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Problem statement and hypothesis

A problem statement may need to be re-worked throughout the process .

The academic problem that you are investigating in your assignment can either take the form of a problem statement, i.e. a question that you want to answer, or it can be a hypothesis that you wish to reject or confirm. How you formulate the problem influences the task you are embarking on. Problem statements as well as hypotheses must be relevant to your area of study, and you must be able to carry out the investigation using the resources and methods available to you.  

Note that a problem statement or a hypothesis often changes during the writing process. Sometimes you have to change the focus of the problem statement/hypothesis, and sometimes you only have to change a single word. The amount of changes required depends on your study programme and the assignment at hand. Therefore, you should always ask your teacher or supervisor for advice.  

Problem statement

A problem statement usually consists of one question to be addressed in your assignment and to be answered in your conclusion. It can include 2-5 sub-questions. A problem statement can take different forms, but generally: 

It uses accurate wording, for example technical terms 

It relates specifically to your project, describing what you want to study (object) and how you want to study it (theories and methods)  

It not only introduces a description of the problem (what is the problem?) but also encourages explanation, reflection and discussion of the problem (how and why does the problem exist?) 

The problem statement as a guiding tool

The problem statement can be a useful tool to guide you through your work process. Whether you are collecting empirical data, searching for literature or reading, always keep your problem statement in mind. This will help you narrow down your searches and your reading, and help you focus on what is relevant in order to answer the question in your problem statement. 

You should also be prepared to revise your problem statement as you go along. For example if you discover a more relevant or interesting question when you start working on the investigation. Always discuss with your teacher or supervisor if you want to make radical changes to your problem statement, and thereby to your assignment.  

Working on your problem statement

The problem statement sets the framework for your assignment .

Your problem statement asks the question that will be answered in the conclusion. The actual assignment - between the problem statement and the conclusion - addresses your main question. There must be a clear link between the problem statement and the conclusion. 

A problem statement must comply with certain specific requirements 

Your problem statement has to meet a number of formal requirements, but there are other elements that you need to consider as well. For example: Is your language clear and unambiguous, and is your topic relevant and interesting? 

Checklist for the problem statement

Checklist for the problem statement .

Use the points in the checklist below to assure the quality of your problem statement. Tick off each of the points that your problem statement complies with. Continue to work on your problem statement until it complies with most or all of the items on the list. This will help you make sure that your problem statement is satisfactory. 

example of statement of the problem and hypothesis

The checklist has been prepared by the editorial team in collaboration with Susanne Højlund, associate professor at the School of Culture and Society - Department of Anthropology, Aarhus University. 

A hypothesis is a theoretical, hypothetical explanation that can be tested. It usually takes the form of a causal relationship or a causal explanation. You can also consider the hypothesis as a preliminary response to a research question or a problem statement. A hypothesis can be expressed in different ways, but generally, the following applies: 

The hypothesis is theoretical and builds on existing knowledge and general principles. 

The hypothesis can be tested through a study or an experiment. 

The hypothesis can either be confirmed or rejected. 

Testing a hypothesis

Your hypothesis can include a prediction of the results of your study based on a logical explanation. Your study will then show whether your hypothesis and your prediction appear to be correct or not. In other words, a good hypothesis is a hypothesis that you can test through a study or an experiment. 

A good hypothesis is theoretical and is based on existing knowledge, general principles and previous research within a similar academic problem area. It can also be a good idea to consider proposing several hypotheses. 

In science, it is generally believed that a hypothesis can turn out to be wrong, but that it can never be conclusively proven to be true. Consequently, your study or experiment should be designed so that it attempts to reject or falsify your hypothesis. If you fail to reject the hypothesis, it is more likely to be "correct". 

Inspiration from assignments by other students

Get a list of thesis titles from your field of study, and draw inspiration from other students’ problem statements. 

Go on to Assignment 1: Try Your Hand at Writing Hypotheses or Go back to Understanding Hypotheses

E-mail M. Dereshiwsky at [email protected] Call M. Dereshiwsky at (520) 523-1892

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  • Knowledge Base

Methodology

  • How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

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 .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, 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 types of variables .

  • An independent variable is something the researcher changes or controls.
  • A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

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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example of statement of the problem and hypothesis

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 ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize 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.

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

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.

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 .

  • H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
  • H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

  • Sampling methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Likert scales
  • Reproducibility

 Statistics

  • Null hypothesis
  • Statistical power
  • Probability distribution
  • Effect size
  • Poisson distribution

Research bias

  • Optimism bias
  • Cognitive bias
  • Implicit bias
  • Hawthorne effect
  • Anchoring bias
  • Explicit bias

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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).

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

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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  • Research Process

What is a Problem Statement? [with examples]

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Table of Contents

The statement of the problem is one of the first things that a colleague or potential client will read. With the vastness of the information available at one’s fingertips in the online9 world, your work may have just a few seconds to draw in a reader to take a deeper look at your proposal before moving on to the next option. It explains quickly to the reader, the problem at hand, the need for research, and how you intend to do it.

A strong, clear description of the problem that drew you to your research has to be straightforward, easy to read and, most important, relevant. Why do you care about this problem? How can solving this problem impact the world? The problem statement is your opportunity to explain why you care and what you propose to do in the way of researching the problem.

A problem statement is an explanation in research that describes the issue that is in need of study . What problem is the research attempting to address? Having a Problem Statement allows the reader to quickly understand the purpose and intent of the research. The importance of writing your research proposal cannot be stressed enough. Check for more information on Writing a Scientific Research Project Proposal .

It is expected to be brief and concise , and should not include the findings of the research or detailed data . The average length of a research statement is generally about one page . It is going to define the problem, which can be thought of as a gap in the information base. There may be several solutions to this gap or lack of information, but that is not the concern of the problem statement. Its purpose is to summarize the current information and where a lack of knowledge may be presenting a problem that needs to be investigated .

The purpose of the problem statement is to identify the issue that is a concern and focus it in a way that allows it to be studied in a systematic way . It defines the problem and proposes a way to research a solution, or demonstrates why further information is needed in order for a solution to become possible.

What is Included in a Problem Statement?

Besides identifying the gap of understanding or the weakness of necessary data, it is important to explain the significance of this lack.

-How will your research contribute to the existing knowledge base in your field of study?

-How is it significant?

-Why does it matter?

Not all problems have only one solution so demonstrating the need for additional research can also be included in your problem statement. Once you identify the problem and the need for a solution, or for further study, then you can show how you intend to collect the needed data and present it.

How to Write a Statement of Problem in Research Proposal

It is helpful to begin with your goal. What do you see as the achievable goal if the problem you outline is solved? How will the proposed research theoretically change anything? What are the potential outcomes?

Then you can discuss how the problem prevents the ability to reach your realistic and achievable solution. It is what stands in the way of changing an issue for the better. Talk about the present state of affairs and how the problem impacts a person’s life, for example.

It’s helpful at this point to generally layout the present knowledge and understanding of the subject at hand, before then describing the gaps of knowledge that are currently in need of study. Your problem statement is a proposed solution to address one of these gaps.

A good problem statement will also layout the repercussions of leaving the problem as it currently stands. What is the significance of not addressing this problem? What are the possible future outcomes?

Example of Problem Statement in Research Proposal

If, for example , you intended to research the effect of vitamin D supplementation on the immune system , you would begin with a review of the current knowledge of vitamin D’s known function in relation to the immune system and how a deficiency of it impacts a person’s defenses.

You would describe the ideal environment in the body when there is a sufficient level of vitamin D. Then, begin to identify the problems associated with vitamin D deficiency and the difficulty of raising the level through supplementation, along with the consequences of that deficiency. Here you are beginning to identify the problem of a common deficiency and the current difficulty of increasing the level of vitamin D in the blood.

At this stage, you may begin to identify the problem and narrow it down in a way that is practical to a research project. Perhaps you are proposing a novel way of introducing Vitamin D in a way that allows for better absorption by the gut, or in a combination with another product that increases its level in the blood.

Describe the way your research in this area will contribute to the knowledge base on how to increase levels of vitamin D in a specific group of subjects, perhaps menopausal women with breast cancer. The research proposal is then described in practical terms.

How to write a problem statement in research?

Problem statements differ depending on the type and topic of research and vary between a few sentences to a few paragraphs.

However, the problem statement should not drag on needlessly. Despite the absence of a fixed format, a good research problem statement usually consists of three main parts:

Context: This section explains the background for your research. It identifies the problem and describes an ideal scenario that could exist in the absence of the problem. It also includes any past attempts and shortcomings at solving the problem.

Significance: This section defines how the problem prevents the ideal scenario from being achieved, including its negative impacts on the society or field of research. It should include who will be the most affected by a solution to the problem, the relevance of the study that you are proposing, and how it can contribute to the existing body of research.

Solution: This section describes the aim and objectives of your research, and your solution to overcome the problem. Finally, it need not focus on the perfect solution, but rather on addressing a realistic goal to move closer to the ideal scenario.

Here is a cheat sheet to help you with formulating a good problem statement.

1. Begin with a clear indication that the problem statement is going to be discussed next. You can start with a generic sentence like, “The problem that this study addresses…” This will inform your readers of what to expect next.

2. Next, mention the consequences of not solving the problem . You can touch upon who is or will be affected if the problem continues, and how.

3. Conclude with indicating the type of research /information that is needed to solve the problem. Be sure to reference authors who may have suggested the necessity of such research.

This will then directly lead to your proposed research objective and workplan and how that is expected to solve the problem i.e., close the research gap.

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Effective problem statements have these 5 components

problem-statement-colleagues-gathered-talking-in-office

We’ve all encountered problems on the job. After all, that’s what a lot of work is about. Solving meaningful problems to help improve something. 

Developing a problem statement that provides a brief description of an issue you want to solve is an important early step in problem-solving .

It sounds deceptively simple. But creating an effective problem statement isn’t that easy, even for a genius like Albert Einstein. Given one hour to work on a problem, he’d spend 55 minutes thinking about the problem and five minutes finding solutions. (Or so the story goes.)

Einstein was probably exaggerating to make a point. But considering his success in solving complex problems, we think he was on to something. 

As humans, we’re wired to jump past the problem and go directly to the solution stage. In emergencies, this behavior can be lifesaving, as in leaping out of the way of a speeding car. But when dealing with longer-range issues in the workplace, this can lead to bad decisions or half-baked solutions. 

That’s where problem statements come in handy. They help to meaningfully outline objectives to reach effective solutions. Knowing how to develop a great problem statement is also a valuable tool for honing your management skills .

But what exactly is a problem statement, when should you use one, and how do you go about writing one? In this article, we'll answer those questions and give you some tips for writing effective problem statements. Then you'll be ready to take on more challenges large and small.

What is a problem statement?

First, let’s start by defining a problem statement. 

A problem statement is a short, clear explanation of an issue or challenge that sums up what you want to change. It helps you, team members, and other stakeholders to focus on the problem, why it’s important, and who it impacts. 

A good problem statement should create awareness and stimulate creative thinking . It should not identify a solution or create a bias toward a specific strategy.

Taking time to work on a problem statement is a great way to short-circuit the tendency to rush to solutions. It helps to make sure you’re focusing on the right problem and have a well-informed understanding of the root causes. The process can also help you take a more proactive than reactive approach to problem-solving . This can help position you and your team to avoid getting stuck in constant fire-fighting mode. That way, you can take advantage of more growth opportunities.  

When to use a problem statement

The best time to create a problem statement is before you start thinking of solutions. If you catch yourself or your team rushing to the solution stage when you’re first discussing a problem, hit the brakes. Go back and work on the statement of the problem to make sure everyone understands and agrees on what the real problem is. 

Here are some common situations where writing problem statements might come in handy: 

  • Writing an executive summary for a project proposal or research project
  • Collaborating   on a cross-functional project with several team members
  • Defining the customer issue that a proposed product or service aims to solve
  • Using design thinking to improve user experience
  • Tackling a problem that previous actions failed to solve 

problem-statement-colleagues-solving-at-laptop

How to identify a problem statement

Like the unseen body of an iceberg, the root cause of a specific problem isn’t always obvious. So when developing a problem statement, how do you go about identifying the true, underlying problem?

These two steps will help you uncover the root cause of a problem :

  • Collect information from the research and previous experience with the problem
  • Talk to multiple stakeholders who are impacted by the problem

People often perceive problems differently. Interviewing stakeholders will help you understand the problem from diverse points of view. It can also help you develop some case studies to illustrate the problem. 

Combining these insights with research data will help you identify root causes more accurately. In turn, this methodology will help you craft a problem statement that will lead to more viable solutions. 

What are problem statements used for?

You can use problem statements for a variety of purposes. For an organization, it might be solving customer and employee issues. For the government, it could be improving public health. For individuals, it can mean enhancing their own personal well-being . Generally, problem statements can be used to:

  • Identify opportunities for improvement
  • Focus on the right problems or issues to launch more successful initiatives – a common challenge in leadership
  • Help you communicate a problem to others who need to be involved in finding a solution
  • Serve as the basis for developing an action plan or goals that need to be accomplished to help solve the problem
  • Stimulate thinking outside the box  and other types of creative brainstorming techniques

3 examples of problem statements

When you want to be sure you understand a concept or tool, it helps to see an example. There can also be some differences in opinion about what a problem statement should look like. For instance, some frameworks include a proposed solution as part of the problem statement. But if the goal is to stimulate fresh ideas, it’s better not to suggest a solution within the problem statement. 

In our experience, an effective problem statement is brief, preferably one sentence. It’s also specific and descriptive without being prescriptive. 

Here are three problem statement examples. While these examples represent three types of problems or goals, keep in mind that there can be many other types of problem statements.        

Example Problem Statement 1: The Status Quo Problem Statement

Example: 

The average customer service on-hold time for Example company exceeds five minutes during both its busy and slow seasons.

This can be used to describe a current pain point within an organization that may need to be addressed. Note that the statement specifies that the issue occurs during the company’s slow time as well as the busy season. This is helpful in performing the root cause analysis and determining how this problem can be solved. 

The average customer service on-hold time for Example company exceeds five minutes during both its busy and slow seasons. The company is currently understaffed and customer service representatives are overwhelmed.

Background:

Example company is facing a significant challenge in managing their customer service on-hold times. In the past, the company had been known for its efficient and timely customer service, but due to a combination of factors, including understaffing and increased customer demand, the on-hold times have exceeded five minutes consistently. This has resulted in frustration and dissatisfaction among customers, negatively impacting the company's reputation and customer loyalty.

Reducing the on-hold times for customer service callers is crucial for Example company. Prolonged waiting times have a detrimental effect on customer satisfaction and loyalty, leading to potential customer churn and loss of revenue. Additionally, the company's declining reputation in terms of customer service can have a lasting impact on its competitive position in the market. Addressing this problem is of utmost importance to improve customer experience and maintain a positive brand image.

Objectives:

The primary objective of this project is to reduce the on-hold times for customer service callers at Example company. The specific objectives include:

  • Analyzing the current customer service workflow and identifying bottlenecks contributing to increased on-hold times.
  • Assessing the staffing levels and resource allocation to determine the extent of understaffing and its impact on customer service.
  • Developing strategies and implementing measures to optimize the customer service workflow and reduce on-hold times.
  • Monitoring and evaluating the effectiveness of the implemented measures through key performance indicators (KPIs) such as average on-hold time, customer satisfaction ratings, and customer feedback.
  • Establishing a sustainable approach to maintain reduced on-hold times, taking into account both busy and slow seasons, through proper resource planning, training, and process improvements.

Example Problem Statement 2: The Destination Problem Statement

Leaders at Example company want to increase net revenue for its premium product line of widgets by 5% for the next fiscal year. 

This approach can be used to describe where an organization wants to be in the future. This type of problem statement is useful for launching initiatives to help an organization achieve its desired state. 

Like creating SMART goals , you want to be as specific as possible. Note that the statement specifies “net revenue” instead of “gross revenue." This will help keep options open for potential actions. It also makes it clear that merely increasing sales is not an acceptable solution if higher marketing costs offset the net gains. 

Leaders at Example company aim to increase net revenue for its premium product line of widgets by 5% for the next fiscal year. However, the company currently lacks the necessary teams to tackle this objective effectively. To achieve this growth target, the company needs to expand its marketing and PR teams, as well as its product development teams, to prepare for scaling. 

Example company faces the challenge of generating a 5% increase in net revenue for its premium product line of widgets in the upcoming fiscal year. Currently, the company lacks the required workforce to drive this growth. Without adequate staff in the marketing, PR, and product development departments, the company's ability to effectively promote, position, and innovate its premium product line will be hindered. To achieve this kind of growth, it is essential that Example company expands teams, enhances capabilities, and strategically taps into the existing pool of loyal customers.

Increasing net revenue for the premium product line is crucial for Example company's overall business success. Failure to achieve the targeted growth rate can lead to missed revenue opportunities and stagnation in the market. By expanding the marketing and PR teams, Example company can strengthen its brand presence, effectively communicate the value proposition of its premium product line, and attract new customers.

Additionally, expanding the product development teams will enable the company to introduce new features and innovations, further enticing existing and potential customers. Therefore, addressing the workforce shortage and investing in the necessary resources are vital for achieving the revenue growth objective.

The primary objective of this project is to increase net revenue for Example company's premium product line of widgets by 5% in the next fiscal year. The specific objectives include:

  • Assessing the current workforce and identifying the gaps in the marketing, PR, and product development teams.
  • Expanding the marketing and PR teams by hiring skilled professionals who can effectively promote the premium product line and engage with the target audience.
  • Strengthening the product development teams by recruiting qualified individuals who can drive innovation, enhance product features, and meet customer demands.
  • Developing a comprehensive marketing and PR strategy to effectively communicate the value proposition of the premium product line and attract new customers.
  • Leveraging the existing base of loyal customers to increase repeat purchases, referrals, and brand advocacy.
  • Allocating sufficient resources, both time and manpower, to support the expansion and scaling efforts required to achieve the ambitious revenue growth target.
  • Monitoring and analyzing key performance indicators (KPIs) such as net revenue, customer acquisition, customer retention, and customer satisfaction to measure the success of the growth initiatives.
  • Establishing a sustainable plan to maintain the increased revenue growth beyond the next fiscal year by implementing strategies for continuous improvement and adaptation to market dynamics.

Example Problem Statement 3 The Stakeholder Problem Statement

In the last three quarterly employee engagement surveys , less than 30% of employees at Eample company stated that they feel valued by the company. This represents a 20% decline compared to the same period in the year prior. 

This strategy can be used to describe how a specific stakeholder group views the organization. It can be useful for exploring issues and potential solutions that impact specific groups of people. 

Note the statement makes it clear that the issue has been present in multiple surveys and it's significantly worse than the previous year. When researching root causes, the HR team will want to zero in on factors that changed since the previous year.

In the last three quarterly employee engagement surveys, less than 30% of employees at the Example company stated that they feel valued by the company. This indicates a significant decline of 20% compared to the same period in the previous year.

The company aspires to reduce this percentage further to under 10%. However, achieving this goal would require filling specialized roles and implementing substantial cultural changes within the organization.

Example company is facing a pressing issue regarding employee engagement and perceived value within the company. Over the past year, there has been a notable decline in the percentage of employees who feel valued. This decline is evident in the results of the quarterly employee engagement surveys, which consistently show less than 30% of employees reporting a sense of value by the company.

This decline of 20% compared to the previous year's data signifies a concerning trend. To address this problem effectively, Example company needs to undertake significant measures that go beyond superficial changes and necessitate filling specialized roles and transforming the company culture.

Employee engagement and a sense of value are crucial for organizational success. When employees feel valued, they tend to be more productive, committed, and motivated. Conversely, a lack of perceived value can lead to decreased morale, increased turnover rates, and diminished overall performance.

By addressing the decline in employees feeling valued, Example company can improve employee satisfaction, retention, and ultimately, overall productivity. Achieving the desired reduction to under 10% is essential to restore a positive work environment and build a culture of appreciation and respect.

The primary objective of this project is to increase the percentage of employees who feel valued by Example company, aiming to reduce it to under 10%. The specific objectives include:

  • Conducting a comprehensive analysis of the factors contributing to the decline in employees feeling valued, including organizational policies, communication practices, leadership styles, and cultural norms.
  • Identifying and filling specialized roles, such as employee engagement specialists or culture change agents, who can provide expertise and guidance in fostering a culture of value and appreciation.
  • Developing a holistic employee engagement strategy that encompasses various initiatives, including training programs, recognition programs, feedback mechanisms, and communication channels, to enhance employee value perception.
  • Implementing cultural changes within the organization that align with the values of appreciation, respect, and recognition, while fostering an environment where employees feel valued.
  • Communicating the importance of employee value and engagement throughout all levels of the organization, including leadership teams, managers, and supervisors, to ensure consistent messaging and support.
  • Monitoring progress through regular employee surveys, feedback sessions, and key performance indicators (KPIs) related to employee satisfaction, turnover rates, and overall engagement levels.
  • Providing ongoing support, resources, and training to managers and supervisors to enable them to effectively recognize and appreciate their teams and foster a culture of value within their respective departments.
  • Establishing a sustainable framework for maintaining high employee value perception in the long term, including regular evaluation and adaptation of employee engagement initiatives to address evolving needs and expectations.

problem-statement-man-with-arms-crossed-smiling

What are the 5 components of a problem statement?

In developing a problem statement, it helps to think like a journalist by focusing on the five Ws: who, what, when, where, and why or how. Keep in mind that every statement may not explicitly include each component. But asking these questions is a good way to make sure you’re covering the key elements:

  • Who: Who are the stakeholders that are affected by the problem?
  • What: What is the current state, desired state, or unmet need? 
  • When: When is the issue occurring or what is the timeframe involved?
  • Where: Where is the problem occurring? For example, is it in a specific department, location, or region?
  • Why: Why is this important or worth solving? How is the problem impacting your customers, employees, other stakeholders, or the organization? What is the magnitude of the problem? How large is the gap between the current and desired state? 

How do you write a problem statement?

There are many frameworks designed to help people write a problem statement. One example is outlined in the book, The Conclusion Trap: Four Steps to Better Decisions, ” by Daniel Markovitz. A faculty member at the Lean Enterprise Institute, the author uses many case studies from his work as a business consultant.

To simplify the process, we’ve broken it down into three steps:

1. Gather data and observe

Use data from research and reports, as well as facts from direct observation to answer the five Ws: who, what, when, where, and why. 

Whenever possible, get out in the field and talk directly with stakeholders impacted by the problem. Get a firsthand look at the work environment and equipment. This may mean spending time on the production floor asking employees questions about their work and challenges. Or taking customer service calls to learn more about customer pain points and problems your employees may be grappling with.    

2. Frame the problem properly  

A well-framed problem will help you avoid cognitive bias and open avenues for discussion. It will also encourage the exploration of more options.

A good way to test a problem statement for bias is to ask questions like these:

3. Keep asking why (and check in on the progress)

When it comes to problem-solving, stay curious. Lean on your growth mindset to keep asking why — and check in on the progress. 

Asking why until you’re satisfied that you’ve uncovered the root cause of the problem will help you avoid ineffective band-aid solutions.

Refining your problem statements

When solving any sort of problem, there’s likely a slew of questions that might arise for you. In order to holistically understand the root cause of the problem at hand, your workforce needs to stay curious. 

An effective problem statement creates the space you and your team need to explore, gain insight, and get buy-in before taking action.

If you have embarked on a proposed solution, it’s also important to understand that solutions are malleable. There may be no single best solution. Solutions can change and adapt as external factors change, too. It’s more important than ever that organizations stay agile . This means that interactive check-ins are critical to solving tough problems. By keeping a good pulse on your course of action, you’ll be better equipped to pivot when the time comes to change. 

BetterUp can help. With access to virtual coaching , your people can get personalized support to help solve tough problems of the future.

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Madeline Miles

Madeline is a writer, communicator, and storyteller who is passionate about using words to help drive positive change. She holds a bachelor's in English Creative Writing and Communication Studies and lives in Denver, Colorado. In her spare time, she's usually somewhere outside (preferably in the mountains) — and enjoys poetry and fiction.

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  • How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

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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."

example of statement of the problem and hypothesis

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.

example of statement of the problem and hypothesis

Verywell / Alex Dos Diaz

  • The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

  • Operationalization

Hypothesis Types

Hypotheses examples.

  • Collecting Data

Frequently Asked Questions

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

Some examples of how to write a hypothesis include:

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

The four parts of a hypothesis are:

(1) The research question

(2) The independent variable (IV)

(3) The dependent variable (DV)

(4) The proposed relationship between the IV and DV

No, a hypothesis and a theory are not the same thing. A hypothesis is a testable prediction about a specific research question. A theory, on the other hand, is an explanation supported by an existing body of scientific research.

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

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

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

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

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

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

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

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SciSpace Resources

The Craft of Writing a Strong Hypothesis

Deeptanshu D

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

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-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.

example of statement of the problem and hypothesis

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

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

What is a Hypothesis

Definition:

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

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

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

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

Null Hypothesis

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

Alternative Hypothesis

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

Directional Hypothesis

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

Non-directional Hypothesis

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

Statistical Hypothesis

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

Composite Hypothesis

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

Empirical Hypothesis

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

Simple Hypothesis

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

Complex Hypothesis

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

Applications of Hypothesis

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

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

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

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

Conduct a Literature Review

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

Determine the Variables

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

Formulate the Hypothesis

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

Write the Null Hypothesis

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

Refine the Hypothesis

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

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

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

Purpose of Hypothesis

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

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

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

When to use Hypothesis

Here are some common situations in which hypotheses are used:

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

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

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

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

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

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

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

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example of statement of the problem and hypothesis

June 11, 2020 | How to's

Problem Statement vs Hypothesis: which ­­is more important for experimentation?

by Sadie Neve

When it comes to experimentation and conversion rate optimisation (CRO), we often see people relying too heavily on their instincts, abandoning logic and data in favour of their gut feelings. But really, nothing in experimentation is certain until tested. This realisation automatically makes you question everything you want to change about your website. This means experimentation should be approached like a scientific experiment that follows three core steps; identify a problem, form a hypothesis, and test that hypothesis.

But when it comes to experimentation, should you value the problem statement over the hypothesis? Or vice versa?

Which is more important: the problem statement or hypothesis?

At CreativeCX, we actually place equal importance on the problem statement and the hypothesis. This ensures that we consider both the customer problem that needs to be solved, as well as the business objectives.

All too often, we see companies either neglect the problem statement and hypothesis entirely or favour one over the other.

But weakness in either of these elements can seriously hinder the success of your experimentation programme.

So how can you structure both statements in such a way that you get the most out of your experiment?

The problem statement

First of all, what is the problem statement? A problem statement is a concise description of an issue that needs to be addressed or improved upon. In the case of digital products and services, this should be related to a problem that the customer has.

In any experiment, the problem statement should always come first. Without a problem, you have no real reason to conduct the experiment or understanding on what to conduct an experiment on.

The problem statement guides the strategic direction of your experiment while ensuring that you are always focusing on the customer.

How do we identify customer problems?

The data and research that you undertake will help you identify customer problems, either for your current customers or for your target audience. Identifying the pain points of your customer’s online behaviour should ideally come from multiple sources of data and research. This enables you to triangulate insights so that you can build a more complete picture of the problem, whilst also gaining an understanding of the magnitude of the issue. When starting your research process, you’ll probably find yourself having more questions than answers at the beginning. That’s fine; in fact, it’s normal at this early stage of the experiment.

Rather than letting this put you off, it is better to dig deeper, ask more questions and achieve a greater understanding of the customer problem before trying to find a solution. A greater understanding of the problem and how it’s affecting your customers will lead to better solutions and a higher win rate with your experiments. With this in mind, it is wise to collaborate with other teams within your business – preferably members of your CX and UX departments – who may be able to share relevant customer insights that they have discovered through their own research.

Once you have sufficient data, it is likely you will start to identify problem themes, which will help you understand the wider issues your customers are facing. This is where we start to create a clear problem statement.

How do you craft a clear problem statement?

A clear problem statement should help you identify what the problem is and the data that backs up your claim. At CreativeCX, we organise each problem statement as follows:

We believe [state the problem identified] because [state the supporting data].

Let’s demonstrate with an example. We work with an e-commerce company that sells women’s loungewear. Through our research, we discovered the following two pieces of data:

Usability testing showed users were moving back and forth between the product details page and the basket page to edit their selected size. Website data showed only 2% of customers engage with the “size guide” text link on the product details page. Based on this analysis, we have inferred a problem: users are struggling to understand which size they should choose. Through this, we are able to make the following problem statement:

We believe that users are struggling to understand which size they should choose because our data shows that users are editing their selected size multiple times on the basket and product details page and only 2% of customers engage with the sizing guide.

Can you see how much better this statement is compared to the following:

We think we have an issue with users understanding which size would fit them best.

Here are our top three questions we suggest you keep in mind when writing a problem statement:

Is my problem statement focused on my customers? Is my problem statement clear and precise? What data do I have to back up this problem? As you can see in the examples above, our first example answers all three questions while the second statement falls short on questions two and three.

Whilst your problem statement identifies the problem you hope to solve, the hypothesis helps you decide on how you will try to solve it.

The hypothesis statement

The hypothesis: you’ve probably come across this word years ago in a science class, and its meaning remains the same even in this context. Essentially, the hypothesis statement is a prediction for what you think will happen if you take a certain type of action to resolve a problem.

The hypothesis usually identifies what is going to be changed and the action’s potential outcome, as well as why you think the change will have that particular result.

Creating a hypothesis is a key part of any quality experiment and shouldn’t be rushed. Rushing over this critical step could mean that you miss out on key actions or insights further down the line.

Similar to the problem statement, the hypothesis should be precisely constructed. Having a vague hypothesis may actually be a sign that your problem statement isn’t as clear as you originally thought. An unclear problem statement or hypothesis could, in turn, result in your proposed solutions not having the desired or expected results.

How do you write a clear hypothesis?

There are many ways to write a strong hypothesis. At CreativeCX, we structure ours using the following formula:

By [state experiment change], we believe [user behaviour change], solving [state problem]. We expect to see [expected results].

Now, some may say this will create a hypothesis that is too lengthy. However, this structure clearly incorporates three key elements of an experiment: the problem we are trying to solve, the specific execution, and the expected result. More importantly, it strikes a balance between focusing on the business goals you want to achieve and optimising your customers’ online experience.

Let’s go back to our previous example. There might be multiple solutions to solving this sizing problem, all of which would require a different hypothesis. However, our problem statement has allowed us to identify that we need to increase user awareness of the sizing guide on the product page.

We have identified this as a top priority, so our hypothesis would be as follows:

By increasing link prominence for the sizing guide, we believe more customers will interact with the link, solving sizing uncertainty. We expect to see an increase in customers engaging with the size guide, as well as an increase in customers progressing from the basket to checkout.

Again, whilst this is lengthy, it is also precise. It clearly defines the experiment’s aim with both the business and its customers in mind.

Compare this to the following:

Making the sizing guide link larger will improve our profits.

Here are our top three questions to bear in mind when you’re writing a hypothesis:

Is my hypothesis a statement or a testable question? Is it clear and precise? Is my hypothesis human-friendly and keeping the customer in mind? As you can see, whilst our first example considered all three questions, the second is relatively vague and doesn’t relate to the customer at all.

What do I do once I have written a problem statement and hypothesis?

With your concise problem statement and hypothesis, you should have a great foundation for your experiment. The next step looks at designing your experiment, not in terms of actual visual designs, but what solutions you will be testing in a hope to validate your hypothesis and gain as much learnings on your customers as possible.

Look out for our future blog around how best to design your experiments and be creative with your potential variations.

If you have any questions about topics that have been covered in this blog or you’d like help with your experimentation or CRO programme, please don’t hesitate to reach out to us.

Interested in working with Creative CX?

example of statement of the problem and hypothesis

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Research Problems, Research Questions, and Hypotheses

  Describe the process of developing and refining a research problem   Distinguish the functions and forms of statements of purpose and research questions for quantitative and qualitative studies   Describe the function and characteristics of research hypotheses   Critique statements of purpose, research questions, and hypotheses in research reports with respect to their placement, clarity, wording, and significance   Define new terms in the chapter Key Terms   Directional hypothesis   Hypothesis   Nondirectional hypothesis   Null hypothesis   Problem statement   Research hypothesis   Research problem   Research question   Statement of purpose OVERVIEW OF RESEARCH PROBLEMS Studies begin in much the same fashion as an evidence-based practice (EBP) effort—as problems that need to be solved or questions that need to be answered. This chapter discusses research problems and research questions. We begin by clarifying some terms. Basic Terminology Researchers begin with a topic on which to focus. Examples of research topics are claustrophobia during magnetic resonance imaging (MRI) tests and pain management for sickle cell disease. Within broad topic areas are many possible research problems. In this section, we illustrate various terms using the topic side effects of chemotherapy. A research problem is an enigmatic or troubling condition. The purpose of research is to “solve” the problem—or to contribute to its solution—by gathering relevant data. A problem statement articulates the problem and an argument that explains the need for a study. Table 6.1 presents a simplified problem statement related to the topic of side effects of chemotherapy. Many reports provide a statement of purpose (or purpose statement ), which is a summary of an overall goal. Sometimes the words aim or objective are used in lieu of purpose. Research questions are the specific queries researchers want to answer. Researchers who make specific predictions about answers to research questions pose hypotheses that are then tested. These terms are not always consistently defined in research textbooks. Table 6.1 illustrates the interrelationships among terms as we define them. Research Problems and Paradigms Some research problems are better suited to qualitative versus quantitative inquiry. Quantitative studies usually involve concepts that are well developed and for which methods of measurement have been (or can be) developed. For example, a quantitative study might be undertaken to assess whether people with chronic illness are more depressed than people without a chronic illness. There are relatively good measures of depression that would yield quantitative data about the level of depression in those with and without a chronic illness. Qualitative studies are undertaken because a researcher wants to develop a rich, context-bound understanding of a poorly understood phenomenon. Qualitative methods would not be well suited to comparing levels of depression among those with and without chronic illness, but they would be ideal for exploring the meaning of depression among chronically ill people. In evaluating a research report, one consideration is whether the research problem is suitable for the chosen paradigm. Sources of Research Problems Where do ideas for research problems come from? At the most basic level, research topics originate with researchers’ interests. Because research is a time-consuming enterprise, curiosity about and interest in a topic are essential to a project’s success. Research reports rarely indicate the source of researchers’ inspiration for a study, but a variety of explicit sources can fuel their curiosity, such as nurses’ clinical experience and readings in the nursing literature. Also, topics are sometimes suggested by global social or political issues of relevance to the health care community (e.g., health disparities). Theories from nursing and other disciplines sometimes suggest a research problem. Additionally, researchers who have developed a program of research may get inspiration for “next steps” from their own findings or from a discussion of those findings with others. Example of a problem source for a quantitative study Beck, one of this book’s authors, has developed a strong research program on postpartum depression (PPD). Beck was approached by Dr. Carol Lammi-Keefe, a professor in nutritional sciences and her PhD student, Michelle Judge, who had been researching the effect of DHA (docosahexaemoic acid, a fat found in cold-water fish) on fetal brain development. The literature suggested that DHA might play a role in reducing the severity of PPD, and so these researchers collaborated in a project to test the effectiveness of dietary supplements of DHA during pregnancy on the incidence and severity of PPD. The researchers found that women in the DHA experimental group had fewer symptoms of PPD compared to women who did not receive the DHA intervention ( Judge et al., 2014 ). Development and Refinement of Research Problems Developing a research problem is a creative process. Researchers often begin with interests in a broad topic area and then develop a more specific researchable problem. For example, suppose a hospital nurse begins to wonder why some patients complain about having to wait for pain medication when certain nurses are assigned to them. The general topic is differences in patients’ complaints about pain medications. The nurse might ask, What accounts for this discrepancy? This broad question may lead to other questions, such as How do the nurses differ? or What characteristics do patients with complaints share? The nurse may then observe that the ethnic background of the patients and nurses could be relevant. This may direct the nurse to look at the literature on nursing behaviors and ethnicity, or it may lead to a discussion with peers. These efforts may result in several research questions, such as the following:   What is the nature of patient complaints among patients of different ethnic backgrounds?   Is the ethnic background of nurses related to the frequency with which they dispense pain medication?   Does the number of patient complaints increase when patients are of dissimilar ethnic backgrounds as opposed to when they are of the same ethnic background as nurses? These questions stem from the same problem, yet each would be studied differently; for example, some suggest a qualitative approach, and others suggest a quantitative one. Both ethnicity and nurses’ dispensing behaviors are variables that can be measured reliably. A qualitative researcher would be more interested in understanding the essence of patients’ complaints, patients’ experience of frustration, or the process by which the problem got resolved. These aspects of the problem would be difficult to measure. Researchers choose a problem to study based on its inherent interest to them and on its fit with a paradigm of preference. COMMUNICATING RESEARCH PROBLEMS AND QUESTIONS Every study needs a problem statement that articulates what is problematic and what must be solved. Most research reports also present either a statement of purpose, research questions, or hypotheses, and often, combinations of these three elements are included. Many students do not really understand problem statements and may have trouble identifying them in a research article. A problem statement is presented early and often begins with the first sentence after the abstract. Research questions, purpose statements, or hypotheses appear later in the introduction. Problem Statements A good problem statement is a declaration of what it is that is problematic, what it is that “needs fixing,” or what it is that is poorly understood. Problem statements, especially for quantitative studies, often have most of the following six components: 1.   Problem identification : What is wrong with the current situation? 2.   Background : What is the nature of the problem, or the context of the situation, that readers need to understand? 3.   Scope of the problem : How big a problem is it, and how many people are affected? 4.   Consequences of the problem : What is the cost of not fixing the problem? 5.   Knowledge gaps : What information about the problem is lacking? 6.   Proposed solution : How will the new study contribute to the solution of the problem? Let us suppose that our topic was humor as a complementary therapy for reducing stress in hospitalized patients with cancer. One research question (discussed later in this section) might be “What is the effect of nurses’ use of humor on stress and natural killer cell activity in hospitalized cancer patients?” Box 6.1 presents a rough draft of a problem statement for such a study. This problem statement is a reasonable draft, but it could be improved. Box 6.1   Draft Problem Statement on Humor and Stress A diagnosis of cancer is associated with high levels of stress. Sizeable numbers of patients who receive a cancer diagnosis describe feelings of uncertainty, fear, anger, and loss of control. Interpersonal relationships, psychological functioning, and role performance have all been found to suffer following cancer diagnosis and treatment. A variety of alternative/complementary therapies have been developed in an effort to decrease the harmful effects of cancer-related stress on psychological and physiological functioning, and resources devoted to these therapies (money and staff) have increased in recent years. However, many of these therapies have not been carefully evaluated to assess their efficacy, safety, or cost-effectiveness. For example, the use of humor has been recommended as a therapeutic device to improve quality of life, decrease stress, and perhaps improve immune functioning, but the evidence to justify its advocacy is scant. Box 6.2 illustrates how the problem statement could be made stronger by adding information about scope (component 3), long-term consequences (component 4), and possible solutions (component 6). This second draft builds a more compelling argument for new research: Millions of people are affected by cancer, and the disease has adverse consequences not only for patients and their families but also for society. The revised problem statement also suggests a basis for the new study by describing a possible solution on which the new study might build. Box 6.2   Some Possible Improvements to Problem Statement on Humor and Stress Each year, more than 1 million people are diagnosed with cancer, which remains one of the top causes of death among both men and women (reference citations). * Numerous studies have documented that a diagnosis of cancer is associated with high levels of stress. Sizeable numbers of patients who receive a cancer diagnosis describe feelings of uncertainty, fear, anger, and loss of control (citations) . Interpersonal relationships, psychological functioning, and role performance have all been found to suffer following cancer diagnosis and treatment (citations). These stressful outcomes can, in turn, adversely affect health, long-term prognosis, and medical costs among cancer survivors (citations). A variety of alternative/complementary therapies have been developed in an effort to decrease the harmful effects of cancer-related stress on psychological and physiological functioning, and resources devoted to these therapies (money and staff) have increased in recent years (citations) . However, many of these therapies have not been carefully evaluated to assess their efficacy, safety, or cost-effectiveness. For example, the use of humor has been recommended as a therapeutic device to improve quality of life, decrease stress, and perhaps improve immune functioning (citations) , but the evidence to justify its advocacy is scant. Preliminary findings from a recent small-scale endocrinology study with a healthy sample exposed to a humorous intervention (citation), however, holds promise for further inquiry with immuno-compromised populations. * Reference citations would be inserted to support the statements. HOW-TO-TELL TIP How can you tell a problem statement? Problem statements are rarely explicitly labeled. The first sentence of a research report is often the starting point of a problem statement. The problem statement is usually interwoven with findings from the research literature. Prior findings provide evidence supporting assertions in the problem statement and suggest gaps in knowledge. In many articles, it is difficult to disentangle the problem statement from the literature review, unless there is a subsection specifically labeled “Literature Review” or something similar. Problem statements for a qualitative study similarly express the nature of the problem, its context, its scope, and information needed to address it. Qualitative studies embedded in a research tradition often incorporate terms and concepts that foreshadow the tradition in their problem statements. For example, a problem statement for a phenomenological study might note the need to know more about people’s experiences or meanings they attribute to those experiences. Statements of Purpose Many researchers articulate their research goals as a statement of purpose. The purpose statement establishes the general direction of the inquiry and captures the study’s substance. It is usually easy to identify a purpose statement because the word purpose is explicitly stated: “The purpose of this study was . . . ”—although sometimes the words aim , goal , or objective are used instead, as in “The aim of this study was . . . .” In a quantitative study, a statement of purpose identifies the key study variables and their possible interrelationships as well as the population of interest (i.e., all the PICO elements). Example of a statement of purpose from a quantitative study The purpose of this study was to examine the effects of an education-support intervention delivered in home settings to people with chronic heart failure, in terms of their functional status, self-efficacy, quality of life, and self-care ability ( Clark et al., 2015 ). This purpose statement identifies the population (P) of interest as patients with heart failure living at home. The key study variables were the patients’ exposure or nonexposure to the special intervention (the independent variable encompassing the I and C components) and the patient’s functional status, self-efficacy, quality of life, and self-care ability (the dependent variables or Os). In qualitative studies, the statement of purpose indicates the nature of the inquiry; the key concept or phenomenon; and the group, community, or setting under study. Example of a statement of purpose from a qualitative study The purpose of this study was to explore the influence of religiosity and spirituality on rural parents’ decision to vaccinate their 9- to 13-year-old children against human papillomavirus (HPV) ( Thomas et al., 2015 ). This statement indicates that the group under study is rural parents with children aged 9 to 13 years and the central phenomenon is the parent’s decision making about vaccinations within the context of their spirituality and religious beliefs. Researchers often communicate information about their approach through their choice of verbs. A study whose purpose is to explore or describe some phenomenon is likely to be an investigation of a little-researched topic, often involving a qualitative approach such as phenomenology or ethnography. A statement of purpose for a qualitative study—especially a grounded theory study—may also use verbs such as understand , discover , or generate . Statements of purpose in qualitative studies also may “encode” the tradition of inquiry through certain terms or “buzz words” associated with those traditions, as follows:    Grounded theory : processes; social structures; social interactions    Phenomenological studies : experience; lived experience; meaning; essence    Ethnographic studies : culture; roles; lifeways; cultural behavior Quantitative researchers also use verbs to communicate the nature of the inquiry. A statement indicating that the study purpose is to test or evaluate something (e.g., an intervention) suggests an experimental design, for example. A study whose purpose is to examine or explore the relationship between two variables is more likely to involve a nonexperimental design. Sometimes the verb is ambiguous: If a purpose statement states that the researcher’s intent is to compare two things, the comparison could involve alternative treatments (using an experimental design) or two preexisting groups such as smokers and nonsmokers (using a nonexperimental design). In any event, verbs such as test , evaluate , and compare suggest quantifiable variables and designs with scientific controls. The verbs in a purpose statement should connote objectivity. A statement of purpose indicating that the study goal was to prove , demonstrate , or show something suggests a bias. Research Questions Research questions are, in some cases, direct rewordings of statements of purpose, phrased interrogatively rather than declaratively, as in the following example:    Purpose : The purpose of this study is to assess the relationship between the functional dependence level of renal transplant recipients and their rate of recovery.    Question : Is the functional dependence level (I) of renal transplant recipients (P) related to their rate of recovery (O)? Some research articles omit a statement of purpose and state only research questions, but in many cases researchers use research questions to add greater specificity to a global purpose statement. Research Questions in Quantitative Studies In Chapter 2 , we discussed clinical foreground questions to guide an EBP inquiry. The EBP question templates in Table 2.1 could yield questions to guide a research project as well, but researchers tend to conceptualize their questions in terms of their variables . Take, for example, the first question in Table 2.1 : “In (population), what is the effect of (intervention) on (outcome)?”A researcher would be more likely to think of the question in these terms: “In (population), what is the effect of (independent variable) on (dependent variable)?” Thinking in terms of variables helps to guide researchers’ decisions about how to operationalize them. Thus, in quantitative studies, research questions identify the population (P) under study, the key study variables (I, C, and O components), and relationships among the variables. Most research questions concern relationships among variables, and thus, many quantitative research questions could be articulated using a general question template: “In (population), what is the relationship between (independent variable or IV) and (dependent variable or DV)?” Examples of variations include the following:    Therapy/treatment/intervention : In (population), what is the effect of (IV: intervention vs. an alternative) on (DV)?    Prognosis : In (population), does (IV: disease or illness vs. its absence) affect or increase the risk of (DV)?    Etiology/harm : In (population), does (IV: exposure vs. nonexposure) cause or increase risk of (DV)? Not all research questions are about relationships—some are descriptive. As examples, here are two descriptive questions that could be answered in a quantitative study on nurses’ use of humor:   What is the frequency with which nurses use humor as a complementary therapy with hospitalized cancer patients?   What are the characteristics of nurses who use humor as a complementary therapy with hospitalized cancer patients? Answers to such questions might be useful in developing effective strategies for reducing stress in patients with cancer. Example of a research question from a quantitative study Chang and colleagues (2015) undertook a study that addressed the following question: Among community-dwelling elders aged 65 years and older, does regular exercise have an association with depressive symptoms?

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Computer Science > Information Theory

Title: finite-sample expansions for the optimal error probability in asymmetric binary hypothesis testing.

Abstract: The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations. Specifically, the asymmetric version of the problem is examined, where different requirements are placed on the two error probabilities. Accurate nonasymptotic expansions with explicit constants are obtained for the error probability, using tools from large deviations and Gaussian approximation. Examples are shown indicating that, in the asymmetric regime, the approximations suggested by the new bounds are significantly more accurate than the approximations provided by either of the two main earlier approaches -- normal approximation and error exponents.

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NPR defends its journalism after senior editor says it has lost the public's trust

David Folkenflik 2018 square

David Folkenflik

example of statement of the problem and hypothesis

NPR is defending its journalism and integrity after a senior editor wrote an essay accusing it of losing the public's trust. Saul Loeb/AFP via Getty Images hide caption

NPR is defending its journalism and integrity after a senior editor wrote an essay accusing it of losing the public's trust.

NPR's top news executive defended its journalism and its commitment to reflecting a diverse array of views on Tuesday after a senior NPR editor wrote a broad critique of how the network has covered some of the most important stories of the age.

"An open-minded spirit no longer exists within NPR, and now, predictably, we don't have an audience that reflects America," writes Uri Berliner.

A strategic emphasis on diversity and inclusion on the basis of race, ethnicity and sexual orientation, promoted by NPR's former CEO, John Lansing, has fed "the absence of viewpoint diversity," Berliner writes.

NPR's chief news executive, Edith Chapin, wrote in a memo to staff Tuesday afternoon that she and the news leadership team strongly reject Berliner's assessment.

"We're proud to stand behind the exceptional work that our desks and shows do to cover a wide range of challenging stories," she wrote. "We believe that inclusion — among our staff, with our sourcing, and in our overall coverage — is critical to telling the nuanced stories of this country and our world."

NPR names tech executive Katherine Maher to lead in turbulent era

NPR names tech executive Katherine Maher to lead in turbulent era

She added, "None of our work is above scrutiny or critique. We must have vigorous discussions in the newsroom about how we serve the public as a whole."

A spokesperson for NPR said Chapin, who also serves as the network's chief content officer, would have no further comment.

Praised by NPR's critics

Berliner is a senior editor on NPR's Business Desk. (Disclosure: I, too, am part of the Business Desk, and Berliner has edited many of my past stories. He did not see any version of this article or participate in its preparation before it was posted publicly.)

Berliner's essay , titled "I've Been at NPR for 25 years. Here's How We Lost America's Trust," was published by The Free Press, a website that has welcomed journalists who have concluded that mainstream news outlets have become reflexively liberal.

Berliner writes that as a Subaru-driving, Sarah Lawrence College graduate who "was raised by a lesbian peace activist mother ," he fits the mold of a loyal NPR fan.

Yet Berliner says NPR's news coverage has fallen short on some of the most controversial stories of recent years, from the question of whether former President Donald Trump colluded with Russia in the 2016 election, to the origins of the virus that causes COVID-19, to the significance and provenance of emails leaked from a laptop owned by Hunter Biden weeks before the 2020 election. In addition, he blasted NPR's coverage of the Israel-Hamas conflict.

On each of these stories, Berliner asserts, NPR has suffered from groupthink due to too little diversity of viewpoints in the newsroom.

The essay ricocheted Tuesday around conservative media , with some labeling Berliner a whistleblower . Others picked it up on social media, including Elon Musk, who has lambasted NPR for leaving his social media site, X. (Musk emailed another NPR reporter a link to Berliner's article with a gibe that the reporter was a "quisling" — a World War II reference to someone who collaborates with the enemy.)

When asked for further comment late Tuesday, Berliner declined, saying the essay spoke for itself.

The arguments he raises — and counters — have percolated across U.S. newsrooms in recent years. The #MeToo sexual harassment scandals of 2016 and 2017 forced newsrooms to listen to and heed more junior colleagues. The social justice movement prompted by the killing of George Floyd in 2020 inspired a reckoning in many places. Newsroom leaders often appeared to stand on shaky ground.

Leaders at many newsrooms, including top editors at The New York Times and the Los Angeles Times , lost their jobs. Legendary Washington Post Executive Editor Martin Baron wrote in his memoir that he feared his bonds with the staff were "frayed beyond repair," especially over the degree of self-expression his journalists expected to exert on social media, before he decided to step down in early 2021.

Since then, Baron and others — including leaders of some of these newsrooms — have suggested that the pendulum has swung too far.

Legendary editor Marty Baron describes his 'Collision of Power' with Trump and Bezos

Author Interviews

Legendary editor marty baron describes his 'collision of power' with trump and bezos.

New York Times publisher A.G. Sulzberger warned last year against journalists embracing a stance of what he calls "one-side-ism": "where journalists are demonstrating that they're on the side of the righteous."

"I really think that that can create blind spots and echo chambers," he said.

Internal arguments at The Times over the strength of its reporting on accusations that Hamas engaged in sexual assaults as part of a strategy for its Oct. 7 attack on Israel erupted publicly . The paper conducted an investigation to determine the source of a leak over a planned episode of the paper's podcast The Daily on the subject, which months later has not been released. The newsroom guild accused the paper of "targeted interrogation" of journalists of Middle Eastern descent.

Heated pushback in NPR's newsroom

Given Berliner's account of private conversations, several NPR journalists question whether they can now trust him with unguarded assessments about stories in real time. Others express frustration that he had not sought out comment in advance of publication. Berliner acknowledged to me that for this story, he did not seek NPR's approval to publish the piece, nor did he give the network advance notice.

Some of Berliner's NPR colleagues are responding heatedly. Fernando Alfonso, a senior supervising editor for digital news, wrote that he wholeheartedly rejected Berliner's critique of the coverage of the Israel-Hamas conflict, for which NPR's journalists, like their peers, periodically put themselves at risk.

Alfonso also took issue with Berliner's concern over the focus on diversity at NPR.

"As a person of color who has often worked in newsrooms with little to no people who look like me, the efforts NPR has made to diversify its workforce and its sources are unique and appropriate given the news industry's long-standing lack of diversity," Alfonso says. "These efforts should be celebrated and not denigrated as Uri has done."

After this story was first published, Berliner contested Alfonso's characterization, saying his criticism of NPR is about the lack of diversity of viewpoints, not its diversity itself.

"I never criticized NPR's priority of achieving a more diverse workforce in terms of race, ethnicity and sexual orientation. I have not 'denigrated' NPR's newsroom diversity goals," Berliner said. "That's wrong."

Questions of diversity

Under former CEO John Lansing, NPR made increasing diversity, both of its staff and its audience, its "North Star" mission. Berliner says in the essay that NPR failed to consider broader diversity of viewpoint, noting, "In D.C., where NPR is headquartered and many of us live, I found 87 registered Democrats working in editorial positions and zero Republicans."

Berliner cited audience estimates that suggested a concurrent falloff in listening by Republicans. (The number of people listening to NPR broadcasts and terrestrial radio broadly has declined since the start of the pandemic.)

Former NPR vice president for news and ombudsman Jeffrey Dvorkin tweeted , "I know Uri. He's not wrong."

Others questioned Berliner's logic. "This probably gets causality somewhat backward," tweeted Semafor Washington editor Jordan Weissmann . "I'd guess that a lot of NPR listeners who voted for [Mitt] Romney have changed how they identify politically."

Similarly, Nieman Lab founder Joshua Benton suggested the rise of Trump alienated many NPR-appreciating Republicans from the GOP.

In recent years, NPR has greatly enhanced the percentage of people of color in its workforce and its executive ranks. Four out of 10 staffers are people of color; nearly half of NPR's leadership team identifies as Black, Asian or Latino.

"The philosophy is: Do you want to serve all of America and make sure it sounds like all of America, or not?" Lansing, who stepped down last month, says in response to Berliner's piece. "I'd welcome the argument against that."

"On radio, we were really lagging in our representation of an audience that makes us look like what America looks like today," Lansing says. The U.S. looks and sounds a lot different than it did in 1971, when NPR's first show was broadcast, Lansing says.

A network spokesperson says new NPR CEO Katherine Maher supports Chapin and her response to Berliner's critique.

The spokesperson says that Maher "believes that it's a healthy thing for a public service newsroom to engage in rigorous consideration of the needs of our audiences, including where we serve our mission well and where we can serve it better."

Disclosure: This story was reported and written by NPR Media Correspondent David Folkenflik and edited by Deputy Business Editor Emily Kopp and Managing Editor Gerry Holmes. Under NPR's protocol for reporting on itself, no NPR corporate official or news executive reviewed this story before it was posted publicly.

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COMMENTS

  1. How to Write a Problem Statement

    Step 3: Set your aims and objectives. Finally, the problem statement should frame how you intend to address the problem. Your goal here should not be to find a conclusive solution, but rather to propose more effective approaches to tackling or understanding it. The research aim is the overall purpose of your research.

  2. Problem statement and hypothesis

    A hypothesis is a theoretical, hypothetical explanation that can be tested. It usually takes the form of a causal relationship or a causal explanation. You can also consider the hypothesis as a preliminary response to a research question or a problem statement. A hypothesis can be expressed in different ways, but generally, the following applies:

  3. Lesson3-2-1

    Example of a problem statement and its related hypothesis: Problem Statement: This study is to determine the effects of a peer-assisted method of teaching reading, as compared to the traditional method, in terms of reading comprehension. ... Key difference between the above two forms (research question/problem statement & its related hypothesis):

  4. How to Write a Strong Hypothesis

    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.

  5. How to Write a Hypothesis in 6 Steps, With Examples

    7 Statistical hypothesis. A statistical hypothesis is when you test only a sample of a population and then apply statistical evidence to the results to draw a conclusion about the entire population. Instead of testing everything, you test only a portion and generalize the rest based on preexisting data. Examples:

  6. What is a Problem Statement? [with examples]

    The purpose of the problem statement is to identify the issue that is a concern and focus it in a way that allows it to be studied in a systematic way. It defines the problem and proposes a way to research a solution, or demonstrates why further information is needed in order for a solution to become possible.

  7. How to Write a Problem Statement (With 3 Examples)

    Example Problem Statement 1: The Status Quo Problem Statement. Example: The average customer service on-hold time for Example company exceeds five minutes during both its busy and slow seasons. This can be used to describe a current pain point within an organization that may need to be addressed.

  8. How to Write a Strong Hypothesis

    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.

  9. PDF DEVELOPING HYPOTHESIS AND RESEARCH QUESTIONS

    Statement of the problem Research hypothesis (a specific deductive prediction) DEVELOPING HYPOTHESES & RESEARCH QUESTIONS. Example: Consider the example of a simple association between two variables, Y and X. 1. Y and X are associated (or, there is an association between Y and X). 2. Y is related to X (or, Y is dependent on X).

  10. How to Write a Statement of the Problem in Research

    Establish relevance: Highlight the importance and significance of the problem in the context of your field or the broader world. Guide inquiry: Formulate the research questions or hypotheses you'll explore. Communicate intent: Succinctly convey the core purpose of your research to stakeholders, peers, and any audience.

  11. Hypothesis Examples: How to Write a Great Research Hypothesis

    What is a hypothesis and how can you write a great one for your research? A hypothesis is a tentative statement about the relationship between two or more variables that can be tested empirically. Find out how to formulate a clear, specific, and testable hypothesis with examples and tips from Verywell Mind, a trusted source of psychology and mental health information.

  12. Research Hypothesis: Definition, Types, Examples and Quick Tips

    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.

  13. What is a Research Hypothesis: How to Write it, Types, and Examples

    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.

  14. Problem Statement

    Here are some general steps to follow when writing a problem statement: Identify the problem: Clearly identify the problem that needs to be addressed. Consider the context, stakeholders, and potential consequences of the problem. Research the problem: Conduct research to gather data and information about the problem.

  15. Research Hypothesis In Psychology: Types, & Examples

    Examples. A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

  16. Problem Statement and Hypothesis

    Learn more about writing a problem statement and hypothesis!Link to Lesson on the Scientific Method: https://www.youtube.com/watch?v=nQuxB7wOBNE&t=37sReferen...

  17. What is a Hypothesis

    Definition: Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation. Hypothesis is often used in scientific research to guide the design of experiments ...

  18. Problem Statement vs Hypothesis: which ­­is more important for

    At CreativeCX, we actually place equal importance on the problem statement and the hypothesis. This ensures that we consider both the customer problem that needs to be solved, as well as the business objectives. All too often, we see companies either neglect the problem statement and hypothesis entirely or favour one over the other.

  19. PDF UNIT 2 PROBLEM AND HYPOTHESIS* Problem and Hypothesis

    problem statement are: The problem should be testable by empirical methods • A problem statement should be solvable. • The data of a scientific problem should be quantitative. • The variable relating to the problem should be clear and definite. 2.2.4 ays in which a Problem is Manifested W A problem is said to exist when we know enough ...

  20. Research Problems, Research Questions, and Hypotheses

    The purpose of research is to "solve" the problem—or to contribute to its solution—by gathering relevant data. A problem statement articulates the problem and an argument that explains the need for a study. Table 6.1 presents a simplified problem statement related to the topic of side effects of chemotherapy.

  21. Problem Statement and Hypothesis

    1. whate is the best things in skaeting and whate is it made of. 2. all of the stuff in the bord is made up of meatle, wood, and rubber. the best is alien workshop. 1. Which type of wood burns the fastest. 2. I believe that the oak will burn the fastest. 2. my hypothesis is notebook paper will hit the ground last.

  22. Statement of The Problem and Hypothesis

    Statement of the problem and hypothesis - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. 1) The document discusses the different types of research questions that can be formulated in a study, including descriptive, exploratory, evaluative, predictive, explanatory, and control questions. 2) Key criteria for evaluating good research questions ...

  23. Finite-sample expansions for the optimal error probability in

    The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of ...

  24. Assessment of non-linear mixed effects model-based approaches ...

    IMA confirmed its status of promising NLMEM-based approach for hypothesis testing of the drug effect and could be used in the future, after further evaluations, as primary analysis in confirmatory trials. ### Competing Interest Statement The authors have declared no competing interest.

  25. NPR responds after editor says it has 'lost America's trust' : NPR

    A veteran NPR editor publicly questions whether the public radio network has, in its push for greater diversity and representation, overlooked conservative viewpoints.