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What Is A Research (Scientific) Hypothesis? A plain-language explainer + examples

By:  Derek Jansen (MBA)  | Reviewed By: Dr Eunice Rautenbach | June 2020

If you’re new to the world of research, or it’s your first time writing a dissertation or thesis, you’re probably noticing that the words “research hypothesis” and “scientific hypothesis” are used quite a bit, and you’re wondering what they mean in a research context .

“Hypothesis” is one of those words that people use loosely, thinking they understand what it means. However, it has a very specific meaning within academic research. So, it’s important to understand the exact meaning before you start hypothesizing. 

Research Hypothesis 101

• What is a hypothesis ?
• What is a research hypothesis (scientific hypothesis)?
• Requirements for a research hypothesis
• Definition of a research hypothesis
• The null hypothesis

What is a hypothesis?

Let’s start with the general definition of a hypothesis (not a research hypothesis or scientific hypothesis), according to the Cambridge Dictionary:

Hypothesis: an idea or explanation for something that is based on known facts but has not yet been proved.

In other words, it’s a statement that provides an explanation for why or how something works, based on facts (or some reasonable assumptions), but that has not yet been specifically tested . For example, a hypothesis might look something like this:

Hypothesis: sleep impacts academic performance.

This statement predicts that academic performance will be influenced by the amount and/or quality of sleep a student engages in – sounds reasonable, right? It’s based on reasonable assumptions , underpinned by what we currently know about sleep and health (from the existing literature). So, loosely speaking, we could call it a hypothesis, at least by the dictionary definition.

But that’s not good enough…

Unfortunately, that’s not quite sophisticated enough to describe a research hypothesis (also sometimes called a scientific hypothesis), and it wouldn’t be acceptable in a dissertation, thesis or research paper . In the world of academic research, a statement needs a few more criteria to constitute a true research hypothesis .

What is a research hypothesis?

A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes – specificity , clarity and testability .

Let’s take a look at these more closely.

Need a helping hand?

Hypothesis Essential #1: Specificity & Clarity

A good research hypothesis needs to be extremely clear and articulate about both what’ s being assessed (who or what variables are involved ) and the expected outcome (for example, a difference between groups, a relationship between variables, etc.).

Let’s stick with our sleepy students example and look at how this statement could be more specific and clear.

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.

As you can see, the statement is very specific as it identifies the variables involved (sleep hours and test grades), the parties involved (two groups of students), as well as the predicted relationship type (a positive relationship). There’s no ambiguity or uncertainty about who or what is involved in the statement, and the expected outcome is clear.

Contrast that to the original hypothesis we looked at – “Sleep impacts academic performance” – and you can see the difference. “Sleep” and “academic performance” are both comparatively vague , and there’s no indication of what the expected relationship direction is (more sleep or less sleep). As you can see, specificity and clarity are key.

Hypothesis Essential #2: Testability (Provability)

A statement must be testable to qualify as a research hypothesis. In other words, there needs to be a way to prove (or disprove) the statement. If it’s not testable, it’s not a hypothesis – simple as that.

For example, consider the hypothesis we mentioned earlier:

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.  

We could test this statement by undertaking a quantitative study involving two groups of students, one that gets 8 or more hours of sleep per night for a fixed period, and one that gets less. We could then compare the standardised test results for both groups to see if there’s a statistically significant difference. 

Again, if you compare this to the original hypothesis we looked at – “Sleep impacts academic performance” – you can see that it would be quite difficult to test that statement, primarily because it isn’t specific enough. How much sleep? By who? What type of academic performance?

So, remember the mantra – if you can’t test it, it’s not a hypothesis 🙂

Defining A Research Hypothesis

You’re still with us? Great! Let’s recap and pin down a clear definition of a hypothesis.

A research hypothesis (or scientific hypothesis) is a statement about an expected relationship between variables, or explanation of an occurrence, that is clear, specific and testable.

So, when you write up hypotheses for your dissertation or thesis, make sure that they meet all these criteria. If you do, you’ll not only have rock-solid hypotheses but you’ll also ensure a clear focus for your entire research project.

What about the null hypothesis?

You may have also heard the terms null hypothesis , alternative hypothesis, or H-zero thrown around. At a simple level, the null hypothesis is the counter-proposal to the original hypothesis.

For example, if the hypothesis predicts that there is a relationship between two variables (for example, sleep and academic performance), the null hypothesis would predict that there is no relationship between those variables.

At a more technical level, the null hypothesis proposes that no statistical significance exists in a set of given observations and that any differences are due to chance alone.

And there you have it – hypotheses in a nutshell. 

If you have any questions, be sure to leave a comment below and we’ll do our best to help you. If you need hands-on help developing and testing your hypotheses, consider our private coaching service , where we hold your hand through the research journey.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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16 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

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2.8: Why Is Research Important?

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Learning outcomes

By the end of this section, you will be able to:

• Explain how scientific research addresses questions about behavior
• Discuss how scientific research guides public policy
• Appreciate how scientific research can be important in making personal decisions

Scientific research is a critical tool for successfully navigating our complex world. Without it, we would be forced to rely solely on intuition, other people’s authority, and blind luck. While many of us feel confident in our abilities to decipher and interact with the world around us, history is filled with examples of how very wrong we can be when we fail to recognize the need for evidence in supporting claims. At various times in history, we would have been certain that the sun revolved around a flat earth, that the earth’s continents did not move, and that mental illness was caused by possession ( Figure ). It is through systematic scientific research that we divest ourselves of our preconceived notions and superstitions and gain an objective understanding of ourselves and our world.

The goal of all scientists is to better understand the world around them. Psychologists focus their attention on understanding behavior, as well as the cognitive (mental) and physiological (body) processes that underlie behavior. In contrast to other methods that people use to understand the behavior of others, such as intuition and personal experience, the hallmark of scientific research is that there is evidence to support a claim. Scientific knowledge is  empirical : It is grounded in objective, tangible evidence that can be observed time and time again, regardless of who is observing.

While behavior is observable, the mind is not. If someone is crying, we can see behavior. However, the reason for the behavior is more difficult to determine. Is the person crying due to being sad, in pain, or happy? Sometimes we can learn the reason for someone’s behavior by simply asking a question, like “Why are you crying?” However, there are situations in which an individual is either uncomfortable or unwilling to answer the question honestly, or is incapable of answering. For example, infants would not be able to explain why they are crying. In such circumstances, the psychologist must be creative in finding ways to better understand behavior. This chapter explores how scientific knowledge is generated, and how important that knowledge is in forming decisions in our personal lives and in the public domain.

USE OF RESEARCH INFORMATION

Trying to determine which theories are and are not accepted by the scientific community can be difficult, especially in an area of research as broad as psychology. More than ever before, we have an incredible amount of information at our fingertips, and a simple internet search on any given research topic might result in a number of contradictory studies. In these cases, we are witnessing the scientific community going through the process of reaching a consensus, and it could be quite some time before a consensus emerges. For example, the hypothesized link between exposure to media violence and subsequent aggression has been debated in the scientific community for roughly 60 years. Even today, we will find detractors, but a consensus is building. Several professional organizations view media violence exposure as a risk factor for actual violence, including the American Medical Association, the American Psychiatric Association, and the American Psychological Association (American Academy of Pediatrics, American Academy of Child & Adolescent Psychiatry, American Psychological Association, American Medical Association, American Academy of Family Physicians, American Psychiatric Association, 2000).

In the meantime, we should strive to think critically about the information we encounter by exercising a degree of healthy skepticism. When someone makes a claim, we should examine the claim from a number of different perspectives: what is the expertise of the person making the claim, what might they gain if the claim is valid, does the claim seem justified given the evidence, and what do other researchers think of the claim? This is especially important when we consider how much information in advertising campaigns and on the internet claims to be based on “scientific evidence” when in actuality it is a belief or perspective of just a few individuals trying to sell a product or draw attention to their perspectives.

We should be informed consumers of the information made available to us because decisions based on this information have significant consequences. One such consequence can be seen in politics and public policy. Imagine that you have been elected as the governor of your state. One of your responsibilities is to manage the state budget and determine how to best spend your constituents’ tax dollars. As the new governor, you need to decide whether to continue funding the  D.A.R.E.  (Drug Abuse Resistance Education) program in public schools ( Figure ). This program typically involves police officers coming into the classroom to educate students about the dangers of becoming involved with alcohol and other drugs. According to the D.A.R.E. website (www.dare.org), this program has been very popular since its inception in 1983, and it is currently operating in 75% of school districts in the United States and in more than 40 countries worldwide. Sounds like an easy decision, right? However, on closer review, you discover that the vast majority of research into this program consistently suggests that participation has little, if any, effect on whether or not someone uses alcohol or other drugs (Clayton, Cattarello, & Johnstone, 1996; Ennett, Tobler, Ringwalt, & Flewelling, 1994; Lynam et al., 1999; Ringwalt, Ennett, & Holt, 1991). If you are committed to being a good steward of taxpayer money, will you fund this particular program, or will you try to find other programs that research has consistently demonstrated to be effective?

Watch this  news report  to learn more about some of the controversial issues surrounding the D.A.R.E. program.

Ultimately, it is not just politicians who can benefit from using research in guiding their decisions. We all might look to research from time to time when making decisions in our lives. Imagine you just found out that a close friend has breast cancer or that one of your young relatives has recently been diagnosed with autism. In either case, you want to know which treatment options are most successful with the fewest side effects. How would you find that out? You would probably talk with your doctor and personally review the research that has been done on various treatment options—always with a critical eye to ensure that you are as informed as possible.

In the end, research is what makes the difference between facts and opinions. Facts are observable realities, and opinions are personal judgments, conclusions, or attitudes that may or may not be accurate. In the scientific community, facts can be established only using evidence collected through empirical research.

THE PROCESS OF SCIENTIFIC RESEARCH

Scientific knowledge is advanced through a process known as the  scientific method . Basically, ideas (in the form of theories and hypotheses) are tested against the real world (in the form of empirical observations), and those empirical observations lead to more ideas that are tested against the real world, and so on. In this sense, the scientific process is circular. The types of reasoning within the circle are called deductive and inductive. In deductive reasoning, ideas are tested against the empirical world; in inductive reasoning, empirical observations lead to new ideas ( Figure ). These processes are inseparable, like inhaling and exhaling, but different research approaches place different emphasis on the deductive and inductive aspects.

In the scientific context, deductive reasoning begins with a generalization—one hypothesis—that is then used to reach logical conclusions about the real world. If the hypothesis is correct, then the logical conclusions reached through deductive reasoning should also be correct. A deductive reasoning argument might go something like this: All living things require energy to survive (this would be your hypothesis). Ducks are living things. Therefore, ducks require energy to survive (logical conclusion). In this example, the hypothesis is correct; therefore, the conclusion is correct as well. Sometimes, however, an incorrect hypothesis may lead to a logical but incorrect conclusion. Consider this argument: all ducks are born with the ability to see. Quackers is a duck. Therefore, Quackers was born with the ability to see. Scientists use deductive reasoning to empirically test their hypotheses. Returning to the example of the ducks, researchers might design a study to test the hypothesis that if all living things require energy to survive, then ducks will be found to require energy to survive.

Deductive reasoning starts with a generalization that is tested against real-world observations; however, inductive reasoning moves in the opposite direction. Inductive reasoning uses empirical observations to construct broad generalizations. Unlike deductive reasoning, conclusions drawn from inductive reasoning may or may not be correct, regardless of the observations on which they are based. For instance, you may notice that your favorite fruits—apples, bananas, and oranges—all grow on trees; therefore, you assume that all fruit must grow on trees. This would be an example of inductive reasoning, and, clearly, the existence of strawberries, blueberries, and kiwi demonstrate that this generalization is not correct despite it being based on a number of direct observations. Scientists use inductive reasoning to formulate theories, which in turn generate hypotheses that are tested with deductive reasoning. In the end, science involves both deductive and inductive processes.

For example, case studies, which you will read about in the next section, are heavily weighted on the side of empirical observations. Thus, case studies are closely associated with inductive processes as researchers gather massive amounts of observations and seek interesting patterns (new ideas) in the data. Experimental research, on the other hand, puts great emphasis on deductive reasoning.

Play this  “Deal Me In” interactive card game  to practice using inductive reasoning.

We’ve stated that theories and hypotheses are ideas, but what sort of ideas are they, exactly? A theory is a well-developed set of ideas that propose an explanation for observed phenomena. Theories are repeatedly checked against the world, but they tend to be too complex to be tested all at once; instead, researchers create hypotheses to test specific aspects of a theory.

A hypothesis is a testable prediction about how the world will behave if our idea is correct, and it is often worded as an if-then statement (e.g., if I study all night, I will get a passing grade on the test). The hypothesis is extremely important because it bridges the gap between the realm of ideas and the real world. As specific hypotheses are tested, theories are modified and refined to reflect and incorporate the result of these tests  Figure .

To see how this process works, let’s consider a specific theory and a hypothesis that might be generated from that theory. As you’ll learn in a later chapter, the James-Lange theory of emotion asserts that emotional experience relies on the physiological arousal associated with the emotional state. If you walked out of your home and discovered a very aggressive snake waiting on your doorstep, your heart would begin to race and your stomach churn. According to the James-Lange theory, these physiological changes would result in your feeling of fear. A hypothesis that could be derived from this theory might be that a person who is unaware of the physiological arousal that the sight of the snake elicits will not feel fear.

A scientific hypothesis is also falsifiable, or capable of being shown to be incorrect. Recall from the introductory chapter that Sigmund  Freud  had lots of interesting ideas to explain various human behaviors ( Figure ). However, a major criticism of Freud’s theories is that many of his ideas are not falsifiable; for example, it is impossible to imagine empirical observations that would disprove the existence of the id, the ego, and the superego—the three elements of personality described in Freud’s theories. Despite this, Freud’s theories are widely taught in introductory psychology texts because of their historical significance for personality psychology and psychotherapy, and these remain the root of all modern forms of therapy.

In contrast, the James-Lange theory does generate falsifiable hypotheses, such as the one described above. Some individuals who suffer significant injuries to their spinal columns are unable to feel the bodily changes that often accompany emotional experiences. Therefore, we could test the hypothesis by determining how emotional experiences differ between individuals who have the ability to detect these changes in their physiological arousal and those who do not. In fact, this research has been conducted and while the emotional experiences of people deprived of an awareness of their physiological arousal may be less intense, they still experience emotion (Chwalisz, Diener, & Gallagher, 1988).

Scientific research’s dependence on falsifiability allows for great confidence in the information that it produces. Typically, by the time information is accepted by the scientific community, it has been tested repeatedly.

Visit this  website  to apply the scientific method and practice its steps by using them to solve a murder mystery, determine why a student is in trouble, and design an experiment to test house paint.

Scientists are engaged in explaining and understanding how the world around them works, and they are able to do so by coming up with theories that generate hypotheses that are testable and falsifiable. Theories that stand up to their tests are retained and refined, while those that do not are discarded or modified. In this way, research enables scientists to separate fact from simple opinion. Having good information generated from research aids in making wise decisions both in public policy and in our personal lives.

Review Questions

Scientific hypotheses are ________ and falsifiable.

________ are defined as observable realities.

Scientific knowledge is ________.

A major criticism of Freud’s early theories involves the fact that his theories ________.

• were too limited in scope
• were too outrageous
• were too broad
• were not testable

Critical Thinking Questions

In this section, the D.A.R.E. program was described as an incredibly popular program in schools across the United States despite the fact that research consistently suggests that this program is largely ineffective. How might one explain this discrepancy?

The scientific method is often described as self-correcting and cyclical. Briefly describe your understanding of the scientific method with regard to these concepts.

Personal Application Questions

Healthcare professionals cite an enormous number of health problems related to obesity, and many people have an understandable desire to attain a healthy weight. There are many diet programs, services, and products on the market to aid those who wish to lose weight. If a close friend was considering purchasing or participating in one of these products, programs, or services, how would you make sure your friend was fully aware of the potential consequences of this decision? What sort of information would you want to review before making such an investment or lifestyle change yourself?

[glossary-page] [glossary-term]deductive reasoning:[/glossary-term] [glossary-definition]results are predicted based on a general premise[/glossary-definition]

[glossary-term]empirical:[/glossary-term] [glossary-definition]grounded in objective, tangible evidence that can be observed time and time again, regardless of who is observing[/glossary-definition]

[glossary-term]fact:[/glossary-term] [glossary-definition]objective and verifiable observation, established using evidence collected through empirical research[/glossary-definition]

[glossary-term]falsifiable:[/glossary-term] [glossary-definition]able to be disproven by experimental results[/glossary-definition]

[glossary-term]hypothesis:[/glossary-term] [glossary-definition](plural: hypotheses) tentative and testable statement about the relationship between two or more variables[/glossary-definition]

[glossary-term]inductive reasoning:[/glossary-term] [glossary-definition]conclusions are drawn from observations[/glossary-definition]

[glossary-term]opinion:[/glossary-term] [glossary-definition]personal judgements, conclusions, or attitudes that may or may not be accurate[/glossary-definition]

[glossary-term]theory:[/glossary-term] [glossary-definition]well-developed set of ideas that propose an explanation for observed phenomena[/glossary-definition] [/glossary-page]

• Why Is Research Important?. Provided by : OpenStax CNX. Located at : https://cnx.org/contents/[email protected]:Hp5zMFYB@3/Why-Is-Research-Important . License : CC BY-SA: Attribution-ShareAlike

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Research Hypothesis: What It Is, Types + How to Develop?

A research study starts with a question. Researchers worldwide ask questions and create research hypotheses. The effectiveness of research relies on developing a good research hypothesis. Examples of research hypotheses can guide researchers in writing effective ones.

In this blog, we’ll learn what a research hypothesis is, why it’s important in research, and the different types used in science. We’ll also guide you through creating your research hypothesis and discussing ways to test and evaluate it.

What is a Research Hypothesis?

A hypothesis is like a guess or idea that you suggest to check if it’s true. A research hypothesis is a statement that brings up a question and predicts what might happen.

It’s really important in the scientific method and is used in experiments to figure things out. Essentially, it’s an educated guess about how things are connected in the research.

A research hypothesis usually includes pointing out the independent variable (the thing they’re changing or studying) and the dependent variable (the result they’re measuring or watching). It helps plan how to gather and analyze data to see if there’s evidence to support or deny the expected connection between these variables.

Importance of Hypothesis in Research

Hypotheses are really important in research. They help design studies, allow for practical testing, and add to our scientific knowledge. Their main role is to organize research projects, making them purposeful, focused, and valuable to the scientific community. Let’s look at some key reasons why they matter:

• A research hypothesis helps test theories.

A hypothesis plays a pivotal role in the scientific method by providing a basis for testing existing theories. For example, a hypothesis might test the predictive power of a psychological theory on human behavior.

• It serves as a great platform for investigation activities.

It serves as a launching pad for investigation activities, which offers researchers a clear starting point. A research hypothesis can explore the relationship between exercise and stress reduction.

• Hypothesis guides the research work or study.

A well-formulated hypothesis guides the entire research process. It ensures that the study remains focused and purposeful. For instance, a hypothesis about the impact of social media on interpersonal relationships provides clear guidance for a study.

• Hypothesis sometimes suggests theories.

In some cases, a hypothesis can suggest new theories or modifications to existing ones. For example, a hypothesis testing the effectiveness of a new drug might prompt a reconsideration of current medical theories.

• It helps in knowing the data needs.

A hypothesis clarifies the data requirements for a study, ensuring that researchers collect the necessary information—a hypothesis guiding the collection of demographic data to analyze the influence of age on a particular phenomenon.

• The hypothesis explains social phenomena.

Hypotheses are instrumental in explaining complex social phenomena. For instance, a hypothesis might explore the relationship between economic factors and crime rates in a given community.

• Hypothesis provides a relationship between phenomena for empirical Testing.

Hypotheses establish clear relationships between phenomena, paving the way for empirical testing. An example could be a hypothesis exploring the correlation between sleep patterns and academic performance.

• It helps in knowing the most suitable analysis technique.

A hypothesis guides researchers in selecting the most appropriate analysis techniques for their data. For example, a hypothesis focusing on the effectiveness of a teaching method may lead to the choice of statistical analyses best suited for educational research.

Characteristics of a Good Research Hypothesis

A hypothesis is a specific idea that you can test in a study. It often comes from looking at past research and theories. A good hypothesis usually starts with a research question that you can explore through background research. For it to be effective, consider these key characteristics:

• Clear and Focused Language: A good hypothesis uses clear and focused language to avoid confusion and ensure everyone understands it.
• Related to the Research Topic: The hypothesis should directly relate to the research topic, acting as a bridge between the specific question and the broader study.
• Testable: An effective hypothesis can be tested, meaning its prediction can be checked with real data to support or challenge the proposed relationship.
• Potential for Exploration: A good hypothesis often comes from a research question that invites further exploration. Doing background research helps find gaps and potential areas to investigate.
• Includes Variables: The hypothesis should clearly state both the independent and dependent variables, specifying the factors being studied and the expected outcomes.
• Ethical Considerations: Check if variables can be manipulated without breaking ethical standards. It’s crucial to maintain ethical research practices.
• Predicts Outcomes: The hypothesis should predict the expected relationship and outcome, acting as a roadmap for the study and guiding data collection and analysis.
• Simple and Concise: A good hypothesis avoids unnecessary complexity and is simple and concise, expressing the essence of the proposed relationship clearly.
• Clear and Assumption-Free: The hypothesis should be clear and free from assumptions about the reader’s prior knowledge, ensuring universal understanding.
• Observable and Testable Results: A strong hypothesis implies research that produces observable and testable results, making sure the study’s outcomes can be effectively measured and analyzed.

When you use these characteristics as a checklist, it can help you create a good research hypothesis. It’ll guide improving and strengthening the hypothesis, identifying any weaknesses, and making necessary changes. Crafting a hypothesis with these features helps you conduct a thorough and insightful research study.

Types of Research Hypotheses

The research hypothesis comes in various types, each serving a specific purpose in guiding the scientific investigation. Knowing the differences will make it easier for you to create your own hypothesis. Here’s an overview of the common types:

01. Null Hypothesis

The null hypothesis states that there is no connection between two considered variables or that two groups are unrelated. As discussed earlier, a hypothesis is an unproven assumption lacking sufficient supporting data. It serves as the statement researchers aim to disprove. It is testable, verifiable, and can be rejected.

For example, if you’re studying the relationship between Project A and Project B, assuming both projects are of equal standard is your null hypothesis. It needs to be specific for your study.

02. Alternative Hypothesis

The alternative hypothesis is basically another option to the null hypothesis. It involves looking for a significant change or alternative that could lead you to reject the null hypothesis. It’s a different idea compared to the null hypothesis.

When you create a null hypothesis, you’re making an educated guess about whether something is true or if there’s a connection between that thing and another variable. If the null view suggests something is correct, the alternative hypothesis says it’s incorrect. 

For instance, if your null hypothesis is “I’m going to be $1000 richer,” the alternative hypothesis would be “I’m not going to get $1000 or be richer.”

03. Directional Hypothesis

The directional hypothesis predicts the direction of the relationship between independent and dependent variables. They specify whether the effect will be positive or negative.

If you increase your study hours, you will experience a positive association with your exam scores. This hypothesis suggests that as you increase the independent variable (study hours), there will also be an increase in the dependent variable (exam scores).

04. Non-directional Hypothesis

The non-directional hypothesis predicts the existence of a relationship between variables but does not specify the direction of the effect. It suggests that there will be a significant difference or relationship, but it does not predict the nature of that difference.

For example, you will find no notable difference in test scores between students who receive the educational intervention and those who do not. However, once you compare the test scores of the two groups, you will notice an important difference.

05. Simple Hypothesis

A simple hypothesis predicts a relationship between one dependent variable and one independent variable without specifying the nature of that relationship. It’s simple and usually used when we don’t know much about how the two things are connected.

For example, if you adopt effective study habits, you will achieve higher exam scores than those with poor study habits.

06. Complex Hypothesis

A complex hypothesis is an idea that specifies a relationship between multiple independent and dependent variables. It is a more detailed idea than a simple hypothesis.

While a simple view suggests a straightforward cause-and-effect relationship between two things, a complex hypothesis involves many factors and how they’re connected to each other.

For example, when you increase your study time, you tend to achieve higher exam scores. The connection between your study time and exam performance is affected by various factors, including the quality of your sleep, your motivation levels, and the effectiveness of your study techniques.

If you sleep well, stay highly motivated, and use effective study strategies, you may observe a more robust positive correlation between the time you spend studying and your exam scores, unlike those who may lack these factors.

07. Associative Hypothesis

An associative hypothesis proposes a connection between two things without saying that one causes the other. Basically, it suggests that when one thing changes, the other changes too, but it doesn’t claim that one thing is causing the change in the other.

For example, you will likely notice higher exam scores when you increase your study time. You can recognize an association between your study time and exam scores in this scenario.

Your hypothesis acknowledges a relationship between the two variables—your study time and exam scores—without asserting that increased study time directly causes higher exam scores. You need to consider that other factors, like motivation or learning style, could affect the observed association.

08. Causal Hypothesis

A causal hypothesis proposes a cause-and-effect relationship between two variables. It suggests that changes in one variable directly cause changes in another variable.

For example, when you increase your study time, you experience higher exam scores. This hypothesis suggests a direct cause-and-effect relationship, indicating that the more time you spend studying, the higher your exam scores. It assumes that changes in your study time directly influence changes in your exam performance.

09. Empirical Hypothesis

An empirical hypothesis is a statement based on things we can see and measure. It comes from direct observation or experiments and can be tested with real-world evidence. If an experiment proves a theory, it supports the idea and shows it’s not just a guess. This makes the statement more reliable than a wild guess.

For example, if you increase the dosage of a certain medication, you might observe a quicker recovery time for patients. Imagine you’re in charge of a clinical trial. In this trial, patients are given varying dosages of the medication, and you measure and compare their recovery times. This allows you to directly see the effects of different dosages on how fast patients recover.

This way, you can create a research hypothesis: “Increasing the dosage of a certain medication will lead to a faster recovery time for patients.”

10. Statistical Hypothesis

A statistical hypothesis is a statement or assumption about a population parameter that is the subject of an investigation. It serves as the basis for statistical analysis and testing. It is often tested using statistical methods to draw inferences about the larger population.

In a hypothesis test, statistical evidence is collected to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.

For example, let’s say you’re testing a new medicine. Your hypothesis could be that the medicine doesn’t really help patients get better. So, you collect data and use statistics to see if your guess is right or if the medicine actually makes a difference.

If the data strongly shows that the medicine does help, you say your guess was wrong, and the medicine does make a difference. But if the proof isn’t strong enough, you can stick with your original guess because you didn’t get enough evidence to change your mind.

How to Develop a Research Hypotheses?

Step 1: identify your research problem or topic..

Define the area of interest or the problem you want to investigate. Make sure it’s clear and well-defined.

Start by asking a question about your chosen topic. Consider the limitations of your research and create a straightforward problem related to your topic. Once you’ve done that, you can develop and test a hypothesis with evidence.

Step 2: Conduct a literature review

Review existing literature related to your research problem. This will help you understand the current state of knowledge in the field, identify gaps, and build a foundation for your hypothesis. Consider the following questions:

• What existing research has been conducted on your chosen topic?
• Are there any gaps or unanswered questions in the current literature?
• How will the existing literature contribute to the foundation of your research?

Step 3: Formulate your research question

Based on your literature review, create a specific and concise research question that addresses your identified problem. Your research question should be clear, focused, and relevant to your field of study.

Step 4: Identify variables

Determine the key variables involved in your research question. Variables are the factors or phenomena that you will study and manipulate to test your hypothesis.

• Independent Variable: The variable you manipulate or control.
• Dependent Variable: The variable you measure to observe the effect of the independent variable.

Step 5: State the Null hypothesis

The null hypothesis is a statement that there is no significant difference or effect. It serves as a baseline for comparison with the alternative hypothesis.

Step 6: Select appropriate methods for testing the hypothesis

Choose research methods that align with your study objectives, such as experiments, surveys, or observational studies. The selected methods enable you to test your research hypothesis effectively.

Creating a research hypothesis usually takes more than one try. Expect to make changes as you collect data. It’s normal to test and say no to a few hypotheses before you find the right answer to your research question.

Testing and Evaluating Hypotheses

Testing hypotheses is a really important part of research. It’s like the practical side of things. Here, real-world evidence will help you determine how different things are connected. Let’s explore the main steps in hypothesis testing:

• State your research hypothesis.

Before testing, clearly articulate your research hypothesis. This involves framing both a null hypothesis, suggesting no significant effect or relationship, and an alternative hypothesis, proposing the expected outcome.

• Collect data strategically.

Plan how you will gather information in a way that fits your study. Make sure your data collection method matches the things you’re studying.

Whether through surveys, observations, or experiments, this step demands precision and adherence to the established methodology. The quality of data collected directly influences the credibility of study outcomes.

• Perform an appropriate statistical test.

Choose a statistical test that aligns with the nature of your data and the hypotheses being tested. Whether it’s a t-test, chi-square test, ANOVA, or regression analysis, selecting the right statistical tool is paramount for accurate and reliable results.

• Decide if your idea was right or wrong.

Following the statistical analysis, evaluate the results in the context of your null hypothesis. You need to decide if you should reject your null hypothesis or not.

• Share what you found.

When discussing what you found in your research, be clear and organized. Say whether your idea was supported or not, and talk about what your results mean. Also, mention any limits to your study and suggest ideas for future research.

The Role of QuestionPro to Develop a Good Research Hypothesis

QuestionPro is a survey and research platform that provides tools for creating, distributing, and analyzing surveys. It plays a crucial role in the research process, especially when you’re in the initial stages of hypothesis development. Here’s how QuestionPro can help you to develop a good research hypothesis:

• Survey design and data collection: You can use the platform to create targeted questions that help you gather relevant data.
• Exploratory research: Through surveys and feedback mechanisms on QuestionPro, you can conduct exploratory research to understand the landscape of a particular subject.
• Literature review and background research: QuestionPro surveys can collect sample population opinions, experiences, and preferences. This data and a thorough literature evaluation can help you generate a well-grounded hypothesis by improving your research knowledge.
• Identifying variables: Using targeted survey questions, you can identify relevant variables related to their research topic.
• Testing assumptions: You can use surveys to informally test certain assumptions or hypotheses before formalizing a research hypothesis.
• Data analysis tools: QuestionPro provides tools for analyzing survey data. You can use these tools to identify the collected data’s patterns, correlations, or trends.
• Refining your hypotheses: As you collect data through QuestionPro, you can adjust your hypotheses based on the real-world responses you receive.

A research hypothesis is like a guide for researchers in science. It’s a well-thought-out idea that has been thoroughly tested. This idea is crucial as researchers can explore different fields, such as medicine, social sciences, and natural sciences. The research hypothesis links theories to real-world evidence and gives researchers a clear path to explore and make discoveries.

QuestionPro Research Suite is a helpful tool for researchers. It makes creating surveys, collecting data, and analyzing information easily. It supports all kinds of research, from exploring new ideas to forming hypotheses. With a focus on using data, it helps researchers do their best work.

Are you interested in learning more about QuestionPro Research Suite? Take advantage of QuestionPro’s free trial to get an initial look at its capabilities and realize the full potential of your research efforts.

LEARN MORE         FREE TRIAL

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What Is Research, and Why Do People Do It?

• Open Access
• First Online: 03 December 2022

Cite this chapter

You have full access to this open access chapter

• James Hiebert 6 ,
• Jinfa Cai 7 ,
• Stephen Hwang 7 ,
• Anne K Morris 6 &
• Charles Hohensee 6  

Part of the book series: Research in Mathematics Education ((RME))

Abstractspiepr Abs1

Every day people do research as they gather information to learn about something of interest. In the scientific world, however, research means something different than simply gathering information. Scientific research is characterized by its careful planning and observing, by its relentless efforts to understand and explain, and by its commitment to learn from everyone else seriously engaged in research. We call this kind of research scientific inquiry and define it as “formulating, testing, and revising hypotheses.” By “hypotheses” we do not mean the hypotheses you encounter in statistics courses. We mean predictions about what you expect to find and rationales for why you made these predictions. Throughout this and the remaining chapters we make clear that the process of scientific inquiry applies to all kinds of research studies and data, both qualitative and quantitative.

You have full access to this open access chapter,  Download chapter PDF

Part I. What Is Research?

Have you ever studied something carefully because you wanted to know more about it? Maybe you wanted to know more about your grandmother’s life when she was younger so you asked her to tell you stories from her childhood, or maybe you wanted to know more about a fertilizer you were about to use in your garden so you read the ingredients on the package and looked them up online. According to the dictionary definition, you were doing research.

Recall your high school assignments asking you to “research” a topic. The assignment likely included consulting a variety of sources that discussed the topic, perhaps including some “original” sources. Often, the teacher referred to your product as a “research paper.”

Were you conducting research when you interviewed your grandmother or wrote high school papers reviewing a particular topic? Our view is that you were engaged in part of the research process, but only a small part. In this book, we reserve the word “research” for what it means in the scientific world, that is, for scientific research or, more pointedly, for scientific inquiry .

Exercise 1.1

Before you read any further, write a definition of what you think scientific inquiry is. Keep it short—Two to three sentences. You will periodically update this definition as you read this chapter and the remainder of the book.

This book is about scientific inquiry—what it is and how to do it. For starters, scientific inquiry is a process, a particular way of finding out about something that involves a number of phases. Each phase of the process constitutes one aspect of scientific inquiry. You are doing scientific inquiry as you engage in each phase, but you have not done scientific inquiry until you complete the full process. Each phase is necessary but not sufficient.

In this chapter, we set the stage by defining scientific inquiry—describing what it is and what it is not—and by discussing what it is good for and why people do it. The remaining chapters build directly on the ideas presented in this chapter.

A first thing to know is that scientific inquiry is not all or nothing. “Scientificness” is a continuum. Inquiries can be more scientific or less scientific. What makes an inquiry more scientific? You might be surprised there is no universally agreed upon answer to this question. None of the descriptors we know of are sufficient by themselves to define scientific inquiry. But all of them give you a way of thinking about some aspects of the process of scientific inquiry. Each one gives you different insights.

Exercise 1.2

As you read about each descriptor below, think about what would make an inquiry more or less scientific. If you think a descriptor is important, use it to revise your definition of scientific inquiry.

Creating an Image of Scientific Inquiry

We will present three descriptors of scientific inquiry. Each provides a different perspective and emphasizes a different aspect of scientific inquiry. We will draw on all three descriptors to compose our definition of scientific inquiry.

Descriptor 1. Experience Carefully Planned in Advance

Sir Ronald Fisher, often called the father of modern statistical design, once referred to research as “experience carefully planned in advance” (1935, p. 8). He said that humans are always learning from experience, from interacting with the world around them. Usually, this learning is haphazard rather than the result of a deliberate process carried out over an extended period of time. Research, Fisher said, was learning from experience, but experience carefully planned in advance.

This phrase can be fully appreciated by looking at each word. The fact that scientific inquiry is based on experience means that it is based on interacting with the world. These interactions could be thought of as the stuff of scientific inquiry. In addition, it is not just any experience that counts. The experience must be carefully planned . The interactions with the world must be conducted with an explicit, describable purpose, and steps must be taken to make the intended learning as likely as possible. This planning is an integral part of scientific inquiry; it is not just a preparation phase. It is one of the things that distinguishes scientific inquiry from many everyday learning experiences. Finally, these steps must be taken beforehand and the purpose of the inquiry must be articulated in advance of the experience. Clearly, scientific inquiry does not happen by accident, by just stumbling into something. Stumbling into something unexpected and interesting can happen while engaged in scientific inquiry, but learning does not depend on it and serendipity does not make the inquiry scientific.

Descriptor 2. Observing Something and Trying to Explain Why It Is the Way It Is

When we were writing this chapter and googled “scientific inquiry,” the first entry was: “Scientific inquiry refers to the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work.” The emphasis is on studying, or observing, and then explaining . This descriptor takes the image of scientific inquiry beyond carefully planned experience and includes explaining what was experienced.

According to the Merriam-Webster dictionary, “explain” means “(a) to make known, (b) to make plain or understandable, (c) to give the reason or cause of, and (d) to show the logical development or relations of” (Merriam-Webster, n.d. ). We will use all these definitions. Taken together, they suggest that to explain an observation means to understand it by finding reasons (or causes) for why it is as it is. In this sense of scientific inquiry, the following are synonyms: explaining why, understanding why, and reasoning about causes and effects. Our image of scientific inquiry now includes planning, observing, and explaining why.

We need to add a final note about this descriptor. We have phrased it in a way that suggests “observing something” means you are observing something in real time—observing the way things are or the way things are changing. This is often true. But, observing could mean observing data that already have been collected, maybe by someone else making the original observations (e.g., secondary analysis of NAEP data or analysis of existing video recordings of classroom instruction). We will address secondary analyses more fully in Chap. 4 . For now, what is important is that the process requires explaining why the data look like they do.

We must note that for us, the term “data” is not limited to numerical or quantitative data such as test scores. Data can also take many nonquantitative forms, including written survey responses, interview transcripts, journal entries, video recordings of students, teachers, and classrooms, text messages, and so forth.

Exercise 1.3

What are the implications of the statement that just “observing” is not enough to count as scientific inquiry? Does this mean that a detailed description of a phenomenon is not scientific inquiry?

Find sources that define research in education that differ with our position, that say description alone, without explanation, counts as scientific research. Identify the precise points where the opinions differ. What are the best arguments for each of the positions? Which do you prefer? Why?

Descriptor 3. Updating Everyone’s Thinking in Response to More and Better Information

This descriptor focuses on a third aspect of scientific inquiry: updating and advancing the field’s understanding of phenomena that are investigated. This descriptor foregrounds a powerful characteristic of scientific inquiry: the reliability (or trustworthiness) of what is learned and the ultimate inevitability of this learning to advance human understanding of phenomena. Humans might choose not to learn from scientific inquiry, but history suggests that scientific inquiry always has the potential to advance understanding and that, eventually, humans take advantage of these new understandings.

Before exploring these bold claims a bit further, note that this descriptor uses “information” in the same way the previous two descriptors used “experience” and “observations.” These are the stuff of scientific inquiry and we will use them often, sometimes interchangeably. Frequently, we will use the term “data” to stand for all these terms.

An overriding goal of scientific inquiry is for everyone to learn from what one scientist does. Much of this book is about the methods you need to use so others have faith in what you report and can learn the same things you learned. This aspect of scientific inquiry has many implications.

One implication is that scientific inquiry is not a private practice. It is a public practice available for others to see and learn from. Notice how different this is from everyday learning. When you happen to learn something from your everyday experience, often only you gain from the experience. The fact that research is a public practice means it is also a social one. It is best conducted by interacting with others along the way: soliciting feedback at each phase, taking opportunities to present work-in-progress, and benefitting from the advice of others.

A second implication is that you, as the researcher, must be committed to sharing what you are doing and what you are learning in an open and transparent way. This allows all phases of your work to be scrutinized and critiqued. This is what gives your work credibility. The reliability or trustworthiness of your findings depends on your colleagues recognizing that you have used all appropriate methods to maximize the chances that your claims are justified by the data.

A third implication of viewing scientific inquiry as a collective enterprise is the reverse of the second—you must be committed to receiving comments from others. You must treat your colleagues as fair and honest critics even though it might sometimes feel otherwise. You must appreciate their job, which is to remain skeptical while scrutinizing what you have done in considerable detail. To provide the best help to you, they must remain skeptical about your conclusions (when, for example, the data are difficult for them to interpret) until you offer a convincing logical argument based on the information you share. A rather harsh but good-to-remember statement of the role of your friendly critics was voiced by Karl Popper, a well-known twentieth century philosopher of science: “. . . if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can” (Popper, 1968, p. 27).

A final implication of this third descriptor is that, as someone engaged in scientific inquiry, you have no choice but to update your thinking when the data support a different conclusion. This applies to your own data as well as to those of others. When data clearly point to a specific claim, even one that is quite different than you expected, you must reconsider your position. If the outcome is replicated multiple times, you need to adjust your thinking accordingly. Scientific inquiry does not let you pick and choose which data to believe; it mandates that everyone update their thinking when the data warrant an update.

Doing Scientific Inquiry

We define scientific inquiry in an operational sense—what does it mean to do scientific inquiry? What kind of process would satisfy all three descriptors: carefully planning an experience in advance; observing and trying to explain what you see; and, contributing to updating everyone’s thinking about an important phenomenon?

We define scientific inquiry as formulating , testing , and revising hypotheses about phenomena of interest.

Of course, we are not the only ones who define it in this way. The definition for the scientific method posted by the editors of Britannica is: “a researcher develops a hypothesis, tests it through various means, and then modifies the hypothesis on the basis of the outcome of the tests and experiments” (Britannica, n.d. ).

Notice how defining scientific inquiry this way satisfies each of the descriptors. “Carefully planning an experience in advance” is exactly what happens when formulating a hypothesis about a phenomenon of interest and thinking about how to test it. “ Observing a phenomenon” occurs when testing a hypothesis, and “ explaining ” what is found is required when revising a hypothesis based on the data. Finally, “updating everyone’s thinking” comes from comparing publicly the original with the revised hypothesis.

Doing scientific inquiry, as we have defined it, underscores the value of accumulating knowledge rather than generating random bits of knowledge. Formulating, testing, and revising hypotheses is an ongoing process, with each revised hypothesis begging for another test, whether by the same researcher or by new researchers. The editors of Britannica signaled this cyclic process by adding the following phrase to their definition of the scientific method: “The modified hypothesis is then retested, further modified, and tested again.” Scientific inquiry creates a process that encourages each study to build on the studies that have gone before. Through collective engagement in this process of building study on top of study, the scientific community works together to update its thinking.

Before exploring more fully the meaning of “formulating, testing, and revising hypotheses,” we need to acknowledge that this is not the only way researchers define research. Some researchers prefer a less formal definition, one that includes more serendipity, less planning, less explanation. You might have come across more open definitions such as “research is finding out about something.” We prefer the tighter hypothesis formulation, testing, and revision definition because we believe it provides a single, coherent map for conducting research that addresses many of the thorny problems educational researchers encounter. We believe it is the most useful orientation toward research and the most helpful to learn as a beginning researcher.

A final clarification of our definition is that it applies equally to qualitative and quantitative research. This is a familiar distinction in education that has generated much discussion. You might think our definition favors quantitative methods over qualitative methods because the language of hypothesis formulation and testing is often associated with quantitative methods. In fact, we do not favor one method over another. In Chap. 4 , we will illustrate how our definition fits research using a range of quantitative and qualitative methods.

Exercise 1.4

Look for ways to extend what the field knows in an area that has already received attention by other researchers. Specifically, you can search for a program of research carried out by more experienced researchers that has some revised hypotheses that remain untested. Identify a revised hypothesis that you might like to test.

Unpacking the Terms Formulating, Testing, and Revising Hypotheses

To get a full sense of the definition of scientific inquiry we will use throughout this book, it is helpful to spend a little time with each of the key terms.

We first want to make clear that we use the term “hypothesis” as it is defined in most dictionaries and as it used in many scientific fields rather than as it is usually defined in educational statistics courses. By “hypothesis,” we do not mean a null hypothesis that is accepted or rejected by statistical analysis. Rather, we use “hypothesis” in the sense conveyed by the following definitions: “An idea or explanation for something that is based on known facts but has not yet been proved” (Cambridge University Press, n.d. ), and “An unproved theory, proposition, or supposition, tentatively accepted to explain certain facts and to provide a basis for further investigation or argument” (Agnes & Guralnik, 2008 ).

We distinguish two parts to “hypotheses.” Hypotheses consist of predictions and rationales . Predictions are statements about what you expect to find when you inquire about something. Rationales are explanations for why you made the predictions you did, why you believe your predictions are correct. So, for us “formulating hypotheses” means making explicit predictions and developing rationales for the predictions.

“Testing hypotheses” means making observations that allow you to assess in what ways your predictions were correct and in what ways they were incorrect. In education research, it is rarely useful to think of your predictions as either right or wrong. Because of the complexity of most issues you will investigate, most predictions will be right in some ways and wrong in others.

By studying the observations you make (data you collect) to test your hypotheses, you can revise your hypotheses to better align with the observations. This means revising your predictions plus revising your rationales to justify your adjusted predictions. Even though you might not run another test, formulating revised hypotheses is an essential part of conducting a research study. Comparing your original and revised hypotheses informs everyone of what you learned by conducting your study. In addition, a revised hypothesis sets the stage for you or someone else to extend your study and accumulate more knowledge of the phenomenon.

We should note that not everyone makes a clear distinction between predictions and rationales as two aspects of hypotheses. In fact, common, non-scientific uses of the word “hypothesis” may limit it to only a prediction or only an explanation (or rationale). We choose to explicitly include both prediction and rationale in our definition of hypothesis, not because we assert this should be the universal definition, but because we want to foreground the importance of both parts acting in concert. Using “hypothesis” to represent both prediction and rationale could hide the two aspects, but we make them explicit because they provide different kinds of information. It is usually easier to make predictions than develop rationales because predictions can be guesses, hunches, or gut feelings about which you have little confidence. Developing a compelling rationale requires careful thought plus reading what other researchers have found plus talking with your colleagues. Often, while you are developing your rationale you will find good reasons to change your predictions. Developing good rationales is the engine that drives scientific inquiry. Rationales are essentially descriptions of how much you know about the phenomenon you are studying. Throughout this guide, we will elaborate on how developing good rationales drives scientific inquiry. For now, we simply note that it can sharpen your predictions and help you to interpret your data as you test your hypotheses.

Hypotheses in education research take a variety of forms or types. This is because there are a variety of phenomena that can be investigated. Investigating educational phenomena is sometimes best done using qualitative methods, sometimes using quantitative methods, and most often using mixed methods (e.g., Hay, 2016 ; Weis et al. 2019a ; Weisner, 2005 ). This means that, given our definition, hypotheses are equally applicable to qualitative and quantitative investigations.

Hypotheses take different forms when they are used to investigate different kinds of phenomena. Two very different activities in education could be labeled conducting experiments and descriptions. In an experiment, a hypothesis makes a prediction about anticipated changes, say the changes that occur when a treatment or intervention is applied. You might investigate how students’ thinking changes during a particular kind of instruction.

A second type of hypothesis, relevant for descriptive research, makes a prediction about what you will find when you investigate and describe the nature of a situation. The goal is to understand a situation as it exists rather than to understand a change from one situation to another. In this case, your prediction is what you expect to observe. Your rationale is the set of reasons for making this prediction; it is your current explanation for why the situation will look like it does.

You will probably read, if you have not already, that some researchers say you do not need a prediction to conduct a descriptive study. We will discuss this point of view in Chap. 2 . For now, we simply claim that scientific inquiry, as we have defined it, applies to all kinds of research studies. Descriptive studies, like others, not only benefit from formulating, testing, and revising hypotheses, but also need hypothesis formulating, testing, and revising.

One reason we define research as formulating, testing, and revising hypotheses is that if you think of research in this way you are less likely to go wrong. It is a useful guide for the entire process, as we will describe in detail in the chapters ahead. For example, as you build the rationale for your predictions, you are constructing the theoretical framework for your study (Chap. 3 ). As you work out the methods you will use to test your hypothesis, every decision you make will be based on asking, “Will this help me formulate or test or revise my hypothesis?” (Chap. 4 ). As you interpret the results of testing your predictions, you will compare them to what you predicted and examine the differences, focusing on how you must revise your hypotheses (Chap. 5 ). By anchoring the process to formulating, testing, and revising hypotheses, you will make smart decisions that yield a coherent and well-designed study.

Exercise 1.5

Compare the concept of formulating, testing, and revising hypotheses with the descriptions of scientific inquiry contained in Scientific Research in Education (NRC, 2002 ). How are they similar or different?

Exercise 1.6

Provide an example to illustrate and emphasize the differences between everyday learning/thinking and scientific inquiry.

Learning from Doing Scientific Inquiry

We noted earlier that a measure of what you have learned by conducting a research study is found in the differences between your original hypothesis and your revised hypothesis based on the data you collected to test your hypothesis. We will elaborate this statement in later chapters, but we preview our argument here.

Even before collecting data, scientific inquiry requires cycles of making a prediction, developing a rationale, refining your predictions, reading and studying more to strengthen your rationale, refining your predictions again, and so forth. And, even if you have run through several such cycles, you still will likely find that when you test your prediction you will be partly right and partly wrong. The results will support some parts of your predictions but not others, or the results will “kind of” support your predictions. A critical part of scientific inquiry is making sense of your results by interpreting them against your predictions. Carefully describing what aspects of your data supported your predictions, what aspects did not, and what data fell outside of any predictions is not an easy task, but you cannot learn from your study without doing this analysis.

Analyzing the matches and mismatches between your predictions and your data allows you to formulate different rationales that would have accounted for more of the data. The best revised rationale is the one that accounts for the most data. Once you have revised your rationales, you can think about the predictions they best justify or explain. It is by comparing your original rationales to your new rationales that you can sort out what you learned from your study.

Suppose your study was an experiment. Maybe you were investigating the effects of a new instructional intervention on students’ learning. Your original rationale was your explanation for why the intervention would change the learning outcomes in a particular way. Your revised rationale explained why the changes that you observed occurred like they did and why your revised predictions are better. Maybe your original rationale focused on the potential of the activities if they were implemented in ideal ways and your revised rationale included the factors that are likely to affect how teachers implement them. By comparing the before and after rationales, you are describing what you learned—what you can explain now that you could not before. Another way of saying this is that you are describing how much more you understand now than before you conducted your study.

Revised predictions based on carefully planned and collected data usually exhibit some of the following features compared with the originals: more precision, more completeness, and broader scope. Revised rationales have more explanatory power and become more complete, more aligned with the new predictions, sharper, and overall more convincing.

Part II. Why Do Educators Do Research?

Doing scientific inquiry is a lot of work. Each phase of the process takes time, and you will often cycle back to improve earlier phases as you engage in later phases. Because of the significant effort required, you should make sure your study is worth it. So, from the beginning, you should think about the purpose of your study. Why do you want to do it? And, because research is a social practice, you should also think about whether the results of your study are likely to be important and significant to the education community.

If you are doing research in the way we have described—as scientific inquiry—then one purpose of your study is to understand , not just to describe or evaluate or report. As we noted earlier, when you formulate hypotheses, you are developing rationales that explain why things might be like they are. In our view, trying to understand and explain is what separates research from other kinds of activities, like evaluating or describing.

One reason understanding is so important is that it allows researchers to see how or why something works like it does. When you see how something works, you are better able to predict how it might work in other contexts, under other conditions. And, because conditions, or contextual factors, matter a lot in education, gaining insights into applying your findings to other contexts increases the contributions of your work and its importance to the broader education community.

Consequently, the purposes of research studies in education often include the more specific aim of identifying and understanding the conditions under which the phenomena being studied work like the observations suggest. A classic example of this kind of study in mathematics education was reported by William Brownell and Harold Moser in 1949 . They were trying to establish which method of subtracting whole numbers could be taught most effectively—the regrouping method or the equal additions method. However, they realized that effectiveness might depend on the conditions under which the methods were taught—“meaningfully” versus “mechanically.” So, they designed a study that crossed the two instructional approaches with the two different methods (regrouping and equal additions). Among other results, they found that these conditions did matter. The regrouping method was more effective under the meaningful condition than the mechanical condition, but the same was not true for the equal additions algorithm.

What do education researchers want to understand? In our view, the ultimate goal of education is to offer all students the best possible learning opportunities. So, we believe the ultimate purpose of scientific inquiry in education is to develop understanding that supports the improvement of learning opportunities for all students. We say “ultimate” because there are lots of issues that must be understood to improve learning opportunities for all students. Hypotheses about many aspects of education are connected, ultimately, to students’ learning. For example, formulating and testing a hypothesis that preservice teachers need to engage in particular kinds of activities in their coursework in order to teach particular topics well is, ultimately, connected to improving students’ learning opportunities. So is hypothesizing that school districts often devote relatively few resources to instructional leadership training or hypothesizing that positioning mathematics as a tool students can use to combat social injustice can help students see the relevance of mathematics to their lives.

We do not exclude the importance of research on educational issues more removed from improving students’ learning opportunities, but we do think the argument for their importance will be more difficult to make. If there is no way to imagine a connection between your hypothesis and improving learning opportunities for students, even a distant connection, we recommend you reconsider whether it is an important hypothesis within the education community.

Notice that we said the ultimate goal of education is to offer all students the best possible learning opportunities. For too long, educators have been satisfied with a goal of offering rich learning opportunities for lots of students, sometimes even for just the majority of students, but not necessarily for all students. Evaluations of success often are based on outcomes that show high averages. In other words, if many students have learned something, or even a smaller number have learned a lot, educators may have been satisfied. The problem is that there is usually a pattern in the groups of students who receive lower quality opportunities—students of color and students who live in poor areas, urban and rural. This is not acceptable. Consequently, we emphasize the premise that the purpose of education research is to offer rich learning opportunities to all students.

One way to make sure you will be able to convince others of the importance of your study is to consider investigating some aspect of teachers’ shared instructional problems. Historically, researchers in education have set their own research agendas, regardless of the problems teachers are facing in schools. It is increasingly recognized that teachers have had trouble applying to their own classrooms what researchers find. To address this problem, a researcher could partner with a teacher—better yet, a small group of teachers—and talk with them about instructional problems they all share. These discussions can create a rich pool of problems researchers can consider. If researchers pursued one of these problems (preferably alongside teachers), the connection to improving learning opportunities for all students could be direct and immediate. “Grounding a research question in instructional problems that are experienced across multiple teachers’ classrooms helps to ensure that the answer to the question will be of sufficient scope to be relevant and significant beyond the local context” (Cai et al., 2019b , p. 115).

As a beginning researcher, determining the relevance and importance of a research problem is especially challenging. We recommend talking with advisors, other experienced researchers, and peers to test the educational importance of possible research problems and topics of study. You will also learn much more about the issue of research importance when you read Chap. 5 .

Exercise 1.7

Identify a problem in education that is closely connected to improving learning opportunities and a problem that has a less close connection. For each problem, write a brief argument (like a logical sequence of if-then statements) that connects the problem to all students’ learning opportunities.

Part III. Conducting Research as a Practice of Failing Productively

Scientific inquiry involves formulating hypotheses about phenomena that are not fully understood—by you or anyone else. Even if you are able to inform your hypotheses with lots of knowledge that has already been accumulated, you are likely to find that your prediction is not entirely accurate. This is normal. Remember, scientific inquiry is a process of constantly updating your thinking. More and better information means revising your thinking, again, and again, and again. Because you never fully understand a complicated phenomenon and your hypotheses never produce completely accurate predictions, it is easy to believe you are somehow failing.

The trick is to fail upward, to fail to predict accurately in ways that inform your next hypothesis so you can make a better prediction. Some of the best-known researchers in education have been open and honest about the many times their predictions were wrong and, based on the results of their studies and those of others, they continuously updated their thinking and changed their hypotheses.

A striking example of publicly revising (actually reversing) hypotheses due to incorrect predictions is found in the work of Lee J. Cronbach, one of the most distinguished educational psychologists of the twentieth century. In 1955, Cronbach delivered his presidential address to the American Psychological Association. Titling it “Two Disciplines of Scientific Psychology,” Cronbach proposed a rapprochement between two research approaches—correlational studies that focused on individual differences and experimental studies that focused on instructional treatments controlling for individual differences. (We will examine different research approaches in Chap. 4 ). If these approaches could be brought together, reasoned Cronbach ( 1957 ), researchers could find interactions between individual characteristics and treatments (aptitude-treatment interactions or ATIs), fitting the best treatments to different individuals.

In 1975, after years of research by many researchers looking for ATIs, Cronbach acknowledged the evidence for simple, useful ATIs had not been found. Even when trying to find interactions between a few variables that could provide instructional guidance, the analysis, said Cronbach, creates “a hall of mirrors that extends to infinity, tormenting even the boldest investigators and defeating even ambitious designs” (Cronbach, 1975 , p. 119).

As he was reflecting back on his work, Cronbach ( 1986 ) recommended moving away from documenting instructional effects through statistical inference (an approach he had championed for much of his career) and toward approaches that probe the reasons for these effects, approaches that provide a “full account of events in a time, place, and context” (Cronbach, 1986 , p. 104). This is a remarkable change in hypotheses, a change based on data and made fully transparent. Cronbach understood the value of failing productively.

Closer to home, in a less dramatic example, one of us began a line of scientific inquiry into how to prepare elementary preservice teachers to teach early algebra. Teaching early algebra meant engaging elementary students in early forms of algebraic reasoning. Such reasoning should help them transition from arithmetic to algebra. To begin this line of inquiry, a set of activities for preservice teachers were developed. Even though the activities were based on well-supported hypotheses, they largely failed to engage preservice teachers as predicted because of unanticipated challenges the preservice teachers faced. To capitalize on this failure, follow-up studies were conducted, first to better understand elementary preservice teachers’ challenges with preparing to teach early algebra, and then to better support preservice teachers in navigating these challenges. In this example, the initial failure was a necessary step in the researchers’ scientific inquiry and furthered the researchers’ understanding of this issue.

We present another example of failing productively in Chap. 2 . That example emerges from recounting the history of a well-known research program in mathematics education.

Making mistakes is an inherent part of doing scientific research. Conducting a study is rarely a smooth path from beginning to end. We recommend that you keep the following things in mind as you begin a career of conducting research in education.

First, do not get discouraged when you make mistakes; do not fall into the trap of feeling like you are not capable of doing research because you make too many errors.

Second, learn from your mistakes. Do not ignore your mistakes or treat them as errors that you simply need to forget and move past. Mistakes are rich sites for learning—in research just as in other fields of study.

Third, by reflecting on your mistakes, you can learn to make better mistakes, mistakes that inform you about a productive next step. You will not be able to eliminate your mistakes, but you can set a goal of making better and better mistakes.

Exercise 1.8

How does scientific inquiry differ from everyday learning in giving you the tools to fail upward? You may find helpful perspectives on this question in other resources on science and scientific inquiry (e.g., Failure: Why Science is So Successful by Firestein, 2015).

Exercise 1.9

Use what you have learned in this chapter to write a new definition of scientific inquiry. Compare this definition with the one you wrote before reading this chapter. If you are reading this book as part of a course, compare your definition with your colleagues’ definitions. Develop a consensus definition with everyone in the course.

Part IV. Preview of Chap. 2

Now that you have a good idea of what research is, at least of what we believe research is, the next step is to think about how to actually begin doing research. This means how to begin formulating, testing, and revising hypotheses. As for all phases of scientific inquiry, there are lots of things to think about. Because it is critical to start well, we devote Chap. 2 to getting started with formulating hypotheses.

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Hiebert, J., Cai, J., Hwang, S., Morris, A.K., Hohensee, C. (2023). What Is Research, and Why Do People Do It?. In: Doing Research: A New Researcher’s Guide. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-19078-0_1

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On the role of hypotheses in science

Harald brüssow.

1 Laboratory of Gene Technology, Department of Biosystems, KU Leuven, Leuven Belgium

Associated Data

Scientific research progresses by the dialectic dialogue between hypothesis building and the experimental testing of these hypotheses. Microbiologists as biologists in general can rely on an increasing set of sophisticated experimental methods for hypothesis testing such that many scientists maintain that progress in biology essentially comes with new experimental tools. While this is certainly true, the importance of hypothesis building in science should not be neglected. Some scientists rely on intuition for hypothesis building. However, there is also a large body of philosophical thinking on hypothesis building whose knowledge may be of use to young scientists. The present essay presents a primer into philosophical thoughts on hypothesis building and illustrates it with two hypotheses that played a major role in the history of science (the parallel axiom and the fifth element hypothesis). It continues with philosophical concepts on hypotheses as a calculus that fits observations (Copernicus), the need for plausibility (Descartes and Gilbert) and for explicatory power imposing a strong selection on theories (Darwin, James and Dewey). Galilei introduced and James and Poincaré later justified the reductionist principle in hypothesis building. Waddington stressed the feed‐forward aspect of fruitful hypothesis building, while Poincaré called for a dialogue between experiment and hypothesis and distinguished false, true, fruitful and dangerous hypotheses. Theoretical biology plays a much lesser role than theoretical physics because physical thinking strives for unification principle across the universe while biology is confronted with a breathtaking diversity of life forms and its historical development on a single planet. Knowledge of the philosophical foundations on hypothesis building in science might stimulate more hypothesis‐driven experimentation that simple observation‐oriented “fishing expeditions” in biological research.

Short abstract

Scientific research progresses by the dialectic dialogue between hypothesis building and the experimental testing of these hypotheses. Microbiologists can rely on an increasing set of sophisticated experimental methods for hypothesis testing but the importance of hypothesis building in science should not be neglected. This Lilliput offers a primer on philosophical concepts on hypotheses in science.

INTRODUCTION

Philosophy of science and the theory of knowledge (epistemology) are important branches of philosophy. However, philosophy has over the centuries lost its dominant role it enjoyed in antiquity and became in Medieval Ages the maid of theology (ancilla theologiae) and after the rise of natural sciences and its technological applications many practising scientists and the general public doubt whether they need philosophical concepts in their professional and private life. This is in the opinion of the writer of this article, an applied microbiologist, shortsighted for several reasons. Philosophers of the 20th century have made important contributions to the theory of knowledge, and many eminent scientists grew interested in philosophical problems. Mathematics which plays such a prominent role in physics and increasingly also in other branches of science is a hybrid: to some extent, it is the paradigm of an exact science while its abstract aspects are deeply rooted in philosophical thinking. In the present essay, the focus is on hypothesis and hypothesis building in science, essentially it is a compilation what philosophers and scientists thought about this subject in past and present. The controversy between the mathematical mind and that of the practical mind is an old one. The philosopher, physicist and mathematician Pascal ( 1623 –1662a) wrote in his Pensées : “Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate. They are only right when the principles are quite clear. And men of intuition cannot have the patience to reach to first principles of things speculative and conceptional, which they have never seen in the world and which are altogether out of the common. The intellect can be strong and narrow, and can be comprehensive and weak.” Hypothesis building is an act both of intuition and exact thinking and I hope that theoretical knowledge about hypothesis building will also profit young microbiologists.

HYPOTHESES AND AXIOMS IN MATHEMATICS

In the following, I will illustrate the importance of hypothesis building for the history of science and the development of knowledge and illustrate it with two famous concepts, the parallel axiom in mathematics and the five elements hypothesis in physics.

Euclidean geometry

The prominent role of hypotheses in the development of science becomes already clear in the first science book of the Western civilization: Euclid's The Elements written about 300 BC starts with a set of statements called Definitions, Postulates and Common Notions that lay out the foundation of geometry (Euclid,  c.323‐c.283 ). This axiomatic approach is very modern as exemplified by the fact that Euclid's book remained for long time after the Bible the most read book in the Western hemisphere and a backbone of school teaching in mathematics. Euclid's twenty‐three definitions start with sentences such as “1. A point is that which has no part; 2. A line is breadthless length; 3. The extremities of a line are points”; and continues with the definition of angles (“8. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line”) and that of circles, triangles and quadrilateral figures. For the history of science, the 23rd definition of parallels is particularly interesting: “Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction”. This is the famous parallel axiom. It is clear that the parallel axiom cannot be the result of experimental observations, but must be a concept created in the mind. Euclid ends with five Common Notions (“1. Things which are equal to the same thing are also equal to one another, to 5. The whole is greater than the part”). The establishment of a contradiction‐free system for a branch of mathematics based on a set of axioms from which theorems were deduced was revolutionary modern. Hilbert ( 1899 ) formulated a sound modern formulation for Euclidian geometry. Hilbert's axiom system contains the notions “point, line and plane” and the concepts of “betweenness, containment and congruence” leading to five axioms, namely the axioms of Incidence (“Verknüpfung”), of Order (“Anordnung”), of Congruence, of Continuity (“Stetigkeit”) and of Parallels.

Origin of axioms

Philosophers gave various explanations for the origin of the Euclidean hypotheses or axioms. Plato considered geometrical figures as related to ideas (the true things behind the world of appearances). Aristoteles considered geometric figures as abstractions of physical bodies. Descartes perceived geometric figures as inborn ideas from extended bodies ( res extensa ), while Pascal thought that the axioms of Euclidian geometry were derived from intuition. Kant reasoned that Euclidian geometry represented a priori perceptions of space. Newton considered geometry as part of general mechanics linked to theories of measurement. Hilbert argued that the axioms of mathematical geometry are neither the result of contemplation (“Anschauung”) nor of psychological source. For him, axioms were formal propositions (“formale Aussageformen”) characterized by consistency (“Widerspruchsfreiheit”, i.e. absence of contradiction) (Mittelstrass,  1980a ).

Definitions

Axioms were also differently defined by philosophers. In Topics , Aristoteles calls axioms the assumptions taken up by one partner of a dialogue to initiate a dialectic discussion. Plato states that an axiom needs to be an acceptable or credible proposition, which cannot be justified by reference to other statements. Yet, a justification is not necessary because an axiom is an evident statement. In modern definition, axioms are methodical first sentences in the foundation of a deductive science (Mittelstrass,  1980a ). In Posterior Analytics , Aristotle defines postulates as positions which are at least initially not accepted by the dialogue partners while hypotheses are accepted for the sake of reasoning. In Euclid's book, postulates are construction methods that assure the existence of the geometric objects. Today postulates and axioms are used as synonyms while the 18th‐century philosophy made differences: Lambert defined axioms as descriptive sentences and postulates as prescriptive sentences. According to Kant, mathematical postulates create (synthesize) concepts (Mittelstrass,  1980b ). Definitions then fix the use of signs; they can be semantic definitions that explain the proper meaning of a sign in common language use (in a dictionary style) or they can be syntactic definitions that regulate the use of these signs in formal operations. Nominal definitions explain the words, while real definitions explain the meaning or the nature of the defined object. Definitions are thus essential for the development of a language of science, assuring communication and mutual understanding (Mittelstrass,  1980c ). Finally, hypotheses are also frequently defined as consistent conjectures that are compatible with the available knowledge. The truth of the hypothesis is only supposed in order to explain true observations and facts. Consequences of this hypothetical assumptions should explain the observed facts. Normally, descriptive hypotheses precede explanatory hypotheses in the development of scientific thought. Sometimes only tentative concepts are introduced as working hypotheses to test whether they have an explanatory capacity for the observations (Mittelstrass,  1980d ).

The Euclidian geometry is constructed along a logical “if→then” concept. The “if‐clause” formulates at the beginning the supposition, the “then clause” formulates the consequences from these axioms which provides a system of geometric theorems or insights. The conclusions do not follow directly from the hypothesis; this would otherwise represent self‐evident immediate conclusions. The “if‐then” concept in geometry is not used as in other branches of science where the consequences deduced from the axioms are checked against reality whether they are true, in order to confirm the validity of the hypothesis. The task in mathematics is: what can be logically deduced from a given set of axioms to build a contradiction‐free system of geometry. Whether this applies to the real world is in contrast to the situation in natural sciences another question and absolutely secondary to mathematics (Syntopicon,  1992 ).

Pascal's rules for hypotheses

In his Scientific Treatises on Geometric Demonstrations , Pascal ( 1623‐1662b ) formulates “Five rules are absolutely necessary and we cannot dispense with them without an essential defect and frequently even error. Do not leave undefined any terms at all obscure or ambiguous. Use in definitions of terms only words perfectly well known or already explained. Do not fail to ask that each of the necessary principles be granted, however clear and evident it may be. Ask only that perfectly self‐evident things be granted as axioms. Prove all propositions, using for their proof only axioms that are perfectly self‐evident or propositions already demonstrated or granted. Never get caught in the ambiguity of terms by failing to substitute in thought the definitions which restrict or define them. One should accept as true only those things whose contradiction appears to be false. We may then boldly affirm the original statement, however incomprehensible it is.”

Kant's rules on hypotheses

Kant ( 1724–1804 ) wrote that the analysis described in his book The Critique of Pure Reason “has now taught us that all its efforts to extend the bounds of knowledge by means of pure speculation, are utterly fruitless. So much the wider field lies open to hypothesis; as where we cannot know with certainty, we are at liberty to make guesses and to form suppositions. Imagination may be allowed, under the strict surveillance of reason, to invent suppositions; but these must be based on something that is perfectly certain‐ and that is the possibility of the object. Such a supposition is termed a hypothesis. We cannot imagine or invent any object or any property of an object not given in experience and employ it in a hypothesis; otherwise we should be basing our chain of reasoning upon mere chimerical fancies and not upon conception of things. Thus, we have no right to assume of new powers, not existing in nature and consequently we cannot assume that there is any other kind of community among substances than that observable in experience, any kind of presence than that in space and any kind of duration than that in time. The conditions of possible experience are for reason the only conditions of the possibility of things. Otherwise, such conceptions, although not self‐contradictory, are without object and without application. Transcendental hypotheses are therefore inadmissible, and we cannot use the liberty of employing in the absence of physical, hyperphysical grounds of explanation because such hypotheses do not advance reason, but rather stop it in its progress. When the explanation of natural phenomena happens to be difficult, we have constantly at hand a transcendental ground of explanation, which lifts us above the necessity of investigating nature. The next requisite for the admissibility of a hypothesis is its sufficiency. That is it must determine a priori the consequences which are given in experience and which are supposed to follow from the hypothesis itself.” Kant stresses another aspect when dealing with hypotheses: “It is our duty to try to discover new objections, to put weapons in the hands of our opponent, and to grant him the most favorable position. We have nothing to fear from these concessions; on the contrary, we may rather hope that we shall thus make ourselves master of a possession which no one will ever venture to dispute.”

For Kant's analytical and synthetical judgements and Difference between philosophy and mathematics (Kant, Whitehead) , see Appendices  S1 and S2 , respectively.

Poincaré on hypotheses

The mathematician‐philosopher Poincaré ( 1854 –1912a) explored the foundation of mathematics and physics in his book Science and Hypothesis . In the preface to the book, he summarizes common thinking of scientists at the end of the 19th century. “To the superficial observer scientific truth is unassailable, the logic of science is infallible, and if scientific men sometimes make mistakes, it is because they have not understood the rules of the game. Mathematical truths are derived from a few self‐evident propositions, by a chain of flawless reasoning, they are imposed not only by us, but on Nature itself. This is for the minds of most people the origin of certainty in science.” Poincaré then continues “but upon more mature reflection the position held by hypothesis was seen; it was recognized that it is as necessary to the experimenter as it is to the mathematician. And then the doubt arose if all these constructions are built on solid foundations.” However, “to doubt everything or to believe everything are two equally convenient solutions: both dispense with the necessity of reflection. Instead, we should examine with the utmost care the role of hypothesis; we shall then recognize not only that it is necessary, but that in most cases it is legitimate. We shall also see that there are several kinds of hypotheses; that some are verifiable and when once confirmed by experiment become truths of great fertility; that others may be useful to us in fixing our ideas; and finally that others are hypotheses only in appearance, and reduce to definitions or to conventions in disguise.” Poincaré argues that “we must seek mathematical thought where it has remained pure‐i.e. in arithmetic, in the proofs of the most elementary theorems. The process is proof by recurrence. We first show that a theorem is true for n  = 1; we then show that if it is true for n –1 it is true for n; and we conclude that it is true for all integers. The essential characteristic of reasoning by recurrence is that it contains, condensed in a single formula, an infinite number of syllogisms.” Syllogism is logical argument that applies deductive reasoning to arrive at a conclusion. Poincaré notes “that here is a striking analogy with the usual process of induction. But an essential difference exists. Induction applied to the physical sciences is always uncertain because it is based on the belief in a general order of the universe, an order which is external to us. Mathematical induction‐ i.e. proof by recurrence – is on the contrary, necessarily imposed on us, because it is only the affirmation of a property of the mind itself. No doubt mathematical recurrent reasoning and physical inductive reasoning are based on different foundations, but they move in parallel lines and in the same direction‐namely, from the particular to the general.”

Non‐Euclidian geometry: from Gauss to Lobatschewsky

Mathematics is an abstract science that intrinsically does not request that the structures described reflect a physical reality. Paradoxically, mathematics is the language of physics since the founder of experimental physics Galilei used Euclidian geometry when exploring the laws of the free fall. In his 1623 treatise The Assayer , Galilei ( 1564 –1642a) famously formulated that the book of Nature is written in the language of mathematics, thus establishing a link between formal concepts in mathematics and the structure of the physical world. Euclid's parallel axiom played historically a prominent role for the connection between mathematical concepts and physical realities. Mathematicians had doubted that the parallel axiom was needed and tried to prove it. In Euclidian geometry, there is a connection between the parallel axiom and the sum of the angles in a triangle being two right angles. It is therefore revealing that the famous mathematician C.F. Gauss investigated in the early 19th century experimentally whether this Euclidian theorem applies in nature. He approached this problem by measuring the sum of angles in a real triangle by using geodetic angle measurements of three geographical elevations in the vicinity of Göttingen where he was teaching mathematics. He reportedly measured a sum of the angles in this triangle that differed from 180°. Gauss had at the same time also developed statistical methods to evaluate the accuracy of measurements. Apparently, the difference of his measured angles was still within the interval of Gaussian error propagation. He did not publish the reasoning and the results for this experiment because he feared the outcry of colleagues about this unorthodox, even heretical approach to mathematical reasoning (Carnap,  1891 ‐1970a). However, soon afterwards non‐Euclidian geometries were developed. In the words of Poincaré, “Lobatschewsky assumes at the outset that several parallels may be drawn through a point to a given straight line, and he retains all the other axioms of Euclid. From these hypotheses he deduces a series of theorems between which it is impossible to find any contradiction, and he constructs a geometry as impeccable in its logic as Euclidian geometry. The theorems are very different, however, from those to which we are accustomed, and at first will be found a little disconcerting. For instance, the sum of the angles of a triangle is always less than two right angles, and the difference between that sum and two right angles is proportional to the area of the triangle. Lobatschewsky's propositions have no relation to those of Euclid, but are none the less logically interconnected.” Poincaré continues “most mathematicians regard Lobatschewsky's geometry as a mere logical curiosity. Some of them have, however, gone further. If several geometries are possible, they say, is it certain that our geometry is true? Experiments no doubt teaches us that the sum of the angles of a triangle is equal to two right angles, but this is because the triangles we deal with are too small” (Poincaré,  1854 ‐1912a)—hence the importance of Gauss' geodetic triangulation experiment. Gauss was aware that his three hills experiment was too small and thought on measurements on triangles formed with stars.

Poincaré vs. Einstein

Lobatschewsky's hyperbolic geometry did not remain the only non‐Euclidian geometry. Riemann developed a geometry without the parallel axiom, while the other Euclidian axioms were maintained with the exception of that of Order (Anordnung). Poincaré notes “so there is a kind of opposition between the geometries. For instance the sum of the angles in a triangle is equal to two right angles in Euclid's geometry, less than two right angles in that of Lobatschewsky, and greater than two right angles in that of Riemann. The number of parallel lines that can be drawn through a given point to a given line is one in Euclid's geometry, none in Riemann's, and an infinite number in the geometry of Lobatschewsky. Let us add that Riemann's space is finite, although unbounded.” As further distinction, the ratio of the circumference to the diameter of a circle is equal to π in Euclid's, greater than π in Lobatschewsky's and smaller than π in Riemann's geometry. A further difference between these geometries concerns the degree of curvature (Krümmungsmass k) which is 0 for a Euclidian surface, smaller than 0 for a Lobatschewsky and greater than 0 for a Riemann surface. The difference in curvature can be roughly compared with plane, concave and convex surfaces. The inner geometric structure of a Riemann plane resembles the surface structure of a Euclidean sphere and a Lobatschewsky plane resembles that of a Euclidean pseudosphere (a negatively curved geometry of a saddle). What geometry is true? Poincaré asked “Ought we then, to conclude that the axioms of geometry are experimental truths?” and continues “If geometry were an experimental science, it would not be an exact science. The geometric axioms are therefore neither synthetic a priori intuitions as affirmed by Kant nor experimental facts. They are conventions. Our choice among all possible conventions is guided by experimental facts; but it remains free and is only limited by the necessity of avoiding contradictions. In other words, the axioms of geometry are only definitions in disguise. What then are we to think of the question: Is Euclidean geometry true? It has no meaning. One geometry cannot be more true than another, it can only be more convenient. Now, Euclidean geometry is, and will remain, the most convenient, 1 st because it is the simplest and 2 nd because it sufficiently agrees with the properties of natural bodies” (Poincaré,  1854 ‐1912a).

Poincaré's book was published in 1903 and only a few years later Einstein published his general theory of relativity ( 1916 ) where he used a non‐Euclidean, Riemann geometry and where he demonstrated a structure of space that deviated from Euclidean geometry in the vicinity of strong gravitational fields. And in 1919, astronomical observations during a solar eclipse showed that light rays from a distant star were indeed “bent” when passing next to the sun. These physical observations challenged the view of Poincaré, and we should now address some aspects of hypotheses in physics (Carnap,  1891 ‐1970b).

HYPOTHESES IN PHYSICS

The long life of the five elements hypothesis.

Physical sciences—not to speak of biological sciences — were less developed in antiquity than mathematics which is already demonstrated by the primitive ideas on the elements constituting physical bodies. Plato and Aristotle spoke of the four elements which they took over from Thales (water), Anaximenes (air) and Parmenides (fire and earth) and add a fifth element (quinta essentia, our quintessence), namely ether. Ether is imagined a heavenly element belonging to the supralunar world. In Plato's dialogue Timaios (Plato,  c.424‐c.348 BC a ), the five elements were associated with regular polyhedra in geometry and became known as Platonic bodies: tetrahedron (fire), octahedron (air), cube (earth), icosahedron (water) and dodecahedron (ether). In regular polyhedra, faces are congruent (identical in shape and size), all angles and all edges are congruent, and the same number of faces meet at each vertex. The number of elements is limited to five because in Euclidian space there are exactly five regular polyhedral. There is in Plato's writing even a kind of geometrical chemistry. Since two octahedra (air) plus one tetrahedron (fire) can be combined into one icosahedron (water), these “liquid” elements can combine while this is not the case for combinations with the cube (earth). The 12 faces of the dodecahedron were compared with the 12 zodiac signs (Mittelstrass,  1980e ). This geometry‐based hypothesis of physics had a long life. As late as 1612, Kepler in his Mysterium cosmographicum tried to fit the Platonic bodies into the planetary shells of his solar system model. The ether theory even survived into the scientific discussion of the 19th‐century physics and the idea of a mathematical structure of the universe dominated by symmetry operations even fertilized 20th‐century ideas about symmetry concepts in the physics of elementary particles.

Huygens on sound waves in air

The ether hypothesis figures prominently in the 1690 Treatise on Light from Huygens ( 1617‐1670 ). He first reports on the transmission of sound by air when writing “this may be proved by shutting up a sounding body in a glass vessel from which the air is withdrawn and care was taken to place the sounding body on cotton that it cannot communicate its tremor to the glass vessel which encloses it. After having exhausted all the air, one hears no sound from the metal though it is struck.” Huygens comes up with some foresight when suspecting “the air is of such a nature that it can be compressed and reduced to a much smaller space than that it normally occupies. Air is made up of small bodies which float about and which are agitated very rapidly. So that the spreading of sound is the effort which these little bodies make in collisions with one another, to regain freedom when they are a little more squeezed together in the circuit of these waves than elsewhere.”

Huygens on light waves in ether

“That is not the same air but another kind of matter in which light spreads; since if the air is removed from the vessel the light does not cease to traverse it as before. The extreme velocity of light cannot admit such a propagation of motion” as sound waves. To achieve the propagation of light, Huygens invokes ether “as a substance approaching to perfect hardness and possessing springiness as prompt as we choose. One may conceive light to spread successively by spherical waves. The propagation consists nowise in the transport of those particles but merely in a small agitation which they cannot help communicate to those surrounding.” The hypothesis of an ether in outer space fills libraries of physical discussions, but all experimental approaches led to contradictions with respect to postulated properties of this hypothetical material for example when optical experiments showed that light waves display transversal and not longitudinal oscillations.

The demise of ether

Mechanical models for the transmission of light or gravitation waves requiring ether were finally put to rest by the theory of relativity from Einstein (Mittelstrass,  1980f ). This theory posits that the speed of light in an empty space is constant and does not depend on movements of the source of light or that of an observer as requested by the ether hypothesis. The theory of relativity also provides an answer how the force of gravitation is transmitted from one mass to another across an essentially empty space. In the non‐Euclidian formulation of the theory of relativity (Einstein used the Riemann geometry), there is no gravitation force in the sense of mechanical or electromagnetic forces. The gravitation force is in this formulation simply replaced by a geometric structure (space curvature near high and dense masses) of a four‐dimensional space–time system (Carnap,  1891 ‐1970c; Einstein & Imfeld,  1956 ) Gravitation waves and gravitation lens effects have indeed been experimental demonstrated by astrophysicists (Dorfmüller et al.,  1998 ).

For Aristotle's on physical hypotheses , see Appendix  S3 .

PHILOSOPHICAL THOUGHTS ON HYPOTHESES

In the following, the opinions of a number of famous scientists and philosophers on hypotheses are quoted to provide a historical overview on the subject.

Copernicus' hypothesis: a calculus which fits observations

In his book Revolutions of Heavenly Spheres Copernicus ( 1473–1543 ) reasoned in the preface about hypotheses in physics. “Since the newness of the hypotheses of this work ‐which sets the earth in motion and puts an immovable sun at the center of the universe‐ has already received a great deal of publicity, I have no doubt that certain of the savants have taken great offense.” He defended his heliocentric thesis by stating “For it is the job of the astronomer to use painstaking and skilled observations in gathering together the history of the celestial movements‐ and then – since he cannot by any line of reasoning reach the true causes of these movements‐ to think up or construct whatever causes or hypotheses he pleases such that, by the assumption of these causes, those same movements can be calculated from the principles of geometry for the past and the future too. This artist is markedly outstanding in both of these respects: for it is not necessary that these hypotheses should be true, or even probable; but it is enough if they provide a calculus which fits the observations.” This preface written in 1543 sounds in its arguments very modern physics. However, historians of science have discovered that it was probably written by a theologian friend of Copernicus to defend the book against the criticism by the church.

Bacon's intermediate hypotheses

In his book Novum Organum , Francis Bacon ( 1561–1626 ) claims for hypotheses and scientific reasoning “that they augur well for the sciences, when the ascent shall proceed by a true scale and successive steps, without interruption or breach, from particulars to the lesser axioms, thence to the intermediates and lastly to the most general.” He then notes “that the lowest axioms differ but little from bare experiments, the highest and most general are notional, abstract, and of no real weight. The intermediate are true, solid, full of life, and up to them depend the business and fortune of mankind.” He warns that “we must not then add wings, but rather lead and ballast to the understanding, to prevent its jumping and flying, which has not yet been done; but whenever this takes place we may entertain greater hopes of the sciences.” With respect to methodology, Bacon claims that “we must invent a different form of induction. The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, …deciding generally from too small a number of facts. Sciences should separate nature by proper rejections and exclusions and then conclude for the affirmative, after collecting a sufficient number of negatives.”

Gilbert and Descartes for plausible hypotheses

William Gilbert introduced in his book On the Loadstone (Gilbert,  1544‐1603 ) the argument of plausibility into physical hypothesis building. “From these arguments, therefore, we infer not with mere probability, but with certainty, the diurnal rotation of the earth; for nature ever acts with fewer than with many means; and because it is more accordant to reason that the one small body, the earth, should make a daily revolution than the whole universe should be whirled around it.”

Descartes ( 1596‐1650 ) reflected on the sources of understanding in his book Rules for Direction and distinguished what “comes about by impulse, by conjecture, or by deduction. Impulse can assign no reason for their belief and when determined by fanciful disposition, it is almost always a source of error.” When speaking about the working of conjectures he quotes thoughts of Aristotle: “water which is at a greater distance from the center of the globe than earth is likewise less dense substance, and likewise the air which is above the water, is still rarer. Hence, we hazard the guess that above the air nothing exists but a very pure ether which is much rarer than air itself. Moreover nothing that we construct in this way really deceives, if we merely judge it to be probable and never affirm it to be true; in fact it makes us better instructed. Deduction is thus left to us as the only means of putting things together so as to be sure of their truth. Yet in it, too, there may be many defects.”

Care in formulating hypotheses

Locke ( 1632‐1704 ) in his treatise Concerning Human Understanding admits that “we may make use of any probable hypotheses whatsoever. Hypotheses if they are well made are at least great helps to the memory and often direct us to new discoveries. However, we should not take up any one too hastily.” Also, practising scientists argued against careless use of hypotheses and proposed remedies. Lavoisier ( 1743‐1794 ) in the preface to his Element of Chemistry warned about beaten‐track hypotheses. “Instead of applying observation to the things we wished to know, we have chosen rather to imagine them. Advancing from one ill‐founded supposition to another, we have at last bewildered ourselves amidst a multitude of errors. These errors becoming prejudices, are adopted as principles and we thus bewilder ourselves more and more. We abuse words which we do not understand. There is but one remedy: this is to forget all that we have learned, to trace back our ideas to their sources and as Bacon says to frame the human understanding anew.”

Faraday ( 1791–1867 ) in a Speculation Touching Electric Conduction and the Nature of Matter highlighted the fundamental difference between hypotheses and facts when noting “that he has most power of penetrating the secrets of nature, and guessing by hypothesis at her mode of working, will also be most careful for his own safe progress and that of others, to distinguish that knowledge which consists of assumption, by which I mean theory and hypothesis, from that which is the knowledge of facts and laws; never raising the former to the dignity or authority of the latter.”

Explicatory power justifies hypotheses

Darwin ( 1809 –1882a) defended the conclusions and hypothesis of his book The Origin of Species “that species have been modified in a long course of descent. This has been affected chiefly through the natural selection of numerous, slight, favorable variations.” He uses a post hoc argument for this hypothesis: “It can hardly be supposed that a false theory would explain, to so satisfactory a manner as does the theory of natural selection, the several large classes of facts” described in his book.

The natural selection of hypotheses

In the concluding chapter of The Descent of Man Darwin ( 1809 –1882b) admits “that many of the views which have been advanced in this book are highly speculative and some no doubt will prove erroneous.” However, he distinguished that “false facts are highly injurious to the progress of science for they often endure long; but false views do little harm for everyone takes a salutory pleasure in proving their falseness; and when this is done, one path to error is closed and the road to truth is often at the same time opened.”

The American philosopher William James ( 1842–1907 ) concurred with Darwin's view when he wrote in his Principles of Psychology “every scientific conception is in the first instance a spontaneous variation in someone'’s brain. For one that proves useful and applicable there are a thousand that perish through their worthlessness. The scientific conceptions must prove their worth by being verified. This test, however, is the cause of their preservation, not of their production.”

The American philosopher J. Dewey ( 1859‐1952 ) in his treatise Experience and Education notes that “the experimental method of science attaches more importance not less to ideas than do other methods. There is no such thing as experiment in the scientific sense unless action is directed by some leading idea. The fact that the ideas employed are hypotheses, not final truths, is the reason why ideas are more jealously guarded and tested in science than anywhere else. As fixed truths they must be accepted and that is the end of the matter. But as hypotheses, they must be continuously tested and revised, a requirement that demands they be accurately formulated. Ideas or hypotheses are tested by the consequences which they produce when they are acted upon. The method of intelligence manifested in the experimental method demands keeping track of ideas, activities, and observed consequences. Keeping track is a matter of reflective review.”

The reductionist principle

James ( 1842‐1907 ) pushed this idea further when saying “Scientific thought goes by selection. We break the solid plenitude of fact into separate essences, conceive generally what only exists particularly, and by our classifications leave nothing in its natural neighborhood. The reality exists as a plenum. All its part are contemporaneous, but we can neither experience nor think this plenum. What we experience is a chaos of fragmentary impressions, what we think is an abstract system of hypothetical data and laws. We must decompose each chaos into single facts. We must learn to see in the chaotic antecedent a multitude of distinct antecedents, in the chaotic consequent a multitude of distinct consequents.” From these considerations James concluded “even those experiences which are used to prove a scientific truth are for the most part artificial experiences of the laboratory gained after the truth itself has been conjectured. Instead of experiences engendering the inner relations, the inner relations are what engender the experience here.“

Following curiosity

Freud ( 1856–1939 ) considered curiosity and imagination as driving forces of hypothesis building which need to be confronted as quickly as possible with observations. In Beyond the Pleasure Principle , Freud wrote “One may surely give oneself up to a line of thought and follow it up as far as it leads, simply out of scientific curiosity. These innovations were direct translations of observation into theory, subject to no greater sources of error than is inevitable in anything of the kind. At all events there is no way of working out this idea except by combining facts with pure imagination and thereby departing far from observation.” This can quickly go astray when trusting intuition. Freud recommends “that one may inexorably reject theories that are contradicted by the very first steps in the analysis of observation and be aware that those one holds have only a tentative validity.”

Feed‐forward aspects of hypotheses

The geneticist Waddington ( 1905–1975 ) in his essay The Nature of Life states that “a scientific theory cannot remain a mere structure within the world of logic, but must have implications for action and that in two rather different ways. It must involve the consequence that if you do so and so, such and such result will follow. That is to say it must give, or at least offer, the possibility of controlling the process. Secondly, its value is quite largely dependent on its power of suggesting the next step in scientific advance. Any complete piece of scientific work starts with an activity essentially the same as that of an artist. It starts by asking a relevant question. The first step may be a new awareness of some facet of the world that no one else had previously thought worth attending to. Or some new imaginative idea which depends on a sensitive receptiveness to the oddity of nature essentially similar to that of the artist. In his logical analysis and manipulative experimentation, the scientist is behaving arrogantly towards nature, trying to force her into his categories of thought or to trick her into doing what he wants. But finally he has to be humble. He has to take his intuition, his logical theory and his manipulative skill to the bar of Nature and see whether she answers yes or no; and he has to abide by the result. Science is often quite ready to tolerate some logical inadequacy in a theory‐or even a flat logical contradiction like that between the particle and wave theories of matter‐so long as it finds itself in the possession of a hypothesis which offers both the possibility of control and a guide to worthwhile avenues of exploration.”

Poincaré: the dialogue between experiment and hypothesis

Poincaré ( 1854 –1912b) also dealt with physics in Science and Hypothesis . “Experiment is the sole source of truth. It alone can teach us certainty. Cannot we be content with experiment alone? What place is left for mathematical physics? The man of science must work with method. Science is built up of facts, as a house is built of stones, but an accumulation of facts is no more a science than a heap of stones is a house. It is often said that experiments should be made without preconceived concepts. That is impossible. Without the hypothesis, no conclusion could have been drawn; nothing extraordinary would have been seen; and only one fact the more would have been catalogued, without deducing from it the remotest consequence.” Poincaré compares science to a library. Experimental physics alone can enrich the library with new books, but mathematical theoretical physics draw up the catalogue to find the books and to reveal gaps which have to be closed by the purchase of new books.

Poincaré: false, true, fruitful and dangerous hypotheses

Poincaré continues “we all know that there are good and bad experiments. The latter accumulate in vain. Whether there are hundred or thousand, one single piece of work will be sufficient to sweep them into oblivion. Bacon invented the term of an experimentum crucis for such experiments. What then is a good experiment? It is that which teaches us something more than an isolated fact. It is that which enables us to predict and to generalize. Experiments only gives us a certain number of isolated points. They must be connected by a continuous line and that is true generalization. Every generalization is a hypothesis. It should be as soon as possible submitted to verification. If it cannot stand the test, it must be abandoned without any hesitation. The physicist who has just given up one of his hypotheses should rejoice, for he found an unexpected opportunity of discovery. The hypothesis took into account all the known factors which seem capable of intervention in the phenomenon. If it is not verified, it is because there is something unexpected. Has the hypothesis thus rejected been sterile? Far from it. It has rendered more service than a true hypothesis.” Poincaré notes that “with a true hypothesis only one fact the more would have been catalogued, without deducing from it the remotest consequence. It may be said that the wrong hypothesis has rendered more service than a true hypothesis.” However, Poincaré warns that “some hypotheses are dangerous – first and foremost those which are tacit and unconscious. And since we make them without knowing them, we cannot get rid of them.” Poincaré notes that here mathematical physics is of help because by its precision one is compelled to formulate all the hypotheses, revealing also the tacit ones.

Arguments for the reductionist principle

Poincaré also warned against multiplying hypotheses indefinitely: “If we construct a theory upon multiple hypotheses, and if experiment condemns it, which of the premisses must be changed?” Poincaré also recommended to “resolve the complex phenomenon given directly by experiment into a very large number of elementary phenomena. First, with respect to time. Instead of embracing in its entirety the progressive development of a phenomenon, we simply try to connect each moment with the one immediately preceding. Next, we try to decompose the phenomenon in space. We must try to deduce the elementary phenomenon localized in a very small region of space.” Poincaré suggested that the physicist should “be guided by the instinct of simplicity, and that is why in physical science generalization so readily takes the mathematical form to state the problem in the form of an equation.” This argument goes back to Galilei ( 1564 –1642b) who wrote in The Two Sciences “when I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? If now we examine the matter carefully we find no addition or increment more simple than that which repeats itself always in the same manner. It seems we shall not be far wrong if we put the increment of speed as proportional to the increment of time.” With a bit of geometrical reasoning, Galilei deduced that the distance travelled by a freely falling body varies as the square of the time. However, Galilei was not naïve and continued “I grant that these conclusions proved in the abstract will be different when applied in the concrete” and considers disturbances cause by friction and air resistance that complicate the initially conceived simplicity.

Four sequential steps of discovery…

Some philosophers of science attributed a fundamental importance to observations for the acquisition of experience in science. The process starts with accidental observations (Aristotle), going to systematic observations (Bacon), leading to quantitative rules obtained with exact measurements (Newton and Kant) and culminating in observations under artificially created conditions in experiments (Galilei) (Mittelstrass,  1980g ).

…rejected by Popper and Kant

In fact, Newton wrote that he had developed his theory of gravitation from experience followed by induction. K. Popper ( 1902‐1994 ) in his book Conjectures and Refutations did not agree with this logical flow “experience leading to theory” and that for several reasons. This scheme is according to Popper intuitively false because observations are always inexact, while theory makes absolute exact assertions. It is also historically false because Copernicus and Kepler were not led to their theories by experimental observations but by geometry and number theories of Plato and Pythagoras for which they searched verifications in observational data. Kepler, for example, tried to prove the concept of circular planetary movement influenced by Greek theory of the circle being a perfect geometric figure and only when he could not demonstrate this with observational data, he tried elliptical movements. Popper noted that it was Kant who realized that even physical experiments are not prior to theories when quoting Kant's preface to the Critique of Pure Reason : “When Galilei let his globes run down an inclined plane with a gravity which he has chosen himself, then a light dawned on all natural philosophers. They learnt that our reason can only understand what it creates according to its own design; that we must compel Nature to answer our questions, rather than cling to Nature's apron strings and allow her to guide us. For purely accidental observations, made without any plan having been thought out in advance, cannot be connected by a law‐ which is what reason is searching for.” From that reasoning Popper concluded that “we ourselves must confront nature with hypotheses and demand a reply to our questions; and that lacking such hypotheses, we can only make haphazard observations which follow no plan and which can therefore never lead to a natural law. Everyday experience, too, goes far beyond all observations. Everyday experience must interpret observations for without theoretical interpretation, observations remain blind and uninformative. Everyday experience constantly operates with abstract ideas, such as that of cause and effect, and so it cannot be derived from observation.” Popper agreed with Kant who said “Our intellect does not draw its laws from nature…but imposes them on nature”. Popper modifies this statement to “Our intellect does not draw its laws from nature, but tries‐ with varying degrees of success – to impose upon nature laws which it freely invents. Theories are seen to be free creations of our mind, the result of almost poetic intuition. While theories cannot be logically derived from observations, they can, however, clash with observations. This fact makes it possible to infer from observations that a theory is false. The possibility of refuting theories by observations is the basis of all empirical tests. All empirical tests are therefore attempted refutations.”

OUTLOOK: HYPOTHESES IN BIOLOGY

Is biology special.

Waddington notes that “living organisms are much more complicated than the non‐living things. Biology has therefore developed more slowly than sciences such as physics and chemistry and has tended to rely on them for many of its basic ideas. These older physical sciences have provided biology with many firm foundations which have been of the greatest value to it, but throughout most of its history biology has found itself faced with the dilemma as to how far its reliance on physics and chemistry should be pushed” both with respect to its experimental methods and its theoretical foundations. Vitalism is indeed such a theory maintaining that organisms cannot be explained solely by physicochemical laws claiming specific biological forces active in organisms. However, efforts to prove the existence of such vital forces have failed and today most biologists consider vitalism a superseded theory.

Biology as a branch of science is as old as physics. If one takes Aristotle as a reference, he has written more on biology than on physics. Sophisticated animal experiments were already conducted in the antiquity by Galen (Brüssow, 2022 ). Alertus Magnus displayed biological research interest during the medieval time. Knowledge on plants provided the basis of medical drugs in early modern times. What explains biology's decreasing influence compared with the rapid development of physics by Galilei and Newton? One reason is the possibility to use mathematical equations to describe physical phenomena which was not possible for biological phenomena. Physics has from the beginning displayed a trend to few fundamental underlying principles. This is not the case for biology. With the discovery of new continents, biologists were fascinated by the diversity of life. Diversity was the conducting line of biological thinking. This changed only when taxonomists and comparative anatomists revealed recurring pattern in this stunning biological variety and when Darwin provided a theoretical concept to understand variation as a driving force in biology. Even when genetics and molecular biology allowed to understand biology from a few universally shared properties, such as a universal genetic code, biology differed in fundamental aspects from physics and chemistry. First, biology is so far restricted to the planet earth while the laws of physic and chemistry apply in principle to the entire universe. Second, biology is to a great extent a historical discipline; many biological processes cannot be understood from present‐day observations because they are the result of historical developments in evolution. Hence, the importance of Dobzhansky's dictum that nothing makes sense in biology except in the light of evolution. The great diversity of life forms, the complexity of processes occurring in cells and their integration in higher organisms and the importance of a historical past for the understanding of extant organisms, all that has delayed the successful application of mathematical methods in biology or the construction of theoretical frameworks in biology. Theoretical biology by far did not achieve a comparable role as theoretical physics which is on equal foot with experimental physics. Many biologists are even rather sceptical towards a theoretical biology and see progress in the development of ever more sophisticated experimental methods instead in theoretical concepts expressed by new hypotheses.

Knowledge from data without hypothesis?

Philosophers distinguish rational knowledge ( cognitio ex principiis ) from knowledge from data ( cognitio ex data ). Kant associates these two branches with natural sciences and natural history, respectively. The latter with descriptions of natural objects as prominently done with systematic classification of animals and plants or, where it is really history, when describing events in the evolution of life forms on earth. Cognitio ex data thus played a much more prominent role in biology than in physics and explains why the compilation of data and in extremis the collection of museum specimen characterizes biological research. To account for this difference, philosophers of the logical empiricism developed a two‐level concept of science languages consisting of a language of observations (Beobachtungssprache) and a language of theories (Theoriesprache) which are linked by certain rules of correspondence (Korrespondenzregeln) (Carnap,  1891 –1970d). If one looks into leading biological research journals, it becomes clear that biology has a sophisticated language of observation and a much less developed language of theories.

Do we need more philosophical thinking in biology or at least a more vigorous theoretical biology? The breathtaking speed of progress in experimental biology seems to indicate that biology can well develop without much theoretical or philosophical thinking. At the same time, one could argue that some fields in biology might need more theoretical rigour. Microbiologists might think on microbiome research—one of the breakthrough developments of microbiology research in recent years. The field teems with fascinating, but ill‐defined terms (our second genome; holobionts; gut–brain axis; dysbiosis, symbionts; probiotics; health benefits) that call for stricter definitions. One might also argue that biologists should at least consider the criticism of Goethe ( 1749–1832 ), a poet who was also an active scientist. In Faust , the devil ironically teaches biology to a young student.

“Wer will was Lebendigs erkennen und beschreiben, Sucht erst den Geist herauszutreiben, Dann hat er die Teile in seiner Hand, Fehlt, leider! nur das geistige Band.” (To docket living things past any doubt. You cancel first the living spirit out: The parts lie in the hollow of your hand, You only lack the living thing you banned).

We probably need both in biology: more data and more theory and hypotheses.

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The author reports no conflict of interest.

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Supporting information

Appendix S1

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2. Psychological Research

Why is research important, learning objectives.

By the end of this section, you will be able to:

• Explain how scientific research addresses questions about behavior
• Discuss how scientific research guides public policy
• Appreciate how scientific research can be important in making personal decisions

Scientific research is a critical tool for successfully navigating our complex world. Without it, we would be forced to rely solely on intuition, other people’s authority, and blind luck. While many of us feel confident in our abilities to decipher and interact with the world around us, history is filled with examples of how very wrong we can be when we fail to recognize the need for evidence in supporting claims. At various times in history, we would have been certain that the sun revolved around a flat earth, that the earth’s continents did not move, and that mental illness was caused by possession ( [link] ). It is through systematic scientific research that we divest ourselves of our preconceived notions and superstitions and gain an objective understanding of ourselves and our world.

Some of our ancestors, across the world and over the centuries, believed that trephination—the practice of making a hole in the skull, as shown here—allowed evil spirits to leave the body, thus curing mental illness and other disorders. (credit: “taiproject”/Flickr)

The goal of all scientists is to better understand the world around them. Psychologists focus their attention on understanding behavior, as well as the cognitive (mental) and physiological (body) processes that underlie behavior. In contrast to other methods that people use to understand the behavior of others, such as intuition and personal experience, the hallmark of scientific research is that there is evidence to support a claim. Scientific knowledge is empirical : It is grounded in objective, tangible evidence that can be observed time and time again, regardless of who is observing.

While behavior is observable, the mind is not. If someone is crying, we can see behavior. However, the reason for the behavior is more difficult to determine. Is the person crying due to being sad, in pain, or happy? Sometimes we can learn the reason for someone’s behavior by simply asking a question, like “Why are you crying?” However, there are situations in which an individual is either uncomfortable or unwilling to answer the question honestly, or is incapable of answering. For example, infants would not be able to explain why they are crying. In such circumstances, the psychologist must be creative in finding ways to better understand behavior. This chapter explores how scientific knowledge is generated, and how important that knowledge is in forming decisions in our personal lives and in the public domain.

USE OF RESEARCH INFORMATION

Trying to determine which theories are and are not accepted by the scientific community can be difficult, especially in an area of research as broad as psychology. More than ever before, we have an incredible amount of information at our fingertips, and a simple internet search on any given research topic might result in a number of contradictory studies. In these cases, we are witnessing the scientific community going through the process of reaching a consensus, and it could be quite some time before a consensus emerges. For example, the hypothesized link between exposure to media violence and subsequent aggression has been debated in the scientific community for roughly 60 years. Even today, we will find detractors, but a consensus is building. Several professional organizations view media violence exposure as a risk factor for actual violence, including the American Medical Association, the American Psychiatric Association, and the American Psychological Association (American Academy of Pediatrics, American Academy of Child & Adolescent Psychiatry, American Psychological Association, American Medical Association, American Academy of Family Physicians, American Psychiatric Association, 2000).

In the meantime, we should strive to think critically about the information we encounter by exercising a degree of healthy skepticism. When someone makes a claim, we should examine the claim from a number of different perspectives: what is the expertise of the person making the claim, what might they gain if the claim is valid, does the claim seem justified given the evidence, and what do other researchers think of the claim? This is especially important when we consider how much information in advertising campaigns and on the internet claims to be based on “scientific evidence” when in actuality it is a belief or perspective of just a few individuals trying to sell a product or draw attention to their perspectives.

We should be informed consumers of the information made available to us because decisions based on this information have significant consequences. One such consequence can be seen in politics and public policy. Imagine that you have been elected as the governor of your state. One of your responsibilities is to manage the state budget and determine how to best spend your constituents’ tax dollars. As the new governor, you need to decide whether to continue funding the D.A.R.E. (Drug Abuse Resistance Education) program in public schools ( [link] ). This program typically involves police officers coming into the classroom to educate students about the dangers of becoming involved with alcohol and other drugs. According to the D.A.R.E. website (www.dare.org), this program has been very popular since its inception in 1983, and it is currently operating in 75% of school districts in the United States and in more than 40 countries worldwide. Sounds like an easy decision, right? However, on closer review, you discover that the vast majority of research into this program consistently suggests that participation has little, if any, effect on whether or not someone uses alcohol or other drugs (Clayton, Cattarello, & Johnstone, 1996; Ennett, Tobler, Ringwalt, & Flewelling, 1994; Lynam et al., 1999; Ringwalt, Ennett, & Holt, 1991). If you are committed to being a good steward of taxpayer money, will you fund this particular program, or will you try to find other programs that research has consistently demonstrated to be effective?

The D.A.R.E. program continues to be popular in schools around the world despite research suggesting that it is ineffective.

Link to Learning

Watch this news report to learn more about some of the controversial issues surrounding the D.A.R.E. program.

Ultimately, it is not just politicians who can benefit from using research in guiding their decisions. We all might look to research from time to time when making decisions in our lives. Imagine you just found out that a close friend has breast cancer or that one of your young relatives has recently been diagnosed with autism. In either case, you want to know which treatment options are most successful with the fewest side effects. How would you find that out? You would probably talk with your doctor and personally review the research that has been done on various treatment options—always with a critical eye to ensure that you are as informed as possible.

In the end, research is what makes the difference between facts and opinions. Facts are observable realities, and opinions are personal judgments, conclusions, or attitudes that may or may not be accurate. In the scientific community, facts can be established only using evidence collected through empirical research.

THE PROCESS OF SCIENTIFIC RESEARCH

Scientific knowledge is advanced through a process known as the scientific method . Basically, ideas (in the form of theories and hypotheses) are tested against the real world (in the form of empirical observations), and those empirical observations lead to more ideas that are tested against the real world, and so on. In this sense, the scientific process is circular. The types of reasoning within the circle are called deductive and inductive. In deductive reasoning , ideas are tested against the empirical world; in inductive reasoning , empirical observations lead to new ideas ( [link] ). These processes are inseparable, like inhaling and exhaling, but different research approaches place different emphasis on the deductive and inductive aspects.

Psychological research relies on both inductive and deductive reasoning.

In the scientific context, deductive reasoning begins with a generalization—one hypothesis—that is then used to reach logical conclusions about the real world. If the hypothesis is correct, then the logical conclusions reached through deductive reasoning should also be correct. A deductive reasoning argument might go something like this: All living things require energy to survive (this would be your hypothesis). Ducks are living things. Therefore, ducks require energy to survive (logical conclusion). In this example, the hypothesis is correct; therefore, the conclusion is correct as well. Sometimes, however, an incorrect hypothesis may lead to a logical but incorrect conclusion. Consider this argument: all ducks are born with the ability to see. Quackers is a duck. Therefore, Quackers was born with the ability to see. Scientists use deductive reasoning to empirically test their hypotheses. Returning to the example of the ducks, researchers might design a study to test the hypothesis that if all living things require energy to survive, then ducks will be found to require energy to survive.

Deductive reasoning starts with a generalization that is tested against real-world observations; however, inductive reasoning moves in the opposite direction. Inductive reasoning uses empirical observations to construct broad generalizations. Unlike deductive reasoning, conclusions drawn from inductive reasoning may or may not be correct, regardless of the observations on which they are based. For instance, you may notice that your favorite fruits—apples, bananas, and oranges—all grow on trees; therefore, you assume that all fruit must grow on trees. This would be an example of inductive reasoning, and, clearly, the existence of strawberries, blueberries, and kiwi demonstrate that this generalization is not correct despite it being based on a number of direct observations. Scientists use inductive reasoning to formulate theories, which in turn generate hypotheses that are tested with deductive reasoning. In the end, science involves both deductive and inductive processes.

For example, case studies, which you will read about in the next section, are heavily weighted on the side of empirical observations. Thus, case studies are closely associated with inductive processes as researchers gather massive amounts of observations and seek interesting patterns (new ideas) in the data. Experimental research, on the other hand, puts great emphasis on deductive reasoning.

We’ve stated that theories and hypotheses are ideas, but what sort of ideas are they, exactly? A theory is a well-developed set of ideas that propose an explanation for observed phenomena. Theories are repeatedly checked against the world, but they tend to be too complex to be tested all at once; instead, researchers create hypotheses to test specific aspects of a theory.

A hypothesis is a testable prediction about how the world will behave if our idea is correct, and it is often worded as an if-then statement (e.g., if I study all night, I will get a passing grade on the test). The hypothesis is extremely important because it bridges the gap between the realm of ideas and the real world. As specific hypotheses are tested, theories are modified and refined to reflect and incorporate the result of these tests [link] .

The scientific method of research includes proposing hypotheses, conducting research, and creating or modifying theories based on results.

To see how this process works, let’s consider a specific theory and a hypothesis that might be generated from that theory. As you’ll learn in a later chapter, the James-Lange theory of emotion asserts that emotional experience relies on the physiological arousal associated with the emotional state. If you walked out of your home and discovered a very aggressive snake waiting on your doorstep, your heart would begin to race and your stomach churn. According to the James-Lange theory, these physiological changes would result in your feeling of fear. A hypothesis that could be derived from this theory might be that a person who is unaware of the physiological arousal that the sight of the snake elicits will not feel fear.

A scientific hypothesis is also falsifiable , or capable of being shown to be incorrect. Recall from the introductory chapter that Sigmund Freud had lots of interesting ideas to explain various human behaviors ( [link] ). However, a major criticism of Freud’s theories is that many of his ideas are not falsifiable; for example, it is impossible to imagine empirical observations that would disprove the existence of the id, the ego, and the superego—the three elements of personality described in Freud’s theories. Despite this, Freud’s theories are widely taught in introductory psychology texts because of their historical significance for personality psychology and psychotherapy, and these remain the root of all modern forms of therapy.

Many of the specifics of (a) Freud’s theories, such as (b) his division of the mind into id, ego, and superego, have fallen out of favor in recent decades because they are not falsifiable. In broader strokes, his views set the stage for much of psychological thinking today, such as the unconscious nature of the majority of psychological processes.

In contrast, the James-Lange theory does generate falsifiable hypotheses, such as the one described above. Some individuals who suffer significant injuries to their spinal columns are unable to feel the bodily changes that often accompany emotional experiences. Therefore, we could test the hypothesis by determining how emotional experiences differ between individuals who have the ability to detect these changes in their physiological arousal and those who do not. In fact, this research has been conducted and while the emotional experiences of people deprived of an awareness of their physiological arousal may be less intense, they still experience emotion (Chwalisz, Diener, & Gallagher, 1988).

Scientific research’s dependence on falsifiability allows for great confidence in the information that it produces. Typically, by the time information is accepted by the scientific community, it has been tested repeatedly.

Visit this website to apply the scientific method and practice its steps by using them to solve a murder mystery, determine why a student is in trouble, and design an experiment to test house paint.

Scientists are engaged in explaining and understanding how the world around them works, and they are able to do so by coming up with theories that generate hypotheses that are testable and falsifiable. Theories that stand up to their tests are retained and refined, while those that do not are discarded or modified. In this way, research enables scientists to separate fact from simple opinion. Having good information generated from research aids in making wise decisions both in public policy and in our personal lives.

Self Check Questions

Critical thinking questions.

1. In this section, the D.A.R.E. program was described as an incredibly popular program in schools across the United States despite the fact that research consistently suggests that this program is largely ineffective. How might one explain this discrepancy?

2. The scientific method is often described as self-correcting and cyclical. Briefly describe your understanding of the scientific method with regard to these concepts.

Personal Application Questions

3. Healthcare professionals cite an enormous number of health problems related to obesity, and many people have an understandable desire to attain a healthy weight. There are many diet programs, services, and products on the market to aid those who wish to lose weight. If a close friend was considering purchasing or participating in one of these products, programs, or services, how would you make sure your friend was fully aware of the potential consequences of this decision? What sort of information would you want to review before making such an investment or lifestyle change yourself?

1. There is probably tremendous political pressure to appear to be hard on drugs. Therefore, even though D.A.R.E. might be ineffective, it is a well-known program with which voters are familiar.

2. This cyclical, self-correcting process is primarily a function of the empirical nature of science. Theories are generated as explanations of real-world phenomena. From theories, specific hypotheses are developed and tested. As a function of this testing, theories will be revisited and modified or refined to generate new hypotheses that are again tested. This cyclical process ultimately allows for more and more precise (and presumably accurate) information to be collected.

• Psychology. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:1/Psychology . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/content/col11629/latest/.

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What is importance of hypothesis in research?

Table of Contents

Importance of Hypothesis: It helps to provide link to the underlying theory and specific research question. It helps in data analysis and measure the validity and reliability of the research. It provides a basis or evidence to prove the validity of the research.

What is a testable hypothesis?

For a hypothesis to be testable means that it is possible to make observations that agree or disagree with it. If a hypothesis cannot be tested by making observations, it is not scientific.

What is the difference between a hypothesis and a theory Brainly?

Answer: A theory is an explanation that why something occurs while the hypothesis is a prediction or guess about what will happen.

How do you write a testable hypothesis?

How to Propose a Testable Hypothesis

• Try to write the hypothesis as an if-then statement.
• Identify the independent and dependent variable in the hypothesis.
• Write the hypothesis in such a way that you can prove or disprove it.
• Make sure you are proposing a hypothesis you can test with reproducible results.

What is an example of a testable question?

How does the weight of a toy car affect the distance the car rolls down a ramp? How does the size of the wheels affect the distance a toy car rolls down a ramp? How does the height of a ramp affect the distance a toy car rolls? How does adding weights affect the distance a toy car travels?

What are the 3 parts of a hypothesis?

A hypothesis is a prediction you create prior to running an experiment. The common format is: If [cause], then [effect], because [rationale]. In the world of experience optimization, strong hypotheses consist of three distinct parts: a definition of the problem, a proposed solution, and a result.

How does a theory differ from a hypothesis quizlet?

A hypothesis is a proposed explanation for a phenomenon. A theory is a hypothesis for natural phenomena that is exceptionally well-supported by the data.

What makes a theory different from a hypothesis?

Hypothesis: What’s the Difference? A hypothesis proposes a tentative explanation or prediction. A scientist bases their hypothesis on a specific observed event, making an educated guess as to how or why that event occurs. A theory, on the other hand, is a substantiated explanation for an occurrence.

What is hypothesis conclusion?

Explanation: And the mark of a good hypothesis is its testability . And a conclusion is drawn AFTER the experiment is performed, and reports whether or not the results of the experiment supported the original hypothesis…

How do you write a hypothesis conclusion?

Restate your hypothesis and then state clearly and concisely whether or not your hypothesis has been supported by the experiment. Was the experiment a success? Use simple language such as, “The results supported the hypothesis,” or “The results did not support the hypothesis.”