the research question and hypothesis

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Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

Research Questions

Clarify the research’s aim (farrugia et al., 2010).

• Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
• Descriptive: “What factors most influence the academic achievement of senior high school students?”
• Comparative: “What is the performance difference between teaching methods A and B?”
• Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
• Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
• Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
• The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
• It’s advisable to focus on a single primary research question for the study.
• The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
• The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.
• The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.
• Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
• The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
• A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
• A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
• An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

Checklist: Good research questions for social science projects (Panke, 2018)

Research Hypotheses

Present the researcher’s predictions based on specific statements.

• These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
• Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
• The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
• Hypotheses can express a single outcome or multiple outcomes.
• After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
• Hypothesis testing helps determine if observed findings are due to true differences and not chance.
• Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
• 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
• A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

Types of Research Hypothesis

• In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
• Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
• Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
• In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
• Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
• Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
• Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
• Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
• Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
• Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
• Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
• Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
• Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
• Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
• Example : “Teaching method A will improve student performance more than method B.”
• Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
• Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
• Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

Tips for developing research questions and hypotheses for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives.  Canadian journal of surgery. Journal canadien de chirurgie ,  53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences.  Research Design & Method Selection , 1-368.

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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

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What is and How to Write a Good Hypothesis in Research?

• 4 minute read

Table of Contents

One of the most important aspects of conducting research is constructing a strong hypothesis. But what makes a hypothesis in research effective? In this article, we’ll look at the difference between a hypothesis and a research question, as well as the elements of a good hypothesis in research. We’ll also include some examples of effective hypotheses, and what pitfalls to avoid.

What is a Hypothesis in Research?

Simply put, a hypothesis is a research question that also includes the predicted or expected result of the research. Without a hypothesis, there can be no basis for a scientific or research experiment. As such, it is critical that you carefully construct your hypothesis by being deliberate and thorough, even before you set pen to paper. Unless your hypothesis is clearly and carefully constructed, any flaw can have an adverse, and even grave, effect on the quality of your experiment and its subsequent results.

Research Question vs Hypothesis

It’s easy to confuse research questions with hypotheses, and vice versa. While they’re both critical to the Scientific Method, they have very specific differences. Primarily, a research question, just like a hypothesis, is focused and concise. But a hypothesis includes a prediction based on the proposed research, and is designed to forecast the relationship of and between two (or more) variables. Research questions are open-ended, and invite debate and discussion, while hypotheses are closed, e.g. “The relationship between A and B will be C.”

A hypothesis is generally used if your research topic is fairly well established, and you are relatively certain about the relationship between the variables that will be presented in your research. Since a hypothesis is ideally suited for experimental studies, it will, by its very existence, affect the design of your experiment. The research question is typically used for new topics that have not yet been researched extensively. Here, the relationship between different variables is less known. There is no prediction made, but there may be variables explored. The research question can be casual in nature, simply trying to understand if a relationship even exists, descriptive or comparative.

How to Write Hypothesis in Research

Writing an effective hypothesis starts before you even begin to type. Like any task, preparation is key, so you start first by conducting research yourself, and reading all you can about the topic that you plan to research. From there, you’ll gain the knowledge you need to understand where your focus within the topic will lie.

Remember that a hypothesis is a prediction of the relationship that exists between two or more variables. Your job is to write a hypothesis, and design the research, to “prove” whether or not your prediction is correct. A common pitfall is to use judgments that are subjective and inappropriate for the construction of a hypothesis. It’s important to keep the focus and language of your hypothesis objective.

An effective hypothesis in research is clearly and concisely written, and any terms or definitions clarified and defined. Specific language must also be used to avoid any generalities or assumptions.

Use the following points as a checklist to evaluate the effectiveness of your research hypothesis:

• Predicts the relationship and outcome
• Simple and concise – avoid wordiness
• Clear with no ambiguity or assumptions about the readers’ knowledge
• Observable and testable results
• Relevant and specific to the research question or problem

Research Hypothesis Example

Perhaps the best way to evaluate whether or not your hypothesis is effective is to compare it to those of your colleagues in the field. There is no need to reinvent the wheel when it comes to writing a powerful research hypothesis. As you’re reading and preparing your hypothesis, you’ll also read other hypotheses. These can help guide you on what works, and what doesn’t, when it comes to writing a strong research hypothesis.

Here are a few generic examples to get you started.

Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits.

Budget airlines are more likely to receive more customer complaints. A budget airline is defined as an airline that offers lower fares and fewer amenities than a traditional full-service airline. (Note that the term “budget airline” is included in the hypothesis.

Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours.

Each of the above examples are specific, observable and measurable, and the statement of prediction can be verified or shown to be false by utilizing standard experimental practices. It should be noted, however, that often your hypothesis will change as your research progresses.

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Research Questions vs Hypothesis: Understanding the Difference Between Them

by  Antony W

August 20, 2021

You’ll need to come up with a research question or a hypothesis to guide your next research project. But what is a hypothesis in the first place? What is the perfect definition for a research question? And, what’s the difference between the two?

In this guide to research questions vs hypothesis, we’ll look at the definition of each component and the difference between the two.

We’ll also look at when a research question and a hypothesis may be useful and provide you with some tips that you can use to come up with hypothesis and research questions that will suit your research topic . 

Let’s get to it.

What’s a Research Question?

We define a research question as the exact question you want to answer on a given topic or research project. Good research questions should be clear and easy to understand, allow for the collection of necessary data, and be specific and relevant to your field of study.

Research questions are part of heuristic research methods, where researchers use personal experiences and observations to understand a research subject. By using such approaches to explore the question, you should be able to provide an analytical justification of why and how you should respond to the question. 

While it’s common for researchers to focus on one question at a time, more complex topics may require two or more questions to cover in-depth.

When is a Research Question Useful? 

A research question may be useful when and if: 

• There isn’t enough previous research on the topic
• You want to report a wider range out of outcome when doing your research project
• You want to conduct a more open ended inquiries 

Perhaps the biggest drawback with research questions is that they tend to researchers in a position to “fish expectations” or excessively manipulate their findings.

Again, research questions sometimes tend to be less specific, and the reason is that there often no sufficient previous research on the questions.

What’s a Hypothesis? 

A hypothesis is a statement you can approve or disapprove. You develop a hypothesis from a research question by changing the question into a statement.

Primarily applied in deductive research, it involves the use of scientific, mathematical, and sociological findings to agree to or write off an assumption.

Researchers use the null approach for statements they can disapprove. They take a hypothesis and add a “not” to it to make it a working null hypothesis.

A null hypothesis is quite common in scientific methods. In this case, you have to formulate a hypothesis, and then conduct an investigation to disapprove the statement.

If you can disapprove the statement, you develop another hypothesis and then repeat the process until you can’t disapprove the statement.

In other words, if a hypothesis is true, then it must have been repeatedly tested and verified.

The consensus among researchers is that, like research questions, a hypothesis should not only be clear and easy to understand but also have a definite focus, answerable, and relevant to your field of study. 

When is a Hypothesis Useful?

A hypothesis may be useful when or if:

• There’s enough previous research on the topic
• You want to test a specific model or a particular theory
• You anticipate a likely outcome in advance 

The drawback to hypothesis as a scientific method is that it can hinder flexibility, or possibly blind a researcher not to see unanticipated results.

Research Question vs Hypothesis: Which One Should Come First 

Researchers use scientific methods to hone on different theories. So if the purpose of the research project were to analyze a concept, a scientific method would be necessary.

Such a case requires coming up with a research question first, followed by a scientific method.

Since a hypothesis is part of a research method, it will come after the research question.

Research Question vs Hypothesis: What’s the Difference? 

The following are the differences between a research question and a hypothesis.

We look at the differences in purpose and structure, writing, as well as conclusion. 

Research Questions vs Hypothesis: Some Useful Advice 

As much as there are differences between hypothesis and research questions, you have to state either one in the introduction and then repeat the same in the conclusion of your research paper.

Whichever element you opt to use, you should clearly demonstrate that you understand your topic, have achieved the goal of your research project, and not swayed a bit in your research process.

If it helps, start and conclude every chapter of your research project by providing additional information on how you’ve or will address the hypothesis or research question.

You should also include the aims and objectives of coming up with the research question or formulating the hypothesis. Doing so will go a long way to demonstrate that you have a strong focus on the research issue at hand. 

Research Questions vs Hypothesis: Conclusion 

If you need help with coming up with research questions, formulating a hypothesis, and completing your research paper writing , feel free to talk to us. 

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

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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.

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How to Write a Good Research Question (w/ Examples)

What is a Research Question?

A research question is the main question that your study sought or is seeking to answer. A clear research question guides your research paper or thesis and states exactly what you want to find out, giving your work a focus and objective. Learning  how to write a hypothesis or research question is the start to composing any thesis, dissertation, or research paper. It is also one of the most important sections of a research proposal . 

A good research question not only clarifies the writing in your study; it provides your readers with a clear focus and facilitates their understanding of your research topic, as well as outlining your study’s objectives. Before drafting the paper and receiving research paper editing (and usually before performing your study), you should write a concise statement of what this study intends to accomplish or reveal.

Research Question Writing Tips

Listed below are the important characteristics of a good research question:

A good research question should:

• Be clear and provide specific information so readers can easily understand the purpose.
• Be focused in its scope and narrow enough to be addressed in the space allowed by your paper
• Be relevant and concise and express your main ideas in as few words as possible, like a hypothesis.
• Be precise and complex enough that it does not simply answer a closed “yes or no” question, but requires an analysis of arguments and literature prior to its being considered acceptable. 
• Be arguable or testable so that answers to the research question are open to scrutiny and specific questions and counterarguments.

Some of these characteristics might be difficult to understand in the form of a list. Let’s go into more detail about what a research question must do and look at some examples of research questions.

The research question should be specific and focused 

Research questions that are too broad are not suitable to be addressed in a single study. One reason for this can be if there are many factors or variables to consider. In addition, a sample data set that is too large or an experimental timeline that is too long may suggest that the research question is not focused enough.

A specific research question means that the collective data and observations come together to either confirm or deny the chosen hypothesis in a clear manner. If a research question is too vague, then the data might end up creating an alternate research problem or hypothesis that you haven’t addressed in your Introduction section .

The research question should be based on the literature 

An effective research question should be answerable and verifiable based on prior research because an effective scientific study must be placed in the context of a wider academic consensus. This means that conspiracy or fringe theories are not good research paper topics.

Instead, a good research question must extend, examine, and verify the context of your research field. It should fit naturally within the literature and be searchable by other research authors.

References to the literature can be in different citation styles and must be properly formatted according to the guidelines set forth by the publishing journal, university, or academic institution. This includes in-text citations as well as the Reference section . 

The research question should be realistic in time, scope, and budget

There are two main constraints to the research process: timeframe and budget.

A proper research question will include study or experimental procedures that can be executed within a feasible time frame, typically by a graduate doctoral or master’s student or lab technician. Research that requires future technology, expensive resources, or follow-up procedures is problematic.

A researcher’s budget is also a major constraint to performing timely research. Research at many large universities or institutions is publicly funded and is thus accountable to funding restrictions. 

The research question should be in-depth

Research papers, dissertations and theses , and academic journal articles are usually dozens if not hundreds of pages in length.

A good research question or thesis statement must be sufficiently complex to warrant such a length, as it must stand up to the scrutiny of peer review and be reproducible by other scientists and researchers.

Research Question Types

Qualitative and quantitative research are the two major types of research, and it is essential to develop research questions for each type of study. 

Quantitative Research Questions

Quantitative research questions are specific. A typical research question involves the population to be studied, dependent and independent variables, and the research design.

In addition, quantitative research questions connect the research question and the research design. In addition, it is not possible to answer these questions definitively with a “yes” or “no” response. For example, scientific fields such as biology, physics, and chemistry often deal with “states,” in which different quantities, amounts, or velocities drastically alter the relevance of the research.

As a consequence, quantitative research questions do not contain qualitative, categorical, or ordinal qualifiers such as “is,” “are,” “does,” or “does not.”

Categories of quantitative research questions

Qualitative research questions.

In quantitative research, research questions have the potential to relate to broad research areas as well as more specific areas of study. Qualitative research questions are less directional, more flexible, and adaptable compared with their quantitative counterparts. Thus, studies based on these questions tend to focus on “discovering,” “explaining,” “elucidating,” and “exploring.”

Categories of qualitative research questions

Quantitative and qualitative research question examples.

Good and Bad Research Question Examples

Below are some good (and not-so-good) examples of research questions that researchers can use to guide them in crafting their own research questions.

Research Question Example 1

The first research question is too vague in both its independent and dependent variables. There is no specific information on what “exposure” means. Does this refer to comments, likes, engagement, or just how much time is spent on the social media platform?

Second, there is no useful information on what exactly “affected” means. Does the subject’s behavior change in some measurable way? Or does this term refer to another factor such as the user’s emotions?

Research Question Example 2

In this research question, the first example is too simple and not sufficiently complex, making it difficult to assess whether the study answered the question. The author could really only answer this question with a simple “yes” or “no.” Further, the presence of data would not help answer this question more deeply, which is a sure sign of a poorly constructed research topic.

The second research question is specific, complex, and empirically verifiable. One can measure program effectiveness based on metrics such as attendance or grades. Further, “bullying” is made into an empirical, quantitative measurement in the form of recorded disciplinary actions.

Steps for Writing a Research Question

Good research questions are relevant, focused, and meaningful. It can be difficult to come up with a good research question, but there are a few steps you can follow to make it a bit easier.

1. Start with an interesting and relevant topic

Choose a research topic that is interesting but also relevant and aligned with your own country’s culture or your university’s capabilities. Popular academic topics include healthcare and medical-related research. However, if you are attending an engineering school or humanities program, you should obviously choose a research question that pertains to your specific study and major.

Below is an embedded graph of the most popular research fields of study based on publication output according to region. As you can see, healthcare and the basic sciences receive the most funding and earn the highest number of publications. 

2. Do preliminary research  

You can begin doing preliminary research once you have chosen a research topic. Two objectives should be accomplished during this first phase of research. First, you should undertake a preliminary review of related literature to discover issues that scholars and peers are currently discussing. With this method, you show that you are informed about the latest developments in the field.

Secondly, identify knowledge gaps or limitations in your topic by conducting a preliminary literature review . It is possible to later use these gaps to focus your research question after a certain amount of fine-tuning.

3. Narrow your research to determine specific research questions

You can focus on a more specific area of study once you have a good handle on the topic you want to explore. Focusing on recent literature or knowledge gaps is one good option. 

By identifying study limitations in the literature and overlooked areas of study, an author can carve out a good research question. The same is true for choosing research questions that extend or complement existing literature.

4. Evaluate your research question

Make sure you evaluate the research question by asking the following questions:

Is my research question clear?

The resulting data and observations that your study produces should be clear. For quantitative studies, data must be empirical and measurable. For qualitative, the observations should be clearly delineable across categories.

Is my research question focused and specific?

A strong research question should be specific enough that your methodology or testing procedure produces an objective result, not one left to subjective interpretation. Open-ended research questions or those relating to general topics can create ambiguous connections between the results and the aims of the study. 

Is my research question sufficiently complex?

The result of your research should be consequential and substantial (and fall sufficiently within the context of your field) to warrant an academic study. Simply reinforcing or supporting a scientific consensus is superfluous and will likely not be well received by most journal editors.  

Editing Your Research Question

Your research question should be fully formulated well before you begin drafting your research paper. However, you can receive English paper editing and proofreading services at any point in the drafting process. Language editors with expertise in your academic field can assist you with the content and language in your Introduction section or other manuscript sections. And if you need further assistance or information regarding paper compositions, in the meantime, check out our academic resources , which provide dozens of articles and videos on a variety of academic writing and publication topics.

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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Formulation of Research Question – Stepwise Approach

Simmi k. ratan.

Department of Pediatric Surgery, Maulana Azad Medical College, New Delhi, India

1 Department of Community Medicine, North Delhi Municipal Corporation Medical College, New Delhi, India

2 Department of Pediatric Surgery, Batra Hospital and Research Centre, New Delhi, India

Formulation of research question (RQ) is an essentiality before starting any research. It aims to explore an existing uncertainty in an area of concern and points to a need for deliberate investigation. It is, therefore, pertinent to formulate a good RQ. The present paper aims to discuss the process of formulation of RQ with stepwise approach. The characteristics of good RQ are expressed by acronym “FINERMAPS” expanded as feasible, interesting, novel, ethical, relevant, manageable, appropriate, potential value, publishability, and systematic. A RQ can address different formats depending on the aspect to be evaluated. Based on this, there can be different types of RQ such as based on the existence of the phenomenon, description and classification, composition, relationship, comparative, and causality. To develop a RQ, one needs to begin by identifying the subject of interest and then do preliminary research on that subject. The researcher then defines what still needs to be known in that particular subject and assesses the implied questions. After narrowing the focus and scope of the research subject, researcher frames a RQ and then evaluates it. Thus, conception to formulation of RQ is very systematic process and has to be performed meticulously as research guided by such question can have wider impact in the field of social and health research by leading to formulation of policies for the benefit of larger population.

I NTRODUCTION

A good research question (RQ) forms backbone of a good research, which in turn is vital in unraveling mysteries of nature and giving insight into a problem.[ 1 , 2 , 3 , 4 ] RQ identifies the problem to be studied and guides to the methodology. It leads to building up of an appropriate hypothesis (Hs). Hence, RQ aims to explore an existing uncertainty in an area of concern and points to a need for deliberate investigation. A good RQ helps support a focused arguable thesis and construction of a logical argument. Hence, formulation of a good RQ is undoubtedly one of the first critical steps in the research process, especially in the field of social and health research, where the systematic generation of knowledge that can be used to promote, restore, maintain, and/or protect health of individuals and populations.[ 1 , 3 , 4 ] Basically, the research can be classified as action, applied, basic, clinical, empirical, administrative, theoretical, or qualitative or quantitative research, depending on its purpose.[ 2 ]

Research plays an important role in developing clinical practices and instituting new health policies. Hence, there is a need for a logical scientific approach as research has an important goal of generating new claims.[ 1 ]

C HARACTERISTICS OF G OOD R ESEARCH Q UESTION

“The most successful research topics are narrowly focused and carefully defined but are important parts of a broad-ranging, complex problem.”

A good RQ is an asset as it:

• Details the problem statement
• Further describes and refines the issue under study
• Adds focus to the problem statement
• Guides data collection and analysis
• Sets context of research.

Hence, while writing RQ, it is important to see if it is relevant to the existing time frame and conditions. For example, the impact of “odd-even” vehicle formula in decreasing the level of air particulate pollution in various districts of Delhi.

A good research is represented by acronym FINERMAPS[ 5 ]

Interesting.

• Appropriate
• Potential value and publishability
• Systematic.

Feasibility means that it is within the ability of the investigator to carry out. It should be backed by an appropriate number of subjects and methodology as well as time and funds to reach the conclusions. One needs to be realistic about the scope and scale of the project. One has to have access to the people, gadgets, documents, statistics, etc. One should be able to relate the concepts of the RQ to the observations, phenomena, indicators, or variables that one can access. One should be clear that the collection of data and the proceedings of project can be completed within the limited time and resources available to the investigator. Sometimes, a RQ appears feasible, but when fieldwork or study gets started, it proves otherwise. In this situation, it is important to write up the problems honestly and to reflect on what has been learned. One should try to discuss with more experienced colleagues or the supervisor so as to develop a contingency plan to anticipate possible problems while working on a RQ and find possible solutions in such situations.

This is essential that one has a real grounded interest in one's RQ and one can explore this and back it up with academic and intellectual debate. This interest will motivate one to keep going with RQ.

The question should not simply copy questions investigated by other workers but should have scope to be investigated. It may aim at confirming or refuting the already established findings, establish new facts, or find new aspects of the established facts. It should show imagination of the researcher. Above all, the question has to be simple and clear. The complexity of a question can frequently hide unclear thoughts and lead to a confused research process. A very elaborate RQ, or a question which is not differentiated into different parts, may hide concepts that are contradictory or not relevant. This needs to be clear and thought-through. Having one key question with several subcomponents will guide your research.

This is the foremost requirement of any RQ and is mandatory to get clearance from appropriate authorities before stating research on the question. Further, the RQ should be such that it minimizes the risk of harm to the participants in the research, protect the privacy and maintain their confidentiality, and provide the participants right to withdraw from research. It should also guide in avoiding deceptive practices in research.

The question should of academic and intellectual interest to people in the field you have chosen to study. The question preferably should arise from issues raised in the current situation, literature, or in practice. It should establish a clear purpose for the research in relation to the chosen field. For example, filling a gap in knowledge, analyzing academic assumptions or professional practice, monitoring a development in practice, comparing different approaches, or testing theories within a specific population are some of the relevant RQs.

Manageable (M): It has the similar essence as of feasibility but mainly means that the following research can be managed by the researcher.

Appropriate (A): RQ should be appropriate logically and scientifically for the community and institution.

Potential value and publishability (P): The study can make significant health impact in clinical and community practices. Therefore, research should aim for significant economic impact to reduce unnecessary or excessive costs. Furthermore, the proposed study should exist within a clinical, consumer, or policy-making context that is amenable to evidence-based change. Above all, a good RQ must address a topic that has clear implications for resolving important dilemmas in health and health-care decisions made by one or more stakeholder groups.

Systematic (S): Research is structured with specified steps to be taken in a specified sequence in accordance with the well-defined set of rules though it does not rule out creative thinking.

Example of RQ: Would the topical skin application of oil as a skin barrier reduces hypothermia in preterm infants? This question fulfills the criteria of a good RQ, that is, feasible, interesting, novel, ethical, and relevant.

Types of research question

A RQ can address different formats depending on the aspect to be evaluated.[ 6 ] For example:

• Existence: This is designed to uphold the existence of a particular phenomenon or to rule out rival explanation, for example, can neonates perceive pain?
• Description and classification: This type of question encompasses statement of uniqueness, for example, what are characteristics and types of neuropathic bladders?
• Composition: It calls for breakdown of whole into components, for example, what are stages of reflux nephropathy?
• Relationship: Evaluate relation between variables, for example, association between tumor rupture and recurrence rates in Wilm's tumor
• Descriptive—comparative: Expected that researcher will ensure that all is same between groups except issue in question, for example, Are germ cell tumors occurring in gonads more aggressive than those occurring in extragonadal sites?
• Causality: Does deletion of p53 leads to worse outcome in patients with neuroblastoma?
• Causality—comparative: Such questions frequently aim to see effect of two rival treatments, for example, does adding surgical resection improves survival rate outcome in children with neuroblastoma than with chemotherapy alone?
• Causality–Comparative interactions: Does immunotherapy leads to better survival outcome in neuroblastoma Stage IV S than with chemotherapy in the setting of adverse genetic profile than without it? (Does X cause more changes in Y than those caused by Z under certain condition and not under other conditions).

How to develop a research question

• Begin by identifying a broader subject of interest that lends itself to investigate, for example, hormone levels among hypospadias
• Do preliminary research on the general topic to find out what research has already been done and what literature already exists.[ 7 ] Therefore, one should begin with “information gaps” (What do you already know about the problem? For example, studies with results on testosterone levels among hypospadias
• What do you still need to know? (e.g., levels of other reproductive hormones among hypospadias)
• What are the implied questions: The need to know about a problem will lead to few implied questions. Each general question should lead to more specific questions (e.g., how hormone levels differ among isolated hypospadias with respect to that in normal population)
• Narrow the scope and focus of research (e.g., assessment of reproductive hormone levels among isolated hypospadias and hypospadias those with associated anomalies)
• Is RQ clear? With so much research available on any given topic, RQs must be as clear as possible in order to be effective in helping the writer direct his or her research
• Is the RQ focused? RQs must be specific enough to be well covered in the space available
• Is the RQ complex? RQs should not be answerable with a simple “yes” or “no” or by easily found facts. They should, instead, require both research and analysis on the part of the writer
• Is the RQ one that is of interest to the researcher and potentially useful to others? Is it a new issue or problem that needs to be solved or is it attempting to shed light on previously researched topic
• Is the RQ researchable? Consider the available time frame and the required resources. Is the methodology to conduct the research feasible?
• Is the RQ measurable and will the process produce data that can be supported or contradicted?
• Is the RQ too broad or too narrow?
• Create Hs: After formulating RQ, think where research is likely to be progressing? What kind of argument is likely to be made/supported? What would it mean if the research disputed the planned argument? At this step, one can well be on the way to have a focus for the research and construction of a thesis. Hs consists of more specific predictions about the nature and direction of the relationship between two variables. It is a predictive statement about the outcome of the research, dictate the method, and design of the research[ 1 ]
• Understand implications of your research: This is important for application: whether one achieves to fill gap in knowledge and how the results of the research have practical implications, for example, to develop health policies or improve educational policies.[ 1 , 8 ]

Brainstorm/Concept map for formulating research question

• First, identify what types of studies have been done in the past?
• Is there a unique area that is yet to be investigated or is there a particular question that may be worth replicating?
• Begin to narrow the topic by asking open-ended “how” and “why” questions
• Evaluate the question
• Develop a Hypothesis (Hs)
• Write down the RQ.

Writing down the research question

• State the question in your own words
• Write down the RQ as completely as possible.

For example, Evaluation of reproductive hormonal profile in children presenting with isolated hypospadias)

• Divide your question into concepts. Narrow to two or three concepts (reproductive hormonal profile, isolated hypospadias, compare with normal/not isolated hypospadias–implied)
• Specify the population to be studied (children with isolated hypospadias)
• Refer to the exposure or intervention to be investigated, if any
• Reflect the outcome of interest (hormonal profile).

Another example of a research question

Would the topical skin application of oil as a skin barrier reduces hypothermia in preterm infants? Apart from fulfilling the criteria of a good RQ, that is, feasible, interesting, novel, ethical, and relevant, it also details about the intervention done (topical skin application of oil), rationale of intervention (as a skin barrier), population to be studied (preterm infants), and outcome (reduces hypothermia).

Other important points to be heeded to while framing research question

• Make reference to a population when a relationship is expected among a certain type of subjects
• RQs and Hs should be made as specific as possible
• Avoid words or terms that do not add to the meaning of RQs and Hs
• Stick to what will be studied, not implications
• Name the variables in the order in which they occur/will be measured
• Avoid the words significant/”prove”
• Avoid using two different terms to refer to the same variable.

Some of the other problems and their possible solutions have been discussed in Table 1 .

Potential problems and solutions while making research question

G OING B EYOND F ORMULATION OF R ESEARCH Q UESTION–THE P ATH A HEAD

Once RQ is formulated, a Hs can be developed. Hs means transformation of a RQ into an operational analog.[ 1 ] It means a statement as to what prediction one makes about the phenomenon to be examined.[ 4 ] More often, for case–control trial, null Hs is generated which is later accepted or refuted.

A strong Hs should have following characteristics:

• Give insight into a RQ
• Are testable and measurable by the proposed experiments
• Have logical basis
• Follows the most likely outcome, not the exceptional outcome.

E XAMPLES OF R ESEARCH Q UESTION AND H YPOTHESIS

Research question-1.

• Does reduced gap between the two segments of the esophagus in patients of esophageal atresia reduces the mortality and morbidity of such patients?

Hypothesis-1

• Reduced gap between the two segments of the esophagus in patients of esophageal atresia reduces the mortality and morbidity of such patients
• In pediatric patients with esophageal atresia, gap of <2 cm between two segments of the esophagus and proper mobilization of proximal pouch reduces the morbidity and mortality among such patients.

Research question-2

• Does application of mitomycin C improves the outcome in patient of corrosive esophageal strictures?

Hypothesis-2

In patients aged 2–9 years with corrosive esophageal strictures, 34 applications of mitomycin C in dosage of 0.4 mg/ml for 5 min over a period of 6 months improve the outcome in terms of symptomatic and radiological relief. Some other examples of good and bad RQs have been shown in Table 2 .

Examples of few bad (left-hand side column) and few good (right-hand side) research questions

R ESEARCH Q UESTION AND S TUDY D ESIGN

RQ determines study design, for example, the question aimed to find the incidence of a disease in population will lead to conducting a survey; to find risk factors for a disease will need case–control study or a cohort study. RQ may also culminate into clinical trial.[ 9 , 10 ] For example, effect of administration of folic acid tablet in the perinatal period in decreasing incidence of neural tube defect. Accordingly, Hs is framed.

Appropriate statistical calculations are instituted to generate sample size. The subject inclusion, exclusion criteria and time frame of research are carefully defined. The detailed subject information sheet and pro forma are carefully defined. Moreover, research is set off few examples of research methodology guided by RQ:

• Incidence of anorectal malformations among adolescent females (hospital-based survey)
• Risk factors for the development of spontaneous pneumoperitoneum in pediatric patients (case–control design and cohort study)
• Effect of technique of extramucosal ureteric reimplantation without the creation of submucosal tunnel for the preservation of upper tract in bladder exstrophy (clinical trial).

The results of the research are then be available for wider applications for health and social life

C ONCLUSION

A good RQ needs thorough literature search and deep insight into the specific area/problem to be investigated. A RQ has to be focused yet simple. Research guided by such question can have wider impact in the field of social and health research by leading to formulation of policies for the benefit of larger population.

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Conflicts of interest.

There are no conflicts of interest.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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Home » Education » Difference Between Hypothesis and Research Question

Difference Between Hypothesis and Research Question

Main difference – hypothesis vs research question.

Research question and hypothesis are the foundations of a research study. Formulating the research question or developing the hypothesis can help you to decide on the approach of the research. A research question is the question the research study sets out to answer. Hypothesis is the statement the research study sets out to prove or disprove. The main difference between hypothesis and research question is that hypothesis is predictive in nature whereas research question is inquisitive in nature.

In this article, we’ll discuss,

1. What is a Hypothesis? – Meaning, Features, Characteristics, and Usage

2. What is a Research Question? – Meaning, Features, Characteristics, and Usage

What is a Hypothesis

A hypothesis is a prediction about the relationship between two or more variables. It can be described as an educated guess about what happens in an experiment. Researchers usually tend to use hypotheses when significant knowledge is already available on the subject. The hypothesis is based on this existing knowledge. After the hypothesis is developed, the researcher can develop data, analyze and use them to support or negate the hypothesis.

Not all studies have hypotheses. They are usually used in experimental quantitative research studies. They are useful in testing a specific theory or model.  A complete hypothesis always includes the variables, population and the predicted relationship between the variables. The main disadvantage of hypotheses is that their tendency to blind a researcher to unexpected results. 

What is a Research Question

A research question is the question a research study sets to answer. However, a research study can have more than one research question. The research methodologies , tools used to collect data, etc. all depend on the research question.

Research questions are often used in qualitative research, which seek to answer open-ended questions . But they can also be used in quantitative studies. Research questions can be used instead of hypotheses when there is little previous research on the subject. Research questions allow the researcher to conduct more open-ended queries, and a wide range of results can be reported.

A properly constructed research question should always be clear and concise. It should include the variables, population and the topic being studied.

Hypothesis is a tentative prediction about the relationship between two or more variables.

Research Question is the question a research study sets to answer.

Hypothesis is predictive in nature.

Research Question is inquisitive in nature.

Existing Research

Hypothesis can be used if there is significant knowledge or previous research on this subject.

Research Question can be used if there is little previous research on the subject.

Quantitative vs Qualitative

Hypothesis is mainly used in experimental quantitative studies.

Research Question can be used in both quantitative and qualitative studies.

Hypothesis doesn’t allow a wide range of outcomes.

Research Question allows a wide range of outcomes.

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Physical Review Research

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Complexity of fermionic states

Tuomas i. vanhala and teemu ojanen, phys. rev. research 6 , 023178 – published 16 may 2024.

• No Citing Articles
• INTRODUCTION
• FERMIONIC COMPLEXITY
• CONCLUSION AND OUTLOOK
• ACKNOWLEDGMENTS

How much information does a fermionic state contain? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock representations. The complexity characterizes the minimum computational and physical resources required to represent the state and store the information obtained from it by measurements. Alternatively, the complexity can be regarded as a Fock space entanglement measure describing the intrinsic many-particle entanglement in the state. We establish a universal lower bound for the complexity in terms of the single-particle correlation matrix eigenvalues and formulate a finite-size complexity scaling hypothesis. Remarkably, numerical studies on interacting lattice models suggest a general model-independent complexity hierarchy: ground states are exponentially less complex than average excited states, which, in turn, are exponentially less complex than generic states in the Fock space. Our work has fundamental implications on how much information is encoded in fermionic states.

• Received 29 June 2023
• Accepted 30 April 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.023178

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

• Research Areas
• Physical Systems

Authors & Affiliations

• Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University , P.O. Box 692, FI-33014 Tampere, Finland and Helsinki Institute of Physics , P.O. Box 64, FI-00014, Finland
• * [email protected]

Article Text

Vol. 6, Iss. 2 — May - July 2024

Subject Areas

• Quantum Physics

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Complexity hierarchy of fermionic states as a function of particles N p and the correlation entropy S c at fixed filling fraction. Ground states and excited states refer to eigenstates of interacting lattice Hamiltonians at strong coupling exceeding the bandwidth and 1 ≤ α g ≤ 2 , depending on the filling.

Complexity of ground states. (a) Ground-state complexity of a half-filled Hubbard chain as a function of interaction. The system length is L = 8 sites ( N o = 16 orbitals). The numerically optimized complexity (black dots) is well approximated from below by the ground-state scaling form S P = 1 2 N p S c (green dashed line). The solid lines correspond to complexities calculated in the momentum and position orbitals. Complexity at weak coupling does not approach zero due to ground-state degeneracy in the noninteracting model. (b) Complexity scaling of the half-filled Hubbard chain as a function of the particle number N p . The complexity S P is approximated by S min = min ( S pos , S mom ) , as we cannot perform the full optimization for large systems. (c) Tentative extrapolation of the coefficient α = S P / ( N p S c ) to infinite system size. The dashed lines are a quadratic fit. At strong coupling the value approaches α ≈ 1 / 2 . [(d–f)] The same quantities for the t − V model but at ν = 1 / 3 filling. Here, we also explicitly include the complexity S nat in natural orbitals, which always gives the approximated minimal complexity S min . Again, the ground-state complexity follows closely the scaling form S P = 1 2 N p S c .

Complexity of excited states in the Hubbard and the t − V model in the ground-state parity and momentum sector. (a) and (b) Comparison of numerically optimized results S opt with S min = min ( S nat , S mom , S pos ) , where S nat , S mom , and S pos are the natural orbital, momentum, and position basis complexities in a Hubbard chain of length L = 8 . (c and d) Distribution of the excited state complexity ratio S / ( N p S c ) for a larger system of L = 12 . (e) and (f) Mean complexity ratio in the ground-state sector of the Hubbard model for filling factors ν = 1 / 2 and ν = 1 / 3 . The colored areas around the mean (dashed line) have a width of one standard deviation. (g) Scaling of the mean complexity with the number of particles N p . For comparison, generic states have α g = 2 at ν = 1 / 2 and α g at ν = 1 / 3 is marked on the axis. [(h–j)] The same as (e) and (f) but for the t , V model instead of the Hubbard model.

Cumulative probability distribution for the ground state of the Hubbard model at U = 10 , as a function of the scaled logarithm of the state index log ( n ) / L . The state probabilities P n have been ordered from the largest to smallest. The vertical lines mark the scaled entropy S P / L and log [ σ ( n ) ] / L , where σ ( n ) is the standard deviation of n . The inset shows a tentative extrapolation of S P / L and log [ σ ( n ) ] / L to infinite system size.

Complexity of generic, Haar-distributed states in different single-particle bases computed as a mean of five samples with the vertical bars giving the sample standard deviation, except at N p = 6 , where we have only computed one realization. A Q -dimensional generic state has logarithmic complexity S C U E = − log ( 2 / Q ) in the limit of large Q . The complexity can be reduced by applying single-particle rotations as demonstrated here by transforming to the natural orbital basis or a numerically optimized basis. However, to conserve information, we expect that the typical reduction in the characteristic number of terms C = exp ( − S ) in the optimal Fock representation of a state with no special structure scales with the number of parameters in the single-particle basis, i.e., polynomially in N p , while C grows exponentially for a fixed filling fraction. S C U E , nat and S C U E , opt are thus expected to approach S C U E for large N p , while the correlation entropy approaches its maximal value − log ( ν ) .

Fractal dimension D 2 , B of the states in the ground-state symmetry block of the 1 / 3 -filled t − V model at different interaction strengths. The left and middle columns show the fractal dimension in the L = 24 model in position and momentum bases. The right column shows the scaling of the maximal fractal dimension (i.e., the highest point in the left and middle panels) as a function of system size. S B is the Renyi-2 entropy of the Slater configuration distribution in the indicated basis and Q is the number of states in the Fock space.

The ratio S min / S c for a range of filling factors ν in a Hubbard model of size L = 12 and t − V models of size L = 20 , 21 . S min is again the minimal S P B chosen from the natural orbital, momentum, and position bases. In some cases the ground state is degenerate, but the degeneracy can be resolved by the total momentum and reflection parity quantum numbers. We find that the complexity for the degenerate ground states is the same in all symmetry sectors. The basis giving the lowest complexity is typically the natural orbital basis in the t − V model or the momentum basis in the Hubbard model, where the natural occupations may become degenerate. The exception is at half-filling (dashed lines) with strong interactions, where the position basis leads to lower complexity (marked with dots), and in the case of the t − V model to an apparent departure from the typical ground-state scaling α ≳ 1 / 2 . This is discussed in Appendix  pp6 .

Fitting Eq. ( G2 ) to ground-state data from the Hubbard model. The numerical results were computed at half-filling for system size L = 10 in momentum orbitals. The dots show the total weight of Slater configurations with a given Hamming distance from the Fermi sea, while the lines represent the model distribution. Note that the weight at Hamming distances not divisible by four is zero in the model of Eq. ( G2 ), because all excitations from the Fermi sea are assumed to be pair excitations. This agrees with the numerical data quite well.

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