hypothesis of research methodology

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.

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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.

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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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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 Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

Prevent plagiarism, run a free check.

Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

Cite this Scribbr article

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

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 30 May 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

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How to Write a Research Hypothesis

• Research Process
• Peer Review

Since grade school, we've all been familiar with hypotheses. The hypothesis is an essential step of the scientific method. But what makes an effective research hypothesis, how do you create one, and what types of hypotheses are there? We answer these questions and more.

Updated on April 27, 2022

What is a research hypothesis?

General hypothesis.

Since grade school, we've all been familiar with the term “hypothesis.” A hypothesis is a fact-based guess or prediction that has not been proven. It is an essential step of the scientific method. The hypothesis of a study is a drive for experimentation to either prove the hypothesis or dispute it.

Research Hypothesis

A research hypothesis is more specific than a general hypothesis. It is an educated, expected prediction of the outcome of a study that is testable.

What makes an effective research hypothesis?

A good research hypothesis is a clear statement of the relationship between a dependent variable(s) and independent variable(s) relevant to the study that can be disproven.

Research hypothesis checklist

Once you've written a possible hypothesis, make sure it checks the following boxes:

• It must be testable: You need a means to prove your hypothesis. If you can't test it, it's not a hypothesis.
• It must include a dependent and independent variable: At least one independent variable ( cause ) and one dependent variable ( effect ) must be included.
• The language must be easy to understand: Be as clear and concise as possible. Nothing should be left to interpretation.
• It must be relevant to your research topic: You probably shouldn't be talking about cats and dogs if your research topic is outer space. Stay relevant to your topic.

How to create an effective research hypothesis

Pose it as a question first.

Start your research hypothesis from a journalistic approach. Ask one of the five W's: Who, what, when, where, or why.

A possible initial question could be: Why is the sky blue?

Do the preliminary research

Once you have a question in mind, read research around your topic. Collect research from academic journals.

If you're looking for information about the sky and why it is blue, research information about the atmosphere, weather, space, the sun, etc.

Write a draft hypothesis

Once you're comfortable with your subject and have preliminary knowledge, create a working hypothesis. Don't stress much over this. Your first hypothesis is not permanent. Look at it as a draft.

Your first draft of a hypothesis could be: Certain molecules in the Earth's atmosphere are responsive to the sky being the color blue.

Make your working draft perfect

Take your working hypothesis and make it perfect. Narrow it down to include only the information listed in the “Research hypothesis checklist” above.

Now that you've written your working hypothesis, narrow it down. Your new hypothesis could be: Light from the sun hitting oxygen molecules in the sky makes the color of the sky appear blue.

Write a null hypothesis

Your null hypothesis should be the opposite of your research hypothesis. It should be able to be disproven by your research.

In this example, your null hypothesis would be: Light from the sun hitting oxygen molecules in the sky does not make the color of the sky appear blue.

Why is it important to have a clear, testable hypothesis?

One of the main reasons a manuscript can be rejected from a journal is because of a weak hypothesis. “Poor hypothesis, study design, methodology, and improper use of statistics are other reasons for rejection of a manuscript,” says Dr. Ish Kumar Dhammi and Dr. Rehan-Ul-Haq in Indian Journal of Orthopaedics.

According to Dr. James M. Provenzale in American Journal of Roentgenology , “The clear declaration of a research question (or hypothesis) in the Introduction is critical for reviewers to understand the intent of the research study. It is best to clearly state the study goal in plain language (for example, “We set out to determine whether condition x produces condition y.”) An insufficient problem statement is one of the more common reasons for manuscript rejection.”

Characteristics that make a hypothesis weak include:

• Unclear variables
• Unoriginality
• Too general
• Too specific

A weak hypothesis leads to weak research and methods . The goal of a paper is to prove or disprove a hypothesis - or to prove or disprove a null hypothesis. If the hypothesis is not a dependent variable of what is being studied, the paper's methods should come into question.

A strong hypothesis is essential to the scientific method. A hypothesis states an assumed relationship between at least two variables and the experiment then proves or disproves that relationship with statistical significance. Without a proven and reproducible relationship, the paper feeds into the reproducibility crisis. Learn more about writing for reproducibility .

In a study published in The Journal of Obstetrics and Gynecology of India by Dr. Suvarna Satish Khadilkar, she reviewed 400 rejected manuscripts to see why they were rejected. Her studies revealed that poor methodology was a top reason for the submission having a final disposition of rejection.

Aside from publication chances, Dr. Gareth Dyke believes a clear hypothesis helps efficiency.

“Developing a clear and testable hypothesis for your research project means that you will not waste time, energy, and money with your work,” said Dyke. “Refining a hypothesis that is both meaningful, interesting, attainable, and testable is the goal of all effective research.”

Types of research hypotheses

There can be overlap in these types of hypotheses.

Simple hypothesis

A simple hypothesis is a hypothesis at its most basic form. It shows the relationship of one independent and one independent variable.

Example: Drinking soda (independent variable) every day leads to obesity (dependent variable).

Complex hypothesis

A complex hypothesis shows the relationship of two or more independent and dependent variables.

Example: Drinking soda (independent variable) every day leads to obesity (dependent variable) and heart disease (dependent variable).

Directional hypothesis

A directional hypothesis guesses which way the results of an experiment will go. It uses words like increase, decrease, higher, lower, positive, negative, more, or less. It is also frequently used in statistics.

Example: Humans exposed to radiation have a higher risk of cancer than humans not exposed to radiation.

Non-directional hypothesis

A non-directional hypothesis says there will be an effect on the dependent variable, but it does not say which direction.

Associative hypothesis

An associative hypothesis says that when one variable changes, so does the other variable.

Alternative hypothesis

An alternative hypothesis states that the variables have a relationship.

• The opposite of a null hypothesis

Example: An apple a day keeps the doctor away.

Null hypothesis

A null hypothesis states that there is no relationship between the two variables. It is posed as the opposite of what the alternative hypothesis states.

Researchers use a null hypothesis to work to be able to reject it. A null hypothesis:

• Can never be proven
• Can only be rejected
• Is the opposite of an alternative hypothesis

Example: An apple a day does not keep the doctor away.

Logical hypothesis

A logical hypothesis is a suggested explanation while using limited evidence.

Example: Bats can navigate in the dark better than tigers.

In this hypothesis, the researcher knows that tigers cannot see in the dark, and bats mostly live in darkness.

Empirical hypothesis

An empirical hypothesis is also called a “working hypothesis.” It uses the trial and error method and changes around the independent variables.

• An apple a day keeps the doctor away.
• Two apples a day keep the doctor away.
• Three apples a day keep the doctor away.

In this case, the research changes the hypothesis as the researcher learns more about his/her research.

Statistical hypothesis

A statistical hypothesis is a look of a part of a population or statistical model. This type of hypothesis is especially useful if you are making a statement about a large population. Instead of having to test the entire population of Illinois, you could just use a smaller sample of people who live there.

Example: 70% of people who live in Illinois are iron deficient.

Causal hypothesis

A causal hypothesis states that the independent variable will have an effect on the dependent variable.

Example: Using tobacco products causes cancer.

Final thoughts

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How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

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It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

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

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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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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

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

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

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

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

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

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

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

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

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

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

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

Elements of a Good Hypothesis

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

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

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

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

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

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

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

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

The Importance of Operational Definitions

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

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

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

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

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

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

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

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

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

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

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

A few examples of simple hypotheses:

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

Examples of a complex hypothesis include:

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

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

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

Descriptive Research Methods

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

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

Experimental Research Methods

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

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

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

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

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

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

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Research Methodology – Types, Examples and writing Guide

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Research Methodology

Definition:

Research Methodology refers to the systematic and scientific approach used to conduct research, investigate problems, and gather data and information for a specific purpose. It involves the techniques and procedures used to identify, collect , analyze , and interpret data to answer research questions or solve research problems . Moreover, They are philosophical and theoretical frameworks that guide the research process.

Structure of Research Methodology

Research methodology formats can vary depending on the specific requirements of the research project, but the following is a basic example of a structure for a research methodology section:

I. Introduction

• Provide an overview of the research problem and the need for a research methodology section
• Outline the main research questions and objectives

II. Research Design

• Explain the research design chosen and why it is appropriate for the research question(s) and objectives
• Discuss any alternative research designs considered and why they were not chosen
• Describe the research setting and participants (if applicable)

III. Data Collection Methods

• Describe the methods used to collect data (e.g., surveys, interviews, observations)
• Explain how the data collection methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or instruments used for data collection

IV. Data Analysis Methods

• Describe the methods used to analyze the data (e.g., statistical analysis, content analysis )
• Explain how the data analysis methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or software used for data analysis

V. Ethical Considerations

• Discuss any ethical issues that may arise from the research and how they were addressed
• Explain how informed consent was obtained (if applicable)
• Detail any measures taken to ensure confidentiality and anonymity

VI. Limitations

• Identify any potential limitations of the research methodology and how they may impact the results and conclusions

VII. Conclusion

• Summarize the key aspects of the research methodology section
• Explain how the research methodology addresses the research question(s) and objectives

Research Methodology Types

Types of Research Methodology are as follows:

Quantitative Research Methodology

This is a research methodology that involves the collection and analysis of numerical data using statistical methods. This type of research is often used to study cause-and-effect relationships and to make predictions.

Qualitative Research Methodology

This is a research methodology that involves the collection and analysis of non-numerical data such as words, images, and observations. This type of research is often used to explore complex phenomena, to gain an in-depth understanding of a particular topic, and to generate hypotheses.

Mixed-Methods Research Methodology

This is a research methodology that combines elements of both quantitative and qualitative research. This approach can be particularly useful for studies that aim to explore complex phenomena and to provide a more comprehensive understanding of a particular topic.

Case Study Research Methodology

This is a research methodology that involves in-depth examination of a single case or a small number of cases. Case studies are often used in psychology, sociology, and anthropology to gain a detailed understanding of a particular individual or group.

Action Research Methodology

This is a research methodology that involves a collaborative process between researchers and practitioners to identify and solve real-world problems. Action research is often used in education, healthcare, and social work.

Experimental Research Methodology

This is a research methodology that involves the manipulation of one or more independent variables to observe their effects on a dependent variable. Experimental research is often used to study cause-and-effect relationships and to make predictions.

Survey Research Methodology

This is a research methodology that involves the collection of data from a sample of individuals using questionnaires or interviews. Survey research is often used to study attitudes, opinions, and behaviors.

Grounded Theory Research Methodology

This is a research methodology that involves the development of theories based on the data collected during the research process. Grounded theory is often used in sociology and anthropology to generate theories about social phenomena.

Research Methodology Example

An Example of Research Methodology could be the following:

Research Methodology for Investigating the Effectiveness of Cognitive Behavioral Therapy in Reducing Symptoms of Depression in Adults

Introduction:

The aim of this research is to investigate the effectiveness of cognitive-behavioral therapy (CBT) in reducing symptoms of depression in adults. To achieve this objective, a randomized controlled trial (RCT) will be conducted using a mixed-methods approach.

Research Design:

The study will follow a pre-test and post-test design with two groups: an experimental group receiving CBT and a control group receiving no intervention. The study will also include a qualitative component, in which semi-structured interviews will be conducted with a subset of participants to explore their experiences of receiving CBT.

Participants:

Participants will be recruited from community mental health clinics in the local area. The sample will consist of 100 adults aged 18-65 years old who meet the diagnostic criteria for major depressive disorder. Participants will be randomly assigned to either the experimental group or the control group.

Intervention :

The experimental group will receive 12 weekly sessions of CBT, each lasting 60 minutes. The intervention will be delivered by licensed mental health professionals who have been trained in CBT. The control group will receive no intervention during the study period.

Data Collection:

Quantitative data will be collected through the use of standardized measures such as the Beck Depression Inventory-II (BDI-II) and the Generalized Anxiety Disorder-7 (GAD-7). Data will be collected at baseline, immediately after the intervention, and at a 3-month follow-up. Qualitative data will be collected through semi-structured interviews with a subset of participants from the experimental group. The interviews will be conducted at the end of the intervention period, and will explore participants’ experiences of receiving CBT.

Data Analysis:

Quantitative data will be analyzed using descriptive statistics, t-tests, and mixed-model analyses of variance (ANOVA) to assess the effectiveness of the intervention. Qualitative data will be analyzed using thematic analysis to identify common themes and patterns in participants’ experiences of receiving CBT.

Ethical Considerations:

This study will comply with ethical guidelines for research involving human subjects. Participants will provide informed consent before participating in the study, and their privacy and confidentiality will be protected throughout the study. Any adverse events or reactions will be reported and managed appropriately.

Data Management:

All data collected will be kept confidential and stored securely using password-protected databases. Identifying information will be removed from qualitative data transcripts to ensure participants’ anonymity.

Limitations:

One potential limitation of this study is that it only focuses on one type of psychotherapy, CBT, and may not generalize to other types of therapy or interventions. Another limitation is that the study will only include participants from community mental health clinics, which may not be representative of the general population.

Conclusion:

This research aims to investigate the effectiveness of CBT in reducing symptoms of depression in adults. By using a randomized controlled trial and a mixed-methods approach, the study will provide valuable insights into the mechanisms underlying the relationship between CBT and depression. The results of this study will have important implications for the development of effective treatments for depression in clinical settings.

How to Write Research Methodology

Writing a research methodology involves explaining the methods and techniques you used to conduct research, collect data, and analyze results. It’s an essential section of any research paper or thesis, as it helps readers understand the validity and reliability of your findings. Here are the steps to write a research methodology:

• Start by explaining your research question: Begin the methodology section by restating your research question and explaining why it’s important. This helps readers understand the purpose of your research and the rationale behind your methods.
• Describe your research design: Explain the overall approach you used to conduct research. This could be a qualitative or quantitative research design, experimental or non-experimental, case study or survey, etc. Discuss the advantages and limitations of the chosen design.
• Discuss your sample: Describe the participants or subjects you included in your study. Include details such as their demographics, sampling method, sample size, and any exclusion criteria used.
• Describe your data collection methods : Explain how you collected data from your participants. This could include surveys, interviews, observations, questionnaires, or experiments. Include details on how you obtained informed consent, how you administered the tools, and how you minimized the risk of bias.
• Explain your data analysis techniques: Describe the methods you used to analyze the data you collected. This could include statistical analysis, content analysis, thematic analysis, or discourse analysis. Explain how you dealt with missing data, outliers, and any other issues that arose during the analysis.
• Discuss the validity and reliability of your research : Explain how you ensured the validity and reliability of your study. This could include measures such as triangulation, member checking, peer review, or inter-coder reliability.
• Acknowledge any limitations of your research: Discuss any limitations of your study, including any potential threats to validity or generalizability. This helps readers understand the scope of your findings and how they might apply to other contexts.
• Provide a summary: End the methodology section by summarizing the methods and techniques you used to conduct your research. This provides a clear overview of your research methodology and helps readers understand the process you followed to arrive at your findings.

When to Write Research Methodology

Research methodology is typically written after the research proposal has been approved and before the actual research is conducted. It should be written prior to data collection and analysis, as it provides a clear roadmap for the research project.

The research methodology is an important section of any research paper or thesis, as it describes the methods and procedures that will be used to conduct the research. It should include details about the research design, data collection methods, data analysis techniques, and any ethical considerations.

The methodology should be written in a clear and concise manner, and it should be based on established research practices and standards. It is important to provide enough detail so that the reader can understand how the research was conducted and evaluate the validity of the results.

Applications of Research Methodology

Here are some of the applications of research methodology:

• To identify the research problem: Research methodology is used to identify the research problem, which is the first step in conducting any research.
• To design the research: Research methodology helps in designing the research by selecting the appropriate research method, research design, and sampling technique.
• To collect data: Research methodology provides a systematic approach to collect data from primary and secondary sources.
• To analyze data: Research methodology helps in analyzing the collected data using various statistical and non-statistical techniques.
• To test hypotheses: Research methodology provides a framework for testing hypotheses and drawing conclusions based on the analysis of data.
• To generalize findings: Research methodology helps in generalizing the findings of the research to the target population.
• To develop theories : Research methodology is used to develop new theories and modify existing theories based on the findings of the research.
• To evaluate programs and policies : Research methodology is used to evaluate the effectiveness of programs and policies by collecting data and analyzing it.
• To improve decision-making: Research methodology helps in making informed decisions by providing reliable and valid data.

Purpose of Research Methodology

Research methodology serves several important purposes, including:

• To guide the research process: Research methodology provides a systematic framework for conducting research. It helps researchers to plan their research, define their research questions, and select appropriate methods and techniques for collecting and analyzing data.
• To ensure research quality: Research methodology helps researchers to ensure that their research is rigorous, reliable, and valid. It provides guidelines for minimizing bias and error in data collection and analysis, and for ensuring that research findings are accurate and trustworthy.
• To replicate research: Research methodology provides a clear and detailed account of the research process, making it possible for other researchers to replicate the study and verify its findings.
• To advance knowledge: Research methodology enables researchers to generate new knowledge and to contribute to the body of knowledge in their field. It provides a means for testing hypotheses, exploring new ideas, and discovering new insights.
• To inform decision-making: Research methodology provides evidence-based information that can inform policy and decision-making in a variety of fields, including medicine, public health, education, and business.

Advantages of Research Methodology

Research methodology has several advantages that make it a valuable tool for conducting research in various fields. Here are some of the key advantages of research methodology:

• Systematic and structured approach : Research methodology provides a systematic and structured approach to conducting research, which ensures that the research is conducted in a rigorous and comprehensive manner.
• Objectivity : Research methodology aims to ensure objectivity in the research process, which means that the research findings are based on evidence and not influenced by personal bias or subjective opinions.
• Replicability : Research methodology ensures that research can be replicated by other researchers, which is essential for validating research findings and ensuring their accuracy.
• Reliability : Research methodology aims to ensure that the research findings are reliable, which means that they are consistent and can be depended upon.
• Validity : Research methodology ensures that the research findings are valid, which means that they accurately reflect the research question or hypothesis being tested.
• Efficiency : Research methodology provides a structured and efficient way of conducting research, which helps to save time and resources.
• Flexibility : Research methodology allows researchers to choose the most appropriate research methods and techniques based on the research question, data availability, and other relevant factors.
• Scope for innovation: Research methodology provides scope for innovation and creativity in designing research studies and developing new research techniques.

Research Methodology Vs Research Methods

About the author.

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing  is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.  

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

• Clear and precise
• Capable of being tested
• Able to relate to a variable
• Stated in simple terms
• Consistent with known facts
• Limited in scope and specific
• Tested in a limited timeframe
• Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A  null hypothesis  is a hypothesis when there is no significant relationship between the dependent and the participants’ independent  variables . 

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

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How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to  gather the data  obtained through a large number of samples from a specific population. 

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many  types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study 

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance. 

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

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Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the  significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided. 

If the significance level is minimum, then it prevents the researchers from false claims. 

The significance level is denoted by  P,  and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the  outcomes of your study . You need to ensure whether you have met the objectives of your research or not. 

In the discussion section and  conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis? 

Always remember that you either conclude to reject Ho in favor of Haor   do not reject Ho . It would help if you never rejected  Ha  or even  accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude  reject Ho in favor of Haor   do not reject Ho,  then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

• One-Sample Test : Compare sample data to a known population value.
• Two-Sample Test : Compare means between two sample groups.
• ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

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What is Research Methodology? Definition, Types, and Examples

Research methodology 1,2 is a structured and scientific approach used to collect, analyze, and interpret quantitative or qualitative data to answer research questions or test hypotheses. A research methodology is like a plan for carrying out research and helps keep researchers on track by limiting the scope of the research. Several aspects must be considered before selecting an appropriate research methodology, such as research limitations and ethical concerns that may affect your research.

The research methodology section in a scientific paper describes the different methodological choices made, such as the data collection and analysis methods, and why these choices were selected. The reasons should explain why the methods chosen are the most appropriate to answer the research question. A good research methodology also helps ensure the reliability and validity of the research findings. There are three types of research methodology—quantitative, qualitative, and mixed-method, which can be chosen based on the research objectives.

What is research methodology ?

A research methodology describes the techniques and procedures used to identify and analyze information regarding a specific research topic. It is a process by which researchers design their study so that they can achieve their objectives using the selected research instruments. It includes all the important aspects of research, including research design, data collection methods, data analysis methods, and the overall framework within which the research is conducted. While these points can help you understand what is research methodology, you also need to know why it is important to pick the right methodology.

Why is research methodology important?

Having a good research methodology in place has the following advantages: 3

• Helps other researchers who may want to replicate your research; the explanations will be of benefit to them.
• You can easily answer any questions about your research if they arise at a later stage.
• A research methodology provides a framework and guidelines for researchers to clearly define research questions, hypotheses, and objectives.
• It helps researchers identify the most appropriate research design, sampling technique, and data collection and analysis methods.
• A sound research methodology helps researchers ensure that their findings are valid and reliable and free from biases and errors.
• It also helps ensure that ethical guidelines are followed while conducting research.
• A good research methodology helps researchers in planning their research efficiently, by ensuring optimum usage of their time and resources.

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Types of research methodology.

There are three types of research methodology based on the type of research and the data required. 1

• Quantitative research methodology focuses on measuring and testing numerical data. This approach is good for reaching a large number of people in a short amount of time. This type of research helps in testing the causal relationships between variables, making predictions, and generalizing results to wider populations.
• Qualitative research methodology examines the opinions, behaviors, and experiences of people. It collects and analyzes words and textual data. This research methodology requires fewer participants but is still more time consuming because the time spent per participant is quite large. This method is used in exploratory research where the research problem being investigated is not clearly defined.
• Mixed-method research methodology uses the characteristics of both quantitative and qualitative research methodologies in the same study. This method allows researchers to validate their findings, verify if the results observed using both methods are complementary, and explain any unexpected results obtained from one method by using the other method.

What are the types of sampling designs in research methodology?

Sampling 4 is an important part of a research methodology and involves selecting a representative sample of the population to conduct the study, making statistical inferences about them, and estimating the characteristics of the whole population based on these inferences. There are two types of sampling designs in research methodology—probability and nonprobability.

• Probability sampling

In this type of sampling design, a sample is chosen from a larger population using some form of random selection, that is, every member of the population has an equal chance of being selected. The different types of probability sampling are:

• Systematic —sample members are chosen at regular intervals. It requires selecting a starting point for the sample and sample size determination that can be repeated at regular intervals. This type of sampling method has a predefined range; hence, it is the least time consuming.
• Stratified —researchers divide the population into smaller groups that don’t overlap but represent the entire population. While sampling, these groups can be organized, and then a sample can be drawn from each group separately.
• Cluster —the population is divided into clusters based on demographic parameters like age, sex, location, etc.
• Convenience —selects participants who are most easily accessible to researchers due to geographical proximity, availability at a particular time, etc.
• Purposive —participants are selected at the researcher’s discretion. Researchers consider the purpose of the study and the understanding of the target audience.
• Snowball —already selected participants use their social networks to refer the researcher to other potential participants.
• Quota —while designing the study, the researchers decide how many people with which characteristics to include as participants. The characteristics help in choosing people most likely to provide insights into the subject.

What are data collection methods?

During research, data are collected using various methods depending on the research methodology being followed and the research methods being undertaken. Both qualitative and quantitative research have different data collection methods, as listed below.

Qualitative research 5

• One-on-one interviews: Helps the interviewers understand a respondent’s subjective opinion and experience pertaining to a specific topic or event
• Document study/literature review/record keeping: Researchers’ review of already existing written materials such as archives, annual reports, research articles, guidelines, policy documents, etc.
• Focus groups: Constructive discussions that usually include a small sample of about 6-10 people and a moderator, to understand the participants’ opinion on a given topic.
• Qualitative observation : Researchers collect data using their five senses (sight, smell, touch, taste, and hearing).

Quantitative research 6

• Sampling: The most common type is probability sampling.
• Interviews: Commonly telephonic or done in-person.
• Observations: Structured observations are most commonly used in quantitative research. In this method, researchers make observations about specific behaviors of individuals in a structured setting.
• Document review: Reviewing existing research or documents to collect evidence for supporting the research.
• Surveys and questionnaires. Surveys can be administered both online and offline depending on the requirement and sample size.

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What are data analysis methods.

The data collected using the various methods for qualitative and quantitative research need to be analyzed to generate meaningful conclusions. These data analysis methods 7 also differ between quantitative and qualitative research.

Quantitative research involves a deductive method for data analysis where hypotheses are developed at the beginning of the research and precise measurement is required. The methods include statistical analysis applications to analyze numerical data and are grouped into two categories—descriptive and inferential.

Descriptive analysis is used to describe the basic features of different types of data to present it in a way that ensures the patterns become meaningful. The different types of descriptive analysis methods are:

• Measures of frequency (count, percent, frequency)
• Measures of central tendency (mean, median, mode)
• Measures of dispersion or variation (range, variance, standard deviation)
• Measure of position (percentile ranks, quartile ranks)

Inferential analysis is used to make predictions about a larger population based on the analysis of the data collected from a smaller population. This analysis is used to study the relationships between different variables. Some commonly used inferential data analysis methods are:

• Correlation: To understand the relationship between two or more variables.
• Cross-tabulation: Analyze the relationship between multiple variables.
• Regression analysis: Study the impact of independent variables on the dependent variable.
• Frequency tables: To understand the frequency of data.
• Analysis of variance: To test the degree to which two or more variables differ in an experiment.

Qualitative research involves an inductive method for data analysis where hypotheses are developed after data collection. The methods include:

• Content analysis: For analyzing documented information from text and images by determining the presence of certain words or concepts in texts.
• Narrative analysis: For analyzing content obtained from sources such as interviews, field observations, and surveys. The stories and opinions shared by people are used to answer research questions.
• Discourse analysis: For analyzing interactions with people considering the social context, that is, the lifestyle and environment, under which the interaction occurs.
• Grounded theory: Involves hypothesis creation by data collection and analysis to explain why a phenomenon occurred.
• Thematic analysis: To identify important themes or patterns in data and use these to address an issue.

How to choose a research methodology?

Here are some important factors to consider when choosing a research methodology: 8

• Research objectives, aims, and questions —these would help structure the research design.
• Review existing literature to identify any gaps in knowledge.
• Check the statistical requirements —if data-driven or statistical results are needed then quantitative research is the best. If the research questions can be answered based on people’s opinions and perceptions, then qualitative research is most suitable.
• Sample size —sample size can often determine the feasibility of a research methodology. For a large sample, less effort- and time-intensive methods are appropriate.
• Constraints —constraints of time, geography, and resources can help define the appropriate methodology.

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How to write a research methodology .

A research methodology should include the following components: 3,9

• Research design —should be selected based on the research question and the data required. Common research designs include experimental, quasi-experimental, correlational, descriptive, and exploratory.
• Research method —this can be quantitative, qualitative, or mixed-method.
• Reason for selecting a specific methodology —explain why this methodology is the most suitable to answer your research problem.
• Research instruments —explain the research instruments you plan to use, mainly referring to the data collection methods such as interviews, surveys, etc. Here as well, a reason should be mentioned for selecting the particular instrument.
• Sampling —this involves selecting a representative subset of the population being studied.
• Data collection —involves gathering data using several data collection methods, such as surveys, interviews, etc.
• Data analysis —describe the data analysis methods you will use once you’ve collected the data.
• Research limitations —mention any limitations you foresee while conducting your research.
• Validity and reliability —validity helps identify the accuracy and truthfulness of the findings; reliability refers to the consistency and stability of the results over time and across different conditions.
• Ethical considerations —research should be conducted ethically. The considerations include obtaining consent from participants, maintaining confidentiality, and addressing conflicts of interest.

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Frequently Asked Questions

Q1. What are the key components of research methodology?

A1. A good research methodology has the following key components:

• Research design
• Data collection procedures
• Data analysis methods
• Ethical considerations

Q2. Why is ethical consideration important in research methodology?

A2. Ethical consideration is important in research methodology to ensure the readers of the reliability and validity of the study. Researchers must clearly mention the ethical norms and standards followed during the conduct of the research and also mention if the research has been cleared by any institutional board. The following 10 points are the important principles related to ethical considerations: 10

• Participants should not be subjected to harm.
• Respect for the dignity of participants should be prioritized.
• Full consent should be obtained from participants before the study.
• Participants’ privacy should be ensured.
• Confidentiality of the research data should be ensured.
• Anonymity of individuals and organizations participating in the research should be maintained.
• The aims and objectives of the research should not be exaggerated.
• Affiliations, sources of funding, and any possible conflicts of interest should be declared.
• Communication in relation to the research should be honest and transparent.
• Misleading information and biased representation of primary data findings should be avoided.

Q3. What is the difference between methodology and method?

A3. Research methodology is different from a research method, although both terms are often confused. Research methods are the tools used to gather data, while the research methodology provides a framework for how research is planned, conducted, and analyzed. The latter guides researchers in making decisions about the most appropriate methods for their research. Research methods refer to the specific techniques, procedures, and tools used by researchers to collect, analyze, and interpret data, for instance surveys, questionnaires, interviews, etc.

Research methodology is, thus, an integral part of a research study. It helps ensure that you stay on track to meet your research objectives and answer your research questions using the most appropriate data collection and analysis tools based on your research design.

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• Research methodologies. Pfeiffer Library website. Accessed August 15, 2023. https://library.tiffin.edu/researchmethodologies/whatareresearchmethodologies
• Types of research methodology. Eduvoice website. Accessed August 16, 2023. https://eduvoice.in/types-research-methodology/
• The basics of research methodology: A key to quality research. Voxco. Accessed August 16, 2023. https://www.voxco.com/blog/what-is-research-methodology/
• Sampling methods: Types with examples. QuestionPro website. Accessed August 16, 2023. https://www.questionpro.com/blog/types-of-sampling-for-social-research/
• What is qualitative research? Methods, types, approaches, examples. Researcher.Life blog. Accessed August 15, 2023. https://researcher.life/blog/article/what-is-qualitative-research-methods-types-examples/
• What is quantitative research? Definition, methods, types, and examples. Researcher.Life blog. Accessed August 15, 2023. https://researcher.life/blog/article/what-is-quantitative-research-types-and-examples/
• Data analysis in research: Types & methods. QuestionPro website. Accessed August 16, 2023. https://www.questionpro.com/blog/data-analysis-in-research/#Data_analysis_in_qualitative_research
• Factors to consider while choosing the right research methodology. PhD Monster website. Accessed August 17, 2023. https://www.phdmonster.com/factors-to-consider-while-choosing-the-right-research-methodology/
• What is research methodology? Research and writing guides. Accessed August 14, 2023. https://paperpile.com/g/what-is-research-methodology/
• Ethical considerations. Business research methodology website. Accessed August 17, 2023. https://research-methodology.net/research-methodology/ethical-considerations/

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Case Study Research Method in Psychology

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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

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

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

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

On This Page:

Case studies are in-depth investigations of a person, group, event, or community. Typically, data is gathered from various sources using several methods (e.g., observations & interviews).

The case study research method originated in clinical medicine (the case history, i.e., the patient’s personal history). In psychology, case studies are often confined to the study of a particular individual.

The information is mainly biographical and relates to events in the individual’s past (i.e., retrospective), as well as to significant events that are currently occurring in his or her everyday life.

The case study is not a research method, but researchers select methods of data collection and analysis that will generate material suitable for case studies.

Freud (1909a, 1909b) conducted very detailed investigations into the private lives of his patients in an attempt to both understand and help them overcome their illnesses.

This makes it clear that the case study is a method that should only be used by a psychologist, therapist, or psychiatrist, i.e., someone with a professional qualification.

There is an ethical issue of competence. Only someone qualified to diagnose and treat a person can conduct a formal case study relating to atypical (i.e., abnormal) behavior or atypical development.

 Famous Case Studies

• Anna O – One of the most famous case studies, documenting psychoanalyst Josef Breuer’s treatment of “Anna O” (real name Bertha Pappenheim) for hysteria in the late 1800s using early psychoanalytic theory.
• Little Hans – A child psychoanalysis case study published by Sigmund Freud in 1909 analyzing his five-year-old patient Herbert Graf’s house phobia as related to the Oedipus complex.
• Bruce/Brenda – Gender identity case of the boy (Bruce) whose botched circumcision led psychologist John Money to advise gender reassignment and raise him as a girl (Brenda) in the 1960s.
• Genie Wiley – Linguistics/psychological development case of the victim of extreme isolation abuse who was studied in 1970s California for effects of early language deprivation on acquiring speech later in life.
• Phineas Gage – One of the most famous neuropsychology case studies analyzes personality changes in railroad worker Phineas Gage after an 1848 brain injury involving a tamping iron piercing his skull.

Clinical Case Studies

• Studying the effectiveness of psychotherapy approaches with an individual patient
• Assessing and treating mental illnesses like depression, anxiety disorders, PTSD
• Neuropsychological cases investigating brain injuries or disorders

Child Psychology Case Studies

• Studying psychological development from birth through adolescence
• Cases of learning disabilities, autism spectrum disorders, ADHD
• Effects of trauma, abuse, deprivation on development

Types of Case Studies

• Explanatory case studies : Used to explore causation in order to find underlying principles. Helpful for doing qualitative analysis to explain presumed causal links.
• Exploratory case studies : Used to explore situations where an intervention being evaluated has no clear set of outcomes. It helps define questions and hypotheses for future research.
• Descriptive case studies : Describe an intervention or phenomenon and the real-life context in which it occurred. It is helpful for illustrating certain topics within an evaluation.
• Multiple-case studies : Used to explore differences between cases and replicate findings across cases. Helpful for comparing and contrasting specific cases.
• Intrinsic : Used to gain a better understanding of a particular case. Helpful for capturing the complexity of a single case.
• Collective : Used to explore a general phenomenon using multiple case studies. Helpful for jointly studying a group of cases in order to inquire into the phenomenon.

Where Do You Find Data for a Case Study?

There are several places to find data for a case study. The key is to gather data from multiple sources to get a complete picture of the case and corroborate facts or findings through triangulation of evidence. Most of this information is likely qualitative (i.e., verbal description rather than measurement), but the psychologist might also collect numerical data.

1. Primary sources

• Interviews – Interviewing key people related to the case to get their perspectives and insights. The interview is an extremely effective procedure for obtaining information about an individual, and it may be used to collect comments from the person’s friends, parents, employer, workmates, and others who have a good knowledge of the person, as well as to obtain facts from the person him or herself.
• Observations – Observing behaviors, interactions, processes, etc., related to the case as they unfold in real-time.
• Documents & Records – Reviewing private documents, diaries, public records, correspondence, meeting minutes, etc., relevant to the case.

2. Secondary sources

• News/Media – News coverage of events related to the case study.
• Academic articles – Journal articles, dissertations etc. that discuss the case.
• Government reports – Official data and records related to the case context.
• Books/films – Books, documentaries or films discussing the case.

3. Archival records

Searching historical archives, museum collections and databases to find relevant documents, visual/audio records related to the case history and context.

Public archives like newspapers, organizational records, photographic collections could all include potentially relevant pieces of information to shed light on attitudes, cultural perspectives, common practices and historical contexts related to psychology.

4. Organizational records

Organizational records offer the advantage of often having large datasets collected over time that can reveal or confirm psychological insights.

Of course, privacy and ethical concerns regarding confidential data must be navigated carefully.

However, with proper protocols, organizational records can provide invaluable context and empirical depth to qualitative case studies exploring the intersection of psychology and organizations.

• Organizational/industrial psychology research : Organizational records like employee surveys, turnover/retention data, policies, incident reports etc. may provide insight into topics like job satisfaction, workplace culture and dynamics, leadership issues, employee behaviors etc.
• Clinical psychology : Therapists/hospitals may grant access to anonymized medical records to study aspects like assessments, diagnoses, treatment plans etc. This could shed light on clinical practices.
• School psychology : Studies could utilize anonymized student records like test scores, grades, disciplinary issues, and counseling referrals to study child development, learning barriers, effectiveness of support programs, and more.

How do I Write a Case Study in Psychology?

Follow specified case study guidelines provided by a journal or your psychology tutor. General components of clinical case studies include: background, symptoms, assessments, diagnosis, treatment, and outcomes. Interpreting the information means the researcher decides what to include or leave out. A good case study should always clarify which information is the factual description and which is an inference or the researcher’s opinion.

1. Introduction

• Provide background on the case context and why it is of interest, presenting background information like demographics, relevant history, and presenting problem.
• Compare briefly to similar published cases if applicable. Clearly state the focus/importance of the case.

2. Case Presentation

• Describe the presenting problem in detail, including symptoms, duration,and impact on daily life.
• Include client demographics like age and gender, information about social relationships, and mental health history.
• Describe all physical, emotional, and/or sensory symptoms reported by the client.
• Use patient quotes to describe the initial complaint verbatim. Follow with full-sentence summaries of relevant history details gathered, including key components that led to a working diagnosis.
• Summarize clinical exam results, namely orthopedic/neurological tests, imaging, lab tests, etc. Note actual results rather than subjective conclusions. Provide images if clearly reproducible/anonymized.
• Clearly state the working diagnosis or clinical impression before transitioning to management.

3. Management and Outcome

• Indicate the total duration of care and number of treatments given over what timeframe. Use specific names/descriptions for any therapies/interventions applied.
• Present the results of the intervention,including any quantitative or qualitative data collected.
• For outcomes, utilize visual analog scales for pain, medication usage logs, etc., if possible. Include patient self-reports of improvement/worsening of symptoms. Note the reason for discharge/end of care.

4. Discussion

• Analyze the case, exploring contributing factors, limitations of the study, and connections to existing research.
• Analyze the effectiveness of the intervention,considering factors like participant adherence, limitations of the study, and potential alternative explanations for the results.
• Identify any questions raised in the case analysis and relate insights to established theories and current research if applicable. Avoid definitive claims about physiological explanations.
• Offer clinical implications, and suggest future research directions.

5. Additional Items

• Thank specific assistants for writing support only. No patient acknowledgments.
• References should directly support any key claims or quotes included.
• Use tables/figures/images only if substantially informative. Include permissions and legends/explanatory notes.
• Provides detailed (rich qualitative) information.
• Provides insight for further research.
• Permitting investigation of otherwise impractical (or unethical) situations.

Case studies allow a researcher to investigate a topic in far more detail than might be possible if they were trying to deal with a large number of research participants (nomothetic approach) with the aim of ‘averaging’.

Because of their in-depth, multi-sided approach, case studies often shed light on aspects of human thinking and behavior that would be unethical or impractical to study in other ways.

Research that only looks into the measurable aspects of human behavior is not likely to give us insights into the subjective dimension of experience, which is important to psychoanalytic and humanistic psychologists.

Case studies are often used in exploratory research. They can help us generate new ideas (that might be tested by other methods). They are an important way of illustrating theories and can help show how different aspects of a person’s life are related to each other.

The method is, therefore, important for psychologists who adopt a holistic point of view (i.e., humanistic psychologists ).

Limitations

• Lacking scientific rigor and providing little basis for generalization of results to the wider population.
• Researchers’ own subjective feelings may influence the case study (researcher bias).
• Difficult to replicate.
• Time-consuming and expensive.
• The volume of data, together with the time restrictions in place, impacted the depth of analysis that was possible within the available resources.

Because a case study deals with only one person/event/group, we can never be sure if the case study investigated is representative of the wider body of “similar” instances. This means the conclusions drawn from a particular case may not be transferable to other settings.

Because case studies are based on the analysis of qualitative (i.e., descriptive) data , a lot depends on the psychologist’s interpretation of the information she has acquired.

This means that there is a lot of scope for Anna O , and it could be that the subjective opinions of the psychologist intrude in the assessment of what the data means.

For example, Freud has been criticized for producing case studies in which the information was sometimes distorted to fit particular behavioral theories (e.g., Little Hans ).

This is also true of Money’s interpretation of the Bruce/Brenda case study (Diamond, 1997) when he ignored evidence that went against his theory.

Breuer, J., & Freud, S. (1895).  Studies on hysteria . Standard Edition 2: London.

Curtiss, S. (1981). Genie: The case of a modern wild child .

Diamond, M., & Sigmundson, K. (1997). Sex Reassignment at Birth: Long-term Review and Clinical Implications. Archives of Pediatrics & Adolescent Medicine , 151(3), 298-304

Freud, S. (1909a). Analysis of a phobia of a five year old boy. In The Pelican Freud Library (1977), Vol 8, Case Histories 1, pages 169-306

Freud, S. (1909b). Bemerkungen über einen Fall von Zwangsneurose (Der “Rattenmann”). Jb. psychoanal. psychopathol. Forsch ., I, p. 357-421; GW, VII, p. 379-463; Notes upon a case of obsessional neurosis, SE , 10: 151-318.

Harlow J. M. (1848). Passage of an iron rod through the head.  Boston Medical and Surgical Journal, 39 , 389–393.

Harlow, J. M. (1868).  Recovery from the Passage of an Iron Bar through the Head .  Publications of the Massachusetts Medical Society. 2  (3), 327-347.

Money, J., & Ehrhardt, A. A. (1972).  Man & Woman, Boy & Girl : The Differentiation and Dimorphism of Gender Identity from Conception to Maturity. Baltimore, Maryland: Johns Hopkins University Press.

Money, J., & Tucker, P. (1975). Sexual signatures: On being a man or a woman.

Further Information

• Case Study Approach
• Case Study Method
• Enhancing the Quality of Case Studies in Health Services Research
• “We do things together” A case study of “couplehood” in dementia
• Using mixed methods for evaluating an integrative approach to cancer care: a case study

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What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

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Criterion Validity: Definition & Examples

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• v.53(4); 2010 Aug

Research questions, hypotheses and objectives

Patricia farrugia.

* Michael G. DeGroote School of Medicine, the

Bradley A. Petrisor

† Division of Orthopaedic Surgery and the

Forough Farrokhyar

‡ Departments of Surgery and

§ Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Ont

Mohit Bhandari

There is an increasing familiarity with the principles of evidence-based medicine in the surgical community. As surgeons become more aware of the hierarchy of evidence, grades of recommendations and the principles of critical appraisal, they develop an increasing familiarity with research design. Surgeons and clinicians are looking more and more to the literature and clinical trials to guide their practice; as such, it is becoming a responsibility of the clinical research community to attempt to answer questions that are not only well thought out but also clinically relevant. The development of the research question, including a supportive hypothesis and objectives, is a necessary key step in producing clinically relevant results to be used in evidence-based practice. A well-defined and specific research question is more likely to help guide us in making decisions about study design and population and subsequently what data will be collected and analyzed. 1

Objectives of this article

In this article, we discuss important considerations in the development of a research question and hypothesis and in defining objectives for research. By the end of this article, the reader will be able to appreciate the significance of constructing a good research question and developing hypotheses and research objectives for the successful design of a research study. The following article is divided into 3 sections: research question, research hypothesis and research objectives.

Research question

Interest in a particular topic usually begins the research process, but it is the familiarity with the subject that helps define an appropriate research question for a study. 1 Questions then arise out of a perceived knowledge deficit within a subject area or field of study. 2 Indeed, Haynes suggests that it is important to know “where the boundary between current knowledge and ignorance lies.” 1 The challenge in developing an appropriate research question is in determining which clinical uncertainties could or should be studied and also rationalizing the need for their investigation.

Increasing one’s knowledge about the subject of interest can be accomplished in many ways. Appropriate methods include systematically searching the literature, in-depth interviews and focus groups with patients (and proxies) and interviews with experts in the field. In addition, awareness of current trends and technological advances can assist with the development of research questions. 2 It is imperative to understand what has been studied about a topic to date in order to further the knowledge that has been previously gathered on a topic. Indeed, some granting institutions (e.g., Canadian Institute for Health Research) encourage applicants to conduct a systematic review of the available evidence if a recent review does not already exist and preferably a pilot or feasibility study before applying for a grant for a full trial.

In-depth knowledge about a subject may generate a number of questions. It then becomes necessary to ask whether these questions can be answered through one study or if more than one study needed. 1 Additional research questions can be developed, but several basic principles should be taken into consideration. 1 All questions, primary and secondary, should be developed at the beginning and planning stages of a study. Any additional questions should never compromise the primary question because it is the primary research question that forms the basis of the hypothesis and study objectives. It must be kept in mind that within the scope of one study, the presence of a number of research questions will affect and potentially increase the complexity of both the study design and subsequent statistical analyses, not to mention the actual feasibility of answering every question. 1 A sensible strategy is to establish a single primary research question around which to focus the study plan. 3 In a study, the primary research question should be clearly stated at the end of the introduction of the grant proposal, and it usually specifies the population to be studied, the intervention to be implemented and other circumstantial factors. 4

Hulley and colleagues 2 have suggested the use of the FINER criteria in the development of a good research question ( Box 1 ). The FINER criteria highlight useful points that may increase the chances of developing a successful research project. A good research question should specify the population of interest, be of interest to the scientific community and potentially to the public, have clinical relevance and further current knowledge in the field (and of course be compliant with the standards of ethical boards and national research standards).

FINER criteria for a good research question

Adapted with permission from Wolters Kluwer Health. 2

Whereas the FINER criteria outline the important aspects of the question in general, a useful format to use in the development of a specific research question is the PICO format — consider the population (P) of interest, the intervention (I) being studied, the comparison (C) group (or to what is the intervention being compared) and the outcome of interest (O). 3 , 5 , 6 Often timing (T) is added to PICO ( Box 2 ) — that is, “Over what time frame will the study take place?” 1 The PICOT approach helps generate a question that aids in constructing the framework of the study and subsequently in protocol development by alluding to the inclusion and exclusion criteria and identifying the groups of patients to be included. Knowing the specific population of interest, intervention (and comparator) and outcome of interest may also help the researcher identify an appropriate outcome measurement tool. 7 The more defined the population of interest, and thus the more stringent the inclusion and exclusion criteria, the greater the effect on the interpretation and subsequent applicability and generalizability of the research findings. 1 , 2 A restricted study population (and exclusion criteria) may limit bias and increase the internal validity of the study; however, this approach will limit external validity of the study and, thus, the generalizability of the findings to the practical clinical setting. Conversely, a broadly defined study population and inclusion criteria may be representative of practical clinical practice but may increase bias and reduce the internal validity of the study.

PICOT criteria 1

A poorly devised research question may affect the choice of study design, potentially lead to futile situations and, thus, hamper the chance of determining anything of clinical significance, which will then affect the potential for publication. Without devoting appropriate resources to developing the research question, the quality of the study and subsequent results may be compromised. During the initial stages of any research study, it is therefore imperative to formulate a research question that is both clinically relevant and answerable.

Research hypothesis

The primary research question should be driven by the hypothesis rather than the data. 1 , 2 That is, the research question and hypothesis should be developed before the start of the study. This sounds intuitive; however, if we take, for example, a database of information, it is potentially possible to perform multiple statistical comparisons of groups within the database to find a statistically significant association. This could then lead one to work backward from the data and develop the “question.” This is counterintuitive to the process because the question is asked specifically to then find the answer, thus collecting data along the way (i.e., in a prospective manner). Multiple statistical testing of associations from data previously collected could potentially lead to spuriously positive findings of association through chance alone. 2 Therefore, a good hypothesis must be based on a good research question at the start of a trial and, indeed, drive data collection for the study.

The research or clinical hypothesis is developed from the research question and then the main elements of the study — sampling strategy, intervention (if applicable), comparison and outcome variables — are summarized in a form that establishes the basis for testing, statistical and ultimately clinical significance. 3 For example, in a research study comparing computer-assisted acetabular component insertion versus freehand acetabular component placement in patients in need of total hip arthroplasty, the experimental group would be computer-assisted insertion and the control/conventional group would be free-hand placement. The investigative team would first state a research hypothesis. This could be expressed as a single outcome (e.g., computer-assisted acetabular component placement leads to improved functional outcome) or potentially as a complex/composite outcome; that is, more than one outcome (e.g., computer-assisted acetabular component placement leads to both improved radiographic cup placement and improved functional outcome).

However, when formally testing statistical significance, the hypothesis should be stated as a “null” hypothesis. 2 The purpose of hypothesis testing is to make an inference about the population of interest on the basis of a random sample taken from that population. The null hypothesis for the preceding research hypothesis then would be that there is no difference in mean functional outcome between the computer-assisted insertion and free-hand placement techniques. After forming the null hypothesis, the researchers would form an alternate hypothesis stating the nature of the difference, if it should appear. The alternate hypothesis would be that there is a difference in mean functional outcome between these techniques. At the end of the study, the null hypothesis is then tested statistically. If the findings of the study are not statistically significant (i.e., there is no difference in functional outcome between the groups in a statistical sense), we cannot reject the null hypothesis, whereas if the findings were significant, we can reject the null hypothesis and accept the alternate hypothesis (i.e., there is a difference in mean functional outcome between the study groups), errors in testing notwithstanding. In other words, hypothesis testing confirms or refutes the statement that the observed findings did not occur by chance alone but rather occurred because there was a true difference in outcomes between these surgical procedures. The concept of statistical hypothesis testing is complex, and the details are beyond the scope of this article.

Another important concept inherent in hypothesis testing is whether the hypotheses will be 1-sided or 2-sided. A 2-sided hypothesis states that there is a difference between the experimental group and the control group, but it does not specify in advance the expected direction of the difference. For example, we asked whether there is there an improvement in outcomes with computer-assisted surgery or whether the outcomes worse with computer-assisted surgery. We presented a 2-sided test in the above example because we did not specify the direction of the difference. A 1-sided hypothesis states a specific direction (e.g., there is an improvement in outcomes with computer-assisted surgery). A 2-sided hypothesis should be used unless there is a good justification for using a 1-sided hypothesis. As Bland and Atlman 8 stated, “One-sided hypothesis testing should never be used as a device to make a conventionally nonsignificant difference significant.”

The research hypothesis should be stated at the beginning of the study to guide the objectives for research. Whereas the investigators may state the hypothesis as being 1-sided (there is an improvement with treatment), the study and investigators must adhere to the concept of clinical equipoise. According to this principle, a clinical (or surgical) trial is ethical only if the expert community is uncertain about the relative therapeutic merits of the experimental and control groups being evaluated. 9 It means there must exist an honest and professional disagreement among expert clinicians about the preferred treatment. 9

Designing a research hypothesis is supported by a good research question and will influence the type of research design for the study. Acting on the principles of appropriate hypothesis development, the study can then confidently proceed to the development of the research objective.

Research objective

The primary objective should be coupled with the hypothesis of the study. Study objectives define the specific aims of the study and should be clearly stated in the introduction of the research protocol. 7 From our previous example and using the investigative hypothesis that there is a difference in functional outcomes between computer-assisted acetabular component placement and free-hand placement, the primary objective can be stated as follows: this study will compare the functional outcomes of computer-assisted acetabular component insertion versus free-hand placement in patients undergoing total hip arthroplasty. Note that the study objective is an active statement about how the study is going to answer the specific research question. Objectives can (and often do) state exactly which outcome measures are going to be used within their statements. They are important because they not only help guide the development of the protocol and design of study but also play a role in sample size calculations and determining the power of the study. 7 These concepts will be discussed in other articles in this series.

From the surgeon’s point of view, it is important for the study objectives to be focused on outcomes that are important to patients and clinically relevant. For example, the most methodologically sound randomized controlled trial comparing 2 techniques of distal radial fixation would have little or no clinical impact if the primary objective was to determine the effect of treatment A as compared to treatment B on intraoperative fluoroscopy time. However, if the objective was to determine the effect of treatment A as compared to treatment B on patient functional outcome at 1 year, this would have a much more significant impact on clinical decision-making. Second, more meaningful surgeon–patient discussions could ensue, incorporating patient values and preferences with the results from this study. 6 , 7 It is the precise objective and what the investigator is trying to measure that is of clinical relevance in the practical setting.

The following is an example from the literature about the relation between the research question, hypothesis and study objectives:

Study: Warden SJ, Metcalf BR, Kiss ZS, et al. Low-intensity pulsed ultrasound for chronic patellar tendinopathy: a randomized, double-blind, placebo-controlled trial. Rheumatology 2008;47:467–71.

Research question: How does low-intensity pulsed ultrasound (LIPUS) compare with a placebo device in managing the symptoms of skeletally mature patients with patellar tendinopathy?

Research hypothesis: Pain levels are reduced in patients who receive daily active-LIPUS (treatment) for 12 weeks compared with individuals who receive inactive-LIPUS (placebo).

Objective: To investigate the clinical efficacy of LIPUS in the management of patellar tendinopathy symptoms.

The development of the research question is the most important aspect of a research project. A research project can fail if the objectives and hypothesis are poorly focused and underdeveloped. Useful tips for surgical researchers are provided in Box 3 . Designing and developing an appropriate and relevant research question, hypothesis and objectives can be a difficult task. The critical appraisal of the research question used in a study is vital to the application of the findings to clinical practice. Focusing resources, time and dedication to these 3 very important tasks will help to guide a successful research project, influence interpretation of the results and affect future publication efforts.

Tips for developing research questions, hypotheses and objectives 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.
• Develop clear and well-defined primary and secondary (if needed) objectives.
• Ensure that the research question and objectives are answerable, feasible and clinically relevant.

FINER = feasible, interesting, novel, ethical, relevant; PICOT = population (patients), intervention (for intervention studies only), comparison group, outcome of interest, time.

Competing interests: No funding was received in preparation of this paper. Dr. Bhandari was funded, in part, by a Canada Research Chair, McMaster University.

Research on the theory and method of reduced-hole blasting for large cross-section tunnel based on explosive energy dissipation

• Open access
• Published: 28 May 2024
• Volume 10 , article number  96 , ( 2024 )

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• Xingchao Tian 1 ,
• Tiejun Tao 2 &
• Caijin Xie 1  

The traditional tunnel drilling and blasting method places cut holes at the lower center of the excavation face, resulting in an excessive number of blasting holes. With the continuous increase in cross-section area, this design concept can no longer meet the requirements of safe and efficient tunnel boring for large cross-section tunnels. This paper puts forward the theory and method of reduced-hole blasting for large cross-section tunnels, as an alternative to the traditional drilling and blasting method of the “more holes, less charge” design concept. Based on the explosion energy dissipation law and rock’s critical crushing energy dissipation characteristics, the calculation method of the extrapolation distance of the wedge-cut holes is given. The optimum extrapolation distance of the wedge-cut holes was verified using numerical simulation and field tests. The results show that the number of drilling holes can be reduced by about 15.8% using the theory and method proposed in this paper, and at the same time, the damage of retained rock can be effectively controlled. The results of this study can provide a reference for the design of blast network parameters for similar large cross-section tunnels.

Article Highlights

This paper put forward the theory and method of reduced hole blasting (RHB) for large cross section tunnels, the number of blasting holes was reduced by an average of 15.8%.

This paper gave the wedge-cut hole extrapolation distance calculation method based on the explosion energy dissipation law and rock’s critical crushing energy dissipation characteristics.

This paper proposed a computational expression for energy dissipation under coupled in-situ stress and blast loading, determined the critical crushing energy dissipation density of gray sandstone under different combined dynamic and static loading conditions.

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1 Introduction

The drilling and blasting method has the advantages of being economic and efficient, and is currently the most commonly used construction method for highway and railroad tunnels, mine shafts, and underground space hard rock excavation. With China’s socio-economic development, as well as the continuous promotion of the Belt and Road initiative and the construction of new infrastructure, large cross-section tunnels have appeared frequently. However, the design of blasting parameters still follows the traditional design concept of small cross-section tunnels, resulting in too many blasting holes, which restricts the quality and duration of tunnel construction. Therefore, there is an urgent need to put forward an innovative theory and method of hole-reduction blasting for large cross-section tunnels, to maximize the outward push of the wedge-cut holes, and to reduce the number of holes while ensuring the quality of blasting, so as to realize the safe and efficient blasting of large cross-section tunnels.

The parameter design of wedge-cut holes is the soul of whether large cross-section tunnels can be successfully blasted to break rocks. Many scholars have conducted research on the hollowing parameters of large cross-section tunnel blasting. Yang et al. ( 2024 ) showed that in large cross-section hard-rock tunnel blasting, using the frames on both sides of the drilling and blasting cart as a reference for the main wedge-cut holes can reduce the number of drilled holes, but the theoretical basis of this design method was not reflected in their study. Ji et al. ( 2020 ) proposed an inverted T-shaped hollowing and blasting method for very large cross-section tunnels, which improved the blasting effect. Mei et al. ( 2021 ) carried out studies on hollowing methods, blast hole placement, charge volume, and charge structure to achieve safe and efficient blasting excavation. Zhang et al. ( 2022 ) proposed an innovative hollowing and blasting technique based on cavity hollowing and debris throwing. Li et al. ( 2023 ) proposed a hollowing out and blasting technique with decentralized charging and staged blasting. Qin and Zhang ( 2020 ) proposed a “three-step + inverted” tunnel blasting excavation method, which effectively controlled the blasting vibration. Cheng et al. ( 2023 ) proposed a medium-deep hole-hollowing and blasting method based on directional pre-cracking with slit charging to improve the tunneling progress. Gao et al. ( 2022 ) improved the hollowing and blasting initiation method and proposed a hybrid initiation method based on the reverse transmission of neighboring holes. Zhang et al. ( 2020a ; b ) analyzed the hollow-hole effect of hollowing and blasting and gave a method for determining the parameters of hollow-hole straight-eye hollowing and blasting. Zhang et al. ( 2020a ; b ) proposed a second-order two-stage hollowing and blasting technique, which effectively improved the efficiency of blasting excavation. Wu et al. ( 2023 ) proposed a zonal blasting excavation scheme for small-spaced large-section tunnels to effectively control blasting vibration and perimeter rock damage. The above research has effectively improved the blasting quality and construction efficiency through the optimization of segmental hollowing blasting technology and hollowing parameters, which is of great significance for the safe and efficient blasting of large cross-section tunnels. However, its parameter design methods are not free from the traditional design concept of small cross-section roadway blasting, the number of blasting holes laid is still high. With the increasing cross-section area of the tunnel excavation, it is possible to extrapolate the placement position of the wedge-cut holes, and utilize the bidirectional critical surface formed after blasting the wedge-cut holes to break the rock effectively. The transformation of design concepts is crucial.

Currently, the wedge-cut holes spacing, angle, and other parameters are determined by the radius of the crushed zone, the radius of the fractured zone, and the geometric relationship, which leads to smaller spacing of the wedge-cut holes and limited hollowing effect. The accumulation, propagation, and dissipation of energy are the driving factors for the destabilization of the medium, and it is more scientific to determine the optimal spacing of the wedge-cut holes based on the explosive energy dissipation. Li et al. ( 2018a ; b ) analyzed the energy evolution law of deep buried tunnels under explosive loading. Leng et al. ( 2016 ) discussed the process of explosive energy transfer during side detonation and end detonation. Sanchidrián et al. ( 2007 ) analyzed the energy distribution pattern within the rock mass after explosive blasting based on single-hole blasting tests. Xia et al. ( 2020 ) analyzed the effect of charge structure on blast energy transfer. Leng et al. ( 2019 ) analyzed the explosion energy transfer law under the condition of double-point detonation in the hole. The above research has conducted a detailed exploration of the transmission and distribution of explosion energy, which is of great significance for exploring the mechanism of rock damage and failure. However, there are few research results on the design of hole network parameters for large cross-section tunnel blasting from the perspective of explosive energy dissipation.

This paper is based on the significant demand for safe and efficient tunnel boring in large cross-section tunnels, and offers the method of wedge-cut hole extrapolation, featuring additional center holes, and adjusts the detonation sequence of large cross-section tunnels according to reduced-hole blasting (RHB) theory and method, completely changing the traditional tunnel blasting "more holes, less charge" design concept. Based on the explosion energy dissipation law and the rock’s critical crushing energy dissipation characteristics, the calculation method of the extrapolation distance of the wedge-cut hole is given. A three-dimensional numerical simulation model was established to compare and analyze the hollowing effect and the damage law of the retained rock body after being subjected to different wedge-cut holes with different extrapolation distances, and the optimal extrapolation distance of the wedge-cut holes was determined. Based on the Gonghe Village Tunnel of the Ludian-Qiaojia Expressway, five on-site blasting tests were carried out to verify the scientific validity of the theory and method proposed in this paper. The results of this study can provide a reference for the design of blast network parameters for similar large cross-section tunnels.

2 Theory and method

2.1 engineering background.

The Gonghe Village Tunnel of the Ludian-Qiaojia Expressway is located in Chongxi Township, Qiaojia County, Yunnan Province. The total length of the right tunnel is 10,698 m, with a maximum depth of about 1320 m, which is a two-way four-lane detached extra-long tunnel. The buried depth of the section used in this study is about 400 m, the surrounding rock level is class III, the surrounding rock lithology is dominated by gray sandstone, and the excavated section area is 99.28 m 2 , which belongs to the large cross-section tunnel. The section used in this study was excavated by blasting using the upper and lower step method, as shown in Fig.  1 .

The Gonghe village tunnel

The originally proposed Gonghe Village Tunnel was constructed by using the traditional drilling and blasting method, which led to the problems of a large number of blasting holes, high drilling intensity, excessive crushing of stones, and serious over excavation, as shown in Fig.  2 . The number of boreholes for conventional tunnel drilling and blasting is estimated on the basis of the tunnel cross-section area S and the rock solidity coefficient f of \(N = 3.3 \cdot \sqrt[3]{{fS^{2} }}\) . The rock solidity coefficient f of the study section of the Gonghe Village Tunnel is 10, the tunnel section area S is 99.28 m 2 , and the number of blasting holes to be drilled in the whole section is 152, which is a huge drilling workload. The current tunnel rock drilling cart is expensive, has a high failure rate, and is limited by the tunnel space, which leads to the automated drilling technology not being mature and still mainly relying on manual drilling. Taking a 4 m depth of the blast hole as an example, the drilling efficiency of the workers is generally about 3 holes/h, and a drilling shift is calculated with 13 people, which takes about 3.9 h of drilling time per cycle, making drilling intense and long, and seriously affecting the construction progress. At the same time, the excessive number of blasting holes laid resulted in high usage of explosives, excessive damage to retained rock, and severe over excavation. The number of blasting holes, drilling time, explosives used, and average over-digging value per cycle of blasting in the upper bench of the study section of the Gonghe Village Tunnel were counted, as shown in Table  1 . Therefore, the traditional drilling and blasting method could not meet the requirements of safe and efficient construction of large cross-section tunnels, and there is an urgent need to put forward innovative theories and methods that can reduce the number of drilled holes, reduce the unit consumption of explosives, and ensure the quality of blasting.

Technical difficulties caused by the traditional drilling and blasting method

2.2 Theory and method of RHB

A typical compound wedge hollowing blast is used as an example to discuss the design method of traditional tunnel blasting parameters, as shown in Fig.  3 . In Fig.  3 , the orifice spacing, bottom spacing, row spacing, hollowing angle, and vertical depth of the first-order wedge-cut holes are S 1 , c , a , β 2 , and h , respectively. The orifice spacing, bottom spacing, row spacing, hollowing angle, and vertical depth of the second-order wedge-cut holes are S 2 , d , b , β 1 , and H , respectively. To determine the above blasting parameters, the following three steps are usually performed: (1) determine the bottom of hole spacing and row spacing based on the radius of the crushed zone and fractured zone, and further determine the orifice spacing based on the geometric relationship. (2) Determine the hollowing angle based on the force relationship of the slot cavity. (3) Determine the rest of the blasting parameters based on the geometry of the slot cavity volume by associating (1)(2).

Duplicate wedge hollowing blast analysis model

The destruction of rock in the slot cavity is based on the principle that the fractured zones of adjacent wedge-cut holes are interconnected, therefore, the row spacing of the wedge-cut holes a should be satisfied:

where R C and R T are the radius of the crushed zone and fractured zone, respectively.

When determining the spacing between the bottoms of the holes in the wedge-cut holes, the principle of overlapping fractured zones is used to ensure that the rock at the bottom of the slot cavity is sufficiently fractured. Therefore, the bottom spacing c and d of the wedge-cut holes should be satisfied:

Combined with the geometric relationship in Fig.  3 , it can be seen that the orifice spacing S 1 and S 2 of the wedge-cut holes should be satisfied:

The force state of the slot cavity lumen is further analyzed. When the wedge-cut hole charging section explosives explosion, the rock around the blasting hole in the strong compression of the explosive shock wave to form a crushed zone. Since the row spacing a of the wedge-cut holes is small, a through surface is formed in the charging section. Subsequently, the rock forms a fractured zone outside of the crushed zone under the combined effect of the blast stress wave and the blast-generated gas. Due to the presence of the hollowing angle, the explosion of the explosive generates a force perpendicular to the free surface outward, forcing the slot cavity to move in the direction normal to the free surface. As a result, the rock in the slot cavity will be damaged by shear with the surrounding rock, forming shear surfaces B 1 C 1 I 1 H 1 , A 1 D 1 J 1 G 1 , A 1 B 1 H 1 G 1 , and D 1 C 1 I 1 J 1 . The bottom of the slot cavity is subjected to large tensile stresses, forming damage surface H 1 I 1 J 1 G 1 .

The total resistance to blasting in the direction of the line of least resistance for the wedge-cut holes is:

where c and ε are rock cohesion and angle of internal friction, respectively. l c is the length of the charge.

The combined force acting on the explosive gas in the direction of the line of least resistance is:

where P is the average burst pressure in the blast hole, P  =  ρ 0 D 2 /8.

When the following conditions are met, the wedge-cut holes blasting is able to throw out the slot cavity smoothly and form a critical surface:

The value of the hollowing angle β 1 can be determined by associating Eqs. ( 6 )–( 8 ).

Ideally, the following relationship exists between the rock volumes V 1 and V 2 for first-order hollowing and second-order hollowing blasts:

From the geometrical relations in Fig.  3 , the values of the remaining parameters can be further determined:

After determining the parameters of the wedge-cut holes according to the above blasting parameter calculation method, the peripheral holes are laid out according to the requirements of contour molding, and finally the auxiliary holes are evenly arranged according to the size of the remaining section area and its location. The above blasting parameters determination method is more applicable to small cross-section tunnels, but with the increase of the tunnel excavation cross-section area, the above blasting parameters will lead to too many blasting holes.

Based on the demand for safe and efficient construction of large cross-section tunnel blasting, this paper proposes the theory and method of RHB for the blasting construction of the tunnel using a step method with more than three levels of surrounding rock, as shown in Figs.  4 and 5 . Central to this method are the extrapolation of wedge-cut holes, the addition of center holes, and the adjustment of the detonation sequence. The methodology is as follows:

The wedge-cut hole is pushed outward. The conventional drilling and blasting method places the wedge-cut holes in the lower middle of the tunnel excavation face, as shown in Fig.  4 a. The spacing of the wedge-cut holes is small, and a large number of auxiliary holes need to be laid to ensure the uniform distribution of the explosive energy, and the number of blasting holes is large. The RHB method pushes the placement of the wedge-cut holes outward to the maximum extent possible and to the minimum distance from the tunnel design contour line. This distance should ensure that blasting of the wedge-cut holes will not cause damage to the retained rock outside the tunnel design contour line, as shown in Fig.  4 b. At this time, the wedge-cut holes blasting forms a two-way critical surface (Lou et al. 2022 ): one provides a critical surface for auxiliary hole blasting; the other provides a critical surface for center holes blasting. From Fig.  4 , it can be seen that the wedge-cut holes are pushed out, which reduces the deployment of auxiliary holes in large quantities and reduces the drilling workload of the up-stage blasting excavation. To ensure the effectiveness of surface blasting, the two methods are consistent in terms of the placement of peripheral holes.

Addition of center holes. In this paper, the blasting holes laid in the center of the tunnel excavation face are defined as the center holes, which need to be loaded with explosives, and are able to break the larger volume of rock in the center of the excavation face by blasting through 2–3 center holes. As a result of the extrapolation of the wedge-cut holes, a large area of rock will be left in the center of the tunnel excavation face waiting to be blasted. After blasting the main wedge-cut holes, the rock in the center of the tunnel excavation face is "isolated" and forms three free surfaces simultaneously, so 2–3 center holes can be used to break this part of the rock. At this point, even if the charge of the center holes is increased, there will be no damage to the retained rock outside the design contour line of the tunnel, as shown in Fig.  4 b. In addition, the deployment of center holes can effectively solve the phenomenon of the "bulging belly" of the tunnel excavation face and improve the digging footage.

Adjustment of the detonation sequence. The traditional tunnel drilling and blasting method in terms of the detonation sequence is as follows: cut hole detonation, auxiliary hole detonation, peripheral hole detonation, bottom hole detonation. This paper optimizes the order of detonation adjustment. The adjusted detonation sequence is as follows: the main wedge-cut holes are detonated first, forming a large volume critical surface in the center of the working face, and providing a free surface for the secondary and tertiary wedge-cut holes, center holes, and collapse holes to be blasted. Then, the secondary wedge-cut holes and center holes are detonated at the same time, the secondary wedge-cut holes blasting for the tertiary level of wedge-cut holes and the collapse holes blasting to provide airspace. After a center hole is detonated, it is possible to fully break up the rock that has not been fully exploded at the bottom of the main wedge-cut holes, providing a larger critical surface. The tertiary wedge-cut holes and collapse holes are then detonated simultaneously to provide a critical surface for auxiliary hole blasting. Finally, the auxiliary holes, peripheral holes, and the bottom holes are detonated in turn, as shown in Fig.  5 .

Wedge-cut hole extrapolation theory and method

Adjustment of the detonation sequence

Compared with the traditional tunnel blasting construction process, the technical advantages of the theory and method proposed in this paper are mainly as follows: (1) the number of blasting holes and the drilling intensity have been reduced, and the construction efficiency has been improved; (2) reduction in the number of blasting holes, improvement in the phenomenon of wrong drilling and leakage, and improvement in the quality of blasting; (3) to curb the phenomenon of bulging belly, this method improves the digging footage to ensure the smoothness of the working face; (4) the order of detonation has been adjusted to change the sequence of energy release from the explosives, and the energy is utilized more efficiently; (5) reduced damage to retained rock outside the tunnel design contour.

2.3 Calculation of extrapolation distance for wedge-cut hole

Energy is an essential feature of the deformation response of rock and is the driving factor for the occurrence of destabilizing damage in rock (Xie et al. 2004 ), explosive blast rock is the result of the joint action of shock wave energy and explosive gas expansion energy (Zhao et al. 2019 ). After the explosion of the explosives, the energy consumed mainly consists of shock waves that expand the explosive cavity of the energy consumption W 1 , stress waves that produce radial fissures of the energy consumption W 2 , stress waves caused by elastic deformation of the energy consumption W 3 , bursting gas that expands the cavity of the energy consumption W 4 , and bursting gas that provides the energy consumption of the thrown rock debris W 5 . Several studies (Zhou and Zhong 2022 ; Leng 2020 ; Raina and Trivedi 2019 ) show that the energy utilization rate of explosive blast crushing rock is only 20–30% of the total release of chemical energy W 0 , and the vast majority of the remaining energy is consumed in other forms. Thus, this paper took 30% W 0 as the total energy of explosive blast crushing rock. The total energy consumed after the explosion of the explosive is W d , and when the residual energy W r (0.3 W 0 - W d ) is greater than the critical crushing energy dissipation density W a0 when the rock is damaged by impact loading, the rock will continue to be damaged.

Therefore, only W d and W a0 need to be determined to calculate the minimum distance of the wedge-cut holes from the tunnel design contour line. In Sect.  3.1 , the explosive energy dissipation law under the coupled action of in-situ stress and explosive loading is discussed, and the computational expression for the energy dissipation of each part under the action of the coupled stress field is proposed. As discussed in Sect.  3.2 , rock impact compression tests under different dynamic static combination loading conditions were designed to determine the critical crushing energy dissipation density W a0 of gray sandstone.

3 Parameter calculation

3.1 explosive energy dissipation law analysis, 3.1.1 calculation of the extent of the crushed and fractured zone under coupled stress field.

Before the tunnel is excavated, the surrounding rock is already in a three-dimensional stress state due to the self-gravitational stresses of the overlying rock. The in-situ stress has an inhibitory effect on the explosive load (Yan et al. 2015 ; Bastante et al. 2012 ; Hamdi et al. 2011 ; Mandal and Singh 2009 ), and the in-situ stress field of the original rock and the dynamic stress field formed after the detonation of explosives are superimposed onto each other to form a secondary coupled stress field. The expression for the stress distribution based on the coupled effect of blast load and in-situ stress is given by:

where r , r 0 are the distance from the calculation point to the center of the packet and the radius of the blast hole, respectively. θ is the angle between the line between any point in the rock and the center of the blast hole in the horizontal direction. P d is the homogeneous force acting on the borehole wall, MPa. α is the pressure attenuation coefficient, for the shock wave region α  ≈ 3 or α  = 2 +  μ /(1— μ ) and for the stress wave region β  = 2 −  μ /(1 −  μ ).

The expression for calculating the radius of the crushed zone R C when considering the effect of in-situ stress is:

where σ cd is the dynamic compressive strength of the rock mass, MPa. Let \(\frac{{r_{0} }}{{R_{C} }} = x\) , then Eq. ( 12 ) becomes:

Equation ( 13 ) can be solved using the MATLAB program, and excluding the limited understanding, the calculation expression of the crushed zone radius R C is obtained:

The expression for calculating the radius R T of the fracture zone when considering the effect of in-situ stress is (Ge 2020 ):

where σ td is the dynamic tensile strength of the rock mass, MPa. m is the coefficient of rock tensile strength enhancement caused by in-situ stress.

Further discussion on the enhancement factor m . The force state of the microelementary point under the action of coupled stress field is analyzed with reference to the research results of Ge ( 2020 ), as shown in Figs.  6 and 7 . According to Dai and Qian ( 2007 ), the initial static load on the rock mass actually increases the dynamic compressive or tensile strength of the rock mass indirectly. It is assumed that when the microelement point is compressed by a concentrated load ( σ V a ) in the vertical direction, the dynamic tensile strength of the rock in that direction is enhanced by 100%, i.e., the dynamic tensile strength in that direction becomes 2 σ td .

Force analysis of rock microelementary points under in-situ stress action ( λ is the lateral pressure coefficient)

Force analysis of rock microelementary points under explosive load

From the force analysis of the microelement points in Figs.  6 and 7 , it can be seen that the tensile stress on each microelement point is ( σa/λ ·sin θ 1  −  σa ·cos θ 1 ). Cracks are most likely to expand when the dynamic tensile strength of the rock is not enhanced, i.e., the crack length is longest when θ 1  = arctan λ . Taking the burial depth of 600 m as an example for analysis, when the lateral pressure coefficients λ are 0.2, 0.4, 0.6, 0.8, and 1.0, the longest cracks are in the directions of 79°, 68°, 59°, 51°, and 45° of the blasting hole, respectively. The values of the enhancement coefficient m in each direction of the borehole are shown in Table  2 , the variation rule of the enhancement coefficient m with θ under different lateral pressure coefficients λ is shown in Fig.  8 , and the variation rule of the enhancement coefficient m with the lateral pressure coefficient λ in the same direction of the blasting hole is shown in Fig.  9 .

Law of change of m with θ for different λ

Law of change of m with λ in the same direction of the blasting hole

3.1.2 Calculation of explosion energy under coupled stress field

After the explosive explodes, the rock around the blast hole in the shock wave produced by the violent compression decays, the hole wall continues to expand outward, and the blast cavity expands. The cavity expansion process ends when the shock wave propagates to the edge of the crushed zone. In the crushed zone, the energy dissipation of the shock wave is equal to the work W 1 performed by the shock wave in the process of cavity expansion:

where the explosion cavity radius \(R_{1} = \left[ {R_{C}^{2} - (R_{C}^{2} - r_{0}^{2} )\frac{{\rho_{m} }}{{\rho_{r} }}} \right]^{\frac{1}{2}}\) . r 1 is the blast cavity radius corresponding to r . ρ m is the original rock density, kg/m 3 . ρ r is the rock density behind the shock wave front at the blast hole wall, \(\rho_{r} = \frac{{(a + bV_{0} )\rho_{m} }}{{a + (b - 1)V_{0} }}\) , kg/m 3 . a and b are the rock test constants, and V 0 is the initial velocity of the rock particle at the blast hole wall. Let \(\frac{{r_{0} }}{{R_{1} }} = x_{1}\) , the calculation expression of shock wave expansion cavity energy dissipation W 1 can be obtained:

The shock wave expanding cavity consumes a large amount of energy and then decays into a stress wave, which has a stretching effect on the rock around the blast hole and forms a large number of radial fractures. The energy dissipation W 2 for the generation of radial cleavage by the stress wave can be expressed as (Zhang 2007 ):

where n is the number of radial fractures, generally taken as 10. K 1 is the stress intensity factor, \(K_{1}^{2} = \pi r\sigma_{\theta }^{2}\) . E m is the dynamic modulus of elasticity, GPa. Let \(\frac{{r_{0} }}{{R_{T} }} = x_{2}\) , the calculation expression of W 2 of the radial crack generated by stress wave can be obtained:

Outside the fractured zone, with the attenuation of the stress wave, the stress wave can only cause elastic deformation of the rock mass. At this time, the elastic deformation energy of the rock in unit volume is:

Let \(\frac{{r_{0} }}{{R_{E} }} = x_{3}\) , the calculation expression of elastic deformation energy dissipation W 3 caused by stress wave can be obtained as:

After the end of the shock wave effect, the explosion gas continues to act in the form of quasi-static pressure on the cavity wall, so that the explosion cavity continues to expand. The energy dissipation W 4 of the expression gas can be expressed as (Zhang 2007 ):

where R 2 is the final radius of the blast chamber, \(R_{2} = \left\{ {\begin{array}{*{20}l} {r_{0} \left( {\frac{{P_{0} }}{{\sigma_{cd} }}} \right)^{\frac{1}{6}} \begin{array}{*{20}c} {} \\ \end{array} \begin{array}{*{20}c} {} \\ \end{array} (\sigma_{cd} \ge P_{k} )} \hfill \\ {r_{0} \left( {\frac{{P_{0} }}{{P_{k} }}} \right)^{\frac{1}{6}} \left( {\frac{{P_{k} }}{{\sigma_{cd} }}} \right)^{\frac{3}{8}} \begin{array}{*{20}c} {} \\ \end{array} \begin{array}{*{20}c} {} \\ \end{array} (\sigma_{cd} < P_{k} )} \hfill \\ \end{array} } \right.\) . P 0 is the explosive gas pressure at the beginning of the expansion, P 0  =  ρ 0 D 2 /4, where ρ 0 is the density of the explosive, kg/m 3 , and D is the bursting speed of the explosive, m/s. P k is the critical pressure, MPa.

In addition to blast cavity expansion, the expression gas also throws the broken rock fragments due to the action of the blast stress wave. The energy dissipation W 5 of the expression gas throwing rock fragments can be expressed as (Zhang 2007 ):

where n 1 is the throwing action index of the blasting funnel, \(n_{1} = \frac{{r_{a} }}{W}\) , r a is the blasting funnel radius, and W is the minimum resistance line. For a standard blasting funnel, n 1 takes 1. \(V_{1} = \frac{{\sigma_{cd} }}{{0.38\rho_{m} C_{p} }}\) , C p is the longitudinal wave velocity. k is a constant related to explosives.

The total chemical energy released per unit length of explosive when it explodes is:

where Q is the explosion heat of the explosive, MJ/kg.

3.2 Critical crushing energy dissipation density of rock

The lithology of the surrounding rock in the study section of the Gonghe Village Tunnel is gray sandstone, and static and kinetic tests were carried out after on-site core drilling and sampling to determine the critical crushing energy dissipation values of the gray sandstone under different stress states. According to the specimen sizes recommended by the International Commission on Rock Dynamics (Zhou et al. 2012 ), the uniaxial compression test and triaxial compression test rock samples were machined as 50 mm × 100 mm cylinders, the Brazilian split test rock samples were machined as 50 mm × 50 mm cylinders, and the impact dynamics test rock samples were machined as 50 mm × 25 mm cylinders. The unevenness and non-perpendicularity of the rock samples were less than 0.02 mm, and the deviation of the end face normal was less than 0.25°. The rock samples are shown in Fig.  10 .

Rock samples

The static tests were carried out using a TAJW-2000 microcomputer-controlled electro-hydraulic servo triaxial rock test system as shown in Fig.  11 a, and the static parameters of the gray sandstone are shown in Table  3 . The impact dynamics tests were carried out on a detached Hopkinson lever test system, ALT100, as shown in Fig.  11 b.

The test systems used in this study

Based on the results of the static tests of the gray sandstone, the axial pressure ( σ V ) was set to 0, 10 MPa, 20 MPa, 30 MPa, and 40 MPa, which are 0%, 9.1%, 18.3%, 27.4%, and 36.6% of the static compressive strength, respectively, and the confining pressure ( σ H ) was set to 0, 4 MPa, 8 MPa, and 12 MPa.

The main purpose of this test is to determine the critical crushing energy density of gray sandstone under different dynamic and static combination loading conditions. Li et al. ( 2010 ) identified the state when the rock is broken into exactly 2–4 pieces as the critical damage state. At the beginning of the test, we set a certain air pressure to impact the rock sample, and if the rock sample is intact or only produces a small amount of cracks, we need to increase the impact air pressure. If a certain impact air pressure, the rock sample is broken into 2–4 pieces, this is the critical damage state. Continue to increase the impact air pressure, if the rock sample crushed, the previous impact air pressure is the critical impact air pressure. So we take the impact air pressure when the rock is exactly broken into 2–4 pieces as the critical impact air pressure, and we take the crushing energy density at this time as the critical crushing energy dissipation density.

During the test, to ensure the reliability of the test results, it is necessary to ensure that the stress on both ends of the rock samples reaches a state of dynamic equilibrium. The stresses, σ 1 and σ 2 , which are applied to the two ends of the rock sample can be calculated from the incident strain signal, \(\varepsilon_{I} \left( t \right)\) , the reflected strain signal, \(\varepsilon_{R} \left( t \right)\) , and the transmitted strain signal, \(\varepsilon_{T} \left( t \right)\) , according to the following equation:

Figure  12 shows the dynamic stress equilibrium curve of gray sandstone (with an axial pressure of 10 MPa, a confining pressure of 4 MPa, and an impact air pressure of 0.4 MPa). The combined stress curves of the incident and reflected waves are fundamentally consistent with the stress curves of the transmitted waves, indicating that the stresses at both ends of the rock samples are virtually in equilibrium during the test, which verifies the validity of the test process and the test results.

The dynamic stress balance curve

The critical crushing energy dissipation density of gray sandstone under the different dynamic and static combinations of loading conditions is shown in Table  4 . The curves of the critical crushing energy dissipation density of gray sandstone according to confining pressure and axial pressure are shown in Figs.  13 and 14 , respectively.

The variation curve of the critical crushing energy dissipation density according to confining pressure

The variation curve of the critical crushing energy dissipation density according to axial pressure

The maximum burial depth of the Gonghe Village Tunnel is about 1320 m. The rock density of the study section is 2.56 g cm −3 and the static Poisson's ratio is 0.37. Assuming that the lithology of the study section is homogeneous, the burial depths corresponding to axial pressures of 0 MPa, 10 MPa, 20 MPa, 30 MPa, and 40 MPa are 0 m, 391 m, 781 m, 1172 m, and 1563 m, respectively, when considering only the effect of gravitational stress. The dynamic Poisson's ratio of the lithology of the study section is 0.296, and the lateral pressure coefficient is 0.42, from which the corresponding confining pressures are 0 MPa, 4 MPa, 8 MPa, 12 MPa, and 16 MPa, respectively. Due to the equipment, the confining pressure of 16 MPa could not be loaded. Setting up the study conditions according to Table  4 can provide a basis for the design of blasting parameters for large cross-section tunnels under different stress states.

From Fig.  13 , it can be seen that the critical crushing energy dissipation density of gray sandstone increases with an increase in the confining pressure. The logarithmic function was used to fit the relationship between the changes; the fitting model and the fitting results are listed in Table  5 . It is evident that the confining pressure exerts a reinforcing effect on the gray sandstone samples; the greater the confining pressure, the more significant the reinforcing effect. The destruction of rock samples is a process of transition from a stable state to an unstable state under energy-driven action. Therefore, to destroy the gray sandstone samples, they must store more energy to reach their energy storage limit. Macroscopically speaking, this is manifested as the critical crushing energy dissipation density of the gray sandstone, which increases along with the increase in the confining pressure. As can be seen from Table  5 , the model’s fits at the axial pressures of 0 MPa and 20 MPa are relatively poor, which may be due to the discrete nature of the gray sandstone samples.

From Fig.  14 , it can be seen that the critical crushing energy dissipation density of the gray sandstone samples increases and then decreases with the increase in axial pressure. A quadratic function is used to fit the relationship between its changes, and the fitting model and fitting results are listed in Table  6 . From the previous analytical results, it is evident that axial pressure exerts a reinforcing effect on the gray sandstone samples when the axial pressure is small, while when the axial pressure continues to increase, the effect of the axial pressure on the gray sandstone samples is converted from a reinforcing to a deteriorating effect. Therefore, when the axial pressure is small, more energy needs to be absorbed to force the gray sandstone to destabilize. When the axial pressure continues to increase, the axial pressure has already caused internal damage within the gray sandstone; therefore, less energy needs to be absorbed in order to force the gray sandstone to destabilize.

From Table  6 , it can be calculated that the critical crushing energy dissipation density of gray sandstone reaches a maximum value of 7.01 J cm −3 when the axial pressure is 25.00 MPa, along with a peripheral pressure of 4 MPa. The critical crushing energy dissipation density of gray sandstone reaches a maximum value of 7.38 J cm −3 when the axial pressure is 28.33 MPa, along with a peripheral pressure of 8 MPa. The critical crushing energy dissipation density of gray sandstone reaches a maximum value of 8.40 J cm −3 when the axial pressure is 20.00 MPa, along with a peripheral pressure of 12 MPa.

3.3 Determination of extrapolation distance for wedge-cut hole

The main wedge-cut holes in the study section of the Gonghe Village Tunnel were loaded with a single charge of 3.0 kg in each hole and a charge length of 3.0 m. From Eq. ( 28 ), W 0 is calculated as 32.85 MJ, and the total chemical energy density is 32.85 J cm −3 , in which the heat of detonation Q of No. 2 rock emulsion explosives is taken as 4.5 MJ/kg. In this section, 30% W 0 is used as the total chemical energy released by the explosives when the main wedge-cut hole explodes, which is 9.86 J cm −3 .

The burial depth of the study section is 400 m, σ V  = 10.24 MPa, and σ H  = 4.3 MPa. The wedge-cut hole has a radius of 25 mm, a depth of 3.5 m, and a charge length of 3.0 m. The site uses No. 2 rock emulsion explosives, explosive density of 1.24 g cm −3 , and bursting speed of 4200 m s −1 . From the results of the study in Sect.  3.1 , it can be seen that the radius of the crushing zone R C is 58.28 mm, the radius of the fissure zone R T is 261.73 mm, the radius of the bursting cavity R 1 is 43.68 mm, and the final radius of the bursting cavity R 2 is 48.05 mm. W 1 , W 2 , W 4 , and W 5 were 1.98 MJ m −3 , 0.59 MJ m −3 , 0.14 MJ m −3 , and 2.08 MJ m −3 , respectively. At this point, the residual energy is 5.07 MJ m −3 . From the test results in Sect.  3.2 , the critical energy dissipation density of gray sandstone under this condition is 4.10 MJ m −3 . The residual energy is greater than the critical energy dissipation density and the rock mass will continue to be destroyed. Therefore, further consumption of explosive energy is required. Backcalculating the joint Eqs. ( 19 ), ( 21 ), ( 24 ), ( 26 ), and ( 27 ), the R E should be a minimum of 2.8 m when the residual energy is 4.10 MJ m −3 . It can be seen that for the upper bench blasting in the study section of the Gonghe Village Tunnel, the minimum distance of the main wedge-cut holes from the tunnel design contour line is 2.8 m. Compared with the conventional tunnel blasting method, the main wedge-cut holes of the RHB method were laid 1.4 m outward, as shown in Fig.  15 .

Schematic diagram of the extrapolation distance of the main wedge-cut holes of the RHB method

4 Parameter validation

4.1 model building.

ANSYS/LS-DYNA numerical simulation software was used to establish a three-dimensional numerical analysis model to compare and analyze the effect of hollowing out and the damage law of the retained rock body after blasting, so as to verify the reasonableness of the theoretical calculation results in Sect.  3.3 . For the main wedge-cut holes 2.4 m, 2.6 m, 2.8 m, 3.0 m, and 3.2 m from the tunnel design contour line, the overall dimensions of the model are 22 m × 18 m × 3.7 m (X × Y × Z), and the radius of the blasting holes and the radius of the pill rolls are 25 mm and 16 mm, respectively. The following simplifications are made to reduce the computational effort of the model: (1) only half of the overall model size is created when modeling, and after the model is calculated, the keyword *CONSTRAINED_GLOBAL is used to analyze the model after symmetry; (2) only primary wedge-cut holes, secondary wedge-cut holes, and center holes are modeled. The mesh size directly affects the accuracy of the simulation results. In this paper, we first refer to the research results of the literature to determine the preliminary grid size (Wang et al. 2016 ), and then comprehensively consider the calculation effect and calculation time, and finally select the rock grid size of 5 mm within the design contour line of the tunnel. The total number of modeled units is approximately 1.93 million. A simplified model is shown in Fig.  16 a, the grid division diagram is shown in Fig.  16 b.

Schematic of the simplified model and the grid division diagram

The in-situ stress σ V  = 10.24 MPa was applied to the upper and lower faces of the model, and the in-situ stress σ H  = 4.3 MPa was applied to the left and right faces (burial depth 400 m). The method of applying the in-situ stress is as follows: Define the load curve CURVE with the keyword *DEFINE, load from 0 to σ V (or σ H ), and use the keyword *INTERFACE to output the DYINA file with the ground stresses, replacing the original k file, to achieve the effect of applying the in-situ stress indicated in the model. The rock material is defined as a solid, the explosive and air material is defined as a fluid, the fluid is meshed in a co-nodal way, and the solid and the fluid are connected by fluid solid coupling. All faces except the free surface are set as non-reflective boundary conditions. The RHT model was used for the rock constitutive model, and the parameters of the RHT constitutive model are shown in Table  7 (Li et al. 2018a ; b ). The explosives, air, and gun clay material models were modeled using *MAT_HIGH_EXPLOSIVE_BURN, *MAT_NULL, and *MAT_SOIL_AND_FOAM material models, respectively, and the material models were taken with reference to the results of several studies in the literature (Liu et al. 2020 ; Wang 2020 ; Li et al. 2018a , b ). The blast parameters of the simplified model are shown in Table  8 .

4.2 Analysis of results

After the wedge-cut hole is extrapolated, whether the slot cavity can be successfully hollowed out is key to the success of blasting. The hollowing effect with different wedge shaped hollowing hole extrapolation distances is shown in Fig.  17 . Due to the clamping function of the rock, the rock in the slot cavity needs to overcome shear resistance and tensile resistance when being hollowed out. As can be seen from Fig.  17 , the hollowing effect gradually deteriorates as the wedge-shaped hollowing hole is extrapolated by an increasing distance. When the distance between the main wedge-cut hole and the design contour line of the tunnel is greater than or equal to 2.8 m, the explosive load can overcome the shear resistance and tensile resistance, and the rock in the slot cavity can be thrown out smoothly. At the same time, due to the role of center holes, the bottom of the hole will not show signs of the bulging belly phenomenon. When the distance between the main wedge-cut holes and the tunnel design contour line is less than 2.8 m, the spacing between the bottom of the wedge-cut holes is large, and the wedge-cut holes are able to form pre-cracking cracks after blasting, but are unable to overcome the tensile resistance of the rock at the bottom of the holes. Even if the center holes blasting can break part of the rock, it cannot also successfully hollow out the slot cavity, resulting in a serious bulging belly phenomenon, or even lead to blasting failure.

Effect of hollowing out

Damage to the retained rock outside the tunnel design contour after the wedge-cut holes have been extrapolated is another area of concern. The damage to the retained rock at different wedge-cut hole extrapolation distances is shown in Fig.  18 . As can be seen from Fig.  18 , when the distance of the main wedge-cut hole from the tunnel design contour line is greater than or equal to 2.8 m, blasting basically will not cause damage to the retained rock outside the tunnel design contour line. However, when the distance of the main wedge-cut hole from the tunnel design contour line is less than 2.8 m, blasting can cause extensive damage to the retained rock in the arch waist area. Peripheral hole blasting and post-blast drainage will result in more severe over excavation and affect the quality of blasting. Therefore, the optimum distance from the main wedge-cut hole to the tunnel design contour line in the study section of the Gonghe Village Tunnel is 2.8 m. The numerical simulation results are in agreement with the theoretical calculations.

Damage to retained rock

5 Field tests

Adopting the theory and method of RHB for large cross-section tunnel blasting proposed in this paper, five on-site blasting tests were carried out in the research section of the Gonghe Village Tunnel, and the plan view of the hole network design, the actual blast hole layout plan, the hole network design section plan, and the schematic diagram of the over-undercutting measurement point layout are shown in Fig.  19 a–d. In order to ensure the hollowing effect, the collapse holes were drilled at a downward inclination of 5°–10°, and the blasting parameters are shown in Table  9 . After the completion of blasting, the quality of blasting was comprehensively evaluated in terms of the excavation effect of the working face, the number of blasting holes, the drilling time, the utilization rate of the blasting holes, the unit consumption of explosives, and the over and under excavation.

Schematic diagram of aperture network design and monitoring point placement

Using the theory and method proposed in this paper for on-site blasting tests, the slot cavity can be successfully hollowed out, and the work surface is relatively flat, with basically no bulging belly phenomenon. After blasting was completed, the value of over undercut was measured at each measurement point, as shown in Fig.  20 . Data on the number of blasting holes, drilling time, utilization rate of blasting holes, unit consumption of explosives, and over and under excavation were collected, as shown in Table  10 .

Measurement of values for over and under excavation

As can be seen from Table  10 , by adopting the theory and method of RHB for large cross-section tunnel blasting proposed in this paper, the number of blasting holes per cycle of step blasting in the study section is reduced by an average of 21 holes, the drilling time is saved by an average of 0.5 h, the explosive unit consumption is reduced by an average of 0.16 kg cm −3 , and the value of over excavation is reduced by an average of 6.6 cm. The main reasons for the better contouring results of the RHB method compared to the conventional blasting method are as follows: (1) the wedge-cut hole pushed out to form a two-way critical surface after blasting, which can effectively block the stress wave during the center holes blasting and reduce the damage of the retained rock mass. (2) The number of auxiliary holes deployed was reduced, effectively minimizing the cumulative damage to the retained rock mass. (3) When the RHB method is applied in the field, the peripheral holes are loaded with axial spacing, and the explosive energy is distributed more evenly.

The cost of explosives on site is RMB 8.4 per kg, and the cost of the digital electronic detonator is RMB 16 each, whereas the research section of the upper step blasting can reduce the digital electronic detonator cost by RMB 320 per cycle while reducing explosives cost by RMB 302.4 per cycle. The total length of the right width of the Gonghe Village Tunnel is 10,698 m; by adopting the theory and method proposed in this paper, it is expected to save 1783 h of drilling time and about RMB 2.22 million on the cost of explosives. After the optimization of the program, the unit consumption of explosives is still high, which is due to the higher compressive strength (109.33 MPa) and better integrity of the rock in the study section, which requires more energy to be consumed to form crushed and fractured zones.

6 Conclusions

This paper put forward an RHB theory and method for large cross-section tunnels. The calculation method of explosion energy dissipation under the action of coupled stress field is given, the critical energy dissipation density of rock under different stress states is determined, and the calculation method of the extrapolation distance of wedge-cut holes is constructed.

The critical crushing energy dissipation density of gray sandstone increases with the increase in peripheral pressure, and the change rule conforms to the logarithmic function relationship. The critical crushing energy dissipation density of the gray sandstone samples increases and then decreases with the increase in axial pressure, and the change rule conforms to the quadratic function relationship. The critical crushing energy dissipation density of the gray sandstone samples under the conditions of confining pressure of 4 MPa axial pressure of 25.00 MPa, confining pressure of 8 MPa axial pressure of 28.33 MPa, and confining pressure of 12 MPa axial pressure of 20.00 MPa reached maximum values of 7.01 J cm −3 , 7.38 J cm −3 , and 8.40 J cm −3 , respectively.

The optimum distance of the main wedge-cut holes in the study section of the Gonghe Village Tunnel from the tunnel design contour is 2.8 m. The number of drill holes per cycle of step blasting in the section used in this study was reduced by about 15.8%, the drilling time was reduced by an average of 0.5 h, the unit consumption of explosives was reduced by an average of 0.16 kg cm −3 , the value of over excavation was reduced by an average of 6.6 cm, and the cost of explosives was reduced by an average of RMB 622.4.

Availability of data and materials

Data will be made available on request.

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This study was supported by the National Natural Science Foundation of China (52064008) and Guizhou Province High-level Innovative Talent Project (Qianke He Platform Talent-GCC [2022] 004-1).

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Xingchao Tian: proposing of the theory and methodology, designing of experimental plan, analysising of experimental data, writing original draft. Tiejun Tao: Editing and checking of manuscript. Caijin Xie: uniaxial compression test, triaxial compression test, brazilian splitting test, and dynamic shock compression test.

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Tian, X., Tao, T. & Xie, C. Research on the theory and method of reduced-hole blasting for large cross-section tunnel based on explosive energy dissipation. Geomech. Geophys. Geo-energ. Geo-resour. 10 , 96 (2024). https://doi.org/10.1007/s40948-024-00816-3

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Received : 24 January 2024

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DOI : https://doi.org/10.1007/s40948-024-00816-3

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