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How to Write a Hypothesis: Step-By-Step Guide

How to Write a Hypothesis: Step-By-Step Guide

A hypothesis is a testable statement that guides scientific research. Want to know how to write a hypothesis for your research paper? This guide will show you the key steps involved, including defining your variables and phrasing your hypothesis correctly.

Key Takeaways

  • A hypothesis is a testable statement proposed for investigation, grounded in existing knowledge, essential for guiding scientific research.
  • Understanding different types of hypotheses, including simple, complex, null, and alternative, is crucial for selecting appropriate research approaches.
  • Crafting a strong hypothesis involves a systematic process including defining variables, phrasing it as an if-then statement, and ensuring it is clear, specific, and testable.

Understanding a Hypothesis

An empirical hypothesis is not just a simple guess. It represents a preliminary concept that stands to be scrutinized through Research and experimentation. A well-constructed hypothesis is a fundamental component of the scientific method, guiding experiments and leading to conclusions. Within the realm of science, such hypotheses are crafted after an extensive examination of current knowledge, ensuring their foundation on already established evidence prior to beginning any new inquiry.

Essentially, a hypothesis in the scientific community must present itself as something capable of being tested, this characteristic distinguishes it from mere speculation by allowing its potential verification or falsification through methodical scrutiny. Hypotheses serve as crucial instruments within scientific studies, directing these investigations toward particular queries and forming the backbone upon which all experiments rest in their pursuit for advancements in comprehension.

When formulating a hypothesis for testing within research activities, one should employ language that remains neutral and detached from subjective bias thereby bolstering the legitimacy of outcomes produced during the study. This precision fosters greater confidence in results obtained under rigorous evaluation standards among peers.

Characteristics of a Good Hypothesis

A good hypothesis is the cornerstone of any successful scientific research. It should be clear, concise, and testable, providing a solid foundation for your investigation. Here are some key characteristics that define a good hypothesis:

  • Clarity : A good hypothesis should be easy to understand and clearly state the expected outcome of the research. For example , “Increased exposure to sunlight will result in taller plant growth” is a clear and straightforward hypothesis.
  • Conciseness : Avoid unnecessary complexity or jargon. A concise hypothesis is brief and to the point, making it easier to test and analyze. For instance, “Exercise improves mental health” is concise and direct.
  • Testability : A good hypothesis must be testable and falsifiable, meaning it can be proven or disproven through scientific research methods. For example, “Consuming vitamin C reduces the duration of the common cold” is a testable hypothesis.
  • Relevance : Ensure your hypothesis is relevant to the research question or problem and aligned with your research objectives. For example, if your research question is about the impact of diet on health, a relevant hypothesis could be “A high-fiber diet reduces the risk of heart disease.”
  • Specificity : A good hypothesis should be specific and focused on a particular aspect of the research question. For example, “Daily meditation reduces stress levels in college students” is specific and targeted.
  • Measurability : Your hypothesis should be measurable, meaning it can be quantified or observed. For example, “Regular physical activity lowers blood pressure” is a measurable hypothesis.

By ensuring your hypothesis possesses these characteristics, you set a strong foundation for your scientific research, guiding your investigation towards meaningful and reliable results.

Types of Hypotheses

Scientific research incorporates a range of research hypotheses, which are crucial for proposing relationships between different variables and steering the direction of the investigation. These seven unique forms of hypotheses cater to diverse needs within the realm of scientific inquiry.

Comprehending these various types is essential in selecting an appropriate method for conducting research. To delve into details, we have simple, complex, null and alternative hypotheses. Each brings its distinct features and practical implications to the table. It underscores why recognizing how they diverge and what purposes they serve is fundamental in any scientific study.

Simple Hypothesis

A basic hypothesis suggests a fundamental relationship between two elements: the independent and dependent variable. Take, for example, a hypothesis that says, “The taller growth of plants (dependent variable) is due to increased exposure to sunlight (independent variable).” Such hypotheses are clear-cut and easily testable as they concentrate on one direct cause-and-effect link.

These types of straightforward hypotheses are very beneficial in scientific experiments because they permit the isolation of variables for precise outcome measurement. Their simplicity lends itself well to being an essential component in conducting scientific research, thanks to their unambiguous nature and targeted focus on specific relationships.

Complex Hypothesis

Alternatively, a complex hypothesis proposes an interconnection amongst several variables. It builds on the concept of numerous variable interactions within research parameters. Take for instance a causal hypothesis which asserts that sustained alcohol consumption (the independent variable) leads to liver impairment (the dependent variable), with additional influences like use duration and general health results impacting this relationship.

Involving various factors, complex hypotheses reveal the nuanced interaction of elements that affect results. Although they provide extensive insight into studied phenomena, such hypotheses necessitate advanced research frameworks and analysis techniques to be understood properly.

Null Hypothesis

In the realm of hypothesis testing, the null hypothesis (H0) serves as a fundamental presumption suggesting that there exists no association between the variables under investigation. It posits that variations within the dependent variable are attributed to random chance and not an influential relationship. Take for instance a null hypothesis which could propose “There is no impact of sleep duration on productivity levels.”

The significance of the null hypothesis lies in its role as a reference point which researchers strive to refute during their investigations. Upon uncovering statistical evidence indicative of a substantial linkage, it becomes necessary to discard the null hypothesis. The act of rejecting this foundational assumption is critical for affirming research findings and assessing their importance with respect to outcomes observed.

Alternative Hypothesis

The alternative hypothesis, often represented by H1 or Ha, contradicts the null hypothesis and proposes a meaningful link between variables under examination. For example, where the null hypothesis asserts that a particular medication is ineffective, the alternative might posit that “Compared to placebo treatment, the new drug yields beneficial effects.”

By claiming outcomes are non-random and carry weight, the alternative hypothesis bolsters theoretical assertions. Its testable prediction propels scientific investigation forward as it aims either to corroborate or debunk what’s posited by the null hypothesis.

Consider an assertive statement like “Productivity is influenced by sleep duration” which serves as a crisp articulation of an alternative hypothesis.

Steps to Write a Hypothesis

Crafting a hypothesis is a methodical process that begins with curiosity and culminates in a testable prediction. Writing a hypothesis involves following structured steps to ensure clarity, focus, and researchability. Steps include asking a research question, conducting preliminary research, defining variables, and phrasing the hypothesis as an if-then statement.

Each step is critical in formulating a strong hypothesis to guide research and lead to meaningful discoveries.

Ask a Research Question

A well-defined research question forms the cornerstone of a strong hypothesis, guiding your investigation towards a significant and targeted exploration. By rooting this question in observations and existing studies, it becomes pertinent and ripe for research. For example, noting that certain snacks are more popular could prompt the inquiry: “Does providing healthy snack options in an office setting enhance employee productivity?”.

Such a thoughtfully constructed question lays the groundwork for your research hypothesis, steering your scholarly work to be concentrated and purposeful.

Conduct Preliminary Research

Begin your research endeavor by conducting preliminary investigations into established theories, past studies, and available data. This initial stage is crucial as it equips you with a comprehensive background to craft an informed hypothesis while pinpointing any existing voids in current knowledge. Understanding the concept of a statistical hypothesis can also be beneficial, as it involves drawing conclusions about a population based on a sample and applying statistical evidence.

By reviewing literature and examining previously published research papers, one can discern the various variables of interest and their interconnections. Should the findings from these early inquiries refute your original hypothesis, adjust it accordingly so that it resonates with already recognized evidence.

Define Your Variables

A well-formed hypothesis should unambiguously identify the independent and dependent variables involved. In an investigation exploring how plant growth is affected by sunlight, for instance, plant height represents the dependent variable, while the quantity of sunlight exposure constitutes the independent variable.

It is essential to explicitly state all the variables included in a study so that the hypothesis can be tested with accuracy and specificity. Defining these variables distinctly facilitates a targeted and quantifiable examination.

Phrase as an If-Then Statement

A good hypothesis is typically structured in the form of if-then statements, allowing for a clear demonstration of the anticipated link between different variables. Take, for example, stating that administering drug X could result in reduced fatigue among patients. This outcome would be especially advantageous to individuals receiving cancer therapy. The structure aids in explicitly defining the cause-and-effect dynamic.

In order to craft a strong hypothesis, it should be capable of being tested and grounded on existing knowledge or theoretical frameworks. It should also be framed as a statement that can potentially be refuted by experimental data, which qualifies it as a solidly formulated hypothesis.

Collect Data to Support Your Hypothesis

Once you have formulated a hypothesis, the next crucial step is to collect data to support or refute it. This involves designing and conducting experiments or studies that test the hypothesis, and collecting and analyzing data to determine whether the hypothesis holds true.

Here are the key steps in collecting data to support your hypothesis:

  • Designing an Experiment or Study : Start by identifying your research question or problem. Design a study or experiment that specifically tests your hypothesis. For example, if your hypothesis is “Daily exercise improves cognitive function,” design an experiment that measures cognitive function in individuals who exercise daily versus those who do not.
  • Collecting Data : Gather data through various methods such as experiments, surveys, observations, or other techniques. Ensure your data collection methods are reliable and valid. For instance, use standardized tests to measure cognitive function in your exercise study.
  • Analyzing Data : Use statistical methods or other techniques to analyze the data. This step involves determining whether the data supports or refutes your hypothesis. For example, use statistical tests to compare cognitive function scores between the exercise and non-exercise groups .
  • Interpreting Results : Interpret the results of your data analysis to determine whether your hypothesis is supported. For instance, if the exercise group shows significantly higher cognitive function scores, your hypothesis is supported. If not, you may need to refine your hypothesis or explore other variables.

By following these steps, you can systematically collect and analyze data to support or refute your hypothesis, ensuring your research is grounded in empirical evidence.

Refining Your Hypothesis

To ensure your hypothesis is precise, comprehensible, verifiable, straightforward, and pertinent, you must refine it meticulously. Creating a compelling hypothesis involves careful consideration of its transparency, purposeful direction and the potential results. This requires unmistakably delineating the subject matter and central point of your experiment.

Your hypothesis should undergo stringent examination to remove any uncertainties and define parameters that guarantee both ethical integrity and scientific credibility. An effective hypothesis not only questions prevailing assumptions, but also maintains an ethically responsible framework.

Testing Your Hypothesis

Having a robust research methodology is essential for efficiently evaluating your hypothesis. It is important to ensure that the integrity and validity of the research are upheld through adherence to ethical standards. The data gathered ought to be both representative and tailored specifically towards validating or invalidating the hypothesis.

In order to ascertain whether there’s any significant difference, statistical analyses measure variations both within and across groups. Frequently, the decision on whether to discard the null hypothesis hinges on establishing a p-value cut-off point, which conventionally stands at 0.05.

Tips for Writing a Research Hypothesis

Writing a research hypothesis can be a challenging task, but with the right approach, you can craft a strong and testable hypothesis. Here are some tips to help you write a research hypothesis:

  • Start with a Research Question : A good hypothesis starts with a clear and focused research question. For example, “Does regular exercise improve mental health?” can lead to a hypothesis like “Regular exercise reduces symptoms of depression.”
  • Conduct Preliminary Research : Conducting preliminary research helps you identify a knowledge gap in your field and develop a hypothesis that is relevant and testable. Review existing literature and studies to inform your hypothesis.
  • Use Clear and Concise Language : A good hypothesis should be easy to understand and use clear and concise language. Avoid jargon and complex terms. For example, “Increased screen time negatively impacts sleep quality” is clear and straightforward.
  • Avoid Ambiguity and Vagueness : Ensure your hypothesis is free from ambiguity and vagueness. Clearly state the expected outcome of the research. For example, “Consuming caffeine before bedtime reduces sleep duration” is specific and unambiguous.
  • Make Sure It Is Testable : A good hypothesis should be testable and falsifiable, meaning it can be proven or disproven through scientific research methods. For example, “A high-protein diet increases muscle mass” is a testable hypothesis.
  • Use Existing Knowledge and Research : Base your hypothesis on existing knowledge and research. Align it with your research objectives and ensure it is grounded in established theories or findings.

Common mistakes to avoid when writing a research hypothesis include:

  • Making It Too Broad or Too Narrow : A good hypothesis should be specific and focused on a particular aspect of the research question. Avoid overly broad or narrow hypotheses.
  • Making It Too Vague or Ambiguous : Ensure your hypothesis is clear and concise, avoiding ambiguity and vagueness.
  • Failing to Make It Testable : A good hypothesis should be testable and falsifiable. Ensure it can be proven or disproven through scientific research methods.
  • Failing to Use Existing Knowledge and Research : Base your hypothesis on existing knowledge and research. Align it with your research objectives and ensure it is grounded in established theories or findings.

By following these tips and avoiding common mistakes, you can write a strong and testable research hypothesis that will guide your scientific investigation towards meaningful and reliable results.

Examples of Good and Bad Hypotheses

A well-constructed hypothesis is distinct, precise, and capable of being empirically verified. To be considered a good hypothesis, it must offer measurable and examinable criteria through experimental means. Take the claim “Working from home boosts job satisfaction” as an example. This posits a testable outcome related to work environments.

On the other hand, a subpar hypothesis such as “Garlic repels vampires” falls short because it hinges on fantastical elements that cannot be substantiated or refuted in reality. The ability to distinguish between strong and weak hypotheses plays an essential role in conducting successful research.

Importance of a Testable Hypothesis

A hypothesis that can be subjected to testing forms the basis of a scientific experiment, outlining anticipated results. For a hypothesis to qualify as testable, it must possess key attributes such as being able to be falsified and verifiable or disprovable via experimental means. It serves as an essential platform for conducting fresh research with the potential to confirm or debunk it.

Crafting a robust testable hypothesis yields clear forecasts derived from previous studies. Should both the predictions and outcomes stemming from a hypothesis lack this critical aspect of testability, they will remain ambiguous, rendering the associated experiment ineffective in conclusively proving or negating anything of substance.

In summary, crafting a strong hypothesis constitutes an essential ability within the realm of scientific research. Grasping the various forms of hypotheses and mastering the process for their formulation and refinement are critical to establishing your research as solid and significant. It is crucial to underscore that having a testable hypothesis serves as the bedrock for successful scientific investigation.

Frequently Asked Questions

How can you formulate a hypothesis.

To formulate a hypothesis, first state the question your experiment aims to answer and identify the independent and dependent variables.

Then create an “If, Then” statement that succinctly defines the relationship between these variables.

What is a hypothesis in scientific research?

In the research process, a hypothesis acts as a tentative concept that is put forward for additional scrutiny and examination, establishing the bedrock upon which scientific experiments are built. It steers the course of research by forecasting possible results.

What are the different types of hypotheses?

Hypotheses can be classified into simple, complex, null, and alternative types, each type fulfilling distinct roles in scientific research.

Understanding these differences is crucial for effective hypothesis formulation.

How do I write a hypothesis?

To write a hypothesis, start by formulating a research question and conducting preliminary research.

Then define your variables and express your hypothesis in the form of an if-then statement.

Why is a testable hypothesis important?

Having a testable hypothesis is vital because it provides a definitive structure for conducting research, allowing for particular predictions that experimentation can either verify or refute.

Such an element significantly improves the process of scientific investigation.

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

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

A hypothesis is a proposed explanation or prediction that seeks to answer a research question. It is a statement that can be tested through empirical observation and analysis. When developing a hypothesis, it is important to have a clear understanding of its role in the research process.

Imagine a group of scientists seeking to understand the effects of a new drug on a specific medical condition. Without a hypothesis, their research would lack focus and purpose. However, with a carefully crafted hypothesis, they can set clear objectives and design experiments that will yield meaningful results. The hypothesis acts as a roadmap, guiding them through the intricate maze of data collection and analysis, ultimately leading to a deeper understanding of the subject matter.

Key Elements of a Strong Hypothesis

Constructing a hypothesis requires careful consideration of several key elements. These elements ensure that the hypothesis is robust and capable of withstanding the rigors of scientific scrutiny:

  • Clarity:  A hypothesis should leave no room for ambiguity or vagueness. It must clearly articulate the expected relationship between variables, allowing for accurate interpretation of results. By providing a precise explanation or prediction, researchers can avoid misinterpretation and ensure that their findings are reliable.
  • Testability:  A hypothesis must be testable through empirical observation or experimentation. It should be possible to collect data that can either support or refute the proposed explanation or prediction. Without testability, a hypothesis becomes nothing more than an abstract concept, devoid of practical value.
  • Falsifiability:  A hallmark of scientific hypotheses is their potential to be proven false. By allowing for the possibility of rejection, hypotheses encourage critical thinking and the pursuit of knowledge. It is through the process of testing and potentially refuting hypotheses that scientific understanding evolves and expands.

By incorporating these key elements into the construction of a hypothesis, researchers can ensure that their work is grounded in scientific rigor. A strong hypothesis sets the stage for meaningful research, paving the way for new discoveries and advancements in our understanding of the world.

Preparing to Write Your Hypothesis

Before diving into the actual formulation of your hypothesis, there are several preparatory steps you should take.

One important step in preparing to write your hypothesis is identifying your research question. This step is crucial because it helps you clearly define what you are seeking to investigate. By asking yourself what specific phenomenon or relationship you are interested in exploring, you lay the foundation for a focused and meaningful hypothesis.

For example, if you are studying the effects of caffeine on memory, your research question might be “Does caffeine enhance memory performance?” This question provides a clear direction for your hypothesis.

Another crucial step in preparing to write your hypothesis is conducting preliminary research. Before formulating your hypothesis, it is important to gather as much information as possible about your topic. This involves reviewing relevant literature, examining existing theories and findings, and familiarizing yourself with the current state of knowledge in your field. By conducting thorough preliminary research, you gain valuable insights that will inform the development of your hypothesis.

  For example, you might come across studies that have already investigated the effects of caffeine on memory and have found mixed results. This information will help you refine your research question and develop a hypothesis that addresses the gaps in existing knowledge.

Additionally, conducting preliminary research allows you to ensure the relevance and novelty of your hypothesis. By familiarizing yourself with the current state of knowledge, you can identify gaps or inconsistencies in the existing literature. These gaps or inconsistencies can serve as the basis for your hypothesis, allowing you to contribute new insights to your field of study. For example, if previous studies have focused on the short-term effects of caffeine on memory, you might decide to investigate the long-term effects, thus adding a novel perspective to the existing body of research.

In conclusion, before formulating your hypothesis, it is important to take  preparatory steps such as identifying your research question  and conducting preliminary research. These steps help you define the scope of your investigation, gather relevant information, and ensure the relevance and novelty of your hypothesis. By investing time and effort into these preparatory steps, you set yourself up for a successful and impactful research project.

Crafting Your Hypothesis

With a solid understanding of the basics and having completed the necessary preparations, it is now time to craft your hypothesis.

When formulating your initial hypothesis, it is important to consider the variables involved in your study. Variables are the factors or characteristics that can change or vary. You need to  identify the independent variable , which is the factor that you manipulate or control, and the dependent variable, which is the factor that you measure or observe to see if it changes in response to the independent variable.

Formulating an Initial Hypothesis

Your initial hypothesis should be based on a logical and informed understanding of the topic you are studying. It should be a clear and concise statement that predicts the relationship between the independent and dependent variables. By formulating a hypothesis, you are making a prediction about what you expect to find in your research.

  For example, if you are studying the effects of caffeine on memory, your initial hypothesis might be: “Consuming caffeine will improve memory performance compared to a control group that does not consume caffeine.”

Remember, your hypothesis is not a random guess. It should be informed by previous research, theories, or observations. It is essential to review the existing literature and scientific studies related to your topic to ensure that your hypothesis is grounded in evidence.

Refining Your Hypothesis for Clarity

After formulating your initial hypothesis, it is crucial to refine it further to ensure clarity and precision. This involves eliminating any ambiguities or imprecise language that could lead to misunderstandings. A well-refined hypothesis allows for a more accurate interpretation of results and facilitates the testing process.

One way to refine your hypothesis is to make it more specific. Instead of making a general prediction, try to narrow down your focus and specify the conditions or variables involved. This will make your hypothesis more testable and increase the precision of your research.

Additionally, it is important to avoid biased language or assumptions in your hypothesis. Your hypothesis should be objective and unbiased, reflecting a neutral stance. This ensures that your research is conducted in a fair and unbiased manner, allowing for reliable and valid results.

Refining your hypothesis also involves considering alternative explanations or variables that could influence your results. By acknowledging potential confounding factors or alternative hypotheses, you demonstrate a thorough understanding of your research topic and strengthen the validity of your study.

Overall, crafting a hypothesis is a critical step in the research process. It allows you to make an informed prediction about the relationship between variables and provides a framework for your investigation. By formulating and refining your hypothesis, you set the stage for a well-designed and meaningful research study.

Testing Your Hypothesis

Once you have crafted your hypothesis, the next step is to test it through empirical observation or experimentation. This phase involves the  design and implementation of a study  aimed at collecting data that can either support or refute your hypothesis.

Designing an Experiment

If your research question lends itself to experimental investigation, designing a controlled experiment is often the most effective approach to test your hypothesis. Careful consideration should be given to selecting appropriate variables, determining the sample size, and ensuring validity and reliability.

Analyzing the Results

Once you have collected the necessary data, the next step is to analyze and interpret your findings.  Statistical methods and data analysis techniques  can help identify patterns, correlations, or significant differences between variables. The results will either support or reject your hypothesis, leading to a deeper understanding of the phenomenon under investigation.

Ready to take your hypothesis from concept to completion? Dissertation by Design is here to support you every step of the way. Whether you need help refining your research proposal, analyzing qualitative data, navigating statistical complexities, or polishing your dissertation with expert editing, our team of experienced academic coaches is ready to guide you. Don’t navigate the dissertation process alone— schedule a free consultation  with us today and move forward with confidence.

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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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