Javan rhino calf spotted in Indonesia

16 hours ago

Scientists investigate information propagation in interacting bosonic systems

22 hours ago

DESI first-year data delivers unprecedented measurements of expanding universe

Apr 6, 2024

Saturday Citations: AI and the prisoner's dilemma; stellar cannibalism; evidence that EVs reduce atmospheric CO₂

Huge star explosion to appear in sky in once-in-a-lifetime event

Innovative sensing platform unlocks ultrahigh sensitivity in conventional sensors

Nonvolatile quantum memory: Discovery points path to flash-like memory for storing qubits

Can language models read the genome? This one decoded mRNA to make better vaccines

A simple, inexpensive way to make carbon atoms bind together

Relevant physicsforums posts, what do large moles on the body indicate.

Mar 30, 2024

Avian flu - A new study led by a team from the University of Maryland

Mar 27, 2024

Are all biological catabolic reactions exergonic?

Mar 20, 2024

A First of Its Kind: A Calcium-based signal in the Human Brain

Mar 18, 2024

Biological culture and cultural biology

Mar 17, 2024

Potentially fatal dog parasite found in the Colorado River

Mar 15, 2024

More from Biology and Medical

Related Stories

Interaction patterns between bumblebees and floral resources revealed during buzz pollination

Mar 22, 2024

Research finds fragrant screw pines are pollinated by sap beetles rather than by wind

How flowers maintain water balance across different angiosperm branches

How flowers adapt to their pollinators

Dec 5, 2019

Scientists describe new orchid species related to famous Darwin's orchid

Mar 14, 2024

How air pollution harms pollination

Feb 7, 2024

Recommended for you

eDNA methods give a real-time look at coral reef health

Apr 5, 2024

Corals can bounce back after heat waves, but only if there's enough time between them

Microorganisms may be essential to the survival of coral reefs threatened by climate change

Amphibians use scream inaudible to humans for self-defense against predators, study suggests

Apr 4, 2024

Study reports that people and environment both benefit from diversified farming, while bottom lines also thrive

Let us know if there is a problem with our content.

Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page. For general inquiries, please use our contact form . For general feedback, use the public comments section below (please adhere to guidelines ).

Please select the most appropriate category to facilitate processing of your request

Thank you for taking time to provide your feedback to the editors.

Your feedback is important to us. However, we do not guarantee individual replies due to the high volume of messages.

E-mail the story

Your email address is used only to let the recipient know who sent the email. Neither your address nor the recipient's address will be used for any other purpose. The information you enter will appear in your e-mail message and is not retained by Phys.org in any form.

Newsletter sign up

Get weekly and/or daily updates delivered to your inbox. You can unsubscribe at any time and we'll never share your details to third parties.

More information Privacy policy

Donate and enjoy an ad-free experience

We keep our content available to everyone. Consider supporting Science X's mission by getting a premium account.

E-mail newsletter

The Federal Register

The daily journal of the united states government, request access.

Due to aggressive automated scraping of FederalRegister.gov and eCFR.gov, programmatic access to these sites is limited to access to our extensive developer APIs.

If you are human user receiving this message, we can add your IP address to a set of IPs that can access FederalRegister.gov & eCFR.gov; complete the CAPTCHA (bot test) below and click "Request Access". This process will be necessary for each IP address you wish to access the site from, requests are valid for approximately one quarter (three months) after which the process may need to be repeated.

An official website of the United States government.

If you want to request a wider IP range, first request access for your current IP, and then use the "Site Feedback" button found in the lower left-hand side to make the request.