## Constructing Hypotheses in Quantitative Research

Hypotheses are the testable statements linked to your research question. Hypotheses bridge the gap from the general question you intend to investigate (i.e., the research question) to concise statements of what you hypothesize the connection between your variables to be. For example, if we were studying the influence of mentoring relationships on first-generation students’ intention to remain at their university, we might have the following research question:

“Does the presence of a mentoring relationship influence first-generation students’ intentions to remain at their university?”

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Although this statement clearly articulates the construct and specific variables we intend to study, we still have not identified exactly what we are testing. We use the hypotheses to make this clear. Specifically, we create null and alternate hypotheses to indicate exactly what we intend to test. In general, the null hypothesis states that there is no observable difference or relationship, and the alternate hypothesis states that there is an observable difference or relationship. In the example above, our hypotheses would be as follows:

Null hypothesis: The presence of a mentoring relationship does not influence first-generation students’ intention to remain at their university.

Alternate hypothesis: The presence of a mentoring relationship influences first-generation students’ intention to remain at their university.

Hypotheses may be worded with or without a direction. As written above, the hypotheses do not have a direction. To give them direction, we would consult previous literature to determine how a mentoring relationship is likely to influence intention to remain in school. If the research indicates that the presence of a mentoring relationship should increase students’ connections to the university and their willingness to remain, our alternate hypothesis would state:

“The presence of a mentoring relationship increases first-generation students’ intention to remain at their university.”

If the research indicates that the presence of a mentoring relationship minimizes students’ desire to make additional connections to the university and in turn decreases their willingness to remain, our alternate hypothesis would state:

“The presence of a mentoring relationship decreases first-generation students’ intention to remain at their university.”

Once you conduct your statistical analysis you will determine if the null hypothesis should be rejected in favor of the alternate hypothesis.

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## Research Questions & Hypotheses

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

## Research Questions

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

- Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
- Descriptive: “What factors most influence the academic achievement of senior high school students?”
- Comparative: “What is the performance difference between teaching methods A and B?”
- Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
- Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
- Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
- The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
- It’s advisable to focus on a single primary research question for the study.
- The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
- The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.

Feasible | ||

Interesting | ||

Novel | ||

Ethical | ||

Relevant |

- The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.

Population (patients) | ||

Intervention (for intervention studies only) | ||

Comparison group | ||

Outcome of interest | ||

Time |

- Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
- The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
- A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
- A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
- An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

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

## Research Hypotheses

Present the researcher’s predictions based on specific statements.

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

## Types of Research Hypothesis

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

## Tips for developing research questions and hypotheses for research studies

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

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

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

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

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

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- How to Write a Strong Hypothesis | Guide & Examples

## How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

## Table of contents

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

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

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

## Variables in hypotheses

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

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

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Step 1: ask a question.

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

## Step 2: Do some preliminary research

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

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

## Step 3: Formulate your hypothesis

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

## Step 4: Refine your hypothesis

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

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

## Step 5: Phrase your hypothesis in three ways

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

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

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

## Step 6. Write a null hypothesis

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

Research question | Hypothesis | Null hypothesis |
---|---|---|

What are the health benefits of eating an apple a day? | Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. | Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits. |

Which airlines have the most delays? | Low-cost airlines are more likely to have delays than premium airlines. | Low-cost and premium airlines are equally likely to have delays. |

Can flexible work arrangements improve job satisfaction? | Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. | There is no relationship between working hour flexibility and job satisfaction. |

How effective is secondary school sex education at reducing teen pregnancies? | Teenagers who received sex education lessons throughout secondary school will have lower rates of unplanned pregnancy than teenagers who did not receive any sex education. | Secondary school sex education has no effect on teen pregnancy rates. |

What effect does daily use of social media have on the attention span of under-16s? | There is a negative correlation between time spent on social media and attention span in under-16s. | There is no relationship between social media use and attention span in under-16s. |

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 4 July 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

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

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## The Craft of Writing a Strong Hypothesis

## Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

## What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

## Different Types of Hypotheses

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

## 1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

## 2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

- Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
- Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

## 3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

## 4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

## 5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

## 6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher the statement after assessing a group of women who take iron tablets and charting the findings.

## 7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

## Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

- A research hypothesis has to be simple yet clear to look justifiable enough.
- It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
- It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
- A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
- If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
- A hypothesis must keep and reflect the scope for further investigations and experiments.

## Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

## Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

## 1. Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

## 2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

## 3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

## 4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

## 5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

## Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

## 2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

## 3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

## 4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

## 5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

## 6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

## 7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

## 8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

## 9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

## 10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

## 11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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## How to Write a Hypothesis: A Step-by-Step Guide

## Introduction

An overview of the research hypothesis, different types of hypotheses, variables in a hypothesis, how to formulate an effective research hypothesis, designing a study around your hypothesis.

The scientific method can derive and test predictions as hypotheses. Empirical research can then provide support (or lack thereof) for the hypotheses. Even failure to find support for a hypothesis still represents a valuable contribution to scientific knowledge. Let's look more closely at the idea of the hypothesis and the role it plays in research.

As much as the term exists in everyday language, there is a detailed development that informs the word "hypothesis" when applied to research. A good research hypothesis is informed by prior research and guides research design and data analysis , so it is important to understand how a hypothesis is defined and understood by researchers.

## What is the simple definition of a hypothesis?

A hypothesis is a testable prediction about an outcome between two or more variables . It functions as a navigational tool in the research process, directing what you aim to predict and how.

## What is the hypothesis for in research?

In research, a hypothesis serves as the cornerstone for your empirical study. It not only lays out what you aim to investigate but also provides a structured approach for your data collection and analysis.

Essentially, it bridges the gap between the theoretical and the empirical, guiding your investigation throughout its course.

## What is an example of a hypothesis?

If you are studying the relationship between physical exercise and mental health, a suitable hypothesis could be: "Regular physical exercise leads to improved mental well-being among adults."

This statement constitutes a specific and testable hypothesis that directly relates to the variables you are investigating.

## What makes a good hypothesis?

A good hypothesis possesses several key characteristics. Firstly, it must be testable, allowing you to analyze data through empirical means, such as observation or experimentation, to assess if there is significant support for the hypothesis. Secondly, a hypothesis should be specific and unambiguous, giving a clear understanding of the expected relationship between variables. Lastly, it should be grounded in existing research or theoretical frameworks , ensuring its relevance and applicability.

Understanding the types of hypotheses can greatly enhance how you construct and work with hypotheses. While all hypotheses serve the essential function of guiding your study, there are varying purposes among the types of hypotheses. In addition, all hypotheses stand in contrast to the null hypothesis, or the assumption that there is no significant relationship between the variables .

Here, we explore various kinds of hypotheses to provide you with the tools needed to craft effective hypotheses for your specific research needs. Bear in mind that many of these hypothesis types may overlap with one another, and the specific type that is typically used will likely depend on the area of research and methodology you are following.

## Null hypothesis

The null hypothesis is a statement that there is no effect or relationship between the variables being studied. In statistical terms, it serves as the default assumption that any observed differences are due to random chance.

For example, if you're studying the effect of a drug on blood pressure, the null hypothesis might state that the drug has no effect.

## Alternative hypothesis

Contrary to the null hypothesis, the alternative hypothesis suggests that there is a significant relationship or effect between variables.

Using the drug example, the alternative hypothesis would posit that the drug does indeed affect blood pressure. This is what researchers aim to prove.

## Simple hypothesis

A simple hypothesis makes a prediction about the relationship between two variables, and only two variables.

For example, "Increased study time results in better exam scores." Here, "study time" and "exam scores" are the only variables involved.

## Complex hypothesis

A complex hypothesis, as the name suggests, involves more than two variables. For instance, "Increased study time and access to resources result in better exam scores." Here, "study time," "access to resources," and "exam scores" are all variables.

This hypothesis refers to multiple potential mediating variables. Other hypotheses could also include predictions about variables that moderate the relationship between the independent variable and dependent variable .

## Directional hypothesis

A directional hypothesis specifies the direction of the expected relationship between variables. For example, "Eating more fruits and vegetables leads to a decrease in heart disease."

Here, the direction of heart disease is explicitly predicted to decrease, due to effects from eating more fruits and vegetables. All hypotheses typically specify the expected direction of the relationship between the independent and dependent variable, such that researchers can test if this prediction holds in their data analysis .

## Statistical hypothesis

A statistical hypothesis is one that is testable through statistical methods, providing a numerical value that can be analyzed. This is commonly seen in quantitative research .

For example, "There is a statistically significant difference in test scores between students who study for one hour and those who study for two."

## Empirical hypothesis

An empirical hypothesis is derived from observations and is tested through empirical methods, often through experimentation or survey data . Empirical hypotheses may also be assessed with statistical analyses.

For example, "Regular exercise is correlated with a lower incidence of depression," could be tested through surveys that measure exercise frequency and depression levels.

## Causal hypothesis

A causal hypothesis proposes that one variable causes a change in another. This type of hypothesis is often tested through controlled experiments.

For example, "Smoking causes lung cancer," assumes a direct causal relationship.

## Associative hypothesis

Unlike causal hypotheses, associative hypotheses suggest a relationship between variables but do not imply causation.

For instance, "People who smoke are more likely to get lung cancer," notes an association but doesn't claim that smoking causes lung cancer directly.

## Relational hypothesis

A relational hypothesis explores the relationship between two or more variables but doesn't specify the nature of the relationship.

For example, "There is a relationship between diet and heart health," leaves the nature of the relationship (causal, associative, etc.) open to interpretation.

## Logical hypothesis

A logical hypothesis is based on sound reasoning and logical principles. It's often used in theoretical research to explore abstract concepts, rather than being based on empirical data.

For example, "If all men are mortal and Socrates is a man, then Socrates is mortal," employs logical reasoning to make its point.

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In any research hypothesis, variables play a critical role. These are the elements or factors that the researcher manipulates, controls, or measures. Understanding variables is essential for crafting a clear, testable hypothesis and for the stages of research that follow, such as data collection and analysis.

In the realm of hypotheses, there are generally two types of variables to consider: independent and dependent. Independent variables are what you, as the researcher, manipulate or change in your study. It's considered the cause in the relationship you're investigating. For instance, in a study examining the impact of sleep duration on academic performance, the independent variable would be the amount of sleep participants get.

Conversely, the dependent variable is the outcome you measure to gauge the effect of your manipulation. It's the effect in the cause-and-effect relationship. The dependent variable thus refers to the main outcome of interest in your study. In the same sleep study example, the academic performance, perhaps measured by exam scores or GPA, would be the dependent variable.

Beyond these two primary types, you might also encounter control variables. These are variables that could potentially influence the outcome and are therefore kept constant to isolate the relationship between the independent and dependent variables . For example, in the sleep and academic performance study, control variables could include age, diet, or even the subject of study.

By clearly identifying and understanding the roles of these variables in your hypothesis, you set the stage for a methodologically sound research project. It helps you develop focused research questions, design appropriate experiments or observations, and carry out meaningful data analysis . It's a step that lays the groundwork for the success of your entire study.

Crafting a strong, testable hypothesis is crucial for the success of any research project. It sets the stage for everything from your study design to data collection and analysis . Below are some key considerations to keep in mind when formulating your hypothesis:

- Be specific : A vague hypothesis can lead to ambiguous results and interpretations . Clearly define your variables and the expected relationship between them.
- Ensure testability : A good hypothesis should be testable through empirical means, whether by observation , experimentation, or other forms of data analysis.
- Ground in literature : Before creating your hypothesis, consult existing research and theories. This not only helps you identify gaps in current knowledge but also gives you valuable context and credibility for crafting your hypothesis.
- Use simple language : While your hypothesis should be conceptually sound, it doesn't have to be complicated. Aim for clarity and simplicity in your wording.
- State direction, if applicable : If your hypothesis involves a directional outcome (e.g., "increase" or "decrease"), make sure to specify this. You also need to think about how you will measure whether or not the outcome moved in the direction you predicted.
- Keep it focused : One of the common pitfalls in hypothesis formulation is trying to answer too many questions at once. Keep your hypothesis focused on a specific issue or relationship.
- Account for control variables : Identify any variables that could potentially impact the outcome and consider how you will control for them in your study.
- Be ethical : Make sure your hypothesis and the methods for testing it comply with ethical standards , particularly if your research involves human or animal subjects.

Designing your study involves multiple key phases that help ensure the rigor and validity of your research. Here we discuss these crucial components in more detail.

## Literature review

Starting with a comprehensive literature review is essential. This step allows you to understand the existing body of knowledge related to your hypothesis and helps you identify gaps that your research could fill. Your research should aim to contribute some novel understanding to existing literature, and your hypotheses can reflect this. A literature review also provides valuable insights into how similar research projects were executed, thereby helping you fine-tune your own approach.

## Research methods

Choosing the right research methods is critical. Whether it's a survey, an experiment, or observational study, the methodology should be the most appropriate for testing your hypothesis. Your choice of methods will also depend on whether your research is quantitative, qualitative, or mixed-methods. Make sure the chosen methods align well with the variables you are studying and the type of data you need.

## Preliminary research

Before diving into a full-scale study, it’s often beneficial to conduct preliminary research or a pilot study . This allows you to test your research methods on a smaller scale, refine your tools, and identify any potential issues. For instance, a pilot survey can help you determine if your questions are clear and if the survey effectively captures the data you need. This step can save you both time and resources in the long run.

## Data analysis

Finally, planning your data analysis in advance is crucial for a successful study. Decide which statistical or analytical tools are most suited for your data type and research questions . For quantitative research, you might opt for t-tests, ANOVA, or regression analyses. For qualitative research , thematic analysis or grounded theory may be more appropriate. This phase is integral for interpreting your results and drawing meaningful conclusions in relation to your research question.

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## Quantitative Research Hypothesis Examples

In general, a researcher arranges hypotheses based on the formulation of problems and theoretical studies. For quantitative research, the hypothesis used is a statistical hypothesis, meaning that the hypothesis must be tested using statistical rules. Whereas for qualitative research does not need to use statistical rules. In a quantitative study, the formulated statistical hypothesis has two forms, the null hypothesis (Ho) and the alternative hypothesis (Ha). In general, hypotheses for quantitative research have three types: Descriptive Hypothesis, Comparative Hypothesis, and Associative Hypothesis.

## Descriptive Hypothesis

Descriptive hypotheses are temporary conjectures about the value of a variable, not expressing relationships or comparisons. Remember, only about the value of a variable. Statistics used to test descriptive hypotheses are sample mean tests or standard deviation tests. A researcher formulates hypothesis based on the problem formulation and theoretical study. Following are some examples of problem formulations (PF), hypotheses (H). PF: What is the percentage of junior high school mathematics mastery in the subject matter of the set? H: Junior high school mathematics teacher mastery in the subject matter reaches 70%.

PF: How good is the grade XI mastery of class XI material? H: mastery of class X material by class XI students reaches 75%.

## Comparative Hypothesis

The comparative hypothesis is a temporary construct that compares the values of two variables. That is, in the comparative hypothesis, we do not determine with certainty the value of the variables we examine, but compare. Means, there are two variables that are the same, but different samples. The statistics used to test this comparative hypothesis are (assuming normality is met) using a t-test. But before that, the normality and homogeneity must be tested first. Following are some examples of problem formulations (PF), hypotheses (H). PF: Is there a difference in the problem-solving abilities of students who got X learning better than students who got Y learning? H: the problem solving ability of students who get learning X is better than students who get learning Y.

PF: Are there differences in the critical thinking skills of students who study during the day are better than students who study in the morning? H: there is no difference in the critical thinking skills of students who study in the afternoon with students who study in the morning.

The two hypothetical examples above are slightly different. In the first hypothesis, we claim that the problem solving ability of students who get learning X is better than students who get learning Y. While in the second hypothesis, there is no one-sided claim that the critical thinking skills of students who learn during the day are better or worse. We only state that there are differences. Which problem is better, it does not concern this hypothesis. The first hypothesis is a one-party test hypothesis, while the second hypothesis is called a two-party test hypothesis.

## Associative Quantitative Hypothesis

The associative hypothesis is a relationship between the relationship between two variables, the dependent variable and the independent variable. The statistics are used to test this comparative hypothesis are (assuming normality is met) using Product Moment Correlation, Double Correlation, or Partial Correlation. The following are examples of problem formulations (PF), hypotheses (H). PF: Is there a relationship between student achievement and the level of student anxiety? H: there is a negative relationship between student achievement with the level of student anxiety.

PF: Is there a relationship between student learning outcomes and seating arrangements? H: there is a positive relationship between student achievement with the level of student anxiety. In the first hypothesis there are the words ‘negative relationship’. Negative relationship means inversely proportional. That is if the level of student anxiety is high, then student achievement is low. Whereas in the second hypothesis there are the words ‘positive relationship’. Positive relationship means directly proportional. It means if the seating arrangement is good, the student learning outcomes are high.

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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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## Exploring Research Question and Hypothesis Examples: A Comprehensive Guide

This comprehensive guide explores the intricacies of formulating research questions and hypotheses across various academic disciplines. By delving into examples and methodological approaches, the article aims to provide scholars and researchers with the tools necessary to develop robust and effective research frameworks. Understanding and crafting well-formed research questions and hypotheses are pivotal in conducting meaningful research that can significantly contribute to knowledge within a field.

## Key Takeaways

- Understand the fundamental differences and connections between research questions and hypotheses.
- Learn how to craft effective and precise research questions that guide the research process.
- Explore various types of hypotheses and methods for testing and refining them.
- Examine practical examples of research questions and hypotheses across multiple disciplines.
- Gain insights into the impact of well-constructed research questions and hypotheses on research outcomes, academic publishing, and grant applications.

## Understanding the Fundamentals of Research Questions and Hypotheses

Defining research questions.

Research questions are the backbone of any scholarly inquiry, guiding you through the exploration of your chosen topic. They help you focus your study and determine the direction of your research. A well-crafted research question should be clear, focused, and answerable within the constraints of your study.

## Characteristics of a Strong Hypothesis

A strong hypothesis provides a specific, testable prediction about the expected outcomes of your research. It is not merely a guess but is grounded in existing literature and theory. To develop a robust hypothesis, consider the variables involved and ensure that it is feasible to test them within your study's design.

## Interrelation Between Research Questions and Hypotheses

Understanding the interrelation between research questions and hypotheses is crucial for structuring your research effectively. Your hypothesis should directly address the gap in the literature highlighted by your research question, providing a clear pathway for investigation. This alignment ensures that your study can contribute valuable insights to your field.

## Crafting Effective Research Questions

Identifying the purpose.

To craft an effective research question , you must first identify the purpose of your study. This involves understanding what you aim to discover or elucidate through your research. Ask yourself what the core of your inquiry is and what outcomes you hope to achieve. This clarity will guide your entire research process, ensuring that your question is not only relevant but also deeply rooted in your specific academic or practical goals.

## Scope and Limitations

It's crucial to define the scope and limitations of your research early on. This helps in setting realistic boundaries and expectations for your study. Consider factors such as time, resources, and the breadth of the subject area. Narrowing down your focus to a manageable scope can prevent the common pitfall of an overly broad or vague question, which can dilute the impact of your findings.

## Formulating Questions that Drive Inquiry

The final step in crafting your research question is formulating it in a way that drives inquiry. This means your question should be clear, concise, and structured to prompt detailed investigation and critical analysis. It should challenge existing knowledge and push the boundaries of what is already known. Utilizing strategies like the Thesis Dialogue Blueprint or the Research Proposal Compass can be instrumental in refining your question to ensure it is both innovative and feasible.

## Developing Hypotheses in Research

From research questions to hypotheses.

When you transition from research questions to hypotheses, you are essentially moving from what you want to know to what you predict will happen. This shift involves formulating a specific, testable prediction that directly stems from your initial question. Ensure your hypothesis is directly linked to and derived from your research question to maintain a coherent research strategy.

## Types of Hypotheses

There are several types of hypotheses you might encounter, including simple, complex, directional, nondirectional, associative, causal, null, and alternative. Each type serves a different purpose and is chosen based on the specifics of the research question and the nature of the study. For instance, a null hypothesis might be used to test the effectiveness of a new teaching method compared to the standard.

## Testing and Refining Hypotheses

Testing your hypothesis is a critical step in the research process. This phase involves collecting data, conducting experiments, or utilizing other research methods to determine the validity of your hypothesis. After testing, you may find that your hypothesis needs refining or even reformation based on the outcomes. This iterative process is essential for narrowing down the most accurate explanation or prediction for your research question.

## Examples of Research Questions in Various Disciplines

Humanities and social sciences.

In the realm of Humanities and Social Sciences, research questions often explore cultural, social, historical, or philosophical aspects. How does gender representation in 20th-century American literature reflect broader social changes? This question not only seeks to uncover specific literary trends but also ties them to societal shifts, offering a rich field for analysis.

## Natural Sciences

Research questions in the Natural Sciences are typically aimed at understanding natural phenomena or solving specific scientific problems. A common question might be, What are the effects of plastic pollutants on marine biodiversity? This inquiry highlights the environmental concerns and seeks empirical data to understand the impact.

## Applied Sciences

In Applied Sciences, the focus is often on improving technology or engineering solutions. A pertinent question could be, How can renewable energy sources be integrated into existing power grids? This question addresses the practical challenges and potential innovations in energy systems, crucial for advancing sustainable technologies.

## Analyzing Hypothesis Examples Across Fields

Case studies in psychology.

In psychology, hypotheses often explore the causal relationships between cognitive functions and behaviors. Consider how a hypothesis might predict the impact of stress on memory recall . By examining various case studies, you can see how hypotheses are specifically tailored to address intricate psychological phenomena.

## Experimental Research in Biology

Biology experiments frequently test hypotheses about physiological processes or genetic information. For instance, a hypothesis might propose that a specific gene influences plant growth rates. Through rigorous testing, these hypotheses contribute significantly to our understanding of biological systems.

## Field Studies in Environmental Science

Field studies in environmental science provide a rich ground for testing hypotheses related to ecosystem dynamics and conservation strategies. A common hypothesis might explore the effects of human activity on biodiversity. These studies often involve complex data collection and analysis, highlighting the interrelation between empirical evidence and theoretical predictions.

## Methodological Approaches to Formulating Hypotheses

Quantitative vs. qualitative research.

When you embark on hypothesis formulation, understanding the distinction between quantitative and qualitative research methodologies is crucial. Quantitative research focuses on numerical data and statistical analysis, ideal for hypotheses that require measurable evidence. In contrast, qualitative research delves into thematic and descriptive data, providing depth and context to hypotheses that explore behaviors, perceptions, and experiences.

## The Role of Theoretical Frameworks

Theoretical frameworks serve as the backbone for developing robust hypotheses. They provide a structured way to align your hypothesis with existing knowledge. By integrating theories and models relevant to your study, you ensure that your hypothesis has a solid foundation and aligns with established academic thought.

## Utilizing Existing Literature to Form Hypotheses

A thorough review of existing literature is indispensable for crafting a well-informed hypothesis. This process not only highlights gaps in current research but also allows you to build on the work of others. By synthesizing findings from previous studies, you can formulate hypotheses that are both innovative and grounded in academic precedent.

## Evaluating the Impact of Well-Formed Research Questions and Hypotheses

On research outcomes.

Understanding the impact of well-formed research questions and hypotheses on research outcomes is crucial. Well-crafted questions and hypotheses serve as a framework that guides the entire research process , ensuring that the study remains focused and relevant. They help in defining the scope of the study and in identifying the variables that need to be measured, thus directly influencing the validity and reliability of the research findings.

## In Academic Publishing

The role of well-defined research questions and hypotheses extends beyond the research process into the realm of academic publishing. A clear hypothesis provides a strong foundation for the research paper, enhancing its chances of acceptance in prestigious journals. The clarity and direction afforded by a solid hypothesis make the research more appealing to a scholarly audience, potentially increasing citation rates and academic recognition.

## In Grant Applications

When applying for research grants, the clarity of your research questions and hypotheses can significantly impact the decision-making process of funding bodies. A well-articulated hypothesis demonstrates a clear vision and a structured approach to addressing a specific issue, which can be crucial in securing funding. Grant reviewers often look for proposals that promise substantial contributions to the field, and a strong hypothesis can be a key factor in showcasing the potential impact of your research.

In our latest article, 'Evaluating the Impact of Well-Formed Research Questions and Hypotheses,' we delve into the crucial role that precise questions and hypotheses play in academic research. Understanding this can significantly enhance your thesis writing process. For a deeper exploration and practical tools to apply these concepts, visit our website and discover how our Thesis Action Plan can transform your academic journey. Don't miss out on our special offers tailored just for you!

In this comprehensive guide, we have explored various examples of research questions and hypotheses, shedding light on their significance and application in academic research. Understanding the distinction between a research question and a hypothesis, as well as knowing how to effectively formulate them, is crucial for conducting methodical and impactful studies. By examining different scenarios and examples, this guide aims to equip researchers with the knowledge to craft well-defined research questions and hypotheses that can drive meaningful investigations and contribute to the broader field of knowledge. As we continue to delve into the intricacies of research design, it is our hope that this guide serves as a valuable resource for both novice and experienced researchers in their scholarly endeavors.

## Frequently Asked Questions

What is a research question.

A research question is a clearly defined query that guides a scientific or academic study. It sets the scope and focus of the research by asking about a specific phenomenon or issue.

## How does a hypothesis differ from a research question?

A hypothesis is a specific, testable prediction about what will happen in a study based on prior knowledge or theory, while a research question is an open query that guides the direction of the investigation.

## What are the characteristics of a strong hypothesis?

A strong hypothesis is clear, testable, based on existing knowledge, and it states an expected relationship between variables.

## How can research questions and hypotheses interrelate?

Research questions define the scope of inquiry, while hypotheses provide a specific prediction about the expected outcomes that can be tested through research methods.

## What should be considered when formulating a research question?

When formulating a research question, consider clarity, focus, relevance, and the feasibility of answering the question through available research methods.

## Why is it important to have a well-formed hypothesis?

A well-formed hypothesis directs the research process, allows for clear testing of assumptions, and helps in drawing meaningful conclusions that can contribute to the body of knowledge.

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

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

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

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

## Research Hypothesis 101

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

## What is a hypothesis?

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

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

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

Hypothesis: sleep impacts academic performance.

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

But that’s not good enough…

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

## What is a research hypothesis?

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

Let’s take a look at these more closely.

## Need a helping hand?

## Hypothesis Essential #1: Specificity & Clarity

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

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

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

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

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

## Hypothesis Essential #2: Testability (Provability)

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

For example, consider the hypothesis we mentioned earlier:

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

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

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

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

## Defining A Research Hypothesis

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

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

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

## What about the null hypothesis?

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

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

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

And there you have it – hypotheses in a nutshell.

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

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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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## How to write a research hypothesis

Last updated

19 January 2023

Reviewed by

Miroslav Damyanov

Start with a broad subject matter that excites you, so your curiosity will motivate your work. Conduct a literature search to determine the range of questions already addressed and spot any holes in the existing research.

Narrow the topics that interest you and determine your research question. Rather than focusing on a hole in the research, you might choose to challenge an existing assumption, a process called problematization. You may also find yourself with a short list of questions or related topics.

Use the FINER method to determine the single problem you'll address with your research. FINER stands for:

I nteresting

You need a feasible research question, meaning that there is a way to address the question. You should find it interesting, but so should a larger audience. Rather than repeating research that others have already conducted, your research hypothesis should test something novel or unique.

The research must fall into accepted ethical parameters as defined by the government of your country and your university or college if you're an academic. You'll also need to come up with a relevant question since your research should provide a contribution to the existing research area.

This process typically narrows your shortlist down to a single problem you'd like to study and the variable you want to test. You're ready to write your hypothesis statements.

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- Types of research hypotheses

It is important to narrow your topic down to one idea before trying to write your research hypothesis. You'll only test one problem at a time. To do this, you'll write two hypotheses – a null hypothesis (H0) and an alternative hypothesis (Ha).

You'll come across many terms related to developing a research hypothesis or referring to a specific type of hypothesis. Let's take a quick look at these terms.

## Null hypothesis

The term null hypothesis refers to a research hypothesis type that assumes no statistically significant relationship exists within a set of observations or data. It represents a claim that assumes that any observed relationship is due to chance. Represented as H0, the null represents the conjecture of the research.

## Alternative hypothesis

The alternative hypothesis accompanies the null hypothesis. It states that the situation presented in the null hypothesis is false or untrue, and claims an observed effect in your test. This is typically denoted by Ha or H(n), where “n” stands for the number of alternative hypotheses. You can have more than one alternative hypothesis.

## Simple hypothesis

The term simple hypothesis refers to a hypothesis or theory that predicts the relationship between two variables - the independent (predictor) and the dependent (predicted).

## Complex hypothesis

The term complex hypothesis refers to a model – either quantitative (mathematical) or qualitative . A complex hypothesis states the surmised relationship between two or more potentially related variables.

## Directional hypothesis

When creating a statistical hypothesis, the directional hypothesis (the null hypothesis) states an assumption regarding one parameter of a population. Some academics call this the “one-sided” hypothesis. The alternative hypothesis indicates whether the researcher tests for a positive or negative effect by including either the greater than (">") or less than ("<") sign.

## Non-directional hypothesis

We refer to the alternative hypothesis in a statistical research question as a non-directional hypothesis. It includes the not equal ("≠") sign to show that the research tests whether or not an effect exists without specifying the effect's direction (positive or negative).

## Associative hypothesis

The term associative hypothesis assumes a link between two variables but stops short of stating that one variable impacts the other. Academic statistical literature asserts in this sense that correlation does not imply causation. So, although the hypothesis notes the correlation between two variables – the independent and dependent - it does not predict how the two interact.

## Logical hypothesis

Typically used in philosophy rather than science, researchers can't test a logical hypothesis because the technology or data set doesn't yet exist. A logical hypothesis uses logic as the basis of its assumptions.

In some cases, a logical hypothesis can become an empirical hypothesis once technology provides an opportunity for testing. Until that time, the question remains too expensive or complex to address. Note that a logical hypothesis is not a statistical hypothesis.

## Empirical hypothesis

When we consider the opposite of a logical hypothesis, we call this an empirical or working hypothesis. This type of hypothesis considers a scientifically measurable question. A researcher can consider and test an empirical hypothesis through replicable tests, observations, and measurements.

## Statistical hypothesis

The term statistical hypothesis refers to a test of a theory that uses representative statistical models to test relationships between variables to draw conclusions regarding a large population. This requires an existing large data set, commonly referred to as big data, or implementing a survey to obtain original statistical information to form a data set for the study.

Testing this type of hypothesis requires the use of random samples. Note that the null and alternative hypotheses are used in statistical hypothesis testing.

## Causal hypothesis

The term causal hypothesis refers to a research hypothesis that tests a cause-and-effect relationship. A causal hypothesis is utilized when conducting experimental or quasi-experimental research.

## Descriptive hypothesis

The term descriptive hypothesis refers to a research hypothesis used in non-experimental research, specifying an influence in the relationship between two variables.

- What makes an effective research hypothesis?

An effective research hypothesis offers a clearly defined, specific statement, using simple wording that contains no assumptions or generalizations, and that you can test. A well-written hypothesis should predict the tested relationship and its outcome. It contains zero ambiguity and offers results you can observe and test.

The research hypothesis should address a question relevant to a research area. Overall, your research hypothesis needs the following essentials:

Hypothesis Essential #1: Specificity & Clarity

Hypothesis Essential #2: Testability (Provability)

- How to develop a good research hypothesis

In developing your hypothesis statements, you must pre-plan some of your statistical analysis. Once you decide on your problem to examine, determine three aspects:

the parameter you'll test

the test's direction (left-tailed, right-tailed, or non-directional)

the hypothesized parameter value

Any quantitative research includes a hypothesized parameter value of a mean, a proportion, or the difference between two proportions. Here's how to note each parameter:

Single mean (μ)

Paired means (μd)

Single proportion (p)

Difference between two independent means (μ1−μ2)

Difference between two proportions (p1−p2)

Simple linear regression slope (β)

Correlation (ρ)

Defining these parameters and determining whether you want to test the mean, proportion, or differences helps you determine the statistical tests you'll conduct to analyze your data. When writing your hypothesis, you only need to decide which parameter to test and in what overarching way.

The null research hypothesis must include everyday language, in a single sentence, stating the problem you want to solve. Write it as an if-then statement with defined variables. Write an alternative research hypothesis that states the opposite.

- What is the correct format for writing a hypothesis?

The following example shows the proper format and textual content of a hypothesis. It follows commonly accepted academic standards.

Null hypothesis (H0): High school students who participate in varsity sports as opposed to those who do not, fail to score higher on leadership tests than students who do not participate.

Alternative hypothesis (H1): High school students who play a varsity sport as opposed to those who do not participate in team athletics will score higher on leadership tests than students who do not participate in athletics.

The research question tests the correlation between varsity sports participation and leadership qualities expressed as a score on leadership tests. It compares the population of athletes to non-athletes.

- What are the five steps of a hypothesis?

Once you decide on the specific problem or question you want to address, you can write your research hypothesis. Use this five-step system to hone your null hypothesis and generate your alternative hypothesis.

Step 1 : Create your research question. This topic should interest and excite you; answering it provides relevant information to an industry or academic area.

Step 2 : Conduct a literature review to gather essential existing research.

Step 3 : Write a clear, strong, simply worded sentence that explains your test parameter, test direction, and hypothesized parameter.

Step 4 : Read it a few times. Have others read it and ask them what they think it means. Refine your statement accordingly until it becomes understandable to everyone. While not everyone can or will comprehend every research study conducted, any person from the general population should be able to read your hypothesis and alternative hypothesis and understand the essential question you want to answer.

Step 5 : Re-write your null hypothesis until it reads simply and understandably. Write your alternative hypothesis.

## What is the Red Queen hypothesis?

Some hypotheses are well-known, such as the Red Queen hypothesis. Choose your wording carefully, since you could become like the famed scientist Dr. Leigh Van Valen. In 1973, Dr. Van Valen proposed the Red Queen hypothesis to describe coevolutionary activity, specifically reciprocal evolutionary effects between species to explain extinction rates in the fossil record.

Essentially, Van Valen theorized that to survive, each species remains in a constant state of adaptation, evolution, and proliferation, and constantly competes for survival alongside other species doing the same. Only by doing this can a species avoid extinction. Van Valen took the hypothesis title from the Lewis Carroll book, "Through the Looking Glass," which contains a key character named the Red Queen who explains to Alice that for all of her running, she's merely running in place.

- Getting started with your research

In conclusion, once you write your null hypothesis (H0) and an alternative hypothesis (Ha), you’ve essentially authored the elevator pitch of your research. These two one-sentence statements describe your topic in simple, understandable terms that both professionals and laymen can understand. They provide the starting point of your research project.

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## What is Quantitative Research? Definition, Methods, Types, and Examples

If you’re wondering what is quantitative research and whether this methodology works for your research study, you’re not alone. If you want a simple quantitative research definition , then it’s enough to say that this is a method undertaken by researchers based on their study requirements. However, to select the most appropriate research for their study type, researchers should know all the methods available.

Selecting the right research method depends on a few important criteria, such as the research question, study type, time, costs, data availability, and availability of respondents. There are two main types of research methods— quantitative research and qualitative research. The purpose of quantitative research is to validate or test a theory or hypothesis and that of qualitative research is to understand a subject or event or identify reasons for observed patterns.

Quantitative research methods are used to observe events that affect a particular group of individuals, which is the sample population. In this type of research, diverse numerical data are collected through various methods and then statistically analyzed to aggregate the data, compare them, or show relationships among the data. Quantitative research methods broadly include questionnaires, structured observations, and experiments.

Here are two quantitative research examples:

- Satisfaction surveys sent out by a company regarding their revamped customer service initiatives. Customers are asked to rate their experience on a rating scale of 1 (poor) to 5 (excellent).
- A school has introduced a new after-school program for children, and a few months after commencement, the school sends out feedback questionnaires to the parents of the enrolled children. Such questionnaires usually include close-ended questions that require either definite answers or a Yes/No option. This helps in a quick, overall assessment of the program’s outreach and success.

Table of Contents

## What is quantitative research ? 1,2

The steps shown in the figure can be grouped into the following broad steps:

- Theory : Define the problem area or area of interest and create a research question.
- Hypothesis : Develop a hypothesis based on the research question. This hypothesis will be tested in the remaining steps.
- Research design : In this step, the most appropriate quantitative research design will be selected, including deciding on the sample size, selecting respondents, identifying research sites, if any, etc.
- Data collection : This process could be extensive based on your research objective and sample size.
- Data analysis : Statistical analysis is used to analyze the data collected. The results from the analysis help in either supporting or rejecting your hypothesis.
- Present results : Based on the data analysis, conclusions are drawn, and results are presented as accurately as possible.

## Quantitative research characteristics 4

- Large sample size : This ensures reliability because this sample represents the target population or market. Due to the large sample size, the outcomes can be generalized to the entire population as well, making this one of the important characteristics of quantitative research .
- Structured data and measurable variables: The data are numeric and can be analyzed easily. Quantitative research involves the use of measurable variables such as age, salary range, highest education, etc.
- Easy-to-use data collection methods : The methods include experiments, controlled observations, and questionnaires and surveys with a rating scale or close-ended questions, which require simple and to-the-point answers; are not bound by geographical regions; and are easy to administer.
- Data analysis : Structured and accurate statistical analysis methods using software applications such as Excel, SPSS, R. The analysis is fast, accurate, and less effort intensive.
- Reliable : The respondents answer close-ended questions, their responses are direct without ambiguity and yield numeric outcomes, which are therefore highly reliable.
- Reusable outcomes : This is one of the key characteristics – outcomes of one research can be used and replicated in other research as well and is not exclusive to only one study.

## Quantitative research methods 5

Quantitative research methods are classified into two types—primary and secondary.

## Primary quantitative research method:

In this type of quantitative research , data are directly collected by the researchers using the following methods.

– Survey research : Surveys are the easiest and most commonly used quantitative research method . They are of two types— cross-sectional and longitudinal.

->Cross-sectional surveys are specifically conducted on a target population for a specified period, that is, these surveys have a specific starting and ending time and researchers study the events during this period to arrive at conclusions. The main purpose of these surveys is to describe and assess the characteristics of a population. There is one independent variable in this study, which is a common factor applicable to all participants in the population, for example, living in a specific city, diagnosed with a specific disease, of a certain age group, etc. An example of a cross-sectional survey is a study to understand why individuals residing in houses built before 1979 in the US are more susceptible to lead contamination.

->Longitudinal surveys are conducted at different time durations. These surveys involve observing the interactions among different variables in the target population, exposing them to various causal factors, and understanding their effects across a longer period. These studies are helpful to analyze a problem in the long term. An example of a longitudinal study is the study of the relationship between smoking and lung cancer over a long period.

– Descriptive research : Explains the current status of an identified and measurable variable. Unlike other types of quantitative research , a hypothesis is not needed at the beginning of the study and can be developed even after data collection. This type of quantitative research describes the characteristics of a problem and answers the what, when, where of a problem. However, it doesn’t answer the why of the problem and doesn’t explore cause-and-effect relationships between variables. Data from this research could be used as preliminary data for another study. Example: A researcher undertakes a study to examine the growth strategy of a company. This sample data can be used by other companies to determine their own growth strategy.

– Correlational research : This quantitative research method is used to establish a relationship between two variables using statistical analysis and analyze how one affects the other. The research is non-experimental because the researcher doesn’t control or manipulate any of the variables. At least two separate sample groups are needed for this research. Example: Researchers studying a correlation between regular exercise and diabetes.

– Causal-comparative research : This type of quantitative research examines the cause-effect relationships in retrospect between a dependent and independent variable and determines the causes of the already existing differences between groups of people. This is not a true experiment because it doesn’t assign participants to groups randomly. Example: To study the wage differences between men and women in the same role. For this, already existing wage information is analyzed to understand the relationship.

– Experimental research : This quantitative research method uses true experiments or scientific methods for determining a cause-effect relation between variables. It involves testing a hypothesis through experiments, in which one or more independent variables are manipulated and then their effect on dependent variables are studied. Example: A researcher studies the importance of a drug in treating a disease by administering the drug in few patients and not administering in a few.

The following data collection methods are commonly used in primary quantitative research :

- Sampling : The most common type is probability sampling, in which 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—simple random, systematic, stratified, and cluster sampling.
- Interviews : These are commonly telephonic or face-to-face.
- 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 quantitative research .
- Surveys and questionnaires : Surveys can be administered both online and offline depending on the requirement and sample size.

The data collected can be analyzed in several ways in quantitative research , as listed below:

- Cross-tabulation —Uses a tabular format to draw inferences among collected data
- MaxDiff analysis —Gauges the preferences of the respondents
- TURF analysis —Total Unduplicated Reach and Frequency Analysis; helps in determining the market strategy for a business
- Gap analysis —Identify gaps in attaining the desired results
- SWOT analysis —Helps identify strengths, weaknesses, opportunities, and threats of a product, service, or organization
- Text analysis —Used for interpreting unstructured data

## Secondary quantitative research methods :

This method involves conducting research using already existing or secondary data. This method is less effort intensive and requires lesser time. However, researchers should verify the authenticity and recency of the sources being used and ensure their accuracy.

The main sources of secondary data are:

- The Internet
- Government and non-government sources
- Public libraries
- Educational institutions
- Commercial information sources such as newspapers, journals, radio, TV

## When to use quantitative research 6

Here are some simple ways to decide when to use quantitative research . Use quantitative research to:

- recommend a final course of action
- find whether a consensus exists regarding a particular subject
- generalize results to a larger population
- determine a cause-and-effect relationship between variables
- describe characteristics of specific groups of people
- test hypotheses and examine specific relationships
- identify and establish size of market segments

## A research case study to understand when to use quantitative research 7

Context: A study was undertaken to evaluate a major innovation in a hospital’s design, in terms of workforce implications and impact on patient and staff experiences of all single-room hospital accommodations. The researchers undertook a mixed methods approach to answer their research questions. Here, we focus on the quantitative research aspect.

Research questions : What are the advantages and disadvantages for the staff as a result of the hospital’s move to the new design with all single-room accommodations? Did the move affect staff experience and well-being and improve their ability to deliver high-quality care?

Method: The researchers obtained quantitative data from three sources:

- Staff activity (task time distribution): Each staff member was shadowed by a researcher who observed each task undertaken by the staff, and logged the time spent on each activity.
- Staff travel distances : The staff were requested to wear pedometers, which recorded the distances covered.
- Staff experience surveys : Staff were surveyed before and after the move to the new hospital design.

Results of quantitative research : The following observations were made based on quantitative data analysis:

- The move to the new design did not result in a significant change in the proportion of time spent on different activities.
- Staff activity events observed per session were higher after the move, and direct care and professional communication events per hour decreased significantly, suggesting fewer interruptions and less fragmented care.
- A significant increase in medication tasks among the recorded events suggests that medication administration was integrated into patient care activities.
- Travel distances increased for all staff, with highest increases for staff in the older people’s ward and surgical wards.
- Ratings for staff toilet facilities, locker facilities, and space at staff bases were higher but those for social interaction and natural light were lower.

## Advantages of quantitative research 1,2

When choosing the right research methodology, also consider the advantages of quantitative research and how it can impact your study.

- Quantitative research methods are more scientific and rational. They use quantifiable data leading to objectivity in the results and avoid any chances of ambiguity.
- This type of research uses numeric data so analysis is relatively easier .
- In most cases, a hypothesis is already developed and quantitative research helps in testing and validatin g these constructed theories based on which researchers can make an informed decision about accepting or rejecting their theory.
- The use of statistical analysis software ensures quick analysis of large volumes of data and is less effort intensive.
- Higher levels of control can be applied to the research so the chances of bias can be reduced.
- Quantitative research is based on measured value s, facts, and verifiable information so it can be easily checked or replicated by other researchers leading to continuity in scientific research.

## Disadvantages of quantitative research 1,2

Quantitative research may also be limiting; take a look at the disadvantages of quantitative research.

- Experiments are conducted in controlled settings instead of natural settings and it is possible for researchers to either intentionally or unintentionally manipulate the experiment settings to suit the results they desire.
- Participants must necessarily give objective answers (either one- or two-word, or yes or no answers) and the reasons for their selection or the context are not considered.
- Inadequate knowledge of statistical analysis methods may affect the results and their interpretation.
- Although statistical analysis indicates the trends or patterns among variables, the reasons for these observed patterns cannot be interpreted and the research may not give a complete picture.
- Large sample sizes are needed for more accurate and generalizable analysis .
- Quantitative research cannot be used to address complex issues.

## Frequently asked questions on quantitative research

Q: What is the difference between quantitative research and qualitative research? 1

A: The following table lists the key differences between quantitative research and qualitative research, some of which may have been mentioned earlier in the article.

Purpose and design | ||

Research question | ||

Sample size | Large | Small |

Data | ||

Data collection method | Experiments, controlled observations, questionnaires and surveys with a rating scale or close-ended questions. The methods can be experimental, quasi-experimental, descriptive, or correlational. | Semi-structured interviews/surveys with open-ended questions, document study/literature reviews, focus groups, case study research, ethnography |

Data analysis |

Q: What is the difference between reliability and validity? 8,9

A: The term reliability refers to the consistency of a research study. For instance, if a food-measuring weighing scale gives different readings every time the same quantity of food is measured then that weighing scale is not reliable. If the findings in a research study are consistent every time a measurement is made, then the study is considered reliable. However, it is usually unlikely to obtain the exact same results every time because some contributing variables may change. In such cases, a correlation coefficient is used to assess the degree of reliability. A strong positive correlation between the results indicates reliability.

Validity can be defined as the degree to which a tool actually measures what it claims to measure. It helps confirm the credibility of your research and suggests that the results may be generalizable. In other words, it measures the accuracy of the research.

The following table gives the key differences between reliability and validity.

Importance | Refers to the consistency of a measure | Refers to the accuracy of a measure |

Ease of achieving | Easier, yields results faster | Involves more analysis, more difficult to achieve |

Assessment method | By examining the consistency of outcomes over time, between various observers, and within the test | By comparing the accuracy of the results with accepted theories and other measurements of the same idea |

Relationship | Unreliable measurements typically cannot be valid | Valid measurements are also reliable |

Types | Test-retest reliability, internal consistency, inter-rater reliability | Content validity, criterion validity, face validity, construct validity |

Q: What is mixed methods research? 10

A: A mixed methods approach combines the characteristics of both quantitative research and qualitative research 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. A mixed methods research design is useful in case of research questions that cannot be answered by either quantitative research or qualitative research alone. However, this method could be more effort- and cost-intensive because of the requirement of more resources. The figure 3 shows some basic mixed methods research designs that could be used.

Thus, quantitative research is the appropriate method for testing your hypotheses and can be used either alone or in combination with qualitative research per your study requirements. We hope this article has provided an insight into the various facets of quantitative research , including its different characteristics, advantages, and disadvantages, and a few tips to quickly understand when to use this research method.

References

- Qualitative vs quantitative research: Differences, examples, & methods. Simply Psychology. Accessed Feb 28, 2023. https://simplypsychology.org/qualitative-quantitative.html#Quantitative-Research
- Your ultimate guide to quantitative research. Qualtrics. Accessed February 28, 2023. https://www.qualtrics.com/uk/experience-management/research/quantitative-research/
- The steps of quantitative research. Revise Sociology. Accessed March 1, 2023. https://revisesociology.com/2017/11/26/the-steps-of-quantitative-research/
- What are the characteristics of quantitative research? Marketing91. Accessed March 1, 2023. https://www.marketing91.com/characteristics-of-quantitative-research/
- Quantitative research: Types, characteristics, methods, & examples. ProProfs Survey Maker. Accessed February 28, 2023. https://www.proprofssurvey.com/blog/quantitative-research/#Characteristics_of_Quantitative_Research
- Qualitative research isn’t as scientific as quantitative methods. Kmusial blog. Accessed March 5, 2023. https://kmusial.wordpress.com/2011/11/25/qualitative-research-isnt-as-scientific-as-quantitative-methods/
- Maben J, Griffiths P, Penfold C, et al. Evaluating a major innovation in hospital design: workforce implications and impact on patient and staff experiences of all single room hospital accommodation. Southampton (UK): NIHR Journals Library; 2015 Feb. (Health Services and Delivery Research, No. 3.3.) Chapter 5, Case study quantitative data findings. Accessed March 6, 2023. https://www.ncbi.nlm.nih.gov/books/NBK274429/
- McLeod, S. A. (2007). What is reliability? Simply Psychology. www.simplypsychology.org/reliability.html
- Reliability vs validity: Differences & examples. Accessed March 5, 2023. https://statisticsbyjim.com/basics/reliability-vs-validity/
- Mixed methods research. Community Engagement Program. Harvard Catalyst. Accessed February 28, 2023. https://catalyst.harvard.edu/community-engagement/mmr

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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."

## Quantitative Research Design

Ai generator.

Quantitative research design is a systematic approach used to investigate phenomena by collecting and analyzing numerical data. It involves the use of structured tools such as surveys, experiments, and statistical analysis to quantify variables and identify patterns, relationships, and cause-and-effect dynamics. This Research design emphasizes objectivity and replicability, allowing researchers to generalize findings across larger populations. By focusing on measurable data, quantitative research design aims to provide precise and reliable results.

## What is Quantitative Research Design?

Quantitative research design is a structured method of inquiry that focuses on quantifying data and analyzing it using statistical techniques. This approach involves collecting numerical data through various tools such as surveys, experiments, and questionnaires to identify patterns, relationships, and causal effects. The design emphasizes objectivity, allowing researchers to generalize findings to larger populations.

## Types of Quantitative Research Design

## 1. Descriptive Research Design

- Purpose: To describe characteristics of a population or phenomenon.
- Methods: Surveys, observational studies, case studies.
- Example: Measuring the prevalence of a particular health behavior in a community.

## 2. Correlational Research Design

- Purpose: To identify and measure the relationship between two or more variables without manipulating them.
- Methods: Surveys, archival data analysis.
- Example: Examining the relationship between study habits and academic performance.

## 3. Experimental Research Design

- Purpose: To determine cause-and-effect relationships by manipulating one or more independent variables and measuring their effect on dependent variables.
- Methods: Randomized controlled trials, laboratory experiments.
- Example: Testing the efficacy of a new drug by randomly assigning participants to treatment and control groups.

## 4. Quasi-Experimental Research Design

- Purpose: To estimate causal relationships when random assignment is not possible.
- Methods: Non-randomized control groups, pre-test/post-test designs.
- Example: Evaluating the impact of an educational intervention in different schools where random assignment is not feasible.

## 5. Cross-Sectional Research Design

- Purpose : To collect data at a single point in time to provide a snapshot of a population or phenomenon.
- Methods : Census surveys, sample surveys.
- Example : Surveying a population to assess the current prevalence of smoking.

## 6. Longitudinal Research Design

- Purpose : To collect data from the same subjects over an extended period to observe changes and developments.
- Methods : Panel studies, cohort studies.
- Example : Following a group of students over several years to track their academic progress.

## 7. Comparative Research Design

- Purpose : To compare two or more groups or variables to identify similarities and differences.
- Methods : Case-control studies, cross-national studies.
- Example : Comparing educational outcomes between students from different countries.

## 8. Meta-Analysis

- Purpose : To combine data from multiple studies to draw more robust conclusions about a research question.
- Methods : Systematic reviews, statistical aggregation.
- Example : Aggregating data from various studies to assess the overall effectiveness of a particular therapy.

## 9. Secondary Data Analysis

- Purpose : To use existing datasets collected by other researchers or organizations to answer new research questions or test different hypotheses.
- Methods : Government surveys, social surveys, market research data.
- Example : Analyzing national health survey data to investigate trends in obesity rates.

## 10. Archival Research

- Purpose : To analyze existing data collected for purposes other than the current study to uncover long-term trends and patterns.
- Methods : Historical documents, government records, public databases.
- Example : Examining historical voting records to understand changes in political participation over time.

## Quantitative Research Design Methods

Surveys involve administering questionnaires or structured interviews to gather data from a sample of participants. Surveys can be implemented through different channels, such as conducting them in person, over the phone, via mail, or utilizing online platforms. Researchers use various question types, such as multiple-choice, Likert scales, or rating scales, to collect quantitative data on attitudes, opinions, behaviors, and demographics.

## 2. Experiments

Experiments involve manipulating one or more independent variables and measuring their effects on dependent variables. To compare outcomes, participants are assigned randomly to various groups, including control and experimental groups. Experimental designs allow researchers to establish cause-and-effect relationships by controlling for confounding factors.

## 3. Observational Studies

Observational studies involve systematically observing and recording behavior, events, or phenomena in natural settings. Researchers can use structured or unstructured quantitative observation methods, depending on the research objectives. Quantitative data can be collected by counting the frequency of specific behaviors or by using coding systems to categorize and analyze observed data.

## 4. Archival Research

Archival research involves analyzing existing data collected for purposes other than the current study. Researchers may use historical documents, government records, public databases, or organizational records to extract data through quantitative research. Archival research allows for large-scale data analysis and can provide insights into long-term trends and patterns.

## 5. Secondary Data Analysis

Similar to archival research, secondary data analysis involves using existing datasets that were collected by other researchers or organizations. Researchers analyze the data to answer new research questions or test different hypotheses. Secondary data sources can include government surveys, social surveys, or market research data.

## 6. Content Analysis

Content analysis is a method used to analyze textual or visual data to identify patterns, themes, or relationships. Researchers code and categorize the content of documents, interviews, articles, or media sources. The coded data is then quantified and statistically analyzed to draw conclusions. Content analysis can be both qualitative and quantitative, depending on the approach used.

## 7. Psychometric Testing

Psychometric testing involves the development and administration of tests or scales to measure psychological constructs, such as intelligence, personality traits, or attitudes. Researchers use statistical techniques to analyze the test data, such as factor analysis, reliability analysis, or item response theory.

## Difference between Quantitative Research Design and Qualitative Research Design

Aspect | Quantitative Research Design | Qualitative Research Design |
---|---|---|

To quantify variables and generalize findings from a sample to a population | To explore and understand meanings, experiences, and concepts | |

Numerical data | Non-numerical data (text, images, etc.) | |

Surveys, experiments, observational studies, archival research, secondary data analysis, psychometric testing | Interviews, focus groups, participant observation, content analysis | |

Structured instruments like questionnaires, tests, or observation checklists | Unstructured or semi-structured techniques like open-ended interviews | |

Statistical methods, mathematical models | Thematic analysis, coding, narrative analysis | |

Objective, measurable results | Subjective insights, detailed descriptions | |

Large, representative samples | Small, purposive samples | |

Tests specific hypotheses | Generates hypotheses during the research process | |

Detached and objective | Involved and subjective | |

Rigid and structured | Flexible and evolving | |

High emphasis on reliability and validity through statistical measures | Emphasis on credibility, transferability, dependability, and confirmability | |

High, due to larger sample sizes and statistical analysis | Low, findings are specific to the context and participants studied | |

Randomized Controlled Trials (RCTs), longitudinal studies, cross-sectional surveys | Ethnographies, case studies, grounded theory studies |

## How to Find Quantitative Research Design

Finding a quantitative research design involves several steps to ensure that the chosen method is suitable for your research question and objectives. Here’s a step-by-step guide:

## 1. Define Your Research Question

- Identify the Problem : Clearly define the problem or phenomenon you want to study.
- Specify Objectives : Determine what you aim to achieve with your research.

## 2. Literature Review

- Search Existing Research : Look for existing studies related to your topic in academic journals, books, and databases.
- Identify Gaps : Note any gaps in the current literature that your research could fill.

## 3. Choose a Suitable Research Design

- Descriptive Design : If your goal is to describe characteristics or functions, consider surveys or observational studies.
- Correlational Design : To explore relationships between variables, use correlational methods.
- Experimental Design : For establishing cause-and-effect relationships, conduct experiments with control and experimental groups.
- Quasi-Experimental Design : When random assignment isn’t feasible, use quasi-experimental designs.
- Longitudinal Design : If you need to study changes over time, choose a longitudinal approach.
- Cross-Sectional Design : For a snapshot of a population at a single point in time, use cross-sectional surveys.

## 4. Develop Your Hypothesis

- Formulate Hypotheses : Based on your research question, develop clear and testable hypotheses.

## 5. Select Your Sample

- Define the Population : Determine the population from which you will draw your sample.
- Sampling Methods : Choose an appropriate sampling method (random, stratified, cluster, etc.) to ensure representativeness.

## 6. Choose Data Collection Methods

- Surveys : Use questionnaires or structured interviews.
- Experiments : Design experiments with independent and dependent variables.
- Observations : Use structured or unstructured observation methods.
- Archival Research : Analyze existing records or databases.
- Secondary Data Analysis : Use pre-existing datasets for new analysis.

## 7. Design the Data Collection Instrument

- Create Surveys/Questionnaires : Develop questions that are clear and unbiased.
- Design Experimental Protocols : Outline the procedures for conducting experiments.
- Develop Observation Checklists : List specific behaviors or events to observe and record.

## 8. Pilot Testing

- Test Instruments : Conduct a pilot test to identify any issues with your data collection instruments or procedures.
- Refine Methods : Make necessary adjustments based on feedback from the pilot test.

## 9. Data Collection

- Implement Your Design : Collect data according to your chosen methods and protocols.
- Ensure Accuracy : Follow ethical guidelines and ensure accurate data recording.

## 10. Data Analysis

- Statistical Techniques : Use appropriate statistical methods to analyze your data.
- Software Tools : Utilize software such as SPSS, R, or Excel for data analysis.

## FAQ’s

What is the purpose of quantitative research.

The purpose is to quantify variables, test hypotheses, and identify patterns, relationships, or causal effects through numerical data analysis.

## What is a descriptive research design?

Descriptive research design aims to describe characteristics or functions of a population or phenomenon, without establishing cause-and-effect relationships.

## What is correlational research design?

Correlational research design examines the relationship between two or more variables to determine if a connection exists, without implying causation.

## What is causal-comparative research design?

Causal-comparative research design seeks to identify cause-and-effect relationships by comparing different groups based on varying independent variables.

## What is an experimental research design?

Experimental research design involves manipulating one variable to determine its effect on another variable, establishing a cause-and-effect relationship.

## What are independent and dependent variables?

Independent variables are manipulated to observe their effect on dependent variables, which are measured to see if they change due to the manipulation.

## Why is random sampling important in quantitative research?

Random sampling ensures each member of a population has an equal chance of being selected, enhancing the generalizability of results.

## What is the role of hypothesis in quantitative research?

A hypothesis is a testable prediction about the relationship between variables, guiding the direction and focus of the study.

## What are common data collection methods in quantitative research?

Common methods include surveys, questionnaires, structured interviews, and standardized tests.

## What is the significance of statistical analysis in quantitative research?

Statistical analysis helps interpret numerical data, identify trends, and test hypotheses, providing a basis for drawing conclusions.

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## Quantitative Research – Methods, Types and Analysis

Table of Contents

## Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

## Quantitative Research Methods

Quantitative Research Methods are as follows:

## Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

## Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

## Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

## Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

## Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

## Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

## Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

## Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

## Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

## Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

## Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

## Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

## Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

- Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
- Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
- Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
- Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
- Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

## Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

- Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
- Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
- Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
- Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
- Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
- Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
- Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

## Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

- Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
- Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
- Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
- Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
- Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
- Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
- Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

## How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

- Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
- Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
- Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
- Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
- Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
- Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

## When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

- To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
- To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
- To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
- To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
- To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

## Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

- Description : To provide a detailed and accurate description of a particular phenomenon or population.
- Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
- Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
- Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

## Advantages of Quantitative Research

There are several advantages of quantitative research, including:

- Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
- Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
- Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
- Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
- Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
- Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

## Limitations of Quantitative Research

There are several limitations of quantitative research, including:

- Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
- Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
- Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
- Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
- Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
- Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

## About the author

## Muhammad Hassan

Researcher, Academic Writer, Web developer

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* 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

Feasible | ||

Interesting | ||

Novel | ||

Ethical | ||

Relevant |

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

Population (patients) | ||

Intervention (for intervention studies only) | ||

Comparison group | ||

Outcome of interest | ||

Time |

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.

## Quantitative Research Methods

- Introduction
- Descriptive and Inferential Statistics
- Hypothesis Testing
- Regression and Correlation
- Time Series
- Meta-Analysis
- Mixed Methods
- Additional Resources
- Get Research Help

## Hypothesis Tests

A hypothesis test is exactly what it sounds like: You make a hypothesis about the parameters of a population, and the test determines whether your hypothesis is consistent with your sample data.

- Hypothesis Testing Penn State University tutorial
- Hypothesis Testing Wolfram MathWorld overview
- Hypothesis Testing Minitab Blog entry
- List of Statistical Tests A list of commonly used hypothesis tests and the circumstances under which they're used.

The p-value of a hypothesis test is the probability that your sample data would have occurred if you hypothesis were not correct. Traditionally, researchers have used a p-value of 0.05 (a 5% probability that your sample data would have occurred if your hypothesis was wrong) as the threshold for declaring that a hypothesis is true. But there is a long history of debate and controversy over p-values and significance levels.

## Nonparametric Tests

Many of the most commonly used hypothesis tests rely on assumptions about your sample data—for instance, that it is continuous, and that its parameters follow a Normal distribution. Nonparametric hypothesis tests don't make any assumptions about the distribution of the data, and many can be used on categorical data.

- Nonparametric Tests at Boston University A lesson covering four common nonparametric tests.
- Nonparametric Tests at Penn State Tutorial covering the theory behind nonparametric tests as well as several commonly used tests.
- << Previous: Descriptive and Inferential Statistics
- Next: Regression and Correlation >>
- Last Updated: Aug 18, 2023 11:55 AM
- URL: https://guides.library.duq.edu/quant-methods

July 1, 2024

## The Biggest Problem in Mathematics Is Finally a Step Closer to Being Solved

Number theorists have been trying to prove a conjecture about the distribution of prime numbers for more than 160 years

By Manon Bischoff

Weiquan Lin/Getty Images

The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It has occupied experts for more than 160 years. And the problem appeared both in mathematician David Hilbert’s groundbreaking speech from 1900 and among the “Millennium Problems” formulated a century later. The person who solves it will win a million-dollar prize.

But the Riemann hypothesis is a tough nut to crack. Despite decades of effort, the interest of many experts and the cash reward, there has been little progress. Now mathematicians Larry Guth of the Massachusetts Institute of Technology and James Maynard of the University of Oxford have posted a sensational new finding on the preprint server arXiv.org. In the paper, “the authors improve a result that seemed insurmountable for more than 50 years,” says number theorist Valentin Blomer of the University of Bonn in Germany.

Other experts agree. The work is “a remarkable breakthrough,” mathematician and Fields Medalist Terence Tao wrote on Mastodon , “though still very far from fully resolving this conjecture.”

## On supporting science journalism

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The Riemann hypothesis concerns the basic building blocks of natural numbers: prime numbers, values only divisible by 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, and so on.

Every other number, such as 15, can be clearly broken down into a product of prime numbers: 15 = 3 x 5. The problem is that the prime numbers do not seem to follow a simple pattern and instead appear randomly among the natural numbers. Nineteenth-century German mathematician Bernhard Riemann proposed a way to deal with this peculiarity that explains how prime numbers are distributed on the number line—at least from a statistical point of view.

## A Periodic Table for Numbers

Proving this conjecture would provide mathematicians with nothing less than a kind of “periodic table of numbers.” Just as the basic building blocks of matter (such as quarks, electrons and photons) help us to understand the universe and our world, prime numbers also play an important role, not just in number theory but in almost all areas of mathematics.

There are now numerous theorems based on the Riemann conjecture. Proof of this conjecture would prove many other theorems as well—yet another incentive to tackle this stubborn problem.

Interest in prime numbers goes back thousands of years. Euclid proved as early as 300 B.C.E. that there are an infinite number of prime numbers. And although interest in prime numbers persisted, it was not until the 18th century that any further significant findings were made about these basic building blocks.

As a 15-year-old, physicist Carl Friedrich Gauss realized that the number of prime numbers decreases along the number line. His so-called prime number theorem (not proven until 100 years later) states that approximately n / ln( n ) prime numbers appear in the interval from 0 to n . In other words, the prime number theorem offers mathematicians a way of estimating the typical distribution of primes along a chunk of the number line.

The exact number of prime numbers may differ from the estimate given by the theorem, however. For example: According to the prime number theorem, there are approximately 100 / ln(100) ≈ 22 prime numbers in the interval between 1 and 100. But in reality there are 25. There is therefore a deviation of 3. This is where the Riemann hypothesis comes in. This hypothesis gives mathematicians a way to estimate the deviation. More specifically, it states that this deviation cannot become arbitrarily large but instead must scale at most with the square root of n , the length of the interval under consideration.

The Riemann hypothesis therefore does not predict exactly where prime numbers are located but posits that their appearance on the number line follows certain rules. According to the Riemann hypothesis, the density of primes decreases according to the prime number theorem, and the primes are evenly distributed according to this density. This means that there are no large areas in which there are no prime numbers at all, while others are full of them.

You can also imagine this idea by thinking about the distribution of molecules in the air of a room: the overall density on the floor is somewhat higher than on the ceiling, but the particles—following this density distribution—are nonetheless evenly scattered, and there is no vacuum anywhere.

## A Strange Connection

Riemann formulated the conjecture named after him in 1859, in a slim, six-page publication (his only contribution to the field of number theory). At first glance, however, his work has little to do with prime numbers.

He dealt with a specific function, the so-called zeta function ζ( s ), an infinitely long sum that adds the reciprocal values of natural numbers that are raised to the power of s :

Even before Riemann’s work, experts knew that such zeta functions are related to prime numbers. Thus, the zeta function can also be expressed as a function of all prime numbers p as follows:

Riemann recognized the full significance of this connection with prime numbers when he used not only real values for s but also complex numbers. These numbers contain both a real part and roots from negative numbers, the so-called imaginary part.

You can imagine complex numbers as a two-dimensional construct. Rather than mark a point on the number line, they instead lie on the plane. The x coordinate corresponds to the real part and the y coordinate to the imaginary part:

Никита Воробьев/Wikimedia

The complex zeta function that Riemann investigated can be visualized as a landscape above the plane. As it turns out, there are certain points amid the mountains and valleys that play an important role in relation to prime numbers. These are the points at which the zeta function becomes zero (so-called zeros), where the landscape sinks to sea level, so to speak.

The colors represent the values of the complex zeta function, with the white dots indicating its zeros.

Jan Homann/Wikimedia

Riemann quickly found that the zeta function has no zeros if the real part is greater than 1. This means that the area of the landscape to the right of the straight line x = 1 never sinks to sea level. The zeros of the zeta function are also known for negative values of the real part. They lie on the real axis at x = –2, –4, –6, and so on. But what really interested Riemann—and all mathematicians since—were the zeros of the zeta function in the “critical strip” between 0 ≤ x ≤ 1.

In the critical strip (dark blue), the Riemann zeta function can have “nontrivial” zeros. The Riemann conjecture states that these are located exclusively on the line x = 1/2 (dashed line).

LoStrangolatore/Wikimedia ( CC BY-SA 3.0 )

Riemann knew that the zeta function has an infinite number of zeros within the critical strip. But interestingly, all appear to lie on the straight line x = 1 / 2 . Thus Riemann hypothesized that all zeros of the zeta function within the critical strip have a real part of x = 1 / 2 . That statement is actually at the crux of understanding the distribution of prime numbers. If correct, then the placement of prime numbers along the number line never deviates too much from the prime number set.

## On the Hunt for Zeros

To date, billions and billions of zeta function zeros have now been examined— more than 10 13 of them —and all lie on the straight line x = 1 / 2 .

But that alone is not a valid proof. You would only have to find a single zero that deviates from this scheme to disprove the Riemann hypothesis. Therefore we are looking for a proof that clearly demonstrates that there are no zeros outside x = 1 / 2 in the critical strip.

Thus far, such a proof has been out of reach, so researchers took a different approach. They tried to show that there is, at most, a certain number N of zeros outside this straight line x = 1 / 2 . The hope is to reduce N until N = 0 at some point, thereby proving the Riemann conjecture. Unfortunately, this path also turns out to be extremely difficult. In 1940 mathematician Albert Ingham was able to show that between 0.75 ≤ x ≤ 1 there are at most y 3/5+ c zeros with an imaginary part of at most y , where c is a constant between 0 and 9.

In the following 80 years, this estimation barely improved. The last notable progress came from mathematician Martin Huxley in 1972 . “This has limited us from doing many things in analytic number theory,” Tao wrote in his social media post . For example, if you wanted to apply the prime number theorem to short intervals of the type [ x , x + x θ ], you were limited by Ingham’s estimate to θ > 1 / 6 .

Yet if Riemann’s conjecture is true, then the prime number theorem applies to any interval (or θ = 0), no matter how small (because [ x , x + x θ ] = [ x , x + 1] applies to θ = 0).

Now Maynard, who was awarded the prestigious Fields Medal in 2022 , and Guth have succeeded in significantly improving Ingham’s estimate for the first time. According to their work, the zeta function in the range 0.75 ≤ x ≤ 1 has at most y (13/25)+ c zeros with an imaginary part of at most y . What does that mean exactly? Blomer explains: “The authors show in a quantitative sense that zeros of the Riemann zeta function become rarer the further away they are from the critical straight line. In other words, the worse the possible violations of the Riemann conjecture are, the more rarely they would occur.”

“This propagates to many corresponding improvements in analytic number theory,” Tao wrote . It makes it possible to reduce the size of the intervals for which the prime number theorem applies. The theorem is valid for [ x , x + x 2/15 ], so θ > 1 / 6 = 0.166... becomes θ > 2 ⁄ 15 = 0.133...

For this advance, Maynard and Guth initially used well-known methods from Fourier analysis for their result. These are similar techniques to what is used to break down a sound into its overtones. “The first few steps are standard, and many analytic number theorists, including myself, who have attempted to break the Ingham bound, will recognize them,” Tao explained . From there, however, Maynard and Guth “do a number of clever and unexpected maneuvers,” Tao wrote.

Blomer agrees. “The work provides a whole new set of ideas that—as the authors rightly say—can probably be applied to other problems. From a research point of view, that’s the most decisive contribution of the work,” he says.

So even if Maynard and Guth have not solved Riemann’s conjecture, they have at least provided new food for thought to tackle the 160-year-old puzzle. And who knows—perhaps their efforts hold the key to finally cracking the conjecture.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

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Methodology

- What Is Quantitative Research? | Definition, Uses & Methods

## What Is Quantitative Research? | Definition, Uses & Methods

Published on June 12, 2020 by Pritha Bhandari . Revised on June 22, 2023.

Quantitative research is the process of collecting and analyzing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analyzing non-numerical data (e.g., text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

- What is the demographic makeup of Singapore in 2020?
- How has the average temperature changed globally over the last century?
- Does environmental pollution affect the prevalence of honey bees?
- Does working from home increase productivity for people with long commutes?

## Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, other interesting articles, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

- In descriptive research , you simply seek an overall summary of your study variables.
- In correlational research , you investigate relationships between your study variables.
- In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalized to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

Research method | How to use | Example |
---|---|---|

Control or manipulate an to measure its effect on a dependent variable. | To test whether an intervention can reduce procrastination in college students, you give equal-sized groups either a procrastination intervention or a comparable task. You compare self-ratings of procrastination behaviors between the groups after the intervention. | |

Ask questions of a group of people in-person, over-the-phone or online. | You distribute with rating scales to first-year international college students to investigate their experiences of culture shock. | |

(Systematic) observation | Identify a behavior or occurrence of interest and monitor it in its natural setting. | To study college classroom participation, you sit in on classes to observe them, counting and recording the prevalence of active and passive behaviors by students from different backgrounds. |

Secondary research | Collect data that has been gathered for other purposes e.g., national surveys or historical records. | To assess whether attitudes towards climate change have changed since the 1980s, you collect relevant questionnaire data from widely available . |

Note that quantitative research is at risk for certain research biases , including information bias , omitted variable bias , sampling bias , or selection bias . Be sure that you’re aware of potential biases as you collect and analyze your data to prevent them from impacting your work too much.

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Once data is collected, you may need to process it before it can be analyzed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualize your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalizations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

First, you use descriptive statistics to get a summary of the data. You find the mean (average) and the mode (most frequent rating) of procrastination of the two groups, and plot the data to see if there are any outliers.

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardize data collection and generalize findings . Strengths of this approach include:

- Replication

Repeating the study is possible because of standardized data collection protocols and tangible definitions of abstract concepts.

- Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

- Large samples

Data from large samples can be processed and analyzed using reliable and consistent procedures through quantitative data analysis.

- Hypothesis testing

Using formalized and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

- Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

- Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

- Structural bias

Despite standardized procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

- Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

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

- Chi square goodness of fit test
- Degrees of freedom
- Null hypothesis
- Discourse analysis
- Control groups
- Mixed methods research
- Non-probability sampling
- Inclusion and exclusion criteria

Research bias

- Rosenthal effect
- Implicit bias
- Cognitive bias
- Selection bias
- Negativity bias
- Status quo bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

- Reliability refers to the consistency of a measure (whether the results can be reproduced under the same conditions).
- Validity refers to the accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

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.

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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 (Quantitative hypothesis-testing research) - Quantitative research uses deductive reasoning. - This involves the formation of a hypothesis, collection of data in the investigation of the problem, analysis and use of the data from the investigation, and drawing of conclusions to validate or nullify the hypotheses.

Hypotheses are the testable statements linked to your research question. Hypotheses bridge the gap from the general question you intend to investigate (i.e., the research question) to concise statements of what you hypothesize the connection between your variables to be. For example, if we were studying the influence of mentoring relationships ...

The primary research question should originate from the hypothesis, not the data, and be established before starting the study. Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.

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. If a first-year student starts attending more lectures, then their exam scores will improve.

3. Simple hypothesis. A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, "Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking. 4.

Step 5: Present your findings. The results of hypothesis testing will be presented in the results and discussion sections of your research paper, dissertation or thesis.. In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p-value).

It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis. 7.

In any research hypothesis, variables play a critical role. These are the elements or factors that the researcher manipulates, controls, or measures. Understanding variables is essential for crafting a clear, testable hypothesis and for the stages of research that follow, such as data collection and analysis. ... For quantitative research, you ...

For quantitative research, the hypothesis used is a statistical hypothesis, meaning that the hypothesis must be tested using statistical rules. Whereas for qualitative research does not need to use statistical rules. In a quantitative study, the formulated statistical hypothesis has two forms, the null hypothesis (Ho) and the alternative ...

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.

Quantitative vs. Qualitative Research. When you embark on hypothesis formulation, understanding the distinction between quantitative and qualitative research methodologies is crucial. Quantitative research focuses on numerical data and statistical analysis, ideal for hypotheses that require measurable evidence. In contrast, qualitative research ...

Most quantitative research falls into one or more of these three categories. The most rigorous form of quantitative research follows from a test of a theory (see Chapter 3) and the specification of research questions or hypotheses that are included in the theory. The independent and dependent variables must be measured sepa-rately.

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.

A research hypothesis defines the theory or problem your research intends to test. It is the "educated guess" of what the final results of your research or experiment will be. ... Any quantitative research includes a hypothesized parameter value of a mean, a proportion, or the difference between two proportions. Here's how to note each ...

The purpose of quantitative research is to validate or test a theory or hypothesis and that of qualitative research is to understand a subject or event or identify reasons for observed patterns. Quantitative research methods are used to observe events that affect a particular group of individuals, which is the sample population.

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.

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 ...

Quantitative research design is a systematic approach used to investigate phenomena by collecting and analyzing numerical data. It involves the use of structured tools such as surveys, experiments, and statistical analysis to quantify variables and identify patterns, relationships, and cause-and-effect dynamics.

Quantitative Research. Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions.This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected.

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 ...

The p-value of a hypothesis test is the probability that your sample data would have occurred if you hypothesis were not correct. Traditionally, researchers have used a p-value of 0.05 (a 5% probability that your sample data would have occurred if your hypothesis was wrong) as the threshold for declaring that a hypothesis is true.

The Riemann hypothesis concerns the basic building blocks of natural numbers: prime numbers, values only divisible by 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, and so on.

Revised on June 22, 2023. Quantitative research is the process of collecting and analyzing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations. Quantitative research is the opposite of qualitative research, which involves collecting and analyzing ...

Clinical Research Institute, Shanghai General Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China ... Academy for Advanced Interdisciplinary Studies, Center for Quantitative Biology (CQB), Peking University, Beijing, China ... hypothesis testing software for mediation analysis in genomic applications. Bioinformatics ...

IET Intelligent Transport Systems is an interdisciplinary journal publishing research on the practical applications of ... This paper proposes a low complexity Gaussian mixture probability hypothesis density (GM-PHD-LC) filter. ... MENet uses a quantitative statistics module to establish regional associations and a maintenance and encouragement ...

The European Commission asked EFSA for a risk assessment on small organoarsenic species in food. For monomethylarsonic acid MMA(V), decreased body weight resulting from diarrhoea in rats was identified as the critical endpoint and a BMDL 10 of 18.2 mg MMA(V)/kg body weight (bw) per day (equivalent to 9.7 mg As/kg bw per day) was calculated as a reference point (RP).