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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

  • At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
  • The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
  • The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)).  The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

One Group Mean
Research Question Is the population mean different from \( \mu_{0} \)? Is the population mean greater than \(\mu_{0}\)? Is the population mean less than \(\mu_{0}\)?
Null Hypothesis, \(H_{0}\) \(\mu=\mu_{0} \) \(\mu=\mu_{0} \) \(\mu=\mu_{0} \)
Alternative Hypothesis, \(H_{a}\) \(\mu\neq \mu_{0} \) \(\mu> \mu_{0} \) \(\mu<\mu_{0} \)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
Paired Means
Research Question Is there a difference in the population? Is there a mean increase in the population? Is there a mean decrease in the population?
Null Hypothesis, \(H_{0}\) \(\mu_d=0 \) \(\mu_d =0 \) \(\mu_d=0 \)
Alternative Hypothesis, \(H_{a}\) \(\mu_d \neq 0 \) \(\mu_d> 0 \) \(\mu_d<0 \)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
One Group Proportion
Research Question Is the population proportion different from \(p_0\)? Is the population proportion greater than \(p_0\)? Is the population proportion less than \(p_0\)?
Null Hypothesis, \(H_{0}\) \(p=p_0\) \(p= p_0\) \(p= p_0\)
Alternative Hypothesis, \(H_{a}\) \(p\neq p_0\) \(p> p_0\) \(p< p_0\)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
Difference between Two Independent Means
Research Question Are the population means different? Is the population mean in group 1 greater than the population mean in group 2? Is the population mean in group 1 less than the population mean in groups 2?
Null Hypothesis, \(H_{0}\) \(\mu_1=\mu_2\) \(\mu_1 = \mu_2 \) \(\mu_1 = \mu_2 \)
Alternative Hypothesis, \(H_{a}\) \(\mu_1 \ne \mu_2 \) \(\mu_1 \gt \mu_2 \) \(\mu_1 \lt \mu_2\)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
Difference between Two Proportions
Research Question Are the population proportions different? Is the population proportion in group 1 greater than the population proportion in groups 2? Is the population proportion in group 1 less than the population proportion in group 2?
Null Hypothesis, \(H_{0}\) \(p_1 = p_2 \) \(p_1 = p_2 \) \(p_1 = p_2 \)
Alternative Hypothesis, \(H_{a}\) \(p_1 \ne p_2\) \(p_1 \gt p_2 \) \(p_1 \lt p_2\)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
Simple Linear Regression: Slope
Research Question Is the slope in the population different from 0? Is the slope in the population positive? Is the slope in the population negative?
Null Hypothesis, \(H_{0}\) \(\beta =0\) \(\beta= 0\) \(\beta = 0\)
Alternative Hypothesis, \(H_{a}\) \(\beta\neq 0\) \(\beta> 0\) \(\beta< 0\)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
Correlation (Pearson's )
Research Question Is the correlation in the population different from 0? Is the correlation in the population positive? Is the correlation in the population negative?
Null Hypothesis, \(H_{0}\) \(\rho=0\) \(\rho= 0\) \(\rho = 0\)
Alternative Hypothesis, \(H_{a}\) \(\rho \neq 0\) \(\rho > 0\) \(\rho< 0\)
Type of Hypothesis Test Two-tailed, non-directional Right-tailed, directional Left-tailed, directional
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Writing Guides  /  How to Write a Hypothesis w/ Strong Examples

How to Write a Hypothesis w/ Strong Examples

hypothesis

A hypothesis is a guess about what’s going to happen.  In research, the hypothesis is what you the researcher expects the outcome of an experiment, a study, a test, or a program to be.  It is a belief based on the evidence you have before you, the reasoning of your mind, and what prior experience tells you.  The hypothesis is not 100% guaranteed—that’s why there are different kinds of hypotheses.  In this article, we’ll explain what those are when they should be used.  So let’s dive in!

What is a Hypothesis / Definition

A hypothesis is like a bet:  you size things up and tell your mates exactly what you think is going to happen with respect to X, Y, Z.  It can also be like an explanation for a phenomenon, or a logical prediction of a possible causal correlation among multiple factors. In science—or, really, in any field, a hypothesis is used as a basis for further investigation.  For example, many qualitative or exploratory studies are conducted just so that the researcher in the end can formulate a hypothesis after all the data is collected an analyzed.

In short, it is an educated guess, based on existing knowledge or observation.  It is a way of proposing a possible explanation for a relationship between variables.

One thing to remember is this:  the key characteristic of a hypothesis is that it must be testable and potentially falsifiable. This means that it should be possible to design an experiment or observation that could potentially prove the hypothesis wrong.  That is a very important point to keep in mind.

For that reason, hypotheses are usually only formulated after conducting a preliminary review of existing literature, observations, or after obtaining a general understanding of the subject area. They are not random guesses.  They are grounded in some form of evidence or understanding of the phenomena being studied. The formulation of a hypothesis is a big step in the scientific method, as it defines the focus and direction of the research.  A lot of time is often spent simply on developing a good hypothesis.

Why?  A well-constructed hypothesis not only proposes an explanation for an observation but also often predicts measurable and testable outcomes. It is not merely a question, but rather a statement that includes a clear explanation or prediction. For example, rather than asking “Does temperature affect the growth of bacteria?”, a hypothesis would be something like this:  “If the temperature increases, then the growth rate of bacteria will increase.”  It is clear, measurable, testable, and potentially falsifiable.

In the scientific community, a hypothesis is respected when it has the potential to advance knowledge, regardless of whether testing proves it to be true or false. The process of testing, refining, or nullifying hypotheses through experimentation and observation is part of what research is all about.

hypothesis essays

 Different types of Hypotheses

Hypotheses can be categorized into several types.  Each type has a unique purpose in scientific research.  Understanding these types is helpful for formulating a hypothesis that is appropriate to your specific research question. The main types of hypotheses include the following:

  • Simple Hypothesis : This formulates a relationship between two variables, one independent and one dependent. It is straightforward and concise, making it easy to test.  It is most often used in basic scientific experiments where the aim is to investigate the relationship between two variables, such as in laboratory experiments or controlled field studies.
  • Complex Hypothesis : Unlike the simple hypothesis, a complex hypothesis involves multiple independent and dependent variables. It is used in studies that are looking at several factors simultaneously, where there is an interplay of multiple variables. These are common in fields like social sciences, behavioral studies, and large-scale environmental research.
  • Directional Hypothesis : This type predicts the nature of the effect of the independent variable on the dependent variable. It specifies the direction of the expected relationship.  It tends to be used studies where prior research or theory has already suggested a specific direction of influence or effect, such as in clinical trials or in studies testing theoretical models.
  • Non-directional Hypothesis : In contrast to the directional hypothesis, a non-directional hypothesis does not specify the direction of the relationship. It simply suggests that there is a relationship between variables without stating whether it is positive or negative.  It is often used in exploratory research where the direction of the relationship is not known, such as in early-stage psychological research or when studying new phenomena.
  • Null Hypothesis : The null hypothesis states that there is no relationship between the variables being studied. It is a default position that assumes no effect until evidence suggests otherwise.  It is also a fundamental aspect of virtually all quantitative research, serving as the hypothesis that there is no effect or no difference, against which the alternative hypothesis is tested.
  • Associative and Causal Hypotheses : Associative hypotheses propose a relationship between variables where changes in one variable correspond with changes in another.  They are common in observational studies, such as epidemiological research or surveys, where the goal is to identify correlations between variables.  Causal hypotheses go a step further by suggesting that one variable causes the change in the other.  They are used in experimental research designed to determine cause-and-effect relationships, such as randomized controlled trials in medical research or controlled experiments in psychology.

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How to Write a Good Hypothesis

Writing a good hypothesis is definitely a good skill to have in scientific research. But it is also one that you can definitely learn with some practice if you don’t already have it.  Just keep in mind that the hypothesis is what sets the stage for the entire investigation.  It guides the methods and analysis.  Everything you do in research stems from your research question and hypothesis.

Here are four essential steps to follow when crafting a hypothesis:

  • Start with a Research Question

Every hypothesis begins with a clear, focused research question. This question should arise from a review of existing literature, some observations you have made in the field, or an information gap that is apparent in current knowledge. The question should be specific and researchable.  For example, instead of a broad question like “What affects plant growth?”, a more specific question would be “How does the amount of water affect the growth of sunflowers?”  This is a specific question, and sets up a stage for a perfect hypothesis.

How did you develop the question?  Easy.  You simply took a broad view first, and then began looking more closely.  You looked into the subject matter.  And, as with anything, the more you look into it, the more likely you are to have questions.  So, the most important step here is to get a sense of your subject.  The more you learn about it, the more likely you will be to have a good research question.  Ask yourself:  what about this subject would I like to know more about?  It helps if you have a genuine interest in the topic!  Say, for example, you want to know more about cryptocurrency security or scalability:  wouldn’t you start asking questions about how to achieve either?  And wouldn’t you need to know a bit about the topic before you can ask the right question?  Of course!  Apply that same logic to whatever subject you are researching and your research question will appear rather quickly.

  • Do Preliminary Research

Before formulating your hypothesis, you of course should conduct preliminary research. This involves reviewing existing literature, understanding the current state of knowledge in the field, doing some critical thinking on the subject, and considering any existing theories and findings that might be relevant. This preliminary research helps in developing an educated guess.  If you do your background research well, your hypothesis will be grounded in existing knowledge.

This is basically the step that comes after you ask your research question but before you make a prediction about the subject matter.  Just like if you went to a racetrack and wanted to place a bet on a horse, you would research the horses, the owners, the teams, and make an educated guess about which one is most likely to win, doing preliminary research is the same:  you want to become very familiar with the topic—know it inside and out.  Then you will have everything you need to formulate your hypothesis.

  • Formulate the Hypothesis

Based on your research question and preliminary research, now you can create your hypothesis. A good hypothesis should be clear, concise, and testable. It typically takes a statement form, predicting a potential outcome or relationship between variables. Make sure that your hypothesis is focused and answers your research question.  For example, a hypothesis for the research question stated above might be:   “If sunflower plants are watered with varying amounts of water, then those watered more frequently will grow taller due to better hydration.”

Keep in mind that when you reach the stage of formulating your hypothesis, you are essentially ready to make a statement that can be tested through research or experimentation. Your hypothesis should be as precise as possible. Don’t ever use ambiguous language in your hypothesis.  Also, you should be very specific about the variables involved and the expected relationship between them (if applicable).  For example, let’s look at the hypothesis we generated above:  “If sunflower plants are watered with varying amounts of water, then those watered more frequently will grow taller due to better hydration.”  We have clearly identified the variables (frequency of watering and plant growth height) and the expected outcome.

But what else should your hypothesis do?  Well, when we say it should address your research question, we mean it should be a logical extension of the question and your preliminary research.  If your research question is about the effect of watering frequency on sunflower growth, your hypothesis should specifically predict how these two variables are related.  It should not get into the types of soil, sunshine, temperature, or other variables unless these were brought up specifically in your research question.

Above all, you want your hypothesis to make a prediction. This means stating an expected outcome based on your understanding of the subject. The prediction is what will be tested through experiments or observations.

  • Ensure Testability and Falsifiability

An important aspect of a good hypothesis is that it must be testable and potentially falsifiable. This means you should be able to conduct experiments or make observations that can support or refute the hypothesis. Avoid vague or broad statements that cannot be empirically tested.  Also, make sure that your hypothesis is potentially falsifiable; i.e., there should exist the possibility that it can be proven wrong.  For example, a hypothesis like “Sunflower plants need water to grow” is not falsifiable, as it is already a well-established fact.  But a hypothesis regarding frequency or amount of watering does have the potential to be nullified.

Therefore, keep that in mind during this step:  for a hypothesis to be testable, there must be a way to conduct an experiment or make observations that can confirm or disprove it. This means you should be able to measure or observe the variables involved. In the sunflower example, you can measure plant growth and control the frequency of watering very easily.  This is precisely what makes the hypothesis testable.

Another important point is falsifiability, as this is what separates scientific hypotheses from non-scientific ones.  If it doesn’t have the potential to be proven wrong, it’s not a hypothesis.  Being falsifiable doesn’t mean a hypothesis is false. It means that if the hypothesis is false, there is a way to demonstrate this. The potential for falsification is what allows researchers to make scientific progress no matter the problem or field.

Also, don’t be vague.  Your hypothesis needs to be specific: hypotheses that are too vague or broad are not useful in research, as there is no way to test them.  For example, saying “Water affects plant growth” is too vague.  How does water affect growth?  Is it the amount, frequency, or type of water?  Such a hypothesis needs to be more specific to be testable.  See what we mean?

Remember:   A hypothesis does not need to be correct.  It just needs to be testable.  It is a starting point for investigation. The value of a hypothesis lies in its ability to be tested.  The results of that test are what can potentially contribute to the existing body of scientific knowledge, regardless of whether the hypothesis is supported or refuted by the resulting data.

hypothesis examples

Hypothesis Examples

Simple hypothesis examples.

  • Increasing the amount of natural light in a classroom will improve students’ test scores.
  • Drinking at least eight glasses of water a day reduces the frequency of headaches in adults.
  • Plant growth is faster when the plant is exposed to music for at least one hour per day.

Complex Hypothesis Examples

  • Students’ academic performance is influenced by their study habits, family income, and the educational level of their parents.
  • Employee productivity is affected by workplace environment, job satisfaction, and the level of personal stress the worker encounters both on the job and at home.
  • The effectiveness of a weight loss program is dependent on the participant’s age, gender, and adherence to an appropriate diet plan.

Directional Hypothesis Examples

  • Exposure to high levels of air pollution during pregnancy will increase the risk of asthma in children.
  • A diet high in antioxidants will decrease the risk of heart disease in middle-aged adults.
  • Regular physical exercise leads to a significant decrease in the symptoms of depression in adults.

Non-directional Hypothesis Examples

  • There is a relationship between the amount of sleep a person gets and their level of stress.
  • A change in classroom environment has an effect on student concentration.
  • The introduction of ergonomics in the workplace environment impacts employee productivity.

Null Hypothesis Examples

  • There is no significant difference in test scores between students who study in groups and those who study alone.
  • Dietary changes have no effect on the improvement of symptoms in patients with type 2 diabetes.
  • The new marketing strategy does not affect the sales numbers of the product.

Associative Hypothesis Examples

  • There is an association between the number of hours spent on social media and the level of anxiety in teenagers.
  • Daily consumption of green tea is associated with weight loss in adults.
  • The frequency of public transport use correlates with the level of urban air pollution.

Causal Hypotheses Examples

  • Implementing a school-based exercise program causes a reduction in obesity rates among children.
  • High levels of job stress cause an increase in blood pressure.
  • Smoking causes an increase in the risk of developing lung cancer.

In conclusion, understanding and effectively formulating a solid hypothesis is what scientific research and inquiry is all about—regardless of the type of work you’re doing.  It may be a simple, complex, directional, non-directional, null, associative, or causal hypothesis—no matter:  each type has its own specific purpose and guides the direction of a study in a different way. A simple hypothesis explores the relationship between two variables, while a complex hypothesis involves multiple variables. Directional hypotheses specify the expected direction of a relationship, whereas non-directional hypotheses do not. The null hypothesis, a fundamental aspect of statistical testing, posits no effect or relationship, serving as a baseline for analysis. Associative hypotheses explore correlations between variables, and causal hypotheses aim to establish cause-and-effect relationships.

The ability to craft a clear, concise, and testable hypothesis is important for any researcher. It is what shapes the course of the investigation.  It is also the backbone of the scientific method itself. A well-formulated hypothesis can lead to groundbreaking research or make significant contributions to knowledge in different fields.

As we have shown you with our examples, the hypothesis is more than a mere guess; it is an educated, testable prediction that guides you through the process of scientific discovery. When you master the art of hypothesis formulation, you can set off on your investigation with a clear roadmap and a clear sense of purpose.

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How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

Research question Hypothesis Null hypothesis
What are the health benefits of eating an apple a day? Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits.
Which airlines have the most delays? Low-cost airlines are more likely to have delays than premium airlines. Low-cost and premium airlines are equally likely to have delays.
Can flexible work arrangements improve job satisfaction? Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. There is no relationship between working hour flexibility and job satisfaction.
How effective is secondary school sex education at reducing teen pregnancies? Teenagers who received sex education lessons throughout secondary school will have lower rates of unplanned pregnancy than teenagers who did not receive any sex education. Secondary school sex education has no effect on teen pregnancy rates.
What effect does daily use of social media have on the attention span of under-16s? There is a negative correlation between time spent on social media and attention span in under-16s. There is no relationship between social media use and attention span in under-16s.

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

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

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

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

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How to Write a Hypothesis? Types and Examples 

how to write a hypothesis for research

All research studies involve the use of the scientific method, which is a mathematical and experimental technique used to conduct experiments by developing and testing a hypothesis or a prediction about an outcome. Simply put, a hypothesis is a suggested solution to a problem. It includes elements that are expressed in terms of relationships with each other to explain a condition or an assumption that hasn’t been verified using facts. 1 The typical steps in a scientific method include developing such a hypothesis, testing it through various methods, and then modifying it based on the outcomes of the experiments.  

A research hypothesis can be defined as a specific, testable prediction about the anticipated results of a study. 2 Hypotheses help guide the research process and supplement the aim of the study. After several rounds of testing, hypotheses can help develop scientific theories. 3 Hypotheses are often written as if-then statements. 

Here are two hypothesis examples: 

Dandelions growing in nitrogen-rich soils for two weeks develop larger leaves than those in nitrogen-poor soils because nitrogen stimulates vegetative growth. 4  

If a company offers flexible work hours, then their employees will be happier at work. 5  

Table of Contents

  • What is a hypothesis? 
  • Types of hypotheses 
  • Characteristics of a hypothesis 
  • Functions of a hypothesis 
  • How to write a hypothesis 
  • Hypothesis examples 
  • Frequently asked questions 

What is a hypothesis?

Figure 1. Steps in research design

A hypothesis expresses an expected relationship between variables in a study and is developed before conducting any research. Hypotheses are not opinions but rather are expected relationships based on facts and observations. They help support scientific research and expand existing knowledge. An incorrectly formulated hypothesis can affect the entire experiment leading to errors in the results so it’s important to know how to formulate a hypothesis and develop it carefully.

A few sources of a hypothesis include observations from prior studies, current research and experiences, competitors, scientific theories, and general conditions that can influence people. Figure 1 depicts the different steps in a research design and shows where exactly in the process a hypothesis is developed. 4  

There are seven different types of hypotheses—simple, complex, directional, nondirectional, associative and causal, null, and alternative. 

Types of hypotheses

The seven types of hypotheses are listed below: 5 , 6,7  

  • Simple : Predicts the relationship between a single dependent variable and a single independent variable. 

Example: Exercising in the morning every day will increase your productivity.  

  • Complex : Predicts the relationship between two or more variables. 

Example: Spending three hours or more on social media daily will negatively affect children’s mental health and productivity, more than that of adults.  

  • Directional : Specifies the expected direction to be followed and uses terms like increase, decrease, positive, negative, more, or less. 

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

  • Non-directional : Does not predict the exact direction, nature, or magnitude of the relationship between two variables but rather states the existence of a relationship. This hypothesis may be used when there is no underlying theory or if findings contradict prior research. 

Example: Cats and dogs differ in the amount of affection they express.  

  • Associative and causal : An associative hypothesis suggests an interdependency between variables, that is, how a change in one variable changes the other.  

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

A causal hypothesis, on the other hand, expresses a cause-and-effect association between variables. 

Example: Long-term alcohol use causes liver damage.  

  • Null : Claims that the original hypothesis is false by showing that there is no relationship between the variables. 

Example: Sleep duration does not have any effect on productivity.  

  • Alternative : States the opposite of the null hypothesis, that is, a relationship exists between two variables. 

Example: Sleep duration affects productivity.  

how to write a math hypothesis

Characteristics of a hypothesis

So, what makes a good hypothesis? Here are some important characteristics of a hypothesis. 8,9  

  • Testable : You must be able to test the hypothesis using scientific methods to either accept or reject the prediction. 
  • Falsifiable : It should be possible to collect data that reject rather than support the hypothesis. 
  • Logical : Hypotheses shouldn’t be a random guess but rather should be based on previous theories, observations, prior research, and logical reasoning. 
  • Positive : The hypothesis statement about the existence of an association should be positive, that is, it should not suggest that an association does not exist. Therefore, the language used and knowing how to phrase a hypothesis is very important. 
  • Clear and accurate : The language used should be easily comprehensible and use correct terminology. 
  • Relevant : The hypothesis should be relevant and specific to the research question. 
  • Structure : Should include all the elements that make a good hypothesis: variables, relationship, and outcome. 

Functions of a hypothesis

The following list mentions some important functions of a hypothesis: 1  

  • Maintains the direction and progress of the research. 
  • Expresses the important assumptions underlying the proposition in a single statement. 
  • Establishes a suitable context for researchers to begin their investigation and for readers who are referring to the final report. 
  • Provides an explanation for the occurrence of a specific phenomenon. 
  • Ensures selection of appropriate and accurate facts necessary and relevant to the research subject. 

To summarize, a hypothesis provides the conceptual elements that complete the known data, conceptual relationships that systematize unordered elements, and conceptual meanings and interpretations that explain the unknown phenomena. 1  

how to write a math hypothesis

How to write a hypothesis

Listed below are the main steps explaining how to write a hypothesis. 2,4,5  

  • Make an observation and identify variables : Observe the subject in question and try to recognize a pattern or a relationship between the variables involved. This step provides essential background information to begin your research.  

For example, if you notice that an office’s vending machine frequently runs out of a specific snack, you may predict that more people in the office choose that snack over another. 

  • Identify the main research question : After identifying a subject and recognizing a pattern, the next step is to ask a question that your hypothesis will answer.  

For example, after observing employees’ break times at work, you could ask “why do more employees take breaks in the morning rather than in the afternoon?” 

  • Conduct some preliminary research to ensure originality and novelty : Your initial answer, which is your hypothesis, to the question is based on some pre-existing information about the subject. However, to ensure that your hypothesis has not been asked before or that it has been asked but rejected by other researchers you would need to gather additional information.  

For example, based on your observations you might state a hypothesis that employees work more efficiently when the air conditioning in the office is set at a lower temperature. However, during your preliminary research you find that this hypothesis was proven incorrect by a prior study. 

  • Develop a general statement : After your preliminary research has confirmed the originality of your proposed answer, draft a general statement that includes all variables, subjects, and predicted outcome. The statement could be if/then or declarative.  
  • Finalize the hypothesis statement : Use the PICOT model, which clarifies how to word a hypothesis effectively, when finalizing the statement. This model lists the important components required to write a hypothesis. 

P opulation: The specific group or individual who is the main subject of the research 

I nterest: The main concern of the study/research question 

C omparison: The main alternative group 

O utcome: The expected results  

T ime: Duration of the experiment 

Once you’ve finalized your hypothesis statement you would need to conduct experiments to test whether the hypothesis is true or false. 

Hypothesis examples

The following table provides examples of different types of hypotheses. 10 ,11  

   
Null Hyperactivity is not related to eating sugar. 
There is no relationship between height and shoe size. 
Alternative Hyperactivity is positively related to eating sugar. 
There is a positive association between height and shoe size. 
Simple Students who eat breakfast perform better in exams than students who don’t eat breakfast. 
Reduced screen time improves sleep quality. 
Complex People with high-sugar diet and sedentary activity levels are more likely to develop depression. 
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. 
Directional As job satisfaction increases, the rate of employee turnover decreases. 
Increase in sun exposure increases the risk of skin cancer. 
Non-directional College students will perform differently from elementary school students on a memory task. 
Advertising exposure correlates with variations in purchase decisions among consumers. 
Associative Hospitals have more sick people in them than other institutions in society. 
Watching TV is related to increased snacking. 
Causal Inadequate sleep decreases memory retention. 
Recreational drugs cause psychosis. 

how to write a math hypothesis

Key takeaways  

Here’s a summary of all the key points discussed in this article about how to write a hypothesis. 

  • A hypothesis is an assumption about an association between variables made based on limited evidence, which should be tested. 
  • A hypothesis has four parts—the research question, independent variable, dependent variable, and the proposed relationship between the variables.   
  • The statement should be clear, concise, testable, logical, and falsifiable. 
  • There are seven types of hypotheses—simple, complex, directional, non-directional, associative and causal, null, and alternative. 
  • A hypothesis provides a focus and direction for the research to progress. 
  • A hypothesis plays an important role in the scientific method by helping to create an appropriate experimental design. 

Frequently asked questions

Hypotheses and research questions have different objectives and structure. The following table lists some major differences between the two. 9  

   
Includes a prediction based on the proposed research No prediction is made  
Designed to forecast the relationship of and between two or more variables Variables may be explored 
Closed ended Open ended, invites discussion 
Used if the research topic is well established and there is certainty about the relationship between the variables Used for new topics that haven’t been researched extensively. The relationship between different variables is less known 

Here are a few examples to differentiate between a research question and hypothesis. 

   
What is the effect of eating an apple a day by adults aged over 60 years on the frequency of physician visits?  Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits 
What is the effect of flexible or fixed working hours on employee job satisfaction? Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours. 
Does drinking coffee in the morning affect employees’ productivity? Drinking coffee in the morning improves employees’ productivity. 

Yes, here’s a simple checklist to help you gauge the effectiveness of your hypothesis. 9   1. When writing a hypothesis statement, check if it:  2. Predicts the relationship between the stated variables and the expected outcome.  3. Uses simple and concise language and is not wordy.  4. Does not assume readers’ knowledge about the subject.  5. Has observable, falsifiable, and testable results. 

As mentioned earlier in this article, a hypothesis is an assumption or prediction about an association between variables based on observations and simple evidence. These statements are usually generic. Research objectives, on the other hand, are more specific and dictated by hypotheses. The same hypothesis can be tested using different methods and the research objectives could be different in each case.     For example, Louis Pasteur observed that food lasts longer at higher altitudes, reasoned that it could be because the air at higher altitudes is cleaner (with fewer or no germs), and tested the hypothesis by exposing food to air cleaned in the laboratory. 12 Thus, a hypothesis is predictive—if the reasoning is correct, X will lead to Y—and research objectives are developed to test these predictions. 

Null hypothesis testing is a method to decide between two assumptions or predictions between variables (null and alternative hypotheses) in a statistical relationship in a sample. The null hypothesis, denoted as H 0 , claims that no relationship exists between variables in a population and any relationship in the sample reflects a sampling error or occurrence by chance. The alternative hypothesis, denoted as H 1 , claims that there is a relationship in the population. In every study, researchers need to decide whether the relationship in a sample occurred by chance or reflects a relationship in the population. This is done by hypothesis testing using the following steps: 13   1. Assume that the null hypothesis is true.  2. Determine how likely the sample relationship would be if the null hypothesis were true. This probability is called the p value.  3. If the sample relationship would be extremely unlikely, reject the null hypothesis and accept the alternative hypothesis. If the relationship would not be unlikely, accept the null hypothesis. 

how to write a math hypothesis

To summarize, researchers should know how to write a good hypothesis to ensure that their research progresses in the required direction. A hypothesis is a testable prediction about any behavior or relationship between variables, usually based on facts and observation, and states an expected outcome.  

We hope this article has provided you with essential insight into the different types of hypotheses and their functions so that you can use them appropriately in your next research project. 

References  

  • Dalen, DVV. The function of hypotheses in research. Proquest website. Accessed April 8, 2024. https://www.proquest.com/docview/1437933010?pq-origsite=gscholar&fromopenview=true&sourcetype=Scholarly%20Journals&imgSeq=1  
  • McLeod S. Research hypothesis in psychology: Types & examples. SimplyPsychology website. Updated December 13, 2023. Accessed April 9, 2024. https://www.simplypsychology.org/what-is-a-hypotheses.html  
  • Scientific method. Britannica website. Updated March 14, 2024. Accessed April 9, 2024. https://www.britannica.com/science/scientific-method  
  • The hypothesis in science writing. Accessed April 10, 2024. https://berks.psu.edu/sites/berks/files/campus/HypothesisHandout_Final.pdf  
  • How to develop a hypothesis (with elements, types, and examples). Indeed.com website. Updated February 3, 2023. Accessed April 10, 2024. https://www.indeed.com/career-advice/career-development/how-to-write-a-hypothesis  
  • Types of research hypotheses. Excelsior online writing lab. Accessed April 11, 2024. https://owl.excelsior.edu/research/research-hypotheses/types-of-research-hypotheses/  
  • What is a research hypothesis: how to write it, types, and examples. Researcher.life website. Published February 8, 2023. Accessed April 11, 2024. https://researcher.life/blog/article/how-to-write-a-research-hypothesis-definition-types-examples/  
  • Developing a hypothesis. Pressbooks website. Accessed April 12, 2024. https://opentext.wsu.edu/carriecuttler/chapter/developing-a-hypothesis/  
  • What is and how to write a good hypothesis in research. Elsevier author services website. Accessed April 12, 2024. https://scientific-publishing.webshop.elsevier.com/manuscript-preparation/what-how-write-good-hypothesis-research/  
  • How to write a great hypothesis. Verywellmind website. Updated March 12, 2023. Accessed April 13, 2024. https://www.verywellmind.com/what-is-a-hypothesis-2795239  
  • 15 Hypothesis examples. Helpfulprofessor.com Published September 8, 2023. Accessed March 14, 2024. https://helpfulprofessor.com/hypothesis-examples/ 
  • Editage insights. What is the interconnectivity between research objectives and hypothesis? Published February 24, 2021. Accessed April 13, 2024. https://www.editage.com/insights/what-is-the-interconnectivity-between-research-objectives-and-hypothesis  
  • Understanding null hypothesis testing. BCCampus open publishing. Accessed April 16, 2024. https://opentextbc.ca/researchmethods/chapter/understanding-null-hypothesis-testing/#:~:text=In%20null%20hypothesis%20testing%2C%20this,said%20to%20be%20statistically%20significant  

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How to Write a Strong Hypothesis in 6 Simple Steps

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A hypothesis is an important part of the scientific method. It’s an idea or a proposal based on limited evidence. What comes next is the exciting part. The idea or proposal must be proven through facts, direct testing and evidence. Since the hypothesis acts as the foundation for future research, learn how to write a hypothesis through steps and examples.

What Is a Hypothesis Statement?

A hypothesis statement tells the world what you predict will happen in research. One of the most important elements of a hypothesis is that it must be able to be tested . Sure, you might hypothesize that unicorn horns are made of white gold. But, if you can’t test the independent and dependent variables , your hypothesis will have to remain in your dreams.

If, however, you hypothesize that rose quartz and other crystals possess healing powers, then you might be able to perform a few tests and carry on with your hypothesis. You will have some evidence that either supports or does not support your hypothesis. Now that you know what it is, it’s time to learn how to write a hypothesis.

Steps for How to Write a Hypothesis

When it comes to writing a hypothesis, there are six basic steps:

  • Ask a question.
  • Gather preliminary research.
  • Formulate an answer.
  • Write a hypothesis.
  • Refine your hypothesis.
  • Create a null hypothesis.

1. Ask a Question

In the scientific method , the first step is to ask a question. Frame this question using the classic six: who, what, where, when, why, or how. Sample questions might include:

  • How long does it take carrots to grow?
  • Why does the sky get darker earlier in winter?
  • What happened to the dinosaurs?
  • How did we evolve from monkeys?
  • Why are students antsier on Friday afternoon?
How does sleep affect motivation?
  • Why do IEP accommodations work in schools?

You want the question to be specific and focused. It also needs to be researchable, of course. Once you know you can research your question from several angles, it’s time to start some preliminary research.

2. Gather Preliminary Research

It’s time to collect data. This will come in the form of case studies and academic journals , as well as your own experiments and observations .

Remember, it’s important to explore your question from all sides. Don’t let conflicting research deter you. You might come upon many naysayers as you gather background information. That doesn’t invalidate your hypothesis. In fact, you can use their findings as potential rebuttals and frame your study in such a way as to address these concerns.

For example, if you are looking at the question: "How does sleep affect motivation?", you might find studies with conflicting research about eight hours vs. six hours of sleep. You can use these conflicting points to help to guide the creation of your hypothesis.

3. Formulate an Answer To Your Question

After completing all your research, think about how you will answer your question and defend your position. For example, say the question you posed was:

As you start to collect basic observations and information, you'll find that a lack of sleep creates a negative impact on learning. It decreases thought processes and makes it harder to learn anything new. Therefore, when you are tired, it's harder to learn and requires more effort. Since it is harder, you can be less motivated to do it. Additionally, you discover that there is a point where sleep affects functioning. You use this research to answer your question.

Getting less than eight hours of sleep makes it harder to learn anything new and make new memories. This makes learning harder so you are less likely to be motivated.

4. Write a Hypothesis

With the answer to your question at the ready, it’s time to formulate your hypothesis. To write a good hypothesis, it should include:

  • Relevant variables
  • Predicted outcome
  • Who/what is being studied

Remember that your hypothesis needs to be a statement, not a question. It’s an idea, proposal or prediction. For example, a research hypothesis is formatted in an if/then statement:

If a person gets less than eight hours of sleep, then they will be less motivated at work or school.

This statement shows you:

  • who is being studied - a person
  • the variables - sleep and motivation
  • your prediction - less sleep means less motivation

5. Refine Your Hypothesis

While you might be able to stop at writing your research hypothesis, some hypotheses might be a correlation study or studying the difference between two groups. In these instances, you want to state the relationship or difference you expect to find.

A correlation hypothesis might be:

Getting less than eight hours of sleep has a negative impact on work or school motivation.

A hypothesis showing difference might be:

Those with seven or fewer hours of sleep are less motivated than those with eight or more to complete tasks.

6. Create a Null Hypothesis

Depending on your study, you may need to perform some statistical analysis on the data you collect. When forming your hypothesis statement using the scientific method, it’s important to know the difference between a null hypothesis vs. the alternative hypothesis, and how to create a null hypothesis.

  • A null hypothesis , often denoted as H 0 , posits that there is no apparent difference or that there is no evidence to support a difference. Using the motivation example above, the null hypothesis would be that sleep hours have no effect on motivation.
  • An alternative hypothesis , often denoted as H 1 , states that there is a statistically significant difference, or there is evidence to support such a difference. Going back to the same carrot example, the alternative hypothesis is that a person getting six hours of sleep has less motivation than someone getting eight hours of sleep.

Good and Bad Hypothesis Examples

Here are a few examples of good and bad hypotheses to get you started.

How long does it take carrots to grow?

If we plant carrots deep in the soil, it will take them longer to grow than in shallow soil.

You can plant carrots deep in the soil. (There’s no predicted outcome.)

Why does the sky get darker earlier in winter?

The Earth's rotation affects the number of daylight hours.

The sun goes down. (This doesn’t clarify variables or what will be studied.)

What happened to the dinosaurs?

If we study marine fossils found in the Arctic, we will see that dinosaurs disappeared when a comet hit the Earth.

Extinction happened thousands of years ago. (This does not name what is being studied nor present clear variables for studying dinosaur history.)

How did we evolve from monkeys?

Human beings are not descended from apes, but share a common ancestor with them.

Human evolution is long. (This does not present clear variables to be studied or a prediction to be tested.)

Why are students antsier on Friday afternoon?

Students are anticipating the coming of the weekend, making them antsier on Friday afternoon.

Students have bad behavior. (This isn't showing what is being tested or clear variables.)

How does sleep affect motivation?

If a person gets less than eight hours of sleep, then they will be less motivated at work or school.

Sleep is important. (While this might be true, it's not setting the variables for the study.)

Why do IEP accommodations work in schools?

If a student gets accommodations for their learning disability, then they will perform better in school.

Accommodations help students. (Again, while this might be true, it's not providing what is being studied or the variables.)

Tips for Writing a Hypothesis

To write a strong hypothesis, keep these important tips in mind.

  • Don’t just choose a topic randomly. Find something that interests you.
  • Keep it clear and to the point.
  • Use your research to guide you.
  • Always clearly define your variables.
  • Write it as an if-then statement. If this, then that is the expected outcome.

How to Make a Hypothesis

A hypothesis involves a statement about what you will do, but also what you expect to happen or speculation about what could occur. Once you’ve written your hypothesis, you’ll need to test it, analyze the data and form your conclusion. To read more about hypothesis testing, explore good examples of hypothesis testing .

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Understanding Hypotheses

how to write a math hypothesis

'What happens if ... ?' to ' This will happen if'

The experimentation of children continually moves on to the exploration of new ideas and the refinement of their world view of previously understood situations. This description of the playtime patterns of young children very nicely models the concept of 'making and testing hypotheses'. It follows this pattern:

  • Make some observations. Collect some data based on the observations.
  • Draw a conclusion (called a 'hypothesis') which will explain the pattern of the observations.
  • Test out your hypothesis by making some more targeted observations.

So, we have

  • A hypothesis is a statement or idea which gives an explanation to a series of observations.

Sometimes, following observation, a hypothesis will clearly need to be refined or rejected. This happens if a single contradictory observation occurs. For example, suppose that a child is trying to understand the concept of a dog. He reads about several dogs in children's books and sees that they are always friendly and fun. He makes the natural hypothesis in his mind that dogs are friendly and fun . He then meets his first real dog: his neighbour's puppy who is great fun to play with. This reinforces his hypothesis. His cousin's dog is also very friendly and great fun. He meets some of his friends' dogs on various walks to playgroup. They are also friendly and fun. He is now confident that his hypothesis is sound. Suddenly, one day, he sees a dog, tries to stroke it and is bitten. This experience contradicts his hypothesis. He will need to amend the hypothesis. We see that

  • Gathering more evidence/data can strengthen a hypothesis if it is in agreement with the hypothesis.
  • If the data contradicts the hypothesis then the hypothesis must be rejected or amended to take into account the contradictory situation.

how to write a math hypothesis

  • A contradictory observation can cause us to know for certain that a hypothesis is incorrect.
  • Accumulation of supporting experimental evidence will strengthen a hypothesis but will never let us know for certain that the hypothesis is true.

In short, it is possible to show that a hypothesis is false, but impossible to prove that it is true!

Whilst we can never prove a scientific hypothesis to be true, there will be a certain stage at which we decide that there is sufficient supporting experimental data for us to accept the hypothesis. The point at which we make the choice to accept a hypothesis depends on many factors. In practice, the key issues are

  • What are the implications of mistakenly accepting a hypothesis which is false?
  • What are the cost / time implications of gathering more data?
  • What are the implications of not accepting in a timely fashion a true hypothesis?

For example, suppose that a drug company is testing a new cancer drug. They hypothesise that the drug is safe with no side effects. If they are mistaken in this belief and release the drug then the results could have a disastrous effect on public health. However, running extended clinical trials might be very costly and time consuming. Furthermore, a delay in accepting the hypothesis and releasing the drug might also have a negative effect on the health of many people.

In short, whilst we can never achieve absolute certainty with the testing of hypotheses, in order to make progress in science or industry decisions need to be made. There is a fine balance to be made between action and inaction.

Hypotheses and mathematics So where does mathematics enter into this picture? In many ways, both obvious and subtle:

  • A good hypothesis needs to be clear, precisely stated and testable in some way. Creation of these clear hypotheses requires clear general mathematical thinking.
  • The data from experiments must be carefully analysed in relation to the original hypothesis. This requires the data to be structured, operated upon, prepared and displayed in appropriate ways. The levels of this process can range from simple to exceedingly complex.

Very often, the situation under analysis will appear to be complicated and unclear. Part of the mathematics of the task will be to impose a clear structure on the problem. The clarity of thought required will actively be developed through more abstract mathematical study. Those without sufficient general mathematical skill will be unable to perform an appropriate logical analysis.

Using deductive reasoning in hypothesis testing

There is often confusion between the ideas surrounding proof, which is mathematics, and making and testing an experimental hypothesis, which is science. The difference is rather simple:

  • Mathematics is based on deductive reasoning : a proof is a logical deduction from a set of clear inputs.
  • Science is based on inductive reasoning : hypotheses are strengthened or rejected based on an accumulation of experimental evidence.

Of course, to be good at science, you need to be good at deductive reasoning, although experts at deductive reasoning need not be mathematicians. Detectives, such as Sherlock Holmes and Hercule Poirot, are such experts: they collect evidence from a crime scene and then draw logical conclusions from the evidence to support the hypothesis that, for example, Person M. committed the crime. They use this evidence to create sufficiently compelling deductions to support their hypotheses beyond reasonable doubt . The key word here is 'reasonable'. There is always the possibility of creating an exceedingly outlandish scenario to explain away any hypothesis of a detective or prosecution lawyer, but judges and juries in courts eventually make the decision that the probability of such eventualities are 'small' and the chance of the hypothesis being correct 'high'.

how to write a math hypothesis

  • If a set of data is normally distributed with mean 0 and standard deviation 0.5 then there is a 97.7% certainty that a measurement will not exceed 1.0.
  • If the mean of a sample of data is 12, how confident can we be that the true mean of the population lies between 11 and 13?

It is at this point that making and testing hypotheses becomes a true branch of mathematics. This mathematics is difficult, but fascinating and highly relevant in the information-rich world of today.

To read more about the technical side of hypothesis testing, take a look at What is a Hypothesis Test?

You might also enjoy reading the articles on statistics on the Understanding Uncertainty website

This resource is part of the collection Statistics - Maths of Real Life

Learn How To Write A Hypothesis For Your Next Research Project!

blog image

Undoubtedly, research plays a crucial role in substantiating or refuting our assumptions. These assumptions act as potential answers to our questions. Such assumptions, also known as hypotheses, are considered key aspects of research. In this blog, we delve into the significance of hypotheses. And provide insights on how to write them effectively. So, let’s dive in and explore the art of writing hypotheses together.

Table of Contents

What is a Hypothesis?

A hypothesis is a crucial starting point in scientific research. It is an educated guess about the relationship between two or more variables. In other words, a hypothesis acts as a foundation for a researcher to build their study.

Here are some examples of well-crafted hypotheses:

  • Increased exposure to natural sunlight improves sleep quality in adults.

A positive relationship between natural sunlight exposure and sleep quality in adult individuals.

  • Playing puzzle games on a regular basis enhances problem-solving abilities in children.

Engaging in frequent puzzle gameplay leads to improved problem-solving skills in children.

  • Students and improved learning hecks.

S tudents using online  paper writing service  platforms (as a learning tool for receiving personalized feedback and guidance) will demonstrate improved writing skills. (compared to those who do not utilize such platforms).

  • The use of APA format in research papers. 

Using the  APA format  helps students stay organized when writing research papers. Organized students can focus better on their topics and, as a result, produce better quality work.

The Building Blocks of a Hypothesis

To better understand the concept of a hypothesis, let’s break it down into its basic components:

  • Variables . A hypothesis involves at least two variables. An independent variable and a dependent variable. The independent variable is the one being changed or manipulated, while the dependent variable is the one being measured or observed.
  • Relationship : A hypothesis proposes a relationship or connection between the variables. This could be a cause-and-effect relationship or a correlation between them.
  • Testability : A hypothesis should be testable and falsifiable, meaning it can be proven right or wrong through experimentation or observation.

Types of Hypotheses

When learning how to write a hypothesis, it’s essential to understand its main types. These include; alternative hypotheses and null hypotheses. In the following section, we explore both types of hypotheses with examples. 

Alternative Hypothesis (H1)

This kind of hypothesis suggests a relationship or effect between the variables. It is the main focus of the study. The researcher wants to either prove or disprove it. Many research divides this hypothesis into two subsections: 

  • Directional 

This type of H1 predicts a specific outcome. Many researchers use this hypothesis to explore the relationship between variables rather than the groups. 

  • Non-directional

You can take a guess from the name. This type of H1 does not provide a specific prediction for the research outcome. 

Here are some examples for your better understanding of how to write a hypothesis.

  • Consuming caffeine improves cognitive performance.  (This hypothesis predicts that there is a positive relationship between caffeine consumption and cognitive performance.)
  • Aerobic exercise leads to reduced blood pressure.  (This hypothesis suggests that engaging in aerobic exercise results in lower blood pressure readings.)
  • Exposure to nature reduces stress levels among employees.  (Here, the hypothesis proposes that employees exposed to natural environments will experience decreased stress levels.)
  • Listening to classical music while studying increases memory retention.  (This hypothesis speculates that studying with classical music playing in the background boosts students’ ability to retain information.)
  • Early literacy intervention improves reading skills in children.  (This hypothesis claims that providing early literacy assistance to children results in enhanced reading abilities.)
  • Time management in nursing students. ( Students who use a  nursing research paper writing service  have more time to focus on their studies and can achieve better grades in other subjects. )

Null Hypothesis (H0)

A null hypothesis assumes no relationship or effect between the variables. If the alternative hypothesis is proven to be false, the null hypothesis is considered to be true. Usually a null hypothesis shows no direct correlation between the defined variables. 

Here are some of the examples

  • The consumption of herbal tea has no effect on sleep quality.  (This hypothesis assumes that herbal tea consumption does not impact the quality of sleep.)
  • The number of hours spent playing video games is unrelated to academic performance.  (Here, the null hypothesis suggests that no relationship exists between video gameplay duration and academic achievement.)
  • Implementing flexible work schedules has no influence on employee job satisfaction.  (This hypothesis contends that providing flexible schedules does not affect how satisfied employees are with their jobs.)
  • Writing ability of a 7th grader is not affected by reading editorial example. ( There is no relationship between reading an  editorial example  and improving a 7th grader’s writing abilities.) 
  • The type of lighting in a room does not affect people’s mood.  (In this null hypothesis, there is no connection between the kind of lighting in a room and the mood of those present.)
  • The use of social media during break time does not impact productivity at work.  (This hypothesis proposes that social media usage during breaks has no effect on work productivity.)

As you learn how to write a hypothesis, remember that aiming for clarity, testability, and relevance to your research question is vital. By mastering this skill, you’re well on your way to conducting impactful scientific research. Good luck!

Importance of a Hypothesis in Research

A well-structured hypothesis is a vital part of any research project for several reasons:

  • It provides clear direction for the study by setting its focus and purpose.
  • It outlines expectations of the research, making it easier to measure results.
  • It helps identify any potential limitations in the study, allowing researchers to refine their approach.

In conclusion, a hypothesis plays a fundamental role in the research process. By understanding its concept and constructing a well-thought-out hypothesis, researchers lay the groundwork for a successful, scientifically sound investigation.

How to Write a Hypothesis?

Here are five steps that you can follow to write an effective hypothesis. 

Step 1: Identify Your Research Question

The first step in learning how to compose a hypothesis is to clearly define your research question. This question is the central focus of your study and will help you determine the direction of your hypothesis.

Step 2: Determine the Variables

When exploring how to write a hypothesis, it’s crucial to identify the variables involved in your study. You’ll need at least two variables:

  • Independent variable : The factor you manipulate or change in your experiment.
  • Dependent variable : The outcome or result you observe or measure, which is influenced by the independent variable.

Step 3: Build the Hypothetical Relationship

In understanding how to compose a hypothesis, constructing the relationship between the variables is key. Based on your research question and variables, predict the expected outcome or connection. This prediction should be specific, testable, and, if possible, expressed in the “If…then” format.

Step 4: Write the Null Hypothesis

When mastering how to write a hypothesis, it’s important to create a null hypothesis as well. The null hypothesis assumes no relationship or effect between the variables, acting as a counterpoint to your primary hypothesis.

Step 5: Review Your Hypothesis

Finally, when learning how to compose a hypothesis, it’s essential to review your hypothesis for clarity, testability, and relevance to your research question. Make any necessary adjustments to ensure it provides a solid basis for your study.

In conclusion, understanding how to write a hypothesis is crucial for conducting successful scientific research. By focusing on your research question and carefully building relationships between variables, you will lay a strong foundation for advancing research and knowledge in your field.

Hypothesis vs. Prediction: What’s the Difference?

Understanding the differences between a hypothesis and a prediction is crucial in scientific research. Often, these terms are used interchangeably, but they have distinct meanings and functions. This segment aims to clarify these differences and explain how to compose a hypothesis correctly, helping you improve the quality of your research projects.

Hypothesis: The Foundation of Your Research

A hypothesis is an educated guess about the relationship between two or more variables. It provides the basis for your research question and is a starting point for an experiment or observational study.

The critical elements for a hypothesis include:

  • Specificity: A clear and concise statement that describes the relationship between variables.
  • Testability: The ability to test the hypothesis through experimentation or observation.

To learn how to write a hypothesis, it’s essential to identify your research question first and then predict the relationship between the variables.

Prediction: The Expected Outcome

A prediction is a statement about a specific outcome you expect to see in your experiment or observational study. It’s derived from the hypothesis and provides a measurable way to test the relationship between variables.

Here’s an example of how to write a hypothesis and a related prediction:

  • Hypothesis: Consuming a high-sugar diet leads to weight gain.
  • Prediction: People who consume a high-sugar diet for six weeks will gain more weight than those who maintain a low-sugar diet during the same period.

Key Differences Between a Hypothesis and a Prediction

While a hypothesis and prediction are both essential components of scientific research, there are some key differences to keep in mind:

  • A hypothesis is an educated guess that suggests a relationship between variables, while a prediction is a specific and measurable outcome based on that hypothesis.
  • A hypothesis can give rise to multiple experiment or observational study predictions.

To conclude, understanding the differences between a hypothesis and a prediction, and learning how to write a hypothesis, are essential steps to form a robust foundation for your research. By creating clear, testable hypotheses along with specific, measurable predictions, you lay the groundwork for scientifically sound investigations.

Here’s a wrap-up for this guide on how to write a hypothesis. We’re confident this article was helpful for many of you. We understand that many students struggle with writing their school research . However, we hope to continue assisting you through our blog tutorial on writing different aspects of academic assignments.

For further information, you can check out our reverent blog or contact our professionals to avail amazing writing services. Paper perk experts tailor assignments to reflect your unique voice and perspectives. Our professionals make sure to stick around till your satisfaction. So what are you waiting for? Pick your required service and order away!

How to write a good hypothesis?

How to write a hypothesis in science, how to write a research hypothesis, how to write a null hypothesis, what is the format for a scientific hypothesis, how do you structure a proper hypothesis, can you provide an example of a hypothesis, what is the ideal hypothesis structure.

The ideal hypothesis structure includes the following;

  • A clear statement of the relationship between variables.
  • testable prediction.
  • falsifiability.

If your hypothesis has all of these, it is both scientifically sound and effective.

How to write a hypothesis for product management?

Writing a hypothesis for product management involves a simple process:

  • First, identify the problem or question you want to address.
  • State your assumption or belief about the solution to that problem. .
  • Make a hypothesis by predicting a specific outcome based on your assumption.
  • Make sure your hypothesis is specific, measurable, and testable.
  • Use experiments, data analysis, or user feedback to validate your hypothesis.
  • Make informed decisions for product improvement.

Following these steps will help you in effectively formulating hypotheses for product management.

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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

  • Cluster sampling
  • Stratified sampling
  • Types of interviews
  • Cohort study
  • Thematic analysis

Research bias

  • Implicit bias
  • Cognitive bias
  • Survivorship bias
  • Availability heuristic
  • Nonresponse bias
  • Regression to the mean

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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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 ).

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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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The Craft of Writing a Strong Hypothesis

Deeptanshu D

Table of Contents

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

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

What is a Hypothesis?

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

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

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

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

Different Types of Hypotheses‌

Types-of-hypotheses

Types of hypotheses

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

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

1. Null hypothesis

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

2. Alternative hypothesis

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

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

3. Simple hypothesis

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

4. Complex hypothesis

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

5. Associative and casual hypothesis

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

6. Empirical hypothesis

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

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

7. Statistical hypothesis

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

Characteristics of a Good Hypothesis

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

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

Separating a Hypothesis from a Prediction

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

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

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

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

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

Finally, How to Write a Hypothesis

Quick-tips-on-how-to-write-a-hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

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

2. Carry out a recce

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

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

3. Create a 3-dimensional hypothesis

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

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

4. Write the first draft

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

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

5. Proof your hypothesis

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

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

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

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

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

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

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

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

2. What is an example of hypothesis?

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

3. What is an example of null hypothesis?

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

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

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

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

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

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

7. Difference between research question and research hypothesis?

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

8. What is plural for hypothesis?

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

9. What is the red queen hypothesis?

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

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

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

11. When to reject null hypothesis?

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

how to write a math hypothesis

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

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

how to write a math hypothesis

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

how to write a math hypothesis

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 1,033,574 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

how to write a math hypothesis

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

how to write a math hypothesis

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Write a Good Lab Conclusion in Science

  • ↑ 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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How to write a research hypothesis

Last updated

19 January 2023

Reviewed by

Miroslav Damyanov

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

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

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

I nteresting

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

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

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

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  • Types of research hypotheses

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

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

Null hypothesis

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

Alternative hypothesis

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

Simple hypothesis

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

Complex hypothesis

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

Directional hypothesis

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

Non-directional hypothesis

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

Associative hypothesis

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

Logical hypothesis

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

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

Empirical hypothesis

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

Statistical hypothesis

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

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

Causal hypothesis

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

Descriptive hypothesis

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

  • What makes an effective research hypothesis?

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

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

Hypothesis Essential #1: Specificity & Clarity

Hypothesis Essential #2: Testability (Provability)

  • How to develop a good research hypothesis

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

the parameter you'll test

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

the hypothesized parameter value

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

Single mean (μ)

Paired means (μd)

Single proportion (p)

Difference between two independent means (μ1−μ2)

Difference between two proportions (p1−p2)

Simple linear regression slope (β)

Correlation (ρ)

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

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

  • What is the correct format for writing a hypothesis?

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

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

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

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

  • What are the five steps of a hypothesis?

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

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

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

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

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

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

What is the Red Queen hypothesis?

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

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

  • Getting started with your research

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

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Hypothesis Testing ( AQA A Level Maths: Statistics )

Revision note.

Amber

Language of Hypothesis Testing

What is a hypothesis test.

  • A hypothesis test uses a sample of data in an experiment to test a statement made about the value of a population parameter
  • A hypothesis test is used when the value of the assumed population parameter is questioned
  • The hypothesis test will look at the which outcomes are unlikely to occur if assumed population parameter is true
  • The probability found will be compared against a given significance level to determine whether there is evidence to believe that the assumed population parameter is not true

What are the key terms used in statistical hypothesis testing?

  • Every hypothesis test must begin with a clear null hypothesis (what we believe to already be true) and alternative hypothesis (how we believe the data pattern or probability distribution might have changed)
  • One example of a population parameter is the probability, p   of an event occurring
  • Another example is the mean of a population
  • The null hypothesis is denoted H 0 and sets out the assumed population parameter given that no change has happened
  • The alternative hypothesis is denoted H 1   and sets out how we think the population parameter could have changed
  • When a hypothesis test is carried out, the null hypothesis is assumed to be true and this assumption will either be accepted or rejected
  • A hypothesis test could be a one-tailed test or a two-tailed test
  • The null hypothesis will always be H 0 : θ = ...
  • The alternative hypothesis, H 1  will be H 1 : θ > ...  or   H 1 : θ < ...
  • The alternative hypothesis,  H 1  will be H 1 : θ ≠ ...    
  • It is important to read the wording of the question carefully to decide whether your hypothesis test should be one-tailed or two-tailed
  • A sample of data is a subset of data taken from the population
  • The test statistic is a numerical value calculated from the of data
  • Any probability smaller than the significance level would suggest that the event is unlikely to have happened by chance
  • The significance level must be set before the hypothesis test is carried out
  • The significance level will usually be 1%, 5% or 10%, however it may vary

Worked example

A hypothesis test is carried out at the 5% level of significance to test if a normal coin is fair or not. 

5-1-1-language-of-hypothesis-testing-we-solution

  • Make sure you read the question carefully to determine whether the test you are carrying out is for a one-tailed or a two-tailed test and use the level of significance accordingly. 

Critical Regions & p-values

How do we decide whether to reject or accept the null hypothesis.

  • If the test is looking for a decrease then extreme values are smaller than the test statistic, so find the probability of less than or equal to the test statistic
  • If the test is looking for an increase then extreme values are bigger than the test statistic, so find the probability of greater than or equal to the test statistic
  • Though for a two-tailed test it is common to half the significance level and compare this with the probability (rather than doubling the probability)
  • If the test statistic falls within the critical region, the null hypothesis would be rejected
  • It is the least extreme value that would lead to the rejection of the null hypothesis
  • The critical value is determined by the significance level
  • In a two-tailed test the significance level is halved and both the upper and the lower tails are tested
  • This probability will be known as the actual significance level
  • The actual significance level is the probability of incorrectly rejecting the null hypothesis
  • Finding the critical region will be different for a two-tailed test than it is for a one-tailed test

For the following situations, state at the 1% and 5% significance levels whether the null hypothesis should be rejected or not.

5-1-1-critical-regions-and-p-values-we-solution

Conclusions of Hypothesis Testing

How is a hypothesis test carried out.

  • There are a number of ways that a hypothesis test can be carried out for different models, however the following steps should form the base for your test:
  • Step 1. Define the test statistic and population parameter
  • Step 2. Write the null and alternative hypotheses clearly
  • Step 3. Calculate the critical value(s) or the p - value for the test
  • Step 4. Compare the observed value of the test statistic with the critical value(s) or the p - value with the significance level
  • Step 5. Decide whether there is enough evidence to reject H 0 or whether it has to be accepted
  •   Step 6. Write a conclusion in context

How should a conclusion be written for a hypothesis test?

  • Your conclusion must be written in the context of the question
  • If rejecting the null hypothesis your conclusion should state that there is sufficient evidence to suggest the alternative hypothesis is true at this level of significance
  • If accepting the null hypothesis your conclusion should state that there is not enough evidence to suggest the alternative hypothesis is true at this level of significance
  • There is a chance that the test has led to an incorrect conclusion
  • The outcome is dependent on the sample, a different sample might lead to a different outcome
  • You should not state whether this change is an increase or decrease

A teacher carried out a hypothesis test at the 10% significance level to test if her students perform better in exams after using a new revision technique. The p – value for her test statistic is 0.09142. Write a conclusion for her hypothesis test.

5-1-1-conclusions-of-hypothesis-testing-we-solution

  • It is best to use the exact wording from the question when writing your conclusion for the hypothesis test, do not be afraid to sound repetitive.

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how to write a math hypothesis

When doing a research action plan students in school would know that the first thing to do is to know your topic well enough. From expecting science projects to work based on your predictions and the results that may have been quite the opposite from how you depicted them. This also rings true in businesses. There is a term for that and it is often associated with the subject Science, but can also be associated with business . Scientific method  or a hypothesis.

What Is a Hypothesis?

A hypothesis is a scientific wild guess, a prediction in research . A wild guess, a say from someone without any known proof.  A hypothesis can also mean a scientific, educated guess that most scientists and researchers do before planning out or doing experiments to check if their guesses or their scientific ideas based on their topics are exact or correct.

Hypothesis Format

A well-structured hypothesis is crucial for guiding scientific research. Here’s a detailed format for writing a hypothesis, along with examples for each step:

1. Start with a Research Question

Before writing a hypothesis, begin with a clear and concise research question . This question identifies the focus of your study.

Example Research Question: Does the amount of daily exercise affect weight loss?

2. Identify the Variables

Identify the independent and dependent variables in your research question.

  • Independent Variable: The variable you manipulate (e.g., amount of daily exercise).
  • Dependent Variable: The variable you measure (e.g., weight loss).

3. Formulate the Hypothesis

Use the identified variables to create a testable statement . This statement should clearly express the expected relationship between the variables.

  • If [independent variable], then [dependent variable].
  • [Independent variable] will [effect] [dependent variable].

Directional vs. Non-Directional Hypothesis:

  • Specifies the direction of the expected relationship.
  • Does not specify the direction of the expected relationship, only that a relationship exists.

4. Example Hypotheses Using the Format

Research question: does caffeine affect cognitive performance, if-then statement:.

  • Example: If individuals consume caffeine, then their cognitive performance will improve.

Direct Statement:

  • Example: Caffeine consumption will improve cognitive performance.

Null Hypothesis (H0):

  • Example: There is no significant effect of caffeine consumption on cognitive performance.

Alternative Hypothesis (H1):

  • Example: There is a significant effect of caffeine consumption on cognitive performance.

Directional Hypothesis:

Non-directional hypothesis:.

  • Example: There is a relationship between caffeine consumption and cognitive performance.

5. Refining the Hypothesis

Ensure that your hypothesis is specific, measurable, and testable. Avoid vague terms and focus on a single independent and dependent variable.

Hypothesis Examples in Research

A hypothesis is a statement that predicts the relationship between variables. It serves as a foundation for research by providing a clear focus and direction for experiments and data analysis . Here are examples of hypotheses from various fields of research:

Research Question:

Does sunlight exposure affect plant growth?

Hypotheses:

  • Null Hypothesis (H0): There is no significant difference in plant growth between plants exposed to sunlight and those kept in the shade.
  • Alternative Hypothesis (H1): Plants exposed to sunlight grow taller than those kept in the shade.
  • Directional Hypothesis: Increased sunlight exposure will lead to increased plant growth.
  • If-Then Statement: If plants are exposed to more sunlight, then they will grow taller.

2. Psychology

Does sleep duration affect memory retention?

  • Null Hypothesis (H0): There is no significant difference in memory retention between individuals who sleep for 8 hours and those who sleep for 4 hours.
  • Alternative Hypothesis (H1): Individuals who sleep for 8 hours will have better memory retention than those who sleep for 4 hours.
  • Directional Hypothesis: Longer sleep duration will improve memory retention.
  • If-Then Statement: If individuals sleep for 8 hours, then their memory retention will improve compared to those who sleep for 4 hours.

3. Education

Do interactive teaching methods improve student engagement?

  • Null Hypothesis (H0): There is no significant difference in student engagement between interactive teaching methods and traditional lecture-based methods.
  • Alternative Hypothesis (H1): Interactive teaching methods result in higher student engagement compared to traditional lecture-based methods.
  • Directional Hypothesis: Interactive teaching methods will increase student engagement.
  • If-Then Statement: If teachers use interactive teaching methods, then student engagement will increase.

4. Medicine

Does a new drug reduce blood pressure more effectively than the standard medication?

  • Null Hypothesis (H0): There is no significant difference in blood pressure reduction between the new drug and the standard medication.
  • Alternative Hypothesis (H1): The new drug reduces blood pressure more effectively than the standard medication.
  • Directional Hypothesis: The new drug will reduce blood pressure more than the standard medication.
  • If-Then Statement: If patients take the new drug, then their blood pressure will decrease more than if they take the standard medication.

5. Sociology

Does socioeconomic status affect access to higher education?

  • Null Hypothesis (H0): There is no significant relationship between socioeconomic status and access to higher education.
  • Alternative Hypothesis (H1): Higher socioeconomic status is associated with greater access to higher education.
  • Directional Hypothesis: Individuals with higher socioeconomic status will have greater access to higher education.
  • If-Then Statement: If individuals have a higher socioeconomic status, then they will have greater access to higher education.

Hypothesis Examples in Psychology

Psychology research often explores the relationships between various cognitive, behavioral, and emotional variables. Here are some well-structured hypothesis examples in psychology:

1. Sleep Duration and Memory Retention

  • Non-Directional Hypothesis: There is a relationship between sleep duration and memory retention.

2. Exercise and Anxiety Levels

Does regular exercise reduce anxiety levels?

  • Null Hypothesis (H0): There is no significant difference in anxiety levels between individuals who exercise regularly and those who do not.
  • Alternative Hypothesis (H1): Individuals who exercise regularly will have lower anxiety levels than those who do not.
  • Directional Hypothesis: Regular exercise will decrease anxiety levels.
  • Non-Directional Hypothesis: There is a relationship between regular exercise and anxiety levels.
  • If-Then Statement: If individuals exercise regularly, then their anxiety levels will decrease.

3. Social Media Usage and Self-Esteem

Does social media usage affect self-esteem in teenagers?

  • Null Hypothesis (H0): There is no significant relationship between social media usage and self-esteem in teenagers.
  • Alternative Hypothesis (H1): High social media usage is associated with lower self-esteem in teenagers.
  • Directional Hypothesis: Increased social media usage will decrease self-esteem in teenagers.
  • Non-Directional Hypothesis: There is a relationship between social media usage and self-esteem in teenagers.
  • If-Then Statement: If teenagers spend more time on social media, then their self-esteem will decrease.

4. Cognitive Behavioral Therapy (CBT) and Depression

Is Cognitive Behavioral Therapy (CBT) effective in reducing symptoms of depression?

  • Null Hypothesis (H0): There is no significant difference in depression symptoms between individuals who undergo CBT and those who do not.
  • Alternative Hypothesis (H1): Individuals who undergo CBT will experience a greater reduction in depression symptoms than those who do not.
  • Directional Hypothesis: CBT will reduce symptoms of depression.
  • Non-Directional Hypothesis: There is a relationship between undergoing CBT and reduction in depression symptoms.
  • If-Then Statement: If individuals undergo CBT, then their symptoms of depression will decrease.

5. Parental Involvement and Academic Achievement

Does parental involvement influence academic achievement in children?

  • Null Hypothesis (H0): There is no significant relationship between parental involvement and academic achievement in children.
  • Alternative Hypothesis (H1): Higher levels of parental involvement are associated with higher academic achievement in children.
  • Directional Hypothesis: Increased parental involvement will improve academic achievement in children.
  • Non-Directional Hypothesis: There is a relationship between parental involvement and academic achievement in children.
  • If-Then Statement: If parents are more involved in their children’s education, then their children will achieve higher academic success.

Hypothesis Examples in Science

Scientific research often involves creating hypotheses to test the relationships between variables. Here are some well-structured hypothesis examples from various fields of science:

1. Biology: Sunlight and Plant Growth

  • Non-Directional Hypothesis: There is a relationship between sunlight exposure and plant growth.

2. Chemistry: Temperature and Reaction Rate

Does temperature affect the rate of a chemical reaction?

  • Null Hypothesis (H0): There is no significant difference in the reaction rate of a chemical reaction at different temperatures.
  • Alternative Hypothesis (H1): Increasing the temperature will increase the reaction rate.
  • Directional Hypothesis: Higher temperatures will increase the reaction rate.
  • Non-Directional Hypothesis: There is a relationship between temperature and the reaction rate.
  • If-Then Statement: If the temperature of a reaction increases, then the reaction rate will increase.

3. Physics: Mass and Free Fall Speed

Does the mass of an object affect its speed when falling?

  • Null Hypothesis (H0): There is no significant difference in the falling speed of objects with different masses.
  • Alternative Hypothesis (H1): Objects with greater mass fall faster than those with lesser mass.
  • Directional Hypothesis: Heavier objects will fall faster than lighter objects.
  • Non-Directional Hypothesis: There is a relationship between the mass of an object and its falling speed.
  • If-Then Statement: If an object’s mass increases, then its falling speed will increase.

4. Environmental Science: Fertilizers and Water Quality

Do chemical fertilizers affect water quality in nearby lakes?

  • Null Hypothesis (H0): There is no significant effect of chemical fertilizers on the water quality of nearby lakes.
  • Alternative Hypothesis (H1): Chemical fertilizers negatively affect the water quality of nearby lakes.
  • Directional Hypothesis: The use of chemical fertilizers will decrease the water quality of nearby lakes.
  • Non-Directional Hypothesis: There is a relationship between the use of chemical fertilizers and the water quality of nearby lakes.
  • If-Then Statement: If chemical fertilizers are used, then the water quality in nearby lakes will decrease.

5. Earth Science: Soil Composition and Erosion Rate

Does soil composition affect the rate of erosion?

  • Null Hypothesis (H0): There is no significant difference in the erosion rate of soils with different compositions.
  • Alternative Hypothesis (H1): Soil composition affects the rate of erosion.
  • Directional Hypothesis: Soils with higher clay content will erode more slowly than sandy soils.
  • Non-Directional Hypothesis: There is a relationship between soil composition and the rate of erosion.
  • If-Then Statement: If soil has a higher clay content, then its erosion rate will be lower compared to sandy soil.

Hypothesis Examples in Biology

In biology, hypotheses are used to explore relationships and effects within biological systems. Here are some well-structured hypothesis examples in various areas of biology:

1. Photosynthesis and Light Intensity

How does light intensity affect the rate of photosynthesis in plants?

  • Null Hypothesis (H0): Light intensity has no significant effect on the rate of photosynthesis in plants.
  • Alternative Hypothesis (H1): Light intensity significantly affects the rate of photosynthesis in plants.
  • Directional Hypothesis: Increased light intensity will increase the rate of photosynthesis in plants.
  • Non-Directional Hypothesis: There is a relationship between light intensity and the rate of photosynthesis in plants.
  • If-Then Statement: If light intensity increases, then the rate of photosynthesis in plants will increase.

2. Temperature and Enzyme Activity

How does temperature affect the activity of the enzyme amylase?

  • Null Hypothesis (H0): Temperature has no significant effect on the activity of the enzyme amylase.
  • Alternative Hypothesis (H1): Temperature significantly affects the activity of the enzyme amylase.
  • Directional Hypothesis: Increasing the temperature will increase the activity of the enzyme amylase up to an optimal point, after which activity will decrease.
  • Non-Directional Hypothesis: There is a relationship between temperature and the activity of the enzyme amylase.
  • If-Then Statement: If the temperature increases, then the activity of the enzyme amylase will increase up to an optimal temperature, after which it will decrease.

3. Nutrient Availability and Plant Growth

Does the availability of nutrients in soil affect the growth of plants?

  • Null Hypothesis (H0): Nutrient availability has no significant effect on the growth of plants.
  • Alternative Hypothesis (H1): Nutrient availability significantly affects the growth of plants.
  • Directional Hypothesis: Increased nutrient availability will enhance plant growth.
  • Non-Directional Hypothesis: There is a relationship between nutrient availability and plant growth.
  • If-Then Statement: If nutrient availability in the soil increases, then the growth of plants will be enhanced.

4. Genetic Variation and Disease Resistance

Does genetic variation in a population affect its resistance to diseases?

  • Null Hypothesis (H0): Genetic variation has no significant effect on disease resistance in a population.
  • Alternative Hypothesis (H1): Genetic variation significantly affects disease resistance in a population.
  • Directional Hypothesis: Populations with greater genetic variation will have higher resistance to diseases.
  • Non-Directional Hypothesis: There is a relationship between genetic variation and disease resistance in a population.
  • If-Then Statement: If a population has greater genetic variation, then its resistance to diseases will be higher.

5. Water pH and Aquatic Life Health

Does the pH level of water affect the health of aquatic life?

  • Null Hypothesis (H0): The pH level of water has no significant effect on the health of aquatic life.
  • Alternative Hypothesis (H1): The pH level of water significantly affects the health of aquatic life.
  • Directional Hypothesis: Extreme pH levels (both high and low) will negatively affect the health of aquatic life.
  • Non-Directional Hypothesis: There is a relationship between the pH level of water and the health of aquatic life.
  • If-Then Statement: If the pH level of water is too high or too low, then the health of aquatic life will be negatively affected.

Hypothesis Examples in Sociology

In sociology, hypotheses are used to explore and explain social phenomena, behaviors, and relationships within societies. Here are some well-structured hypothesis examples in various areas of sociology:

1. Education and Social Mobility

Does access to higher education affect social mobility?

  • Null Hypothesis (H0): Access to higher education has no significant effect on social mobility.
  • Alternative Hypothesis (H1): Access to higher education significantly affects social mobility.
  • Directional Hypothesis: Increased access to higher education will improve social mobility.
  • Non-Directional Hypothesis: There is a relationship between access to higher education and social mobility.
  • If-Then Statement: If individuals have increased access to higher education, then their social mobility will improve.

2. Income Inequality and Crime Rates

Does income inequality influence crime rates in urban areas?

  • Null Hypothesis (H0): Income inequality has no significant effect on crime rates in urban areas.
  • Alternative Hypothesis (H1): Income inequality significantly affects crime rates in urban areas.
  • Directional Hypothesis: Higher income inequality will lead to higher crime rates in urban areas.
  • Non-Directional Hypothesis: There is a relationship between income inequality and crime rates in urban areas.
  • If-Then Statement: If income inequality increases, then crime rates in urban areas will increase.

3. Social Media Use and Social Interaction

Does the use of social media affect face-to-face social interactions among teenagers?

  • Null Hypothesis (H0): The use of social media has no significant effect on face-to-face social interactions among teenagers.
  • Alternative Hypothesis (H1): The use of social media significantly affects face-to-face social interactions among teenagers.
  • Directional Hypothesis: Increased use of social media will decrease face-to-face social interactions among teenagers.
  • Non-Directional Hypothesis: There is a relationship between the use of social media and face-to-face social interactions among teenagers.
  • If-Then Statement: If teenagers use social media more frequently, then their face-to-face social interactions will decrease.

4. Gender Roles and Career Choices

Do traditional gender roles influence career choices among young adults?

  • Null Hypothesis (H0): Traditional gender roles have no significant effect on career choices among young adults.
  • Alternative Hypothesis (H1): Traditional gender roles significantly affect career choices among young adults.
  • Directional Hypothesis: Adherence to traditional gender roles will limit career choices among young adults.
  • Non-Directional Hypothesis: There is a relationship between traditional gender roles and career choices among young adults.
  • If-Then Statement: If young adults adhere to traditional gender roles, then their career choices will be limited.

5. Cultural Diversity and Workplace Productivity

Does cultural diversity in the workplace affect productivity levels?

  • Null Hypothesis (H0): Cultural diversity in the workplace has no significant effect on productivity levels.
  • Alternative Hypothesis (H1): Cultural diversity in the workplace significantly affects productivity levels.
  • Directional Hypothesis: Increased cultural diversity will improve productivity levels in the workplace.
  • Non-Directional Hypothesis: There is a relationship between cultural diversity in the workplace and productivity levels.
  • If-Then Statement: If the workplace has increased cultural diversity, then productivity levels will improve.

More Hypothesis Samples & Examples in PDF

1. research hypothesis.

Research Hypothesis

2. Education Hypothesis

Education Hypothesis

3. Basic Hypothesis

Basic Hypothesis

4. Hypothesis Statement Template

Hypothesis Statement Template

5. Hypothesis in PDF

Hypothesis in PDF

6. Hypothesis Format

Hypothesis Format

7. Hypothesis Examples

Hypothesis Examples

8. Simple Hypothesis

Simple Hypothesis

Types of Hypothesis

Types of Hypothesis

A hypothesis is a statement that can be tested and is often used in scientific research to propose a relationship between two or more variables. Understanding the different types of hypotheses is essential for conducting effective research. Below are the main types of hypotheses:

1. Null Hypothesis (H0)

The null hypothesis states that there is no relationship between the variables being studied. It assumes that any observed effect is due to chance. Researchers often aim to disprove the null hypothesis.

Example: There is no significant difference in test scores between students who study with music and those who study in silence.

2. Alternative Hypothesis (H1 or Ha)

The alternative hypothesis suggests that there is a relationship between the variables being studied. It is what researchers seek to prove.

Example: Students who study with music have higher test scores than those who study in silence.

3. Simple Hypothesis

A simple hypothesis predicts a relationship between a single independent variable and a single dependent variable.

Example: Increasing the amount of sunlight will increase the growth rate of plants.

4. Complex Hypothesis

A complex hypothesis predicts a relationship involving two or more independent variables and/or two or more dependent variables.

Example: Increasing sunlight and water will increase the growth rate and height of plants.

5. Directional Hypothesis

A directional hypothesis specifies the direction of the expected relationship between variables. It suggests whether the relationship is positive or negative.

Example: Students who study for more hours will score higher on exams.

6. Non-Directional Hypothesis

A non-directional hypothesis does not specify the direction of the relationship. It only states that a relationship exists.

Example: There is a difference in test scores between students who study with music and those who study in silence.

7. Statistical Hypothesis

A statistical hypothesis involves quantitative data and can be tested using statistical methods. It often includes both null and alternative hypotheses.

Example: The mean test scores of students who study with music are significantly different from those who study in silence.

8. Causal Hypothesis

A causal hypothesis proposes a cause-and-effect relationship between variables. It suggests that one variable causes a change in another.

Example: Smoking causes lung cancer.

9. Associative Hypothesis

An associative hypothesis suggests that variables are related but does not imply causation.

Example: There is an association between physical activity levels and body weight.

10. Research Hypothesis

A research hypothesis is a broad statement that serves as the foundation for the research study. It is often the same as the alternative hypothesis.

Example: Implementing a new teaching strategy will improve student engagement and performance.

How To Use Hypothesis for Research?

A hypothesis is a critical component of the research process, providing a clear direction for the study and forming the basis for drawing conclusions. Here’s a step-by-step guide on how to use a hypothesis in research:

1. Identify the Research Problem

Before formulating a hypothesis, clearly define the research problem or question. This step involves understanding what you aim to investigate and why it is significant.

Example: You want to study the impact of sleep on academic performance among college students.

2. Review Existing Literature

Conduct a thorough review of existing literature to understand what is already known about the topic. This helps in identifying gaps in knowledge and forming a basis for your hypothesis.

Example: Previous studies suggest a positive correlation between sleep duration and academic performance but lack specific data on college students.

Based on the research problem and literature review, formulate a clear and testable hypothesis. Ensure it is specific and relates directly to the variables being studied.

Types of Hypotheses:

  • Null Hypothesis (H0): There is no significant relationship between sleep duration and academic performance among college students.
  • Alternative Hypothesis (H1): There is a significant relationship between sleep duration and academic performance among college students.

4. Define Variables

Clearly define the independent and dependent variables involved in the hypothesis.

  • Independent Variable: Sleep duration
  • Dependent Variable: Academic performance (e.g., GPA)

5. Design the Study

Choose an appropriate research design to test the hypothesis. This could be experimental, correlational, or observational, depending on the nature of your research question.

Example: Conduct a correlational study to examine the relationship between sleep duration and GPA among college students.

6. Collect Data

Gather data through surveys, experiments, or secondary data sources. Ensure the data collection methods are reliable and valid to accurately test the hypothesis.

Example: Use a questionnaire to collect data on students’ sleep duration and their GPAs.

7. Analyze the Data

Use appropriate statistical methods to analyze the data. This step involves testing the hypothesis to determine whether to accept or reject the null hypothesis.

Example: Perform a Pearson correlation analysis to examine the relationship between sleep duration and GPA.

8. Interpret the Results

Interpret the results of the statistical analysis. Determine if the data supports the alternative hypothesis or if the null hypothesis cannot be rejected.

Example: If the analysis shows a significant positive correlation, you can reject the null hypothesis and accept the alternative hypothesis that sleep duration is related to academic performance.

9. Draw Conclusions

Draw conclusions based on the results of the hypothesis testing. Discuss the implications of the findings and how they contribute to the existing body of knowledge.

Example: Conclude that longer sleep duration is associated with higher GPA among college students and discuss potential implications for student health and academic policies.

10. Report and Share Findings

Write a detailed report or research paper presenting the hypothesis, methodology, results, and conclusions. Share your findings with the academic community or relevant stakeholders.

Example: Publish the study in a peer-reviewed journal or present it at an academic conference.

How to Write a Hypothesis?

Writing a hypothesis is a crucial step in the scientific method. A well-constructed hypothesis guides your research, helping you design experiments and analyze results. Here’s a step-by-step guide on how to write an effective hypothesis:

1. Understand the Research Question

Start by clearly understanding the research question or problem you want to address. This helps in formulating a focused hypothesis.

Example: How does sunlight exposure affect plant growth?

2. Conduct Preliminary Research

Review existing literature related to your research question. This helps in understanding what is already known and identifying gaps in knowledge.

Example: Studies show that plants generally grow better with more sunlight, but the optimal amount varies.

3. Identify Variables

Determine the independent and dependent variables for your study.

  • Independent Variable: The factor you manipulate (e.g., sunlight exposure).
  • Dependent Variable: The factor you measure (e.g., plant growth).

4. Formulate a Simple Hypothesis

A simple hypothesis involves one independent and one dependent variable. Clearly state the expected relationship between these variables.

Example: Increasing sunlight exposure will increase plant growth.

5. Choose the Type of Hypothesis

Decide whether your hypothesis will be null or alternative, directional or non-directional.

  • Null Hypothesis (H0): There is no relationship between the variables.
  • Alternative Hypothesis (H1): There is a relationship between the variables.
  • Directional Hypothesis: Specifies the direction of the relationship.
  • Non-Directional Hypothesis: Does not specify the direction.

Example of Directional Hypothesis: Plants exposed to more sunlight will grow taller than those exposed to less sunlight.

6. Ensure Testability

Make sure your hypothesis can be tested through experiments or observations. It should be measurable and falsifiable.

Example: Plants will be grown under different levels of sunlight, and their growth will be measured over time.

7. Write the Hypothesis

Write your hypothesis in a clear, concise, and specific manner. It should include the variables and the expected relationship between them.

Example: If plants are exposed to increased sunlight, then they will grow taller compared to plants that receive less sunlight.

8. Refine the Hypothesis

Ensure that your hypothesis is specific and narrow enough to be testable but broad enough to cover the scope of your research.

Example: If tomato plants are exposed to 8 hours of sunlight per day, then they will grow taller and produce more fruit compared to tomato plants exposed to 4 hours of sunlight per day.

How Do You Formulate a Hypothesis?

To formulate a hypothesis, identify the research question, review existing literature, define variables, and create a testable statement predicting the relationship between the variables.

What Is the Difference Between Null and Alternative Hypotheses?

The null hypothesis (H0) states there is no effect or relationship, while the alternative hypothesis (H1) proposes that there is an effect or relationship.

Why Is a Hypothesis Important in Research?

A hypothesis provides a clear focus for the study, guiding the research design, data collection, and analysis, ultimately helping to draw meaningful conclusions.

Can a Hypothesis Be Proven True?

A hypothesis cannot be proven true; it can only be supported or refuted through experimentation and analysis. Even if supported, it remains open to further testing.

What Makes a Good Hypothesis?

A good hypothesis is clear, concise, specific, testable, and based on existing knowledge. It should predict a relationship between variables that can be measured.

How Is a Hypothesis Tested?

A hypothesis is tested through experiments or observations, collecting and analyzing data to determine if the results support or refute the hypothesis.

What Are the Types of Hypotheses?

Types of hypotheses include null, alternative, simple, complex, directional, non-directional, statistical, causal, and associative.

What Is a Directional Hypothesis?

A directional hypothesis specifies the expected direction of the relationship between variables, indicating whether the effect will be positive or negative.

What Is a Non-Directional Hypothesis?

A non-directional hypothesis states that a relationship exists between variables but does not specify the direction of the relationship.

How Do You Refine a Hypothesis?

Refine a hypothesis by ensuring it is specific, measurable, and testable. Remove any vague terms and focus on a single independent and dependent variable.

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How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =,  ≤, ≥ some value

H A  (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data  does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

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how to write a math hypothesis

Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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you are amazing, thank you so much

Say I am a botanist hypothesizing the average height of daisies is 20 inches, or not? Does T = (ave – 20 inches) / √ variance / (80 / 4)? … This assumes 40 real measures + 40 fake = 80 n, but that seems questionable. Please advise.

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how to write a math hypothesis

A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false.

In statistics, a hypothesis (sometimes called a statistical hypothesis) refers to a statement on which hypothesis testing will be based. Particularly important statistical hypotheses include the null hypothesis and alternative hypothesis .

In symbolic logic , a hypothesis is the first part of an implication (with the second part being known as the predicate ).

In general mathematical usage, "hypothesis" is roughly synonymous with " conjecture ."

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How the Square Root of 2 Became a Number

June 21, 2024

how to write a math hypothesis

Nico Roper/ Quanta Magazine

Introduction

The ancient Greeks wanted to believe that the universe could be described in its entirety using only whole numbers and the ratios between them — fractions, or what we now call rational numbers. But this aspiration was undermined when they considered a square with sides of length 1, only to find that the length of its diagonal couldn’t possibly be written as a fraction.

The first proof of this (there would be several) is commonly attributed to Pythagoras, a 6th-century BCE philosopher, even though none of his writings survive and little is known about him. Nevertheless, “it was the first crisis in what we call the foundations of mathematics,” said John Bell , a professor emeritus at Western University in London, Ontario.

That crisis would not be resolved for a long time. Though the ancient Greeks could establish what $latex \sqrt{2}$ was not, they didn’t have a language for explaining what it was.

For millennia, this sufficed. Renaissance mathematicians manipulated what they came to call irrational numbers while trying to solve algebraic equations. The modern notation for square roots came into use in the 16th and 17th centuries. But still, there was something slippery about them. Does $latex \sqrt{2}$ exist in the same way that 2 does? It wasn’t clear.

Mathematicians continued to live with that ambiguity. Then, in the mid-1800s, Richard Dedekind, among others, realized that calculus — which had been developed 200 years earlier by Isaac Newton and Gottfried Leibniz — stood on a shaky foundation. A reserved but gifted mathematician who worked slowly and published relatively little, Dedekind was preparing to teach his students about continuous functions when he realized that he couldn’t give a satisfactory explanation of what it meant for a function to be continuous.

He hadn’t even seen functions properly defined. And that, he argued, required a good understanding of how numbers worked — something mathematicians seemed to have taken for granted. How, he asked, could you know for sure that $latex \sqrt{2}$ multiplied by $latex \sqrt{3}$ equals $latex \sqrt{6}$? He wanted to provide some answers.

And so he introduced a way to define and construct the irrational numbers using only the rationals. Here’s how it works: First, split all the rational numbers into two sets, so that all of the fractions in one set are smaller than those in the other. For instance, in one group, collect all rationals that, when squared, are less than 2; in the other, put all rationals whose squares are greater than 2. Exactly one number plugs the hole between these two sets. Mathematicians give it the label $latex \sqrt{2}$. For Dedekind, then, an irrational number is defined by a pair of infinite sets of rational numbers, which create what he called a cut. “It’s a very lovely idea,” said Ian Stewart of the University of Warwick. “You can pin down the missing irrational numbers not by describing them, but by describing the gap in which they have to sit.”

Dedekind showed that you can fill in the entire number line this way, rigorously defining for the first time what are now called real numbers (the rationals and the irrationals combined).

At around the same time that Dedekind introduced his cuts, his friend and collaborator Georg Cantor also began to think about irrational numbers. The overlap made their relationship complicated. “They were good friends, and they hated each other. They cooperated, and they ignored each other,” said Leo Corry , a historian of science who is the president of the Open University of Israel.

Cantor came up with a different definition of irrational numbers. He expressed each in terms of sequences of rational numbers that approached, or “converged” to, a particular irrational value. Though Cantor’s irrational numbers initially looked different from Dedekind’s, later work proved that they are mathematically equivalent.

Cantor’s work led him to ask how many numbers exist. The question might at first seem strange. There are infinitely many whole numbers — you can always keep adding one more. Presumably, that’s as big as a set of numbers can get. But Cantor showed that, paradoxically, though the number of fractions is the same as the number of integers, there are demonstrably more irrational numbers. He was the first to realize that infinity comes in many sizes .

The number line was more crowded, and weirder, than anyone had imagined. But mathematicians were only able to see that after a change in perspective.

Dedekind’s cuts are arguably the beginning of modern mathematics. “It’s really the first point in the history of mathematics where mathematicians actually know what they’re talking about,” Stewart said. Dedekind and others used his definition to prove major theorems in calculus for the first time — which allowed them not just to strengthen the edifice that Leibniz and Newton had built, but to add to it. Dedekind’s work enabled mathematicians to better understand sequences and functions. His influence ranged across many fields of math. Emmy Noether, a prolific mathematician who helped shape the field of abstract algebra in the early 20th century, is said to have told her students that “everything is already in Dedekind.”

A formal definition of $latex \sqrt{2}$ opened new horizons for exploration beyond the topics in calculus that initially motivated Dedekind. As Stewart put it, “After Dedekind, mathematicians started to realize that you can invent new concepts altogether. … The whole idea of what mathematics is about becomes much broader and more flexible.”

Clarification:  June 24, 2024 Emmy Noether’s remark about Richard Dedekind was in reference to his work in algebraic number theory. This article has been revised to eliminate the implication that it was in connection to his work on defining real numbers.

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AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 11.

  • Hypotheses for a two-sample t test
  • Example of hypotheses for paired and two-sample t tests

Writing hypotheses to test the difference of means

  • Two-sample t test for difference of means
  • Test statistic in a two-sample t test
  • P-value in a two-sample t test
  • Conclusion for a two-sample t test using a P-value
  • Conclusion for a two-sample t test using a confidence interval
  • Making conclusions about the difference of means

how to write a math hypothesis

  • (Choice A)   Paired t ‍   test with H a :  μ after − before > 0 ‍   A Paired t ‍   test with H a :  μ after − before > 0 ‍  
  • (Choice B)   Paired t ‍   test with H a :  μ after − before ≠ 0 ‍   B Paired t ‍   test with H a :  μ after − before ≠ 0 ‍  
  • (Choice C)   Two-sample t ‍   test with H a :  μ before > μ after ‍   C Two-sample t ‍   test with H a :  μ before > μ after ‍  
  • (Choice D)   Two-sample t ‍   test with H a :  μ before ≠ μ after ‍   D Two-sample t ‍   test with H a :  μ before ≠ μ after ‍  
  • (Choice E)   Two-sample t ‍   test with H a :  μ before < μ after ‍   E Two-sample t ‍   test with H a :  μ before < μ after ‍  

a planet with stars and a galaxy

Human Consciousness Is an Illusion, Scientists Say

The entire universe may have an internal mind—or the whole idea of consciousness could be a sham. Here’s why scientists still can’t agree.

The concept of panpsychism has been around for hundreds of years. Italian philosopher Francesco Patrizi coined the term in the late 16th century. He combined the Greek words παν (pronounced “pan,” and meaning everything) and ψυχή (psyche, meaning “soul” or “mind”) to describe a distinctive soulfulness inherent to each and every order of creation. The idea dates back even further, though, to ancient Greece, when astronomer, mathematician, and pre-Socratic philosopher Thales said “that everything is full of gods,” and one of the world’s best-studied philosophers, Plato, said that the world is indeed a living being endowed with a soul and intelligence.

In the 19th century, panpsychism took off in the West, championed by the likes of the great philosopher of pessimism, Arthur Schopenhauer, and the father of modern psychology, William James. Then came the philosophical movement that emerged in Vienna, Italy, in the 1920s, called logical positivism: the idea that scientific knowledge—empirically proven knowledge—was the only kind of acceptable knowledge, the rest being metaphysical mumbo-jumbo. It was game over for panpsychism.

Until recently.

The inability of empirical sciences to figure out why and how matter gives rise to the experiences of consciousness has recently rekindled an interest in panpsychism. So have developments in the fields of neuroscience, psychology, and quantum physics.

In 2004, Italian neuroscientist and psychiatrist Giulio Tononi, Ph.D., proposed the integrated information theory of consciousness, which says that consciousness is widespread and can be found even in some simple systems. In his article in Scientific American , leading American neuroscientist Christof Koch, Ph.D., bashed materialism and its view of emerging consciousness 10 years later. The notion of subjective feelings springing from physical stuff is at odds with a commonly applied axiom in philosophy and modern science: the “ ex nihilo nihil fit ,” or that “out of nothing, nothing comes, ” Koch wrote . He argued that elementary particles either have some charge, or they have none; similarly, where there are organized lumps of matter, consciousness follows.

.css-2l0eat{font-family:UnitedSans,UnitedSans-roboto,UnitedSans-local,Helvetica,Arial,Sans-serif;font-size:1.625rem;line-height:1.2;margin:0rem;padding:0.9rem 1rem 1rem;}@media(max-width: 48rem){.css-2l0eat{font-size:1.75rem;line-height:1;}}@media(min-width: 48rem){.css-2l0eat{font-size:1.875rem;line-height:1;}}@media(min-width: 64rem){.css-2l0eat{font-size:2.25rem;line-height:1;}}.css-2l0eat b,.css-2l0eat strong{font-family:inherit;font-weight:bold;}.css-2l0eat em,.css-2l0eat i{font-style:italic;font-family:inherit;} “Consciousness doesn’t exist, and we only think it does because we are under a sort of illusion about our own minds.”

Not everyone agrees though. Keith Frankish, Ph.D., a professor of philosophy at the University of Sheffield, believes today’s panpsychism is in a “metaphysical limbo,” a direct result of what he calls the “ depsychologization of consciousness .” This means that we try to grasp consciousness through what our senses perceive or through our immediate experiences, and that we refuse to acknowledge it as a psychological function. “The thought is that, if consciousness is not essentially connected to brain processes, then there’s no reason to think it must be restricted to brains . Maybe everything has a little inner glow to it, ” Frankish says. But it is exactly this view that tends to undermine the significance of consciousness. “If my consciousness makes no difference to how I react, why should I or anyone else care about it?” he asks. Frankish proposes a mirror image of panpsychism.

“Whereas panpsychists think that consciousness is everywhere, I think that consciousness—of the non-functional, inner glow kind—is nowhere,” he explains. “Consciousness doesn’t exist, and we only think it does because we are under a sort of illusion about our own minds, a view I call illusionism,” he continues. In other words, we humans have vastly extended the power of our biological brains and, through powerful tricks like self-manipulation or solid problem-solving skills, we have convinced ourselves we have a unified, conscious mind, a self, a soul—but it’s all an illusion, according to Frankish.

But illusionism is a view antithetical to what well-known biologist and author Rupert Sheldrake, Ph.D., believes. For Sheldrake, it’s an irrefutable fact that not only do we humans have consciousness, but the whole galaxy has consciousness, too. Sheldrake is best known for his hypothesis of morphic resonance, a process through which self-organizing systems (picture termite colonies or insulin molecules) inherit a memory from previous, similar systems. Similar organisms share mysterious telepathic interconnections, and species share collective memories: this is how your dog foretells when you’re coming home and why you feel awkward when someone is staring at you, according to Sheldrake. In a paper he published in the Journal of Consciousness Studies in 2021, Sheldrake asked “Is the sun conscious?” For him, it most certainly is.

“Consciousness does not need to be confined to brains,” Sheldrake says. “The link between minds and physical systems seems to be through rhythmic electromagnetic fields, which of course are present in our brains. They are also present in and around the sun, and these could be the interface between the solar mind and the body of the sun.” So, if the sun is conscious, it’s likely to be aware of activities within the solar system, continues Sheldrake, including here on Earth, and also of its relationship with other stars within the galaxy and the galaxy as a whole.

Perhaps it’s a matter of personal positioning in the world. Is nothing around me conscious? Is everything around me conscious? If the latter is true, where does my consciousness end and yours begin, and why is an intact brain conscious, whereas the same brain, pureed to goo inside a blender, is not ( as Koch ponders )? Will we ever know? No wonder scientists describe consciousness as the granddaddy of all mysteries of human behavior. If you subscribe to the panpsychist view, however, you may be startled to know that the conscious sun makes choices. “It may be able to choose in which direction to send out solar flares or coronal mass ejections, which can have an enormous effect on life on Earth, and to which our technologies are very vulnerable,” Sheldrake says.

Headshot of Stav Dimitropoulos

Stav Dimitropoulos’s science writing has appeared online or in print for the BBC, Discover, Scientific American, Nature, Science, Runner’s World, The Daily Beast and others. Stav disrupted an athletic and academic career to become a journalist and get to know the world.

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IMAGES

  1. How to write a hypothesis in 3 steps!

    how to write a math hypothesis

  2. How to Identify Hypotheses in Algebra

    how to write a math hypothesis

  3. hypothesis math definition example

    how to write a math hypothesis

  4. How to Write a Hypothesis 101: A Step-by-Step Guide

    how to write a math hypothesis

  5. 🏷️ Formulation of hypothesis in research. How to Write a Strong

    how to write a math hypothesis

  6. How to Write a Hypothesis: The Ultimate Guide with Examples

    how to write a math hypothesis

VIDEO

  1. Hypothesis testing

  2. How To Formulate The Hypothesis/What is Hypothesis?

  3. Hypothesis testing

  4. What Is A Hypothesis?

  5. The Math Hypothesis That Could Break the World! #maths #riemann #curiousminds #mystery

  6. How to write null and alternative hypotheses #statistics

COMMENTS

  1. How to Write a Strong Hypothesis

    Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question.

  2. 5.2

    5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). Null Hypothesis. The statement that there is not a difference in the population (s), denoted as H 0.

  3. How to Write a Hypothesis w/ Strong Examples

    Simple Hypothesis Examples. Increasing the amount of natural light in a classroom will improve students' test scores. Drinking at least eight glasses of water a day reduces the frequency of headaches in adults. Plant growth is faster when the plant is exposed to music for at least one hour per day.

  4. How to Write a Strong Hypothesis

    Step 5: Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.

  5. Null & Alternative Hypotheses

    Null hypothesis (H 0): Independent variable does not affect dependent variable. Alternative hypothesis (H a): Independent variable affects dependent variable. Test-specific template sentences. Once you know the statistical test you'll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose ...

  6. How to Write a Hypothesis? Types and Examples

    Here are two hypothesis examples: Dandelions growing in nitrogen-rich soils for two weeks develop larger leaves than those in nitrogen-poor soils because nitrogen stimulates vegetative growth.4. If a company offers flexible work hours, then their employees will be happier at work.5.

  7. How to Write a Strong Hypothesis in 6 Simple Steps

    Learning how to write a hypothesis comes down to knowledge and strategy. So where do you start? Learn how to make your hypothesis strong step-by-step here.

  8. Understanding Hypotheses

    A hypothesis is a statement or idea which gives an explanation to a series of observations. Sometimes, following observation, a hypothesis will clearly need to be refined or rejected. This happens if a single contradictory observation occurs. For example, suppose that a child is trying to understand the concept of a dog.

  9. How to Write a Hypothesis 101: A Step-by-Step Guide

    Step 3: Build the Hypothetical Relationship. In understanding how to compose a hypothesis, constructing the relationship between the variables is key. Based on your research question and variables, predict the expected outcome or connection.

  10. Hypothesis Testing

    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.

  11. What Is a Hypothesis and How Do I Write One?

    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. The Craft of Writing a Strong Hypothesis

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

  13. Hypothesis testing and p-values (video)

    Then, if the null hypothesis is wrong, then the data will tend to group at a point that is not the value in the null hypothesis (1.2), and then our p-value will wind up being very small. If the null hypothesis is correct, or close to being correct, then the p-value will be larger, because the data values will group around the value we hypothesized.

  14. Examples of null and alternative hypotheses

    The null hypothesis is what happens at baseline. It is the uninteresting hypothesis--the boring hypothesis. Usually, it is the hypothesis that assumes no difference. It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove.

  15. Hypothesis: Definition, Examples, and Types

    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 ...

  16. How to Write a Hypothesis: 13 Steps (with Pictures)

    1. Select a topic. Pick a topic that interests you, and that you think it would be good to know more about. [2] If you are writing a hypothesis for a school assignment, this step may be taken care of for you. 2. Read existing research. Gather all the information you can about the topic you've selected.

  17. How to Write a Research Hypothesis

    Step 2: Conduct a literature review to gather essential existing research. Step 3: Write a clear, strong, simply worded sentence that explains your test parameter, test direction, and hypothesized parameter. Step 4: Read it a few times. Have others read it and ask them what they think it means.

  18. 5.1.1 Hypothesis Testing

    There are a number of ways that a hypothesis test can be carried out for different models, however the following steps should form the base for your test: Step 1. Define the test statistic and population parameter. Step 2. Write the null and alternative hypotheses clearly.

  19. Hypothesis

    A well-structured hypothesis is crucial for guiding scientific research. Here's a detailed format for writing a hypothesis, along with examples for each step: 1. Start with a Research Question. Before writing a hypothesis, begin with a clear and concise research question. This question identifies the focus of your study.

  20. How to Write a Null Hypothesis (5 Examples)

    Example 1: Weight of Turtles. A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles. Here is how to write the null and alternative hypotheses for this scenario: H0: μ = 300 (the true mean weight is equal to ...

  21. Hypothesis -- from Wolfram MathWorld

    A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false. In statistics, a hypothesis (sometimes called a statistical hypothesis) refers to a statement on which hypothesis testing will be based. Particularly important statistical hypotheses include the null hypothesis and alternative hypothesis. In symbolic logic, a hypothesis is the ...

  22. Significance tests (hypothesis testing)

    Unit 12: Significance tests (hypothesis testing) Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values ...

  23. How the Square Root of 2 Became a Number

    Dedekind and others used his definition to prove major theorems in calculus for the first time — which allowed them not just to strengthen the edifice that Leibniz and Newton had built, but to add to it. Dedekind's work enabled mathematicians to better understand sequences and functions. His influence ranged across many fields of math.

  24. Writing hypotheses to test the difference of means

    Writing hypotheses to test the difference of means. An exercise scientist wanted to test the effectiveness of a new program designed to increase the flexibility of senior citizens. They recruited participants and rated their flexibility according to a standard scale before starting the program. The participants all went through the program and ...

  25. Human Consciousness Is an Illusion, Scientists Say

    Stav Dimitropoulos's science writing has appeared online or in print for the BBC, Discover, Scientific American, Nature, Science, Runner's World, The Daily Beast and others.