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How Do You Write an Hypothesis? Detailed Explanation and Examples

Writing a hypothesis is a fundamental step in the scientific research process. It serves as a tentative explanation or prediction that can be tested through experimentation and observation. A well-crafted hypothesis provides a clear direction for research and helps in drawing meaningful conclusions. This article will guide you through the process of writing a hypothesis, including understanding its concept, formulating it, and avoiding common pitfalls, with illustrative examples from various fields of study.

Key Takeaways

  • A hypothesis is a testable and falsifiable statement that predicts an outcome based on certain conditions.
  • There are different types of hypotheses, including null, alternative, and directional hypotheses, each serving a specific purpose in research.
  • Formulating a hypothesis involves identifying research questions, conducting preliminary research, and crafting a clear and precise statement.
  • A strong hypothesis is characterized by its testability, clarity, precision, and relevance to the research objectives.
  • Common pitfalls in hypothesis writing include vague statements, overly complex hypotheses, and lack of testability.

Understanding the Concept of a Hypothesis

A hypothesis is a foundational element in scientific research, serving as a preliminary statement that proposes a potential relationship between variables. It is essential for guiding the direction of your study and providing a basis for data collection and analysis.

Steps to Formulate a Hypothesis

Identifying research questions.

The first step in formulating a hypothesis is to identify your research question . This involves observing the subject matter and recognizing patterns or relationships between variables. Crafting a clear, testable, and grounded hypothesis is essential for research success. By pinpointing the exact question you aim to answer, you lay the foundation for a focused and effective hypothesis.

Conducting Preliminary Research

Once you have your research question, the next step is to conduct preliminary research. This involves gathering as much information as possible about the topic. Evaluate these observations to identify potential causes and effects related to your research question. This stage helps you understand the existing knowledge and gaps, which is crucial for developing a well-informed hypothesis.

Formulating the Hypothesis Statement

After conducting preliminary research, you can begin formulating your hypothesis statement. This statement should clearly define the variables involved and the expected relationship between them. Ensure that your hypothesis is specific, testable, and falsifiable. A well-crafted hypothesis not only guides your research but also provides a clear direction for your experimental design and data collection methods.

Characteristics of a Strong Hypothesis

A strong hypothesis is essential for guiding your research and ensuring that your study is both meaningful and scientifically valid. Here are the key characteristics that define a robust hypothesis:

Testability and Falsifiability

A strong hypothesis must be testable, meaning you can design experiments to verify or refute it. Falsifiability is equally important; there should be a possibility to collect data that could disprove the hypothesis. This ensures that your hypothesis is grounded in empirical research rather than mere speculation.

Clarity and Precision

Your hypothesis should be clear and precise, leaving no room for ambiguity. This clarity helps in designing experiments and interpreting results. A well-defined hypothesis often begins with a specific research question and is articulated in simple, straightforward language.

Relevance to Research Objectives

A strong hypothesis is directly related to your research objectives. It should address the core question of your study and be aligned with the goals you aim to achieve. This relevance ensures that your hypothesis is not just an isolated statement but a crucial part of your overall research framework.

Common Pitfalls in Hypothesis Writing

When crafting a hypothesis, it's crucial to avoid common mistakes that can undermine your research. Vague statements are a frequent issue; they lack the specificity needed to be testable. For instance, saying "exercise improves health" is too broad. Instead, specify the type of exercise and the health outcome you are measuring.

Overly complex hypotheses can also be problematic. A hypothesis should be straightforward and focused. If it includes too many variables or conditions, it becomes difficult to test and analyze. Simplify your hypothesis to ensure clarity and feasibility.

Another major pitfall is the lack of testability. A hypothesis must be testable through empirical methods. If you cannot design an experiment or collect data to support or refute your hypothesis, it is not scientifically valid. Ensure your hypothesis can be tested with the resources and methods available to you.

Examples of Well-Written Hypotheses

In this section, you will explore various examples of well-crafted hypotheses across different fields of study. Understanding these examples will help you grasp the nuances of formulating a strong hypothesis.

Hypotheses in Natural Sciences

A well-written hypothesis in the natural sciences is both specific and testable. For instance, consider the hypothesis: "If plants are exposed to higher levels of sunlight, then their growth rate will increase." This statement clearly defines the variables and the expected relationship between them, making it a robust hypothesis for experimental testing.

Hypotheses in Social Sciences

In the social sciences, hypotheses often address complex human behaviors and societal trends. An example of a good hypothesis in this field is: "Individuals who participate in regular physical activity are more likely to report higher levels of mental well-being." This hypothesis is specific, testable, and relevant to the research objectives, providing a clear direction for the study.

Hypotheses in Applied Research

Applied research focuses on practical problem-solving. A strong hypothesis in this area might be: "Implementing a new software system will reduce the time required to complete administrative tasks by 20%." This hypothesis is not only testable but also directly applicable to real-world scenarios, making it highly valuable for applied research.

By examining these examples, you can better understand how to construct hypotheses that are clear, precise, and aligned with your research goals.

Testing and Refining Your Hypothesis

Designing experiments.

Before you dive into any experiment, you first formulate what you think will happen. This is where your hypothesis comes into play. A hypothesis in experimental design is essentially a testable prediction. Ensure that your hypothesis has clear and relevant variables, identifies the relationship between its variables, and is specific and testable. Designing a robust experiment involves controlling the independent variable and observing the dependent variable to validate or refute your hypothesis.

Data Collection Methods

Once your experiment is designed, the next step is to collect data. This involves choosing appropriate methods to gather data that will support or refute your hypothesis. Whether you use surveys, observations, or experiments, the key is to ensure that your data collection methods are reliable and valid. Remember, the priority of any scientific research is the conclusion, so collect data meticulously.

Analyzing Results and Making Adjustments

After data collection, the next step is to analyze the results. This involves statistical analysis to determine whether the data supports your hypothesis. If the data does not support your hypothesis, do not worry. This is a normal part of the scientific method. You may need to refine your hypothesis based on the findings. Use the results to identify weaknesses in your hypothesis and revise it if necessary. This iterative process helps in honing a more accurate and testable hypothesis.

The Importance of Hypotheses in Academic Writing

In academic writing, hypotheses serve as foundational elements that guide the direction and structure of your research. A well-formulated hypothesis not only provides a clear focus for your study but also helps in organizing your research methods and analysis. This is crucial for ensuring that your research remains coherent and targeted.

Guiding Research Direction

A hypothesis plays an important role in the scientific method by helping to create an appropriate experimental design. By establishing a specific, testable statement, you can streamline your research process and avoid unnecessary detours. This focused approach is essential for producing meaningful and reliable results.

Facilitating Critical Thinking

Formulating a hypothesis requires you to engage in critical thinking and problem-solving. This process helps you to clarify your research questions and objectives, making your study more robust and intellectually rigorous. It also encourages you to consider various outcomes and their implications, thereby enhancing the depth of your analysis.

Enhancing Academic Rigor

A well-constructed hypothesis adds a layer of academic rigor to your work. It demonstrates that you have a clear understanding of the theoretical framework and existing literature related to your topic. This not only strengthens your argument but also makes your research more credible and persuasive. In essence, a strong hypothesis is a testament to the quality and seriousness of your academic endeavor.

In academic writing, hypotheses play a crucial role in guiding research and providing a clear focus for your study. They help in formulating research questions and determining the direction of your investigation. If you're struggling with your thesis and need a structured approach, our Thesis Action Plan is here to help. Visit our website to claim your special offer now and overcome the challenges of thesis writing with ease.

In conclusion, writing a hypothesis is a fundamental step in the scientific research process that requires careful consideration and a structured approach. By observing the subject, identifying variables, and formulating a clear and testable statement, researchers can lay a solid foundation for their experiments. A well-crafted hypothesis not only guides the research but also provides a framework for analyzing results and drawing meaningful conclusions. As demonstrated in this article, understanding the components and steps involved in hypothesis writing is crucial for academic success and contributes significantly to the advancement of knowledge in various fields. By following the detailed explanations and examples provided, students and researchers can enhance their ability to construct effective hypotheses, thereby improving the quality and impact of their scientific inquiries.

Frequently Asked Questions

What is a hypothesis.

A hypothesis is a statement that predicts the outcome of a scientific study. It is an educated guess based on prior knowledge and observations.

Why is a hypothesis important in scientific research?

A hypothesis provides a focused direction for research. It helps researchers make predictions that can be tested through experiments and observations, thereby advancing scientific knowledge.

What are the types of hypotheses?

There are several types of hypotheses, including null hypotheses, alternative hypotheses, directional hypotheses, and non-directional hypotheses. Each serves a different purpose in research.

How do you formulate a hypothesis?

Formulating a hypothesis involves identifying a research question, conducting preliminary research, and then crafting a clear and testable statement that predicts an outcome.

What makes a hypothesis strong?

A strong hypothesis is testable, falsifiable, clear, precise, and relevant to the research objectives. It should be specific enough to be tested but broad enough to cover the scope of the research.

What are common pitfalls in writing a hypothesis?

Common pitfalls include making vague statements, creating overly complex hypotheses, and failing to ensure that the hypothesis is testable.

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Research hypothesis: What it is, how to write it, types, and examples

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

hypothesis image example

Any research begins with a research question and a research hypothesis . A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis ? A hypothesis is a testable statement that proposes a possible explanation to a phenomenon, and it may include a prediction. Next, you may ask what is a research hypothesis ? Simply put, a research hypothesis is a prediction or educated guess about the relationship between the variables that you want to investigate.  

It is important to be thorough when developing your research hypothesis. Shortcomings in the framing of a hypothesis can affect the study design and the results. A better understanding of the research hypothesis definition and characteristics of a good hypothesis will make it easier for you to develop your own hypothesis for your research. Let’s dive in to know more about the types of research hypothesis , how to write a research hypothesis , and some research hypothesis examples .  

Table of Contents

What is a hypothesis ?  

A hypothesis is based on the existing body of knowledge in a study area. Framed before the data are collected, a hypothesis states the tentative relationship between independent and dependent variables, along with a prediction of the outcome.  

What is a research hypothesis ?  

Young researchers starting out their journey are usually brimming with questions like “ What is a hypothesis ?” “ What is a research hypothesis ?” “How can I write a good research hypothesis ?”   

A research hypothesis is a statement that proposes a possible explanation for an observable phenomenon or pattern. It guides the direction of a study and predicts the outcome of the investigation. A research hypothesis is testable, i.e., it can be supported or disproven through experimentation or observation.     

hypothesis image example

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

  • Clearly formulated and free of language errors and ambiguity  
  • Concise and not unnecessarily verbose  
  • Has clearly defined variables  
  • Testable and stated in a way that allows for it to be disproven  
  • Can be tested using a research design that is feasible, ethical, and practical   
  • Specific and relevant to the research problem  
  • Rooted in a thorough literature search  
  • Can generate new knowledge or understanding.  

How to create an effective research hypothesis  

A study begins with the formulation of a research question. A researcher then performs background research. This background information forms the basis for building a good research hypothesis . The researcher then performs experiments, collects, and analyzes the data, interprets the findings, and ultimately, determines if the findings support or negate the original hypothesis.  

Let’s look at each step for creating an effective, testable, and good research hypothesis :  

  • Identify a research problem or question: Start by identifying a specific research problem.   
  • Review the literature: Conduct an in-depth review of the existing literature related to the research problem to grasp the current knowledge and gaps in the field.   
  • Formulate a clear and testable hypothesis : Based on the research question, use existing knowledge to form a clear and testable hypothesis . The hypothesis should state a predicted relationship between two or more variables that can be measured and manipulated. Improve the original draft till it is clear and meaningful.  
  • State the null hypothesis: The null hypothesis is a statement that there is no relationship between the variables you are studying.   
  • Define the population and sample: Clearly define the population you are studying and the sample you will be using for your research.  
  • Select appropriate methods for testing the hypothesis: Select appropriate research methods, such as experiments, surveys, or observational studies, which will allow you to test your research hypothesis .  

Remember that creating a research hypothesis is an iterative process, i.e., you might have to revise it based on the data you collect. You may need to test and reject several hypotheses before answering the research problem.  

How to write a research hypothesis  

When you start writing a research hypothesis , you use an “if–then” statement format, which states the predicted relationship between two or more variables. Clearly identify the independent variables (the variables being changed) and the dependent variables (the variables being measured), as well as the population you are studying. Review and revise your hypothesis as needed.  

An example of a research hypothesis in this format is as follows:  

“ If [athletes] follow [cold water showers daily], then their [endurance] increases.”  

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

You may have understood the characteristics of a good hypothesis . But note that a research hypothesis is not always confirmed; a researcher should be prepared to accept or reject the hypothesis based on the study findings.  

hypothesis image example

Research hypothesis checklist  

Following from above, here is a 10-point checklist for a good research hypothesis :  

  • Testable: A research hypothesis should be able to be tested via experimentation or observation.  
  • Specific: A research hypothesis should clearly state the relationship between the variables being studied.  
  • Based on prior research: A research hypothesis should be based on existing knowledge and previous research in the field.  
  • Falsifiable: A research hypothesis should be able to be disproven through testing.  
  • Clear and concise: A research hypothesis should be stated in a clear and concise manner.  
  • Logical: A research hypothesis should be logical and consistent with current understanding of the subject.  
  • Relevant: A research hypothesis should be relevant to the research question and objectives.  
  • Feasible: A research hypothesis should be feasible to test within the scope of the study.  
  • Reflects the population: A research hypothesis should consider the population or sample being studied.  
  • Uncomplicated: A good research hypothesis is written in a way that is easy for the target audience to understand.  

By following this research hypothesis checklist , you will be able to create a research hypothesis that is strong, well-constructed, and more likely to yield meaningful results.  

Research hypothesis: What it is, how to write it, types, and examples

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

A null hypothesis states that there is no change in the dependent variable due to changes to the independent variable. This means that the results are due to chance and are not significant. A null hypothesis is denoted as H0 and is stated as the opposite of what the alternative hypothesis states.   

Example: “ The newly identified virus is not zoonotic .”  

2. Alternative hypothesis:

This states that there is a significant difference or relationship between the variables being studied. It is denoted as H1 or Ha and is usually accepted or rejected in favor of the null hypothesis.  

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

This specifies the direction of the relationship or difference between variables; therefore, it tends to use terms like increase, decrease, positive, negative, more, or less.   

Example: “ The inclusion of intervention X decreases infant mortality compared to the original treatment .”   

4. Non-directional hypothesis:

While it does not predict the exact direction or nature of the relationship between the two variables, a non-directional hypothesis states the existence of a relationship or difference between variables but not the direction, nature, or magnitude of the relationship. A non-directional hypothesis may be used when there is no underlying theory or when findings contradict previous research.  

Example, “ Cats and dogs differ in the amount of affection they express .”  

5. Simple hypothesis :

A simple hypothesis only predicts the relationship between one independent and another independent variable.  

Example: “ Applying sunscreen every day slows skin aging .”  

6 . Complex hypothesis :

A complex hypothesis states the relationship or difference between two or more independent and dependent variables.   

Example: “ Applying sunscreen every day slows skin aging, reduces sun burn, and reduces the chances of skin cancer .” (Here, the three dependent variables are slowing skin aging, reducing sun burn, and reducing the chances of skin cancer.)  

7. Associative hypothesis:  

An associative hypothesis states that a change in one variable results in the change of the other variable. The associative hypothesis defines interdependency between variables.  

Example: “ There is a positive association between physical activity levels and overall health .”  

8 . Causal hypothesis:

A causal hypothesis proposes a cause-and-effect interaction between variables.  

Example: “ Long-term alcohol use causes liver damage .”  

Note that some of the types of research hypothesis mentioned above might overlap. The types of hypothesis chosen will depend on the research question and the objective of the study.  

hypothesis image example

Research hypothesis examples  

Here are some good research hypothesis examples :  

“The use of a specific type of therapy will lead to a reduction in symptoms of depression in individuals with a history of major depressive disorder.”  

“Providing educational interventions on healthy eating habits will result in weight loss in overweight individuals.”  

“Plants that are exposed to certain types of music will grow taller than those that are not exposed to music.”  

“The use of the plant growth regulator X will lead to an increase in the number of flowers produced by plants.”  

Characteristics that make a research hypothesis weak are unclear variables, unoriginality, being too general or too vague, and being untestable. A weak hypothesis leads to weak research and improper methods.   

Some bad research hypothesis examples (and the reasons why they are “bad”) are as follows:  

“This study will show that treatment X is better than any other treatment . ” (This statement is not testable, too broad, and does not consider other treatments that may be effective.)  

“This study will prove that this type of therapy is effective for all mental disorders . ” (This statement is too broad and not testable as mental disorders are complex and different disorders may respond differently to different types of therapy.)  

“Plants can communicate with each other through telepathy . ” (This statement is not testable and lacks a scientific basis.)  

Importance of testable hypothesis  

If a research hypothesis is not testable, the results will not prove or disprove anything meaningful. The conclusions will be vague at best. A testable hypothesis helps a researcher focus on the study outcome and understand the implication of the question and the different variables involved. A testable hypothesis helps a researcher make precise predictions based on prior research.  

To be considered testable, there must be a way to prove that the hypothesis is true or false; further, the results of the hypothesis must be reproducible.  

Research hypothesis: What it is, how to write it, types, and examples

Frequently Asked Questions (FAQs) on research hypothesis  

1. What is the difference between research question and research hypothesis ?  

A research question defines the problem and helps outline the study objective(s). It is an open-ended statement that is exploratory or probing in nature. Therefore, it does not make predictions or assumptions. It helps a researcher identify what information to collect. A research hypothesis , however, is a specific, testable prediction about the relationship between variables. Accordingly, it guides the study design and data analysis approach.

2. When to reject null hypothesis ?

A null hypothesis should be rejected when the evidence from a statistical test shows that it is unlikely to be true. This happens when the test statistic (e.g., p -value) is less than the defined significance level (e.g., 0.05). Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it simply means that the evidence found is not compatible with the null hypothesis.  

3. How can I be sure my hypothesis is testable?  

A testable hypothesis should be specific and measurable, and it should state a clear relationship between variables that can be tested with data. To ensure that your hypothesis is testable, consider the following:  

  • Clearly define the key variables in your hypothesis. You should be able to measure and manipulate these variables in a way that allows you to test the hypothesis.  
  • The hypothesis should predict a specific outcome or relationship between variables that can be measured or quantified.   
  • You should be able to collect the necessary data within the constraints of your study.  
  • It should be possible for other researchers to replicate your study, using the same methods and variables.   
  • Your hypothesis should be testable by using appropriate statistical analysis techniques, so you can draw conclusions, and make inferences about the population from the sample data.  
  • The hypothesis should be able to be disproven or rejected through the collection of data.  

4. How do I revise my research hypothesis if my data does not support it?  

If your data does not support your research hypothesis , you will need to revise it or develop a new one. You should examine your data carefully and identify any patterns or anomalies, re-examine your research question, and/or revisit your theory to look for any alternative explanations for your results. Based on your review of the data, literature, and theories, modify your research hypothesis to better align it with the results you obtained. Use your revised hypothesis to guide your research design and data collection. It is important to remain objective throughout the process.  

5. I am performing exploratory research. Do I need to formulate a research hypothesis?  

As opposed to “confirmatory” research, where a researcher has some idea about the relationship between the variables under investigation, exploratory research (or hypothesis-generating research) looks into a completely new topic about which limited information is available. Therefore, the researcher will not have any prior hypotheses. In such cases, a researcher will need to develop a post-hoc hypothesis. A post-hoc research hypothesis is generated after these results are known.  

6. How is a research hypothesis different from a research question?

A research question is an inquiry about a specific topic or phenomenon, typically expressed as a question. 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. Can a research hypothesis change during the research process?

Yes, research hypotheses can change during the research process. As researchers collect and analyze data, new insights and information may emerge that require modification or refinement of the initial hypotheses. This can be due to unexpected findings, limitations in the original hypotheses, or the need to explore additional dimensions of the research topic. Flexibility is crucial in research, allowing for adaptation and adjustment of hypotheses to align with the evolving understanding of the subject matter.

8. How many hypotheses should be included in a research study?

The number of research hypotheses in a research study varies depending on the nature and scope of the research. It is not necessary to have multiple hypotheses in every study. Some studies may have only one primary hypothesis, while others may have several related hypotheses. The number of hypotheses should be determined based on the research objectives, research questions, and the complexity of the research topic. It is important to ensure that the hypotheses are focused, testable, and directly related to the research aims.

9. Can research hypotheses be used in qualitative research?

Yes, research hypotheses can be used in qualitative research, although they are more commonly associated with quantitative research. In qualitative research, hypotheses may be formulated as tentative or exploratory statements that guide the investigation. Instead of testing hypotheses through statistical analysis, qualitative researchers may use the hypotheses to guide data collection and analysis, seeking to uncover patterns, themes, or relationships within the qualitative data. The emphasis in qualitative research is often on generating insights and understanding rather than confirming or rejecting specific research hypotheses through statistical testing.

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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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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."

hypothesis image example

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.

hypothesis image example

Verywell / Alex Dos Diaz

  • The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

  • Operationalization

Hypothesis Types

Hypotheses examples.

  • Collecting Data

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

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

At a Glance

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

The Hypothesis in the Scientific Method

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

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

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

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

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

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

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

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

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

Elements of a Good Hypothesis

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

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

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

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

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

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

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

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

The Importance of Operational Definitions

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

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

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

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

Replicability

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

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

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

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

Hypothesis Checklist

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

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

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

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

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

A few examples of simple hypotheses:

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

Examples of a complex hypothesis include:

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

Examples of a null hypothesis include:

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

Examples of an alternative hypothesis:

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

Collecting Data on Your Hypothesis

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

Descriptive Research Methods

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

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

Experimental Research Methods

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

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

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

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

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

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

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

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

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

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

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How to Write a Hypothesis

Last Updated: May 2, 2023 Fact Checked

This article was co-authored by Bess Ruff, MA . Bess Ruff is a Geography PhD student at Florida State University. She received her MA in Environmental Science and Management from the University of California, Santa Barbara in 2016. She has conducted survey work for marine spatial planning projects in the Caribbean and provided research support as a graduate fellow for the Sustainable Fisheries Group. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,033,913 times.

A hypothesis is a description of a pattern in nature or an explanation about some real-world phenomenon that can be tested through observation and experimentation. The most common way a hypothesis is used in scientific research is as a tentative, testable, and falsifiable statement that explains some observed phenomenon in nature. [1] X Research source Many academic fields, from the physical sciences to the life sciences to the social sciences, use hypothesis testing as a means of testing ideas to learn about the world and advance scientific knowledge. Whether you are a beginning scholar or a beginning student taking a class in a science subject, understanding what hypotheses are and being able to generate hypotheses and predictions yourself is very important. These instructions will help get you started.

Preparing to Write a Hypothesis

Step 1 Select a topic.

  • If you are writing a hypothesis for a school assignment, this step may be taken care of for you.

Step 2 Read existing research.

  • Focus on academic and scholarly writing. You need to be certain that your information is unbiased, accurate, and comprehensive. Scholarly search databases such as Google Scholar and Web of Science can help you find relevant articles from reputable sources.
  • You can find information in textbooks, at a library, and online. If you are in school, you can also ask for help from teachers, librarians, and your peers.

Step 3 Analyze the literature.

  • For example, if you are interested in the effects of caffeine on the human body, but notice that nobody seems to have explored whether caffeine affects males differently than it does females, this could be something to formulate a hypothesis about. Or, if you are interested in organic farming, you might notice that no one has tested whether organic fertilizer results in different growth rates for plants than non-organic fertilizer.
  • You can sometimes find holes in the existing literature by looking for statements like “it is unknown” in scientific papers or places where information is clearly missing. You might also find a claim in the literature that seems far-fetched, unlikely, or too good to be true, like that caffeine improves math skills. If the claim is testable, you could provide a great service to scientific knowledge by doing your own investigation. If you confirm the claim, the claim becomes even more credible. If you do not find support for the claim, you are helping with the necessary self-correcting aspect of science.
  • Examining these types of questions provides an excellent way for you to set yourself apart by filling in important gaps in a field of study.

Step 4 Generate questions.

  • Following the examples above, you might ask: "How does caffeine affect females as compared to males?" or "How does organic fertilizer affect plant growth compared to non-organic fertilizer?" The rest of your research will be aimed at answering these questions.

Step 5 Look for clues as to what the answer might be.

  • Following the examples above, if you discover in the literature that there is a pattern that some other types of stimulants seem to affect females more than males, this could be a clue that the same pattern might be true for caffeine. Similarly, if you observe the pattern that organic fertilizer seems to be associated with smaller plants overall, you might explain this pattern with the hypothesis that plants exposed to organic fertilizer grow more slowly than plants exposed to non-organic fertilizer.

Formulating Your Hypothesis

Step 1 Determine your variables.

  • You can think of the independent variable as the one that is causing some kind of difference or effect to occur. In the examples, the independent variable would be biological sex, i.e. whether a person is male or female, and fertilizer type, i.e. whether the fertilizer is organic or non-organically-based.
  • The dependent variable is what is affected by (i.e. "depends" on) the independent variable. In the examples above, the dependent variable would be the measured impact of caffeine or fertilizer.
  • Your hypothesis should only suggest one relationship. Most importantly, it should only have one independent variable. If you have more than one, you won't be able to determine which one is actually the source of any effects you might observe.

Step 2 Generate a simple hypothesis.

  • Don't worry too much at this point about being precise or detailed.
  • In the examples above, one hypothesis would make a statement about whether a person's biological sex might impact the way the person is affected by caffeine; for example, at this point, your hypothesis might simply be: "a person's biological sex is related to how caffeine affects his or her heart rate." The other hypothesis would make a general statement about plant growth and fertilizer; for example your simple explanatory hypothesis might be "plants given different types of fertilizer are different sizes because they grow at different rates."

Step 3 Decide on direction.

  • Using our example, our non-directional hypotheses would be "there is a relationship between a person's biological sex and how much caffeine increases the person's heart rate," and "there is a relationship between fertilizer type and the speed at which plants grow."
  • Directional predictions using the same example hypotheses above would be : "Females will experience a greater increase in heart rate after consuming caffeine than will males," and "plants fertilized with non-organic fertilizer will grow faster than those fertilized with organic fertilizer." Indeed, these predictions and the hypotheses that allow for them are very different kinds of statements. More on this distinction below.
  • If the literature provides any basis for making a directional prediction, it is better to do so, because it provides more information. Especially in the physical sciences, non-directional predictions are often seen as inadequate.

Step 4 Get specific.

  • Where necessary, specify the population (i.e. the people or things) about which you hope to uncover new knowledge. For example, if you were only interested the effects of caffeine on elderly people, your prediction might read: "Females over the age of 65 will experience a greater increase in heart rate than will males of the same age." If you were interested only in how fertilizer affects tomato plants, your prediction might read: "Tomato plants treated with non-organic fertilizer will grow faster in the first three months than will tomato plants treated with organic fertilizer."

Step 5 Make sure it is testable.

  • For example, you would not want to make the hypothesis: "red is the prettiest color." This statement is an opinion and it cannot be tested with an experiment. However, proposing the generalizing hypothesis that red is the most popular color is testable with a simple random survey. If you do indeed confirm that red is the most popular color, your next step may be to ask: Why is red the most popular color? The answer you propose is your explanatory hypothesis .

Step 6 Write a research hypothesis.

  • An easy way to get to the hypothesis for this method and prediction is to ask yourself why you think heart rates will increase if children are given caffeine. Your explanatory hypothesis in this case may be that caffeine is a stimulant. At this point, some scientists write a research hypothesis , a statement that includes the hypothesis, the experiment, and the prediction all in one statement.
  • For example, If caffeine is a stimulant, and some children are given a drink with caffeine while others are given a drink without caffeine, then the heart rates of those children given a caffeinated drink will increase more than the heart rate of children given a non-caffeinated drink.

Step 7 Contextualize your hypothesis.

  • Using the above example, if you were to test the effects of caffeine on the heart rates of children, evidence that your hypothesis is not true, sometimes called the null hypothesis , could occur if the heart rates of both the children given the caffeinated drink and the children given the non-caffeinated drink (called the placebo control) did not change, or lowered or raised with the same magnitude, if there was no difference between the two groups of children.
  • It is important to note here that the null hypothesis actually becomes much more useful when researchers test the significance of their results with statistics. When statistics are used on the results of an experiment, a researcher is testing the idea of the null statistical hypothesis. For example, that there is no relationship between two variables or that there is no difference between two groups. [8] X Research source

Step 8 Test your hypothesis.

Hypothesis Examples

hypothesis image example

Community Q&A

Community Answer

  • Remember that science is not necessarily a linear process and can be approached in various ways. [10] X Research source Thanks Helpful 0 Not Helpful 0
  • When examining the literature, look for research that is similar to what you want to do, and try to build on the findings of other researchers. But also look for claims that you think are suspicious, and test them yourself. Thanks Helpful 0 Not Helpful 0
  • Be specific in your hypotheses, but not so specific that your hypothesis can't be applied to anything outside your specific experiment. You definitely want to be clear about the population about which you are interested in drawing conclusions, but nobody (except your roommates) will be interested in reading a paper with the prediction: "my three roommates will each be able to do a different amount of pushups." Thanks Helpful 0 Not Helpful 0

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Write up a Science Experiment

  • ↑ https://undsci.berkeley.edu/for-educators/prepare-and-plan/correcting-misconceptions/#a4
  • ↑ https://owl.purdue.edu/owl/general_writing/common_writing_assignments/research_papers/choosing_a_topic.html
  • ↑ https://owl.purdue.edu/owl/subject_specific_writing/writing_in_the_social_sciences/writing_in_psychology_experimental_report_writing/experimental_reports_1.html
  • ↑ https://www.grammarly.com/blog/how-to-write-a-hypothesis/
  • ↑ https://grammar.yourdictionary.com/for-students-and-parents/how-create-hypothesis.html
  • ↑ https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/1.19/primary/lesson/hypothesis-ms-ps/
  • ↑ https://iastate.pressbooks.pub/preparingtopublish/chapter/goal-1-contextualize-the-studys-methods/
  • ↑ http://mathworld.wolfram.com/NullHypothesis.html
  • ↑ http://undsci.berkeley.edu/article/scienceflowchart

About This Article

Bess Ruff, MA

Before writing a hypothesis, think of what questions are still unanswered about a specific subject and make an educated guess about what the answer could be. Then, determine the variables in your question and write a simple statement about how they might be related. Try to focus on specific predictions and variables, such as age or segment of the population, to make your hypothesis easier to test. For tips on how to test your hypothesis, read on! Did this summary help you? Yes No

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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

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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.

hypothesis image example

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Hypothesis Examples

Hypothesis Examples

A hypothesis is a prediction of the outcome of a test. It forms the basis for designing an experiment in the scientific method . A good hypothesis is testable, meaning it makes a prediction you can check with observation or experimentation. Here are different hypothesis examples.

Null Hypothesis Examples

The null hypothesis (H 0 ) is also known as the zero-difference or no-difference hypothesis. It predicts that changing one variable ( independent variable ) will have no effect on the variable being measured ( dependent variable ). Here are null hypothesis examples:

  • Plant growth is unaffected by temperature.
  • If you increase temperature, then solubility of salt will increase.
  • Incidence of skin cancer is unrelated to ultraviolet light exposure.
  • All brands of light bulb last equally long.
  • Cats have no preference for the color of cat food.
  • All daisies have the same number of petals.

Sometimes the null hypothesis shows there is a suspected correlation between two variables. For example, if you think plant growth is affected by temperature, you state the null hypothesis: “Plant growth is not affected by temperature.” Why do you do this, rather than say “If you change temperature, plant growth will be affected”? The answer is because it’s easier applying a statistical test that shows, with a high level of confidence, a null hypothesis is correct or incorrect.

Research Hypothesis Examples

A research hypothesis (H 1 ) is a type of hypothesis used to design an experiment. This type of hypothesis is often written as an if-then statement because it’s easy identifying the independent and dependent variables and seeing how one affects the other. If-then statements explore cause and effect. In other cases, the hypothesis shows a correlation between two variables. Here are some research hypothesis examples:

  • If you leave the lights on, then it takes longer for people to fall asleep.
  • If you refrigerate apples, they last longer before going bad.
  • If you keep the curtains closed, then you need less electricity to heat or cool the house (the electric bill is lower).
  • If you leave a bucket of water uncovered, then it evaporates more quickly.
  • Goldfish lose their color if they are not exposed to light.
  • Workers who take vacations are more productive than those who never take time off.

Is It Okay to Disprove a Hypothesis?

Yes! You may even choose to write your hypothesis in such a way that it can be disproved because it’s easier to prove a statement is wrong than to prove it is right. In other cases, if your prediction is incorrect, that doesn’t mean the science is bad. Revising a hypothesis is common. It demonstrates you learned something you did not know before you conducted the experiment.

Test yourself with a Scientific Method Quiz .

  • Mellenbergh, G.J. (2008). Chapter 8: Research designs: Testing of research hypotheses. In H.J. Adèr & G.J. Mellenbergh (eds.), Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing.
  • Popper, Karl R. (1959). The Logic of Scientific Discovery . Hutchinson & Co. ISBN 3-1614-8410-X.
  • Schick, Theodore; Vaughn, Lewis (2002). How to think about weird things: critical thinking for a New Age . Boston: McGraw-Hill Higher Education. ISBN 0-7674-2048-9.
  • Tobi, Hilde; Kampen, Jarl K. (2018). “Research design: the methodology for interdisciplinary research framework”. Quality & Quantity . 52 (3): 1209–1225. doi: 10.1007/s11135-017-0513-8

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What Is a Hypothesis and How Do I Write One?

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General Education

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Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

  • Defining the term “hypothesis” 
  • Providing hypothesis examples 
  • Giving you tips for how to write your own hypothesis

So let’s get started!

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What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

  • Observation
  • Asking questions
  • Forming a hypothesis
  • Analyze the data
  • Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

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Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

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The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

  • If I get enough sleep, I’ll be able to get more work done tomorrow.
  • If the bus is on time, I can make it to my friend’s birthday party. 
  • If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

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4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

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Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

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Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

body-bird-feeder

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

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What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

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15 Hypothesis Examples

15 Hypothesis Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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hypothesis definition and example, explained below

A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021).  SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance.  Sleep medicine reviews ,  10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression.  Psychiatry Research ,  309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease.  Molecular nutrition & food research ,  49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.

Chris

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experiments disproving spontaneous generation

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experiments disproving spontaneous generation

scientific hypothesis , an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an “If…then” statement summarizing the idea and in the ability to be supported or refuted through observation and experimentation. The notion of the scientific hypothesis as both falsifiable and testable was advanced in the mid-20th century by Austrian-born British philosopher Karl Popper .

The formulation and testing of a hypothesis is part of the scientific method , the approach scientists use when attempting to understand and test ideas about natural phenomena. The generation of a hypothesis frequently is described as a creative process and is based on existing scientific knowledge, intuition , or experience. Therefore, although scientific hypotheses commonly are described as educated guesses, they actually are more informed than a guess. In addition, scientists generally strive to develop simple hypotheses, since these are easier to test relative to hypotheses that involve many different variables and potential outcomes. Such complex hypotheses may be developed as scientific models ( see scientific modeling ).

Depending on the results of scientific evaluation, a hypothesis typically is either rejected as false or accepted as true. However, because a hypothesis inherently is falsifiable, even hypotheses supported by scientific evidence and accepted as true are susceptible to rejection later, when new evidence has become available. In some instances, rather than rejecting a hypothesis because it has been falsified by new evidence, scientists simply adapt the existing idea to accommodate the new information. In this sense a hypothesis is never incorrect but only incomplete.

The investigation of scientific hypotheses is an important component in the development of scientific theory . Hence, hypotheses differ fundamentally from theories; whereas the former is a specific tentative explanation and serves as the main tool by which scientists gather data, the latter is a broad general explanation that incorporates data from many different scientific investigations undertaken to explore hypotheses.

Countless hypotheses have been developed and tested throughout the history of science . Several examples include the idea that living organisms develop from nonliving matter, which formed the basis of spontaneous generation , a hypothesis that ultimately was disproved (first in 1668, with the experiments of Italian physician Francesco Redi , and later in 1859, with the experiments of French chemist and microbiologist Louis Pasteur ); the concept proposed in the late 19th century that microorganisms cause certain diseases (now known as germ theory ); and the notion that oceanic crust forms along submarine mountain zones and spreads laterally away from them ( seafloor spreading hypothesis ).

Hypothesis definition and example

Hypothesis n., plural: hypotheses [/haɪˈpɑːθəsɪs/] Definition: Testable scientific prediction

Table of Contents

What Is Hypothesis?

A scientific hypothesis is a foundational element of the scientific method . It’s a testable statement proposing a potential explanation for natural phenomena. The term hypothesis means “little theory” . A hypothesis is a short statement that can be tested and gives a possible reason for a phenomenon or a possible link between two variables . In the setting of scientific research, a hypothesis is a tentative explanation or statement that can be proven wrong and is used to guide experiments and empirical research.

What is Hypothesis

It is an important part of the scientific method because it gives a basis for planning tests, gathering data, and judging evidence to see if it is true and could help us understand how natural things work. Several hypotheses can be tested in the real world, and the results of careful and systematic observation and analysis can be used to support, reject, or improve them.

Researchers and scientists often use the word hypothesis to refer to this educated guess . These hypotheses are firmly established based on scientific principles and the rigorous testing of new technology and experiments .

For example, in astrophysics, the Big Bang Theory is a working hypothesis that explains the origins of the universe and considers it as a natural phenomenon. It is among the most prominent scientific hypotheses in the field.

“The scientific method: steps, terms, and examples” by Scishow:

Biology definition: A hypothesis  is a supposition or tentative explanation for (a group of) phenomena, (a set of) facts, or a scientific inquiry that may be tested, verified or answered by further investigation or methodological experiment. It is like a scientific guess . It’s an idea or prediction that scientists make before they do experiments. They use it to guess what might happen and then test it to see if they were right. It’s like a smart guess that helps them learn new things. A scientific hypothesis that has been verified through scientific experiment and research may well be considered a scientific theory .

Etymology: The word “hypothesis” comes from the Greek word “hupothesis,” which means “a basis” or “a supposition.” It combines “hupo” (under) and “thesis” (placing). Synonym:   proposition; assumption; conjecture; postulate Compare:   theory See also: null hypothesis

Characteristics Of Hypothesis

A useful hypothesis must have the following qualities:

  • It should never be written as a question.
  • You should be able to test it in the real world to see if it’s right or wrong.
  • It needs to be clear and exact.
  • It should list the factors that will be used to figure out the relationship.
  • It should only talk about one thing. You can make a theory in either a descriptive or form of relationship.
  • It shouldn’t go against any natural rule that everyone knows is true. Verification will be done well with the tools and methods that are available.
  • It should be written in as simple a way as possible so that everyone can understand it.
  • It must explain what happened to make an answer necessary.
  • It should be testable in a fair amount of time.
  • It shouldn’t say different things.

Sources Of Hypothesis

Sources of hypothesis are:

  • Patterns of similarity between the phenomenon under investigation and existing hypotheses.
  • Insights derived from prior research, concurrent observations, and insights from opposing perspectives.
  • The formulations are derived from accepted scientific theories and proposed by researchers.
  • In research, it’s essential to consider hypothesis as different subject areas may require various hypotheses (plural form of hypothesis). Researchers also establish a significance level to determine the strength of evidence supporting a hypothesis.
  • Individual cognitive processes also contribute to the formation of hypotheses.

One hypothesis is a tentative explanation for an observation or phenomenon. It is based on prior knowledge and understanding of the world, and it can be tested by gathering and analyzing data. Observed facts are the data that are collected to test a hypothesis. They can support or refute the hypothesis.

For example, the hypothesis that “eating more fruits and vegetables will improve your health” can be tested by gathering data on the health of people who eat different amounts of fruits and vegetables. If the people who eat more fruits and vegetables are healthier than those who eat less fruits and vegetables, then the hypothesis is supported.

Hypotheses are essential for scientific inquiry. They help scientists to focus their research, to design experiments, and to interpret their results. They are also essential for the development of scientific theories.

Types Of Hypothesis

In research, you typically encounter two types of hypothesis: the alternative hypothesis (which proposes a relationship between variables) and the null hypothesis (which suggests no relationship).

Hypothesis testing

Simple Hypothesis

It illustrates the association between one dependent variable and one independent variable. For instance, if you consume more vegetables, you will lose weight more quickly. Here, increasing vegetable consumption is the independent variable, while weight loss is the dependent variable.

Complex Hypothesis

It exhibits the relationship between at least two dependent variables and at least two independent variables. Eating more vegetables and fruits results in weight loss, radiant skin, and a decreased risk of numerous diseases, including heart disease.

Directional Hypothesis

It shows that a researcher wants to reach a certain goal. The way the factors are related can also tell us about their nature. For example, four-year-old children who eat well over a time of five years have a higher IQ than children who don’t eat well. This shows what happened and how it happened.

Non-directional Hypothesis

When there is no theory involved, it is used. It is a statement that there is a connection between two variables, but it doesn’t say what that relationship is or which way it goes.

Null Hypothesis

It says something that goes against the theory. It’s a statement that says something is not true, and there is no link between the independent and dependent factors. “H 0 ” represents the null hypothesis.

Associative and Causal Hypothesis

When a change in one variable causes a change in the other variable, this is called the associative hypothesis . The causal hypothesis, on the other hand, says that there is a cause-and-effect relationship between two or more factors.

Examples Of Hypothesis

Examples of simple hypotheses:

  • Students who consume breakfast before taking a math test will have a better overall performance than students who do not consume breakfast.
  • Students who experience test anxiety before an English examination 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, is a statement that suggests that drivers who talk on the phone while driving are more likely to make mistakes.

Examples of a complex hypothesis:

  • Individuals who consume a lot of sugar and don’t get much exercise are at an increased risk of developing depression.
  • Younger people who are routinely exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces, according to a new study.
  • Increased levels of air pollution led to higher rates of respiratory illnesses, which in turn resulted in increased costs for healthcare for the affected communities.

Examples of Directional Hypothesis:

  • The crop yield will go up a lot if the amount of fertilizer is increased.
  • Patients who have surgery and are exposed to more stress will need more time to get better.
  • Increasing the frequency of brand advertising on social media will lead to a significant increase in brand awareness among the target audience.

Examples of Non-Directional Hypothesis (or Two-Tailed Hypothesis):

  • The test scores of two groups of students are very different from each other.
  • There is a link between gender and being happy at work.
  • There is a correlation between the amount of caffeine an individual consumes and the speed with which they react.

Examples of a null hypothesis:

  • Children who receive a new reading intervention will have scores that are different than students who do not receive the intervention.
  • The results of a memory recall test will not reveal any significant gap in performance between children and adults.
  • There is not a significant relationship between the number of hours spent playing video games and academic performance.

Examples of Associative Hypothesis:

  • There is a link between how many hours you spend studying and how well you do in school.
  • Drinking sugary drinks is bad for your health as a whole.
  • There is an association between socioeconomic status and access to quality healthcare services in urban neighborhoods.

Functions Of Hypothesis

The research issue can be understood better with the help of a hypothesis, which is why developing one is crucial. The following are some of the specific roles that a hypothesis plays: (Rashid, Apr 20, 2022)

  • A hypothesis gives a study a point of concentration. It enlightens us as to the specific characteristics of a study subject we need to look into.
  • It instructs us on what data to acquire as well as what data we should not collect, giving the study a focal point .
  • The development of a hypothesis improves objectivity since it enables the establishment of a focal point.
  • A hypothesis makes it possible for us to contribute to the development of the theory. Because of this, we are in a position to definitively determine what is true and what is untrue .

How will Hypothesis help in the Scientific Method?

  • The scientific method begins with observation and inquiry about the natural world when formulating research questions. Researchers can refine their observations and queries into specific, testable research questions with the aid of hypothesis. They provide an investigation with a focused starting point.
  • Hypothesis generate specific predictions regarding the expected outcomes of experiments or observations. These forecasts are founded on the researcher’s current knowledge of the subject. They elucidate what researchers anticipate observing if the hypothesis is true.
  • Hypothesis direct the design of experiments and data collection techniques. Researchers can use them to determine which variables to measure or manipulate, which data to obtain, and how to conduct systematic and controlled research.
  • Following the formulation of a hypothesis and the design of an experiment, researchers collect data through observation, measurement, or experimentation. The collected data is used to verify the hypothesis’s predictions.
  • Hypothesis establish the criteria for evaluating experiment results. The observed data are compared to the predictions generated by the hypothesis. This analysis helps determine whether empirical evidence supports or refutes the hypothesis.
  • The results of experiments or observations are used to derive conclusions regarding the hypothesis. If the data support the predictions, then the hypothesis is supported. If this is not the case, the hypothesis may be revised or rejected, leading to the formulation of new queries and hypothesis.
  • The scientific approach is iterative, resulting in new hypothesis and research issues from previous trials. This cycle of hypothesis generation, testing, and refining drives scientific progress.

Hypothesis

Importance Of Hypothesis

  • Hypothesis are testable statements that enable scientists to determine if their predictions are accurate. This assessment is essential to the scientific method, which is based on empirical evidence.
  • Hypothesis serve as the foundation for designing experiments or data collection techniques. They can be used by researchers to develop protocols and procedures that will produce meaningful results.
  • Hypothesis hold scientists accountable for their assertions. They establish expectations for what the research should reveal and enable others to assess the validity of the findings.
  • Hypothesis aid in identifying the most important variables of a study. The variables can then be measured, manipulated, or analyzed to determine their relationships.
  • Hypothesis assist researchers in allocating their resources efficiently. They ensure that time, money, and effort are spent investigating specific concerns, as opposed to exploring random concepts.
  • Testing hypothesis contribute to the scientific body of knowledge. Whether or not a hypothesis is supported, the results contribute to our understanding of a phenomenon.
  • Hypothesis can result in the creation of theories. When supported by substantive evidence, hypothesis can serve as the foundation for larger theoretical frameworks that explain complex phenomena.
  • Beyond scientific research, hypothesis play a role in the solution of problems in a variety of domains. They enable professionals to make educated assumptions about the causes of problems and to devise solutions.

Research Hypotheses: Did you know that a hypothesis refers to an educated guess or prediction about the outcome of a research study?

It’s like a roadmap guiding researchers towards their destination of knowledge. Just like a compass points north, a well-crafted hypothesis points the way to valuable discoveries in the world of science and inquiry.

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Further Reading

  • RNA-DNA World Hypothesis
  • BYJU’S. (2023). Hypothesis. Retrieved 01 Septermber 2023, from https://byjus.com/physics/hypothesis/#sources-of-hypothesis
  • Collegedunia. (2023). Hypothesis. Retrieved 1 September 2023, from https://collegedunia.com/exams/hypothesis-science-articleid-7026#d
  • Hussain, D. J. (2022). Hypothesis. Retrieved 01 September 2023, from https://mmhapu.ac.in/doc/eContent/Management/JamesHusain/Research%20Hypothesis%20-Meaning,%20Nature%20&%20Importance-Characteristics%20of%20Good%20%20Hypothesis%20Sem2.pdf
  • Media, D. (2023). Hypothesis in the Scientific Method. Retrieved 01 September 2023, from https://www.verywellmind.com/what-is-a-hypothesis-2795239#toc-hypotheses-examples
  • Rashid, M. H. A. (Apr 20, 2022). Research Methodology. Retrieved 01 September 2023, from https://limbd.org/hypothesis-definitions-functions-characteristics-types-errors-the-process-of-testing-a-hypothesis-hypotheses-in-qualitative-research/#:~:text=Functions%20of%20a%20Hypothesis%3A&text=Specifically%2C%20a%20hypothesis%20serves%20the,providing%20focus%20to%20the%20study.

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Last updated on September 8th, 2023

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A hypothesis is an educated guess about what you think will happen in a scientific experiment, based on your observations. Before conducting the experiment, you propose a hypothesis so that you can determine if your prediction is supported.

There are several ways you can state a hypothesis, but the best hypotheses are ones you can test and easily refute. Why would you want to disprove or discard your own hypothesis? Well, it is the easiest way to demonstrate that two factors are related. Here are some good scientific hypothesis examples:

  • Hypothesis: All forks have three tines. This would be disproven if you find any fork with a different number of tines.
  • Hypothesis: There is no relationship between smoking and lung cancer. While it is difficult to establish cause and effect in health issues, you can apply statistics to data to discredit or support this hypothesis.
  • Hypothesis: Plants require liquid water to survive. This would be disproven if you find a plant that doesn't need it.
  • Hypothesis: Cats do not show a paw preference (equivalent to being right- or left-handed). You could gather data around the number of times cats bat at a toy with either paw and analyze the data to determine whether cats, on the whole, favor one paw over the other. Be careful here, because individual cats, like people, might (or might not) express a preference. A large sample size would be helpful.
  • Hypothesis: If plants are watered with a 10% detergent solution, their growth will be negatively affected. Some people prefer to state a hypothesis in an "If, then" format. An alternate hypothesis might be: Plant growth will be unaffected by water with a 10% detergent solution.
  • Null Hypothesis Examples
  • Scientific Hypothesis, Model, Theory, and Law
  • What Are the Elements of a Good Hypothesis?
  • Understanding Simple vs Controlled Experiments
  • What Is a Hypothesis? (Science)
  • Six Steps of the Scientific Method
  • What Is a Testable Hypothesis?
  • Null Hypothesis Definition and Examples
  • What Are Examples of a Hypothesis?
  • Theory Definition in Science
  • How To Design a Science Fair Experiment
  • Science Projects for Every Subject
  • What 'Fail to Reject' Means in a Hypothesis Test
  • Middle School Science Fair Project Ideas
  • Effect of Acids and Bases on the Browning of Apples

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

  • State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
  • Collect data in a way designed to test the hypothesis.
  • Perform an appropriate statistical test .
  • Decide whether to reject or fail to reject your null hypothesis.
  • Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

  • H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

  • an estimate of the difference in average height between the two groups.
  • a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

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

  • Normal distribution
  • Descriptive statistics
  • Measures of central tendency
  • Correlation coefficient

Methodology

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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 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).

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.

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100 Hypothesis Examples Across Various Academic Fields

David Costello

A hypothesis is a statement or proposition that is made for the purpose of testing through empirical research. It represents an educated guess or prediction that can be tested through observation and experimentation. A hypothesis is often formulated using a logical construct of "if-then" statements, allowing researchers to set up experiments to determine its validity. It serves as the foundation of a scientific inquiry, providing a clear focus and direction for the study. In essence, a hypothesis is a provisional answer to a research question , which is then subjected to rigorous testing to determine its accuracy.

In this blog post, we'll explore 100 different hypothesis examples, showing you how these simple statements set the stage for discovery in various academic fields. From the mysteries of chemical reactions to the complexities of human behavior, hypotheses are used to kickstart research in numerous disciplines. Whether you're new to the world of academia or just curious about how ideas are tested, these examples will offer insight into the fundamental role hypotheses play in learning and exploration.

  • If a plant is given more sunlight, then it will grow faster.
  • If an animal's environment is altered, then its behavior will change.
  • If a cell is exposed to a toxin, then its function will be impaired.
  • If a species is introduced to a new ecosystem, then it may become invasive.
  • If an antibiotic is applied to a bacterial culture, then growth will be inhibited.
  • If a gene is mutated, then the corresponding protein may become nonfunctional.
  • If a pond's water temperature rises, then the algae population will increase.
  • If a bird species' habitat is destroyed, then its population will decrease.
  • If a mammal is given a high-fat diet, then its cholesterol levels will rise.
  • If human stem cells are treated with specific factors, then they will differentiate into targeted cell types.
  • If the concentration of a reactant is increased, then the rate of reaction will increase.
  • If a metal is placed in a solution of a salt of a less reactive metal, then a displacement reaction will occur.
  • If a solution's pH is lowered, then the concentration of hydrogen ions will increase.
  • If a gas is cooled at constant pressure, then its volume will decrease according to Charles's law.
  • If an endothermic reaction is heated, then the equilibrium position will shift to favor the products.
  • If an enzyme is added to a reaction, then the reaction rate will increase due to the lower activation energy.
  • If the pressure on a gas is increased at constant temperature, then the volume will decrease according to Boyle's law.
  • If a non-polar molecule is added to water, then it will not dissolve due to water's polarity.
  • If a piece of litmus paper is placed in a basic solution, then the color of the paper will turn blue.
  • If an electric current is passed through a salt solution, then the solution will undergo electrolysis and break down into its components.

Computer science

  • If a new algorithm is applied to a sorting problem, then the computational complexity will decrease.
  • If multi-factor authentication is implemented, then the security of a system will increase.
  • If a machine learning model is trained with more diverse data, then its predictive accuracy will improve.
  • If the bandwidth of a network is increased, then the data transmission rate will be faster.
  • If a user interface is redesigned following usability guidelines, then user satisfaction and efficiency will increase.
  • If a specific optimization technique is applied to a database query, then the retrieval time will be reduced.
  • If a new cooling system is used in a data center, then energy consumption will decrease.
  • If parallel processing is implemented in a computational task, then the processing time will be reduced.
  • If a software development team adopts Agile methodologies, then the project delivery time will be shortened.
  • If a more advanced error correction code is used in data transmission, then the error rate will decrease.
  • If the interest rate is lowered, then consumer spending will increase.
  • If the minimum wage is raised, then unemployment may increase among low-skilled workers.
  • If government spending is increased, then the Gross Domestic Product (GDP) may grow.
  • If taxes on luxury goods are raised, then consumption of those goods may decrease.
  • If a country's currency is devalued, then its exports will become more competitive.
  • If inflation is high, then the central bank may increase interest rates to control it.
  • If consumer confidence is high, then spending in the economy will likely increase.
  • If barriers to entry in a market are reduced, then competition will likely increase.
  • If a firm engages in monopolistic practices, then consumer welfare may decrease.
  • If unemployment benefits are extended, then the unemployment rate may be temporarily affected.
  • If class sizes are reduced, then individual student performance may improve.
  • If teachers receive ongoing professional development, then teaching quality will increase.
  • If schools implement a comprehensive literacy program, then reading levels among students will rise.
  • If parents are actively involved in their children's education, then students' academic achievement may increase.
  • If schools provide more access to extracurricular activities, then student engagement and retention may improve.
  • If educational technology is integrated into the classroom, then learning outcomes may enhance.
  • If a school adopts a zero-tolerance policy on bullying, then the incidence of bullying will decrease.
  • If schools provide nutritious meals, then student concentration and performance may improve.
  • If a curriculum is designed to include diverse cultural perspectives, then student understanding of different cultures will increase.
  • If schools implement individualized learning plans, then students with special needs will achieve better educational outcomes.

Environmental science

  • If deforestation rates continue to rise, then biodiversity in the area will decrease.
  • If carbon dioxide emissions are reduced, then the rate of global warming may decrease.
  • If a water body is polluted with nutrients, then algal blooms may occur, leading to eutrophication.
  • If renewable energy sources are used more extensively, then dependency on fossil fuels will decrease.
  • If urban areas implement green spaces, then the urban heat island effect may be reduced.
  • If protective measures are not implemented, then endangered species may become extinct.
  • If waste recycling practices are increased, then landfill usage and waste pollution may decrease.
  • If air quality regulations are enforced, then respiratory health issues in the population may decrease.
  • If soil erosion control measures are not implemented, then agricultural land fertility may decrease.
  • If ocean temperatures continue to rise, then coral reefs may experience more frequent bleaching events.
  • If a new chemotherapy drug is administered to cancer patients, then tumor size will decrease more effectively.
  • If a specific exercise regimen is followed by osteoarthritis patients, then joint mobility will improve.
  • If a population is exposed to higher levels of air pollution, then respiratory diseases such as asthma will increase.
  • If a novel surgical technique is utilized in cardiac surgery, then patient recovery times will be shortened.
  • If a targeted screening program is implemented for a specific genetic disorder, then early detection and intervention rates will increase.
  • If a community's water supply is fortified with fluoride, then dental cavity rates in children will decrease.
  • If an improved vaccination schedule is followed in a pediatric population, then the incidence of preventable childhood diseases will decline.
  • If nutritional supplements are provided to malnourished individuals, then general health and immune function will improve.
  • If stricter infection control protocols are implemented in hospitals, then the rate of hospital-acquired infections will decrease.
  • If organ transplant recipients are given a new immunosuppressant drug, then organ rejection rates will decrease.
  • If a person is exposed to violent media, then their aggression levels may increase.
  • If a child is given positive reinforcement, then desired behaviors will be more likely to be repeated.
  • If an individual suffers from anxiety, then their performance on tasks under pressure may decrease.
  • If a patient is treated with cognitive-behavioral therapy, then symptoms of depression may reduce.
  • If a person lacks sleep, then their cognitive functions and decision-making abilities will decline.
  • If an individual's self-esteem is increased, then their overall life satisfaction may improve.
  • If a person is exposed to a traumatic event, then they may develop symptoms of PTSD.
  • If social support is provided to an individual, then their ability to cope with stress will improve.
  • If a group works collaboratively, then they may exhibit improved problem-solving abilities.
  • If an individual is given autonomy in their work, then their job satisfaction and motivation will increase.
  • If the velocity of an object is increased, then the kinetic energy will also increase.
  • If the temperature of a gas is increased at constant pressure, then the volume will increase.
  • If the mass of an object is doubled, then the gravitational force it exerts will also double.
  • If the frequency of a wave is increased, then the energy it carries will increase.
  • If a magnet's distance from a metal object is decreased, then the magnetic force will increase.
  • If the angle of incidence equals the angle of reflection, then the law of reflection holds true.
  • If the resistance in an electrical circuit is increased, then the current will decrease.
  • If the force applied to a spring is doubled, then the extension of the spring will also double.
  • If a mirror is concave, then it will focus parallel rays to a point.
  • If a body is in uniform circular motion, then the net force toward the center is providing the centripetal acceleration.
  • If educational opportunities are equally distributed in a society, then social mobility will increase.
  • If community policing strategies are implemented, then trust between law enforcement and the community may improve.
  • If social media usage increases among teenagers, then face-to-face social interaction may decrease.
  • If gender wage gap policies are enforced, then disparities in earnings between men and women will decrease.
  • If a society emphasizes individualistic values, then community engagement and collective responsibility may decline.
  • If affordable housing initiatives are implemented in urban areas, then homelessness rates may decrease.
  • If a minority group is represented in media, then stereotypes and prejudices toward that group may decrease.
  • If a culture promotes work-life balance, then overall life satisfaction among its citizens may increase.
  • If increased funding is provided to community centers in underserved neighborhoods, then social cohesion and community engagement may improve.
  • If legislation is passed to protect the rights of LGBTQ+ individuals, then discrimination and stigma may decrease in society.

In the exploration of various academic disciplines, hypotheses play a crucial role as foundational statements that guide research and inquiry. From understanding complex biological processes to navigating the nuances of human behavior in sociology, hypotheses serve as testable predictions that shape the direction of scientific investigation. The examples provided across the fields of medicine, computer science, sociology, and education illustrate the diverse applications and importance of hypotheses in shaping our understanding of the world. Whether improving medical treatments, enhancing technological systems, fostering social equality, or elevating educational practices, hypotheses remain central to scientific progress and societal advancement. By formulating clear and measurable hypotheses, researchers can continue to unravel complex phenomena, contribute to their fields, and ultimately enrich human knowledge and well-being.

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Biology archive

Course: biology archive   >   unit 1, the scientific method.

  • Controlled experiments
  • The scientific method and experimental design

hypothesis image example

Introduction

  • Make an observation.
  • Ask a question.
  • Form a hypothesis , or testable explanation.
  • Make a prediction based on the hypothesis.
  • Test the prediction.
  • Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation., 2. ask a question., 3. propose a hypothesis., 4. make predictions., 5. test the predictions..

  • If the toaster does toast, then the hypothesis is supported—likely correct.
  • If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

  • If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
  • If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Incredible Answer

Understand Hypothesis testing with real-life examples

hypothesis-testing-real-life-example

If you are learning or working in the field of Data Science, you should have clear understanding of what are hypothesis testing and p values in statistics. If you learn those two things then understanding any basic machine learning algorithms like linear regression, and logistic regression will be easier for you. In this tutorial I will explain hypothesis testing with real life examples.

Many people have lots of confusion about hypothesis testing and p value. In this tutorial, I will explain you what is hypothesis testing in statistics with a very simple and real life example.

What is Hypothesis

Hypothesis testing is a statistical method to evaluate or investigate the validity of a claim or assumption about something based on sample data.

In simple English, meaning of Hypothesis is guess . Now a guess can be anything like: With a ladder tall enough, I could touch the sky or If I had wings, I could fly to the moon, If I had a time machine, I could travel to any point in history, etc.

Some guesses are just imagination, you can not prove or investigate them with anything. If we can investigate or test any guesses with data, that test is called Hypothesis testing in statistics.

Types of Hypothesis Testing

At this point, we know what is hypothesis testing and its use. Now there are two types of hypotheses:

  • Null Hypothesis ( H 0 )
  • Alternative Hypothesis ( H 1 )

Null Hypothesis

In general programming language, we denote Null as empty or zero. In statistics, Null hypothesis means default hypothesis , the hypothesis or guess which is already established for a certain question.

Why it is called “Null”? We call it Null Hypothesis because we always want to nullify the existing theory with something else. This is why we perform any test right? If we do not want to prove something new then why should we put effort into doing any new test?

In statistics, Null Hypothesis is denoted as H 0

Alternative Hypothesis

The alternative hypothesis (H 1 ) is the opposite of the null hypothesis. The alternative hypothesis is the hypothesis that we want to or try to prove .

For example, previously, people believed that the sun is rotating around the Earth until Galileo, an Italian astronomer, proved through his observations that the Earth is actually revolving around the sun . This discovery challenged the widely accepted belief of geocentrism, which people used to believe for centuries.

Here previously believed theory (the Sun is rotating around the Earth) is the Null Hypothesis and the theory Galileo wanted to prove (Earth is rotating around the Sun) is the Alternative Hypothesis. Here the test or observation Galileo perform can be called a Hypothesis testing.

In statistics, Alternative Hypothesis is denoted as H 1

Hypothesis testing example

Let me now give your rela life example where you can implement hypothesis testing as a data science professional. Let’s say for a particular candy manufacturing company, it is believed that a candy machine makes chocolate bars that are an average of 5 grams . That candy manufacturing plant has been making chocolate bars for 10 years now suddenly a worker claims that the machine no longer makes 5 grams of each chocolate bar .

real-life-application-of-hypothesis-testing

So is the worker wrong or the machine is not functioning properly? To answer those questions the owner of that candy company should perform Hypothesis testing.

Here the Null Hypothesis is the statement “The machine is functioning correctly and making each chocolate bar 5 grams” and the alternative hypothesis is the statement of the worker “The machine no longer makes 5 grams of each chocolate bar”.

If we want to write above English text into math then we can write like below:

hypothesis-testing-in-statistics

Pass outcome of Hypothesis testing

There are only two outcomes of hypothesis testing in statistics those are:

  • Reject Null Hypothesis (H 0 ) – the machine is producing each chocolate bar with 5g of weight
  • Fail to reject null hypothesis – In other words, alternative hypothesis (H 1 ) is proven or new theory is established

Application of Hypothesis Testing

Like the above example, there are so many places we can implement hypothesis testing in real life problems. Let’s also see some other important areas where we can apply hypothesis testing.

  • Medicine: Hypothesis testing used to determine effectiveness of new treatments or drugs.
  • Marketing: You can understand the effectiveness of advertising campaigns or new product launches.
  • Quality Control: Find out whether a manufacturing process is producing products within acceptable quality limits. This is the example I explained above.
  • Environmental Science: You can test the effects of pollutants on ecosystems using hypothesis testing

Terminologies to know

Before calculating hypothesis testing you should know some statistical terminologies, let’s understand those.

Statistical Significance

Statistically Significant is a term used to describe whether a result from a statistical test or analysis is likely to be real or just by chance. It is the point where we can draw the line to make a decision. Again the decision is whether we are rejecting the null hypothesis or not.

Level of Confidence

The Level of Confidence (c) says that, how much confident are we when taking our decision to reject null hypothesis or fail to reject the null hypothesis. Level of confidence is measured as a probability value. Now when you are trying to prove something new (rejecting null hypo), you must have high confidence in your test so that people or statistics can believe in your new theory. Good confidence level is more than 95%.

Level of Significance

Level of Significance is a probability value used in hypothesis testing to determine if the results of a statistical test are statistically significant or not. This level of significance is also known as the p-value, which I will explain in a later post. The equation of LOS is as follows:

Level of Significance = 1 – Level of confidence

Now if for some test, level of confidence = 95%

Then, Level of Significance = 1 – 95 = 0.05

Similarly, if LOC = 99% then LOS = 0.01.

You can see sum of Level of Significance and Level of confidence is equal to 1 ( LOS + LOC = 1 ). The sum should always be 1.

Good level of significance score is less than 0.05 (which is greater than 95% of LOS).

Level of Confidence vs Level of Significance

In general, there is no difference between level of confidence and level of significance. They are both the same thing. Different problems or research papers may use different parameters to indicate significance. But both will tell you the same thing, how sure are you to make any statistical decision?

Degrees of Freedom

In statistics, degrees of freedom (df) is the number of values in a sample that are free to vary after imposing certain restrictions or constraints.

In simple words, Degrees of freedom represents the number of independent observations or data points that can be used to estimate statistical parameters or test hypotheses. The more degrees of freedom available, the more reliable and accurate the statistical analysis is likely to be.

The equation for degrees of freedom is as follows:

DF = number of sample data (n) – 1

Hypothesis Testing Formula

Before we calculate hypothesis testing in hand from scratch, we should know the equation to test hypothesis. There are mainly two ways to calculate hypothesis those are t-test and z-test .

t-test equation

t-test equation is: t = ( x̅ – μ 0 ) / (s / √n)

  • Where x̅ is sample mean
  • μ 0 is already proven value (you can say null hypothesis value)
  • s sample standard deviation
  • n is the sample size

z-test equation

z-test equation is: Z = ( x̅ – μ0 ) / (σ / √n)

  • σ is the population standard deviation

Difference between sample SD and population SD

For t-test, I mentioned sample standard deviation and for z-test, I mentioned population standard deviation. Now, what is the difference between sample SD and population SD?

The main difference between sample standard deviation (SD) and population standard deviation (SD) is the data set they are calculated from.

Sample standard deviation (SD) is calculated from a subset of the population data called a sample. A sample is a smaller group of data selected from the entire population for statistical analysis.

On the other hand Population standard deviation (SD) is calculated from the entire population or entire data set.

Z-Test vs. T-Test: When to Use Which?

The z-test and t-test are both statistical tests used to calculate hypothesis testing. The z-test is used when the population standard deviation is known and the sample size is large (typically n > 30).

On the other hand, t-test is used when the population standard deviation is unknown, and the sample size is small (typically n < 30).

In general, if the sample size is large and the population standard deviation is known then the z-test is preferred. If the sample size is small and the population standard deviation is unknown, then the t-test is more appropriate (you can use sample standard deviation).

How to calculate Hypothesis Testing in Excel

So we understand what is hypothesis. Now how to calculate it? or how do you actually determine if you reject the null hypothesis or not? For that, you need to perform some statistical test using some sample data.

Data Collection

Coming back to our main example of a candy-making factory where a worker suddenly made a statement that “the candy making machine is no longer makes 5 grams of chocolate bars”.

Now, this is a big and scary statement for the owner of that factory. So the owner assigned a quality inspector to inspect this.

The quality inspector checked the weight of ten chocolate randomly . I mentioned randomly which means the sample data should be normally distributed . Now the quality inspector can bring this randomness in various ways like he can check chocolate weight at different time of a day or week or check weight while different worker is working etc.

Now let’s say the quality inspector collected following ten random samples:

Candy NumberCandy Weight (in grams)
15.2
24.8
35
44.9
55.2
64.7
75
84.8
94.9
105.1

Selecting Test Type

As I explained earlier since the data or samle size is less and we do not know the population standard deviation so we will use T-test to calculate hypothesis for this problem .

Note: To solve almost all real life problem, we use t-test to calculate hypothesis testing because of lack of overall information (unknown population standard deviation).

Calculate required Parameters

So to apply t-test, now we need to calculate sample standard distribution for our example. You can do it easily in Excel. Now in excel, there are mainly two formulas for standard deviation. Those are:

  • STDEV.S => To calculate standard deviation for sample
  • STDEV.P +> To calculate population standard deviation

We can find our sample standard deviation value is 0.171 (using STDEV.S method in excel)

An our sample mean (x̅) = (5.2 + 4.8 + 5 + 4.9 + 5.2 + 4.7 + 5 + 4.8 + 4.9 + 5.1) / 10 = 4.96

So let’s now list down all required information to calculate hypothesis testing for our problem (measure likelihood of the worker’s claim). Informations are:

  • Already proven value (μ 0 ) = 5 grams
  • Sample standard deviation (s) = 0.171
  • Number of samples collected (n) = 10
  • Degrees of Freedom (DF) = (n-1) = 9
  • Sample mean (x̅) = 4.96

Assuming that the company’s claim of a chocolate bar weight being 5 grams each is true, We need to prove that:

  • Either H0: μ=μ0 (null hypothesis is true – fail to reject null hypothesis – worker’s claimed information is not correct)
  • Or H 1 : μ≠μ0 (Rejecting null hypothesis – worker’s claim is correct)

Draw distribution graph

So our sample mean at 4.96 and our sample standard deviation at 0.171. Now if you draw the distribution of the possible values of our sample mean given the population mean is 5 (already proven weight of a chocolate bar which is 5 grams each). Assuming the null hypothesis is true, below would be the distribution:

standard-normal-distribution-gaussian-bell-graph-curve-concept-hypothesis-testing-gauss-distribution

So basically this hypothesis test is really going to be asking how extreme is this value of 4.96 (sample mean x̅) if the null hypothesis is true. Is it too extreme for us to accept null hypothesis or closer to population mean (already proven value 5) to reject null hypothesis? To answer this question we need to calculate a test statistic here using all provided or known informations.

Apply T test

Applying the T-test formula:

t = ( x̅ – μ 0 ) / (s / √n)

t = (4.96 – 5) / (0.171 / √ 10) = -0.04/0.054 = -0.74074

Decision Rule

So we have our T score which is -0.74074. Now the next thing we need to do is to consider our decision rule. Like normal distribution, T distribution is also a bell curve type shape. The only difference is that the T distribution is defined by its number of degrees of freedom. In our example, degrees of freedom (DF) is 9.

So if degree of freedom is 9 and if we want 95% level of confidence or 0.05 level of significance, we can reject null hypothesis if our calculated T score lies in the green region on the negative side.

t-distribution-bell-curve-for-hypothesis-testing-with-005-level-of-significance

Output of Hypothesis Testing

Now from the T Critical values table, we can find that if degrees of freedom = 9 and Level of significance = 0.05, then T score should be greater than -1.833 (we will keep this value negative because our T score is negative) then only we can reject the null hypothesis.

Note: This is just a one-tailed test as we are only looking at one direction from our expected value (in the negative direction). If we were looking for both the direction of distribution bell curve then we could call it a two-tailed test.

Below is the T Critical values table for your reference.

T distribution table

Conf. Level50%80%90%95%98%99%
One Tail0.250.10.050.0250.010.005
Two Tail0.50.20.10.050.020.01
df = 113.0786.31412.70631.82163.657
20.8161.8862.924.3036.9659.925
30.7651.6382.3533.1824.5415.841
40.7411.5332.1322.7763.7474.604
50.7271.4762.0152.5713.3654.032
60.7181.441.9432.4473.1433.707
70.7111.4151.8952.3652.9983.499
80.7061.3971.862.3062.8963.355
90.7031.3831.8332.2622.8213.25
100.71.3721.8122.2282.7643.169
110.6971.3631.7962.2012.7183.106
120.6951.3561.7822.1792.6813.055
130.6941.351.7712.162.653.012
140.6921.3451.7612.1452.6242.977
150.6911.3411.7532.1312.6022.947
160.691.3371.7462.122.5832.921
170.6891.3331.742.112.5672.898
180.6881.331.7342.1012.5522.878
190.6881.3281.7292.0932.5392.861
200.6871.3251.7252.0862.5282.845
210.6861.3231.7212.082.5182.831
220.6861.3211.7172.0742.5082.819
230.6851.3191.7142.0692.52.807
240.6851.3181.7112.0642.4922.797
250.6841.3161.7082.062.4852.787
260.6841.3151.7062.0562.4792.779
270.6841.3141.7032.0522.4732.771
280.6831.3131.7012.0482.4672.763
290.6831.3111.6992.0452.4622.756
300.6831.311.6972.0422.4572.75
400.6811.3031.6842.0212.4232.704
500.6791.2991.6762.0092.4032.678
600.6791.2961.67122.392.66
700.6781.2941.6671.9942.3812.648
800.6781.2921.6641.992.3742.639
900.6771.2911.6621.9872.3682.632
1000.6771.291.661.9842.3642.626
z0.6741.2821.6451.962.3262.576

The calculated T score for our example is -0.74074 > -1.833, therefore the null hypothesis is true (we failed to reject the null hypothesis). That means the claim by the worker is not true . The candy machine is working properly and it is still producing each chocolate bar around 5 grams.

Graph interpretation

We can see the above interpretation in the below T distribution bell curve:

output-decision-of-hypothesis-testing-calculation-in-hand-and-excel-from-scratch

In statistics, we should always test a hypothesis to make a proper judgment. Now there are two types of hypotheses. The first one is the Null Hypothesis, which is an already established concept. The second one is the Alternative Hypothesis, which is a new concept that we are trying to establish by proving the Null Hypothesis wrong.

We are making these decisions (rejecting null hypothesis or not) based on Level of confidence or Level of Significance score. Good score for those parameters are more than 95% for LOC or less than 0.05 for LOS.

In this post, I tried to explain Hypothesis testing with easy and real life examples. Please let me know if you have any questions or suggestions regarding this tutorial.

Anindya Naskar

Hi there, I’m Anindya Naskar, Data Science Engineer. I created this website to show you what I believe is the best possible way to get your start in the field of Data Science.

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July 1, 2024

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

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

By Manon Bischoff

Abstract purple lines funnelling towards the right with white dotted light sources becoming smaller towards the right.

Weiquan Lin/Getty Images

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

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

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

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

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

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

A Periodic Table for Numbers

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

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

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

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

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

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

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

A Strange Connection

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

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

The zeta function

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

The zeta function as a function of all prime numbers

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

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

The coordinates of z = x + iy illustrate a complex number

Никита Воробьев/Wikimedia

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

A visual mapping of the zeta function looks like a mountainscape with peaks and troughs

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

Jan Homann/Wikimedia

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

The dark blue area demarcates a stretch along the x axis where the Riemann zeta function contains nontrivial zeros

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

LoStrangolatore/Wikimedia ( CC BY-SA 3.0 )

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

On the Hunt for Zeros

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

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

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

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

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

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

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

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

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

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

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

*Editor’s Note (7/9/24): This sentence was edited after posting to better clarify that prime numbers exclude 1.

‘The First Descendant’ Is Using Barely-Changed ‘Destiny 2’ Icons

While The First Descendant is mostly built from Warframe DNA, players have noticed that a number of in-game icons look awfully like ones from Destiny 2. One would be a coincidence, maybe, but there are many, and this is without checking more than a low % of all the icons in the game.

In this case, you can see that there are tiny tweaks to almost all of them, a “copy my homework without making it look like you copied it” type situation, but it’s pretty clear that if these weren’t flat-out taken from Destiny they were copied almost exactly with those small additions or subtractions added.

Different Dream

While I’m not sure anything else is 1:1 like this in the game, played have noticed a gun that looks a lot like a Destiny 2 design. The gun in question is the Different Dream, which you can see above. And the idea is that it has taken its design aesthetic from the IKELOS series of weapons in Destiny 2, namely the IKELOS sniper:

And more so the Sleeper Simulant.

The question is whether it was taken or a tribute. I don’t know. It certainly resembles the aesthetic, but it’s definitely not an exact copy. That barrel and Sleeper’s look extremely close, obviously. Though the fact that the gun is called “Different Dream” makes me think it could be a tribute rather than a rip-off. I am…almost willing to give them the benefit of the doubt. The icon thing is worse, if you ask me, and if they did it there…

There are a few other things, so far. There’s one shielded enemy with a weak spot in the center that reacts essentially identically to a Cabal Phalanx when it’s struck. There is of course one of the main pieces of art of the game that was compared to Destiny ahead of release, though that’s a little freeze orb, not a ghost.

The First Descendant

Generally speaking, The First Descendant feels like an amalgam of a bunch of games with relatively few original concepts. Again, it is at least 85% Warframe DNA in almost every possible way, with more intrusive and expensive microtransactions (though even those are mostly from Warframe too).

I think a lot of this could be overlooked even if the “inspiration” is clear, if you can call it that. But the icons are problematic and I do wonder if Bungie will try to do anything about it. I do not know if other icons may be from other games I don’t play. I will continue looking for more comparison points, and submit any you may have to me on Twitter.

I’ve reached out to Nexon and Bungie for comment, and will update if I hear back.

Update : Adding more as they come in:

Follow me on Twitter , YouTube , and Instagram .

Pick up my sci-fi novels the Herokiller series and The Earthborn Trilogy .

COMMENTS

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  9. 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.

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    Merriam Webster defines a hypothesis as "an assumption or concession made for the sake of argument.". In other words, a hypothesis is an educated guess. Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it's true or not.

  12. 15 Hypothesis Examples (2024)

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    hypothesis. science. scientific hypothesis, an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an "If…then" statement summarizing the idea and in the ...

  14. What Are Examples of a Hypothesis?

    Examples of Null Hypotheses. Hyperactivity is unrelated to eating sugar. All daisies have the same number of petals. The number of pets in a household is unrelated to the number of people living in it. A person's preference for a shirt is unrelated to its color.

  15. Hypothesis

    Figure 1: What is Hypothesis. Image Credit: medium.com . It is an important part of the scientific method because it gives a basis for planning tests, gathering data, and judging evidence to see if it is true and could help us understand how natural things work. ... For example, the hypothesis that "eating more fruits and vegetables will ...

  16. Scientific Hypothesis Examples

    Scientific Hypothesis Examples . Hypothesis: All forks have three tines. This would be disproven if you find any fork with a different number of tines. Hypothesis: There is no relationship between smoking and lung cancer.While it is difficult to establish cause and effect in health issues, you can apply statistics to data to discredit or support this hypothesis.

  17. Hypothesis Testing

    There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1 ). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ...

  18. 100 Hypothesis Examples Across Various Academic Fields

    100 Hypothesis Examples Across Various Academic Fields. David Costello. July 28, 2023 PDT. A hypothesis is a statement or proposition that is made for the purpose of testing through empirical research. It represents an educated guess or prediction that can be tested through observation and experimentation. A hypothesis is often formulated using ...

  19. The scientific method (article)

    The scientific method. At the core of biology and other sciences lies a problem-solving approach called the scientific method. The scientific method has five basic steps, plus one feedback step: Make an observation. Ask a question. Form a hypothesis, or testable explanation. Make a prediction based on the hypothesis.

  20. 9 Hypothesis Examples Explained for Beginner

    The key to these measurable hypotheses is the ability to quantify and measure the variables involved. For example: Test scores can be measured by assigning numerical values to correct answers. Sales can be measured by counting the number of units sold. Blood pressure can be measured with a blood pressure monitor.

  21. Problem-Solving for Anyone: How to Use Hypotheses Like Top Strategy

    Example hypothesis-pyramid for problem-solving — image created by the author based on the 4S-Method in Miro. For sub-hypothesis 1, The UK is a good market; it looks as follows:. EH 1.1: There is enough demand for online coaching EH 1.2: There are enough coaches to satisfy the demand EH 1.3: Coaches are willing to collaborate via an online platform EH 1.4: There isn't too much competition

  22. Understand Hypothesis testing with real-life examples

    There are mainly two ways to calculate hypothesis those are t-test and z-test. t-test equation. t-test equation is: t = ( x̅ - μ0 ) / (s / √n) Where x̅ is sample mean. μ0 is already proven value (you can say null hypothesis value) s sample standard deviation. n is the sample size. z-test equation.

  23. The Riemann Hypothesis, the Biggest Problem in Mathematics, Is a Step

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

  24. Project 2025 Disavowed By Trump: 'I Have Nothing To Do With Them'

    AFP via Getty Images. Key Facts. Trump said in a Truth Social post he has "no idea who is behind" Project 2025, adding he disagrees with some of the project's proposals for the next GOP ...

  25. 'The First Descendant' Is Using Barely-Changed 'Destiny 2' Icons

    The question is whether it was taken or a tribute. I don't know. It certainly resembles the aesthetic, but it's definitely not an exact copy. That barrel and Sleeper's look extremely close ...