- Scientific Methods

## What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

## Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

- The hypothesis should be clear and precise to consider it to be reliable.
- If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
- The hypothesis must be specific and should have scope for conducting more tests.
- The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

## Sources of Hypothesis

Following are the sources of hypothesis:

- The resemblance between the phenomenon.
- Observations from past studies, present-day experiences and from the competitors.
- Scientific theories.
- General patterns that influence the thinking process of people.

## Types of Hypothesis

There are six forms of hypothesis and they are:

- Simple hypothesis
- Complex hypothesis
- Directional hypothesis
- Non-directional hypothesis
- Null hypothesis
- Associative and casual hypothesis

## Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

## Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

## Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

## Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

## Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

## Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

## Examples of Hypothesis

Following are the examples of hypotheses based on their types:

- Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
- All lilies have the same number of petals is an example of a null hypothesis.
- If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

## Functions of Hypothesis

Following are the functions performed by the hypothesis:

- Hypothesis helps in making an observation and experiments possible.
- It becomes the start point for the investigation.
- Hypothesis helps in verifying the observations.
- It helps in directing the inquiries in the right direction.

## How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

- Formation of question
- Doing background research
- Creation of hypothesis
- Designing an experiment
- Collection of data
- Result analysis
- Summarizing the experiment
- Communicating the results

## Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

## Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

- Associative and Casual hypothesis

## State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

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

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## What is hypothesis in Machine Learning?

The hypothesis is a word that is frequently used in Machine Learning and data science initiatives. As we all know, machine learning is one of the most powerful technologies in the world, allowing us to anticipate outcomes based on previous experiences. Moreover, data scientists and ML specialists undertake experiments with the goal of solving an issue. These ML experts and data scientists make an initial guess on how to solve the challenge.

## What is a Hypothesis?

A hypothesis is a conjecture or proposed explanation that is based on insufficient facts or assumptions. It is only a conjecture based on certain known facts that have yet to be confirmed. A good hypothesis is tested and yields either true or erroneous outcomes.

Let's look at an example to better grasp the hypothesis. According to some scientists, ultraviolet (UV) light can harm the eyes and induce blindness.

In this case, a scientist just states that UV rays are hazardous to the eyes, but people presume they can lead to blindness. Yet, it is conceivable that it will not be achievable. As a result, these kinds of assumptions are referred to as hypotheses.

## Defining Hypothesis in Machine Learning

In machine learning, a hypothesis is a mathematical function or model that converts input data into output predictions. The model's first belief or explanation is based on the facts supplied. The hypothesis is typically expressed as a collection of parameters characterizing the behavior of the model.

If we're building a model to predict the price of a property based on its size and location. The hypothesis function may look something like this −

$$\mathrm{h(x)\:=\:θ0\:+\:θ1\:*\:x1\:+\:θ2\:*\:x2}$$

The hypothesis function is h(x), its input data is x, the model's parameters are 0, 1, and 2, and the features are x1 and x2.

The machine learning model's purpose is to discover the optimal values for parameters 0 through 2 that minimize the difference between projected and actual output labels.

To put it another way, we're looking for the hypothesis function that best represents the underlying link between the input and output data.

## Types of Hypotheses in Machine Learning

The next step is to build a hypothesis after identifying the problem and obtaining evidence. A hypothesis is an explanation or solution to a problem based on insufficient data. It acts as a springboard for further investigation and experimentation. A hypothesis is a machine learning function that converts inputs to outputs based on some assumptions. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. Several machine learning theories are as follows −

## 1. Null Hypothesis

A null hypothesis is a basic hypothesis that states that no link exists between the independent and dependent variables. In other words, it assumes the independent variable has no influence on the dependent variable. It is symbolized by the symbol H0. If the p-value falls outside the significance level, the null hypothesis is typically rejected (). If the null hypothesis is correct, the coefficient of determination is the probability of rejecting it. A null hypothesis is involved in test findings such as t-tests and ANOVA.

## 2. Alternative Hypothesis

An alternative hypothesis is a hypothesis that contradicts the null hypothesis. It assumes that there is a relationship between the independent and dependent variables. In other words, it assumes that there is an effect of the independent variable on the dependent variable. It is denoted by Ha. An alternative hypothesis is generally accepted if the p-value is less than the significance level (α). An alternative hypothesis is also known as a research hypothesis.

## 3. One-tailed Hypothesis

A one-tailed test is a type of significance test in which the region of rejection is located at one end of the sample distribution. It denotes that the estimated test parameter is more or less than the crucial value, implying that the alternative hypothesis rather than the null hypothesis should be accepted. It is most commonly used in the chi-square distribution, where all of the crucial areas, related to, are put in either of the two tails. Left-tailed or right-tailed one-tailed tests are both possible.

## 4. Two-tailed Hypothesis

The two-tailed test is a hypothesis test in which the region of rejection or critical area is on both ends of the normal distribution. It determines whether the sample tested falls within or outside a certain range of values, and an alternative hypothesis is accepted if the calculated value falls in either of the two tails of the probability distribution. α is bifurcated into two equal parts, and the estimated parameter is either above or below the assumed parameter, so extreme values work as evidence against the null hypothesis.

Overall, the hypothesis plays a critical role in the machine learning model. It provides a starting point for the model to make predictions and helps to guide the learning process. The accuracy of the hypothesis is evaluated using various metrics like mean squared error or accuracy.

The hypothesis is a mathematical function or model that converts input data into output predictions, typically expressed as a collection of parameters characterizing the behavior of the model. It is an explanation or solution to a problem based on insufficient data. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. A two-tailed hypothesis is used when there is no prior knowledge or theoretical basis to infer a certain direction of the link.

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The majority of statements in mathematics can be written in the form: "If A, then B." For example: "If a function is differentiable, then it is continuous". In this example, the "A" part is "a function is differentiable" and the "B" part is "a function is continuous." The "A" part of the statement is called the "hypothesis", and the "B" part of the statement is called the "conclusion". Thus the hypothesis is what we must assume in order to be positive that the conclusion will hold.

Whenever you are asked to state a theorem, be sure to include the hypothesis. In order to know when you may apply the theorem, you need to know what constraints you have. So in the example above, if we know that a function is differentiable, we may assume that it is continuous. However, if we do not know that a function is differentiable, continuity may not hold. Some theorems have MANY hypotheses, some of which are written in sentences before the ultimate "if, then" statement. For example, there might be a sentence that says: "Assume n is even." which is then followed by an if,then statement. Include all hypotheses and assumptions when asked to state theorems and definitions!

Still have questions? Please ask!

## Definition of a Hypothesis

What it is and how it's used in sociology

- Key Concepts
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A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence.

Within social science, a hypothesis can take two forms. It can predict that there is no relationship between two variables, in which case it is a null hypothesis . Or, it can predict the existence of a relationship between variables, which is known as an alternative hypothesis.

In either case, the variable that is thought to either affect or not affect the outcome is known as the independent variable, and the variable that is thought to either be affected or not is the dependent variable.

Researchers seek to determine whether or not their hypothesis, or hypotheses if they have more than one, will prove true. Sometimes they do, and sometimes they do not. Either way, the research is considered successful if one can conclude whether or not a hypothesis is true.

## Null Hypothesis

A researcher has a null hypothesis when she or he believes, based on theory and existing scientific evidence, that there will not be a relationship between two variables. For example, when examining what factors influence a person's highest level of education within the U.S., a researcher might expect that place of birth, number of siblings, and religion would not have an impact on the level of education. This would mean the researcher has stated three null hypotheses.

## Alternative Hypothesis

Taking the same example, a researcher might expect that the economic class and educational attainment of one's parents, and the race of the person in question are likely to have an effect on one's educational attainment. Existing evidence and social theories that recognize the connections between wealth and cultural resources , and how race affects access to rights and resources in the U.S. , would suggest that both economic class and educational attainment of the one's parents would have a positive effect on educational attainment. In this case, economic class and educational attainment of one's parents are independent variables, and one's educational attainment is the dependent variable—it is hypothesized to be dependent on the other two.

Conversely, an informed researcher would expect that being a race other than white in the U.S. is likely to have a negative impact on a person's educational attainment. This would be characterized as a negative relationship, wherein being a person of color has a negative effect on one's educational attainment. In reality, this hypothesis proves true, with the exception of Asian Americans , who go to college at a higher rate than whites do. However, Blacks and Hispanics and Latinos are far less likely than whites and Asian Americans to go to college.

## Formulating a Hypothesis

Formulating a hypothesis can take place at the very beginning of a research project , or after a bit of research has already been done. Sometimes a researcher knows right from the start which variables she is interested in studying, and she may already have a hunch about their relationships. Other times, a researcher may have an interest in a particular topic, trend, or phenomenon, but he may not know enough about it to identify variables or formulate a hypothesis.

Whenever a hypothesis is formulated, the most important thing is to be precise about what one's variables are, what the nature of the relationship between them might be, and how one can go about conducting a study of them.

Updated by Nicki Lisa Cole, Ph.D

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## Research Hypothesis In Psychology: Types, & Examples

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

## Some key points about hypotheses:

- A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
- It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
- A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
- Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
- For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
- Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

## Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

- Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

## Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

## Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

## Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

## Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

## Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

- Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
- However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

## How to Write a Hypothesis

- Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
- Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
- Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
- Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
- Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

- The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
- The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

## More Examples

- Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
- Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
- Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
- Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
- Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
- Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
- Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
- Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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

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

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

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

## Research Hypothesis 101

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

## What is a hypothesis?

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

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

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

Hypothesis: sleep impacts academic performance.

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

But that’s not good enough…

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

## What is a research hypothesis?

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

Let’s take a look at these more closely.

## Need a helping hand?

## Hypothesis Essential #1: Specificity & Clarity

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

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

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

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

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

## Hypothesis Essential #2: Testability (Provability)

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

For example, consider the hypothesis we mentioned earlier:

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

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

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

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

## Defining A Research Hypothesis

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

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

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

## What about the null hypothesis?

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

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

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

And there you have it – hypotheses in a nutshell.

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

## Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

## 17 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

Hi” best wishes to you and your very nice blog”

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- How to Write a Strong Hypothesis | Steps & Examples

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

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

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

## Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

## Table of contents

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

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

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

## Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

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

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

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

## Prevent plagiarism. Run a free check.

Step 1. ask a question.

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

## Step 2. Do some preliminary research

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

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

## Step 3. Formulate your hypothesis

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

## 4. Refine your hypothesis

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

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

## 5. Phrase your hypothesis in three ways

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

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

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

## 6. Write a null hypothesis

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

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

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 high school sex education at reducing teen pregnancies? | Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. | High 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 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. |

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

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

Statistics

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

Research bias

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

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

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

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

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## What is Hypothesis in Machine Learning? How to Form a Hypothesis?

Hypothesis Testing is a broad subject that is applicable to many fields. When we study statistics, the Hypothesis Testing there involves data from multiple populations and the test is to see how significant the effect is on the population.

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This involves calculating the p-value and comparing it with the critical value or the alpha. When it comes to Machine Learning, Hypothesis Testing deals with finding the function that best approximates independent features to the target. In other words, map the inputs to the outputs.

By the end of this tutorial, you will know the following:

- What is Hypothesis in Statistics vs Machine Learning
- What is Hypothesis space?

## Process of Forming a Hypothesis

Trending machine learning skills.

## Hypothesis in Statistics

A Hypothesis is an assumption of a result that is falsifiable, meaning it can be proven wrong by some evidence. A Hypothesis can be either rejected or failed to be rejected. We never accept any hypothesis in statistics because it is all about probabilities and we are never 100% certain. Before the start of the experiment, we define two hypotheses:

1. Null Hypothesis: says that there is no significant effect

2. Alternative Hypothesis: says that there is some significant effect

In statistics, we compare the P-value (which is calculated using different types of statistical tests) with the critical value or alpha. The larger the P-value, the higher is the likelihood, which in turn signifies that the effect is not significant and we conclude that we fail to reject the null hypothesis .

In other words, the effect is highly likely to have occurred by chance and there is no statistical significance of it. On the other hand, if we get a P-value very small, it means that the likelihood is small. That means the probability of the event occurring by chance is very low.

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## Significance Level

The Significance Level is set before starting the experiment. This defines how much is the tolerance of error and at which level can the effect can be considered significant. A common value for significance level is 95% which also means that there is a 5% chance of us getting fooled by the test and making an error. In other words, the critical value is 0.05 which acts as a threshold. Similarly, if the significance level was set at 99%, it would mean a critical value of 0.01%.

A statistical test is carried out on the population and sample to find out the P-value which then is compared with the critical value. If the P-value comes out to be less than the critical value, then we can conclude that the effect is significant and hence reject the Null Hypothesis (that said there is no significant effect). If P-Value comes out to be more than the critical value, we can conclude that there is no significant effect and hence fail to reject the Null Hypothesis.

Now, as we can never be 100% sure, there is always a chance of our tests being correct but the results being misleading. This means that either we reject the null when it is actually not wrong. It can also mean that we don’t reject the null when it is actually false. These are type 1 and type 2 errors of Hypothesis Testing.

## Example

Consider you’re working for a vaccine manufacturer and your team develops the vaccine for Covid-19. To prove the efficacy of this vaccine, it needs to statistically proven that it is effective on humans. Therefore, we take two groups of people of equal size and properties. We give the vaccine to group A and we give a placebo to group B. We carry out analysis to see how many people in group A got infected and how many in group B got infected.

We test this multiple times to see if group A developed any significant immunity against Covid-19 or not. We calculate the P-value for all these tests and conclude that P-values are always less than the critical value. Hence, we can safely reject the null hypothesis and conclude there is indeed a significant effect.

Read: Machine Learning Models Explained

## Hypothesis in Machine Learning

Hypothesis in Machine Learning is used when in a Supervised Machine Learning, we need to find the function that best maps input to output. This can also be called function approximation because we are approximating a target function that best maps feature to the target.

1. Hypothesis(h): A Hypothesis can be a single model that maps features to the target, however, may be the result/metrics. A hypothesis is signified by “ h ”.

2. Hypothesis Space(H): A Hypothesis space is a complete range of models and their possible parameters that can be used to model the data. It is signified by “ H ”. In other words, the Hypothesis is a subset of Hypothesis Space.

In essence, we have the training data (independent features and the target) and a target function that maps features to the target. These are then run on different types of algorithms using different types of configuration of their hyperparameter space to check which configuration produces the best results. The training data is used to formulate and find the best hypothesis from the hypothesis space. The test data is used to validate or verify the results produced by the hypothesis.

Consider an example where we have a dataset of 10000 instances with 10 features and one target. The target is binary, which means it is a binary classification problem. Now, say, we model this data using Logistic Regression and get an accuracy of 78%. We can draw the regression line which separates both the classes. This is a Hypothesis(h). Then we test this hypothesis on test data and get a score of 74%.

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Now, again assume we fit a RandomForests model on the same data and get an accuracy score of 85%. This is a good improvement over Logistic Regression already. Now we decide to tune the hyperparameters of RandomForests to get a better score on the same data. We do a grid search and run multiple RandomForest models on the data and check their performance. In this step, we are essentially searching the Hypothesis Space(H) to find a better function. After completing the grid search, we get the best score of 89% and we end the search.

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Now we also try more models like XGBoost, Support Vector Machine and Naive Bayes theorem to test their performances on the same data. We then pick the best performing model and test it on the test data to validate its performance and get a score of 87%.

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## Before you go

The hypothesis is a crucial aspect of Machine Learning and Data Science. It is present in all the domains of analytics and is the deciding factor of whether a change should be introduced or not. Be it pharma, software, sales, etc. A Hypothesis covers the complete training dataset to check the performance of the models from the Hypothesis space.

A Hypothesis must be falsifiable, which means that it must be possible to test and prove it wrong if the results go against it. The process of searching for the best configuration of the model is time-consuming when a lot of different configurations need to be verified. There are ways to speed up this process as well by using techniques like Random Search of hyperparameters.

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There are many reasons to do open-source projects. You are learning new things, you are helping others, you are networking with others, you are creating a reputation and many more. Open source is fun, and eventually you will get something back. One of the most important reasons is that it builds a portfolio of great work that you can present to companies and get hired. Open-source projects are a wonderful way to learn new things. You could be enhancing your knowledge of software development or you could be learning a new skill. There is no better way to learn than to teach.

Yes. Open-source projects do not discriminate. The open-source communities are made of people who love to write code. There is always a place for a newbie. You will learn a lot and also have the chance to participate in a variety of open-source projects. You will learn what works and what doesn't and you will also have the chance to make your code used by a large community of developers. There is a list of open-source projects that are always looking for new contributors.

GitHub offers developers a way to manage projects and collaborate with each other. It also serves as a sort of resume for developers, with a project's contributors, documentation, and releases listed. Contributions to a project show potential employers that you have the skills and motivation to work in a team. Projects are often more than code, so GitHub has a way that you can structure your project just like you would structure a website. You can manage your website with a branch. A branch is like an experiment or a copy of your website. When you want to experiment with a new feature or fix something, you make a branch and experiment there. If the experiment is successful, you can merge the branch back into the original website.

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## Definition of hypothesis

Did you know.

The Difference Between Hypothesis and Theory

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

- proposition
- supposition

hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.

hypothesis implies insufficient evidence to provide more than a tentative explanation.

theory implies a greater range of evidence and greater likelihood of truth.

law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.

## Examples of hypothesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do

1641, in the meaning defined at sense 1a

## Phrases Containing hypothesis

- counter - hypothesis
- nebular hypothesis
- null hypothesis
- planetesimal hypothesis
- Whorfian hypothesis

## Articles Related to hypothesis

This is the Difference Between a...

## This is the Difference Between a Hypothesis and a Theory

In scientific reasoning, they're two completely different things

## Dictionary Entries Near hypothesis

hypothermia

hypothesize

## Cite this Entry

“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 13 Aug. 2024.

## Kids Definition

Kids definition of hypothesis, medical definition, medical definition of hypothesis, more from merriam-webster on hypothesis.

Nglish: Translation of hypothesis for Spanish Speakers

Britannica English: Translation of hypothesis for Arabic Speakers

Britannica.com: Encyclopedia article about hypothesis

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## The Craft of Writing a Strong Hypothesis

## Table of Contents

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

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

## What is a Hypothesis?

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

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

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

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

## Different Types of Hypotheses

Types of hypotheses

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

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

## 1. Null hypothesis

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

## 2. Alternative hypothesis

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

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

## 3. Simple hypothesis

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

## 4. Complex hypothesis

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

## 5. Associative and casual hypothesis

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

## 6. Empirical hypothesis

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

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

## 7. Statistical hypothesis

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

## Characteristics of a Good Hypothesis

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

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

## Separating a Hypothesis from a Prediction

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

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

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

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

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

## Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

## 1. Be clear about your research question

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

## 2. Carry out a recce

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

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

## 3. Create a 3-dimensional hypothesis

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

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

## 4. Write the first draft

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

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

## 5. Proof your hypothesis

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

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

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

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

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

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

## Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

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

## 2. What is an example of hypothesis?

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

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

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

## 4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

## 5. How to write a hypothesis?

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

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

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

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

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

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

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

## 8. What is plural for hypothesis?

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

## 9. What is the red queen hypothesis?

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

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

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

## 11. When to reject null hypothesis?

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

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

## What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

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

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

## Types of Hypothesis

Types of Hypothesis are as follows:

## Research Hypothesis

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

## Null Hypothesis

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

## Alternative Hypothesis

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

## Directional Hypothesis

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

## Non-directional Hypothesis

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

## Statistical Hypothesis

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

## Composite Hypothesis

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

## Empirical Hypothesis

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

## Simple Hypothesis

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

## Complex Hypothesis

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

## Applications of Hypothesis

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

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

## How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

## Identify the Research Question

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

## Conduct a Literature Review

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

## Determine the Variables

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

## Formulate the Hypothesis

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

## Write the Null Hypothesis

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

## Refine the Hypothesis

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

## Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

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

## Purpose of Hypothesis

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

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

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

## When to use Hypothesis

Here are some common situations in which hypotheses are used:

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

## Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

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

## Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

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

## Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

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

## About the author

## Muhammad Hassan

Researcher, Academic Writer, Web developer

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Basic Elements of the Scientific Method: Hypotheses

## The Function of the Hypotheses

A hypothesis states what one is looking for in an experiment. When facts are assembled, ordered, and seen in a relationship, they build up to become a theory. This theory needs to be deduced for further confirmation of the facts, this formulation of the deductions constitutes of a hypothesis. As a theory states a logical relationship between facts and from this, the propositions which are deduced should be true. Hence, these deduced prepositions are called hypotheses.

## Problems in Formulating the Hypothesis

There are three major difficulties in the formulation of a hypothesis, they are as follows:

Sometimes the deduction of a hypothesis may be difficult as there would be many variables and the necessity to take them all into consideration becomes a challenge. For instance, observing two cases:

Deduction: This situation holds much more sense to the people who are in professions such as psychotherapy, psychiatry and law to some extent. They possess a very intimate relationship with their clients, thus are more susceptible to issues regarding emotional strains in the client-practitioner relationship and more implicit and explicit controls over both participants in comparison to other professions.

2. Principle: Extensive but relatively systematized data show the correlation between members of the upper occupational class and less unhappiness and worry. Also, they are subjected to more formal controls than members of the lower strata.

Deduction: There can numerous ways to approach this principle, one could go with the comparison applying to martial relationships of the members and further argue that such differential pressures could be observed through divorce rates. This hypothesis would show inverse correlations between class position and divorce rates. There would be a very strong need to define the terms carefully to show the deduction from the principle problem.

## Types of Hypothesis

Science and hypothesis.

“The general culture in which a science develops furnishes many of its basic hypotheses” holds true as science has developed more in the West and is no accident that it is a function of culture itself. This is quite evident with the culture of the West as they read for morals, science and happiness. After the examination of a bunch of variables, it is quite easy to say that the cultural emphasis upon happiness has been productive of an almost limitless range.

The hypotheses originate from science; a key example in the form of “socialization” may be taken. The socialization process in learning science involves a feedback mechanism between the scientist and the student. The student learns from the scientist and then tests for results with his own experience, and the scientist in turn has to do the same with his colleagues.

Analogies are a source of useful hypotheses but not without its dangers as all variables may not be accounted for it as no civilization has a perfect system.

Hypotheses are also the consequence of personal, idiosyncratic experience as the manner in which the individual reacts to the hypotheses is also important and should be accounted for in the experiment.

## The Characteristics for Usable Hypotheses

The formulation of a hypothesis is probably the most necessary step in good research practice and it is very essential to get the thought process started. It helps the researcher to have a specific goal in mind and deduce the end result of an experiment with ease and efficiency. History is evident that asking the right questions always works out fine.

Also Read: Research Methods – Basics

Kartik is studying BA in International Relations at Amity and Dropped out of engineering from NIT Hamirpur and he lived in over 5 different countries.

## What is Hypothesis? Definition, Meaning, Characteristics, Sources

- Post last modified: 10 January 2022
- Reading time: 18 mins read
- Post category: Research Methodology

## What is Hypothesis?

Hypothesis is a prediction of the outcome of a study. Hypotheses are drawn from theories and research questions or from direct observations. In fact, a research problem can be formulated as a hypothesis. To test the hypothesis we need to formulate it in terms that can actually be analysed with statistical tools.

As an example, if we want to explore whether using a specific teaching method at school will result in better school marks (research question), the hypothesis could be that the mean school marks of students being taught with that specific teaching method will be higher than of those being taught using other methods.

In this example, we stated a hypothesis about the expected differences between groups. Other hypotheses may refer to correlations between variables.

Table of Content

- 1 What is Hypothesis?
- 2 Hypothesis Definition
- 3 Meaning of Hypothesis
- 4.1 Conceptual Clarity
- 4.2 Need of empirical referents
- 4.3 Hypothesis should be specific
- 4.4 Hypothesis should be within the ambit of the available research techniques
- 4.5 Hypothesis should be consistent with the theory
- 4.6 Hypothesis should be concerned with observable facts and empirical events
- 4.7 Hypothesis should be simple
- 5.1 Observation
- 5.2 Analogies
- 5.4 State of Knowledge
- 5.5 Culture
- 5.6 Continuity of Research
- 6.1 Null Hypothesis
- 6.2 Alternative Hypothesis

Thus, to formulate a hypothesis, we need to refer to the descriptive statistics (such as the mean final marks), and specify a set of conditions about these statistics (such as a difference between the means, or in a different example, a positive or negative correlation). The hypothesis we formulate applies to the population of interest.

The null hypothesis makes a statement that no difference exists (see Pyrczak, 1995, pp. 75-84).

## Hypothesis Definition

A hypothesis is ‘a guess or supposition as to the existence of some fact or law which will serve to explain a connection of facts already known to exist.’ – J. E. Creighton & H. R. Smart

Hypothesis is ‘a proposition not known to be definitely true or false, examined for the sake of determining the consequences which would follow from its truth.’ – Max Black

Hypothesis is ‘a proposition which can be put to a test to determine validity and is useful for further research.’ – W. J. Goode and P. K. Hatt

A hypothesis is a proposition, condition or principle which is assumed, perhaps without belief, in order to draw out its logical consequences and by this method to test its accord with facts which are known or may be determined. – Webster’s New International Dictionary of the English Language (1956)

## Meaning of Hypothesis

From the above mentioned definitions of hypothesis, its meaning can be explained in the following ways.

- At the primary level, a hypothesis is the possible and probable explanation of the sequence of happenings or data.
- Sometimes, hypothesis may emerge from an imagination, common sense or a sudden event.
- Hypothesis can be a probable answer to the research problem undertaken for study. 4. Hypothesis may not always be true. It can get disproven. In other words, hypothesis need not always be a true proposition.
- Hypothesis, in a sense, is an attempt to present the interrelations that exist in the available data or information.
- Hypothesis is not an individual opinion or community thought. Instead, it is a philosophical means which is to be used for research purpose. Hypothesis is not to be considered as the ultimate objective; rather it is to be taken as the means of explaining scientifically the prevailing situation.

The concept of hypothesis can further be explained with the help of some examples. Lord Keynes, in his theory of national income determination, made a hypothesis about the consumption function. He stated that the consumption expenditure of an individual or an economy as a whole is dependent on the level of income and changes in a certain proportion.

Later, this proposition was proved in the statistical research carried out by Prof. Simon Kuznets. Matthus, while studying the population, formulated a hypothesis that population increases faster than the supply of food grains. Population studies of several countries revealed that this hypothesis is true.

Validation of the Malthus’ hypothesis turned it into a theory and when it was tested in many other countries it became the famous Malthus’ Law of Population. It thus emerges that when a hypothesis is tested and proven, it becomes a theory. The theory, when found true in different times and at different places, becomes the law. Having understood the concept of hypothesis, few hypotheses can be formulated in the areas of commerce and economics.

- Population growth moderates with the rise in per capita income.
- Sales growth is positively linked with the availability of credit.
- Commerce education increases the employability of the graduate students.
- High rates of direct taxes prompt people to evade taxes.
- Good working conditions improve the productivity of employees.
- Advertising is the most effecting way of promoting sales than any other scheme.
- Higher Debt-Equity Ratio increases the probability of insolvency.
- Economic reforms in India have made the public sector banks more efficient and competent.
- Foreign direct investment in India has moved in those sectors which offer higher rate of profit.
- There is no significant association between credit rating and investment of fund.

## Characteristics of Hypothesis

Not all the hypotheses are good and useful from the point of view of research. It is only a few hypotheses satisfying certain criteria that are good, useful and directive in the research work undertaken. The characteristics of such a useful hypothesis can be listed as below:

## Conceptual Clarity

Need of empirical referents, hypothesis should be specific, hypothesis should be within the ambit of the available research techniques, hypothesis should be consistent with the theory, hypothesis should be concerned with observable facts and empirical events, hypothesis should be simple.

The concepts used while framing hypothesis should be crystal clear and unambiguous. Such concepts must be clearly defined so that they become lucid and acceptable to everyone. How are the newly developed concepts interrelated and how are they linked with the old one is to be very clear so that the hypothesis framed on their basis also carries the same clarity.

A hypothesis embodying unclear and ambiguous concepts can to a great extent undermine the successful completion of the research work.

A hypothesis can be useful in the research work undertaken only when it has links with some empirical referents. Hypothesis based on moral values and ideals are useless as they cannot be tested. Similarly, hypothesis containing opinions as good and bad or expectation with respect to something are not testable and therefore useless.

For example, ‘current account deficit can be lowered if people change their attitude towards gold’ is a hypothesis encompassing expectation. In case of such a hypothesis, the attitude towards gold is something which cannot clearly be described and therefore a hypothesis which embodies such an unclean thing cannot be tested and proved or disproved. In short, the hypothesis should be linked with some testable referents.

For the successful conduction of research, it is necessary that the hypothesis is specific and presented in a precise manner. Hypothesis which is general, too ambitious and grandiose in scope is not to be made as such hypothesis cannot be easily put to test. A hypothesis is to be based on such concepts which are precise and empirical in nature. A hypothesis should give a clear idea about the indicators which are to be used.

For example, a hypothesis that economic power is increasingly getting concentrated in a few hands in India should enable us to define the concept of economic power. It should be explicated in terms of measurable indicator like income, wealth, etc. Such specificity in the formulation of a hypothesis ensures that the research is practicable and significant.

While framing the hypothesis, the researcher should be aware of the available research techniques and should see that the hypothesis framed is testable on the basis of them. In other words, a hypothesis should be researchable and for this it is important that a due thought has been given to the methods and techniques which can be used to measure the concepts and variables embodied in the hypothesis.

It does not however mean that hypotheses which are not testable with the available techniques of research are not to be made. If the problem is too significant and therefore the hypothesis framed becomes too ambitious and complex, it’s testing becomes possible with the development of new research techniques or the hypothesis itself leads to the development of new research techniques.

A hypothesis must be related to the existing theory or should have a theoretical orientation. The growth of knowledge takes place in the sequence of facts, hypothesis, theory and law or principles. It means the hypothesis should have a correspondence with the existing facts and theory.

If the hypothesis is related to some theory, the research work will enable us to support, modify or refute the existing theory. Theoretical orientation of the hypothesis ensures that it becomes scientifically useful. According to Prof. Goode and Prof. Hatt, research work can contribute to the existing knowledge only when the hypothesis is related with some theory.

This enables us to explain the observed facts and situations and also verify the framed hypothesis. In the words of Prof. Cohen and Prof. Nagel, “hypothesis must be formulated in such a manner that deduction can be made from it and that consequently a decision can be reached as to whether it does or does not explain the facts considered.”

If the research work based on a hypothesis is to be successful, it is necessary that the later is as simple and easy as possible. An ambition of finding out something new may lead the researcher to frame an unrealistic and unclear hypothesis. Such a temptation is to be avoided. Framing a simple, easy and testable hypothesis requires that the researcher is well acquainted with the related concepts.

## Sources of Hypothesis

Hypotheses can be derived from various sources. Some of the sources is given below:

## Observation

State of knowledge, continuity of research.

Hypotheses can be derived from observation from the observation of price behavior in a market. For example the relationship between the price and demand for an article is hypothesized.

Analogies are another source of useful hypotheses. Julian Huxley has pointed out that casual observations in nature or in the framework of another science may be a fertile source of hypotheses. For example, the hypotheses that similar human types or activities may be found in similar geophysical regions come from plant ecology.

This is one of the main sources of hypotheses. It gives direction to research by stating what is known logical deduction from theory lead to new hypotheses. For example, profit / wealth maximization is considered as the goal of private enterprises. From this assumption various hypotheses are derived’.

An important source of hypotheses is the state of knowledge in any particular science where formal theories exist hypotheses can be deduced. If the hypotheses are rejected theories are scarce hypotheses are generated from conception frameworks.

Another source of hypotheses is the culture on which the researcher was nurtured. Western culture has induced the emergence of sociology as an academic discipline over the past decade, a large part of the hypotheses on American society examined by researchers were connected with violence. This interest is related to the considerable increase in the level of violence in America.

The continuity of research in a field itself constitutes an important source of hypotheses. The rejection of some hypotheses leads to the formulation of new ones capable of explaining dependent variables in subsequent research on the same subject.

## Null and Alternative Hypothesis

Null hypothesis.

The hypothesis that are proposed with the intent of receiving a rejection for them are called Null Hypothesis . This requires that we hypothesize the opposite of what is desired to be proved. For example, if we want to show that sales and advertisement expenditure are related, we formulate the null hypothesis that they are not related.

Similarly, if we want to conclude that the new sales training programme is effective, we formulate the null hypothesis that the new training programme is not effective, and if we want to prove that the average wages of skilled workers in town 1 is greater than that of town 2, we formulate the null hypotheses that there is no difference in the average wages of the skilled workers in both the towns.

Since we hypothesize that sales and advertisement are not related, new training programme is not effective and the average wages of skilled workers in both the towns are equal, we call such hypotheses null hypotheses and denote them as H 0 .

## Alternative Hypothesis

Rejection of null hypotheses leads to the acceptance of alternative hypothesis . The rejection of null hypothesis indicates that the relationship between variables (e.g., sales and advertisement expenditure) or the difference between means (e.g., wages of skilled workers in town 1 and town 2) or the difference between proportions have statistical significance and the acceptance of the null hypotheses indicates that these differences are due to chance.

As already mentioned, the alternative hypotheses specify that values/relation which the researcher believes hold true. The alternative hypotheses can cover a whole range of values rather than a single point. The alternative hypotheses are denoted by H 1 .

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## Understanding Hypothesis Testing

Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

## What is Hypothesis Testing?

A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.

To test the validity of the claim or assumption about the population parameter:

- A sample is drawn from the population and analyzed.
- The results of the analysis are used to decide whether the claim is true or not.

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

## Defining Hypotheses

- Null hypothesis (H 0 ): In statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured cases or no relationship among groups. In other words, it is a basic assumption or made based on the problem knowledge. Example : A company’s mean production is 50 units/per da H 0 : [Tex]\mu [/Tex] = 50.
- Alternative hypothesis (H 1 ): The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. Example: A company’s production is not equal to 50 units/per day i.e. H 1 : [Tex]\mu [/Tex] [Tex]\ne [/Tex] 50.

## Key Terms of Hypothesis Testing

- Level of significance : It refers to the degree of significance in which we accept or reject the null hypothesis. 100% accuracy is not possible for accepting a hypothesis, so we, therefore, select a level of significance that is usually 5%. This is normally denoted with [Tex]\alpha[/Tex] and generally, it is 0.05 or 5%, which means your output should be 95% confident to give a similar kind of result in each sample.
- P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
- Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
- Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
- Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

## Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing.

## One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

## One-Tailed Test

There are two types of one-tailed test:

- Left-Tailed (Left-Sided) Test: The alternative hypothesis asserts that the true parameter value is less than the null hypothesis. Example: H 0 : [Tex]\mu \geq 50 [/Tex] and H 1 : [Tex]\mu < 50 [/Tex]
- Right-Tailed (Right-Sided) Test : The alternative hypothesis asserts that the true parameter value is greater than the null hypothesis. Example: H 0 : [Tex]\mu \leq50 [/Tex] and H 1 : [Tex]\mu > 50 [/Tex]

## Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]

To delve deeper into differences into both types of test: Refer to link

## What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

- Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha( [Tex]\alpha [/Tex] ).
- Type II errors : When we accept the null hypothesis, but it is false. Type II errors are denoted by beta( [Tex]\beta [/Tex] ).

Null Hypothesis is True | Null Hypothesis is False | |
---|---|---|

Null Hypothesis is True (Accept) | Correct Decision | Type II Error (False Negative) |

Alternative Hypothesis is True (Reject) | Type I Error (False Positive) | Correct Decision |

## How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ), suggesting an effect or difference.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

## Step 2 – Choose significance level

Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.

## Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

## Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

- Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
- t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
- Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
- F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

## Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

## Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

- If Test Statistic>Critical Value: Reject the null hypothesis.
- If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

## Method B: Using P-values

We can also come to an conclusion using the p-value,

- If the p-value is less than or equal to the significance level i.e. ( [Tex]p\leq\alpha [/Tex] ), you reject the null hypothesis. This indicates that the observed results are unlikely to have occurred by chance alone, providing evidence in favor of the alternative hypothesis.
- If the p-value is greater than the significance level i.e. ( [Tex]p\geq \alpha[/Tex] ), you fail to reject the null hypothesis. This suggests that the observed results are consistent with what would be expected under the null hypothesis.

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

## Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

## Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

## 1. Z-statistics:

When population means and standard deviations are known.

[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]

- [Tex]\bar{x} [/Tex] is the sample mean,
- μ represents the population mean,
- σ is the standard deviation
- and n is the size of the sample.

## 2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]

- t = t-score,
- x̄ = sample mean
- μ = population mean,
- s = standard deviation of the sample,
- n = sample size

## 3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]

- [Tex]O_{ij}[/Tex] is the observed frequency in cell [Tex]{ij} [/Tex]
- i,j are the rows and columns index respectively.
- [Tex]E_{ij}[/Tex] is the expected frequency in cell [Tex]{ij}[/Tex] , calculated as : [Tex]\frac{{\text{{Row total}} \times \text{{Column total}}}}{{\text{{Total observations}}}}[/Tex]

## Real life Examples of Hypothesis Testing

Let’s examine hypothesis testing using two real life situations,

## Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

- Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
- After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

## Step 1 : Define the Hypothesis

- Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
- Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

## Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

## Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

- m = mean of the difference i.e X after, X before
- s = standard deviation of the difference (d) i.e d i = X after, i − X before,
- n = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

## Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

- If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
- If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

## Python Implementation of Case A

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

import numpy as np from scipy import stats # Data before_treatment = np . array ([ 120 , 122 , 118 , 130 , 125 , 128 , 115 , 121 , 123 , 119 ]) after_treatment = np . array ([ 115 , 120 , 112 , 128 , 122 , 125 , 110 , 117 , 119 , 114 ]) # Step 1: Null and Alternate Hypotheses # Null Hypothesis: The new drug has no effect on blood pressure. # Alternate Hypothesis: The new drug has an effect on blood pressure. null_hypothesis = "The new drug has no effect on blood pressure." alternate_hypothesis = "The new drug has an effect on blood pressure." # Step 2: Significance Level alpha = 0.05 # Step 3: Paired T-test t_statistic , p_value = stats . ttest_rel ( after_treatment , before_treatment ) # Step 4: Calculate T-statistic manually m = np . mean ( after_treatment - before_treatment ) s = np . std ( after_treatment - before_treatment , ddof = 1 ) # using ddof=1 for sample standard deviation n = len ( before_treatment ) t_statistic_manual = m / ( s / np . sqrt ( n )) # Step 5: Decision if p_value <= alpha : decision = "Reject" else : decision = "Fail to reject" # Conclusion if decision == "Reject" : conclusion = "There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different." else : conclusion = "There is insufficient evidence to claim a significant difference in average blood pressure before and after treatment with the new drug." # Display results print ( "T-statistic (from scipy):" , t_statistic ) print ( "P-value (from scipy):" , p_value ) print ( "T-statistic (calculated manually):" , t_statistic_manual ) print ( f "Decision: { decision } the null hypothesis at alpha= { alpha } ." ) print ( "Conclusion:" , conclusion )

T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05.

- The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
- The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

## Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

## Step 1: Define the Hypothesis

- Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
- Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] and we get accordingly , Z =2.039999999999992.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

## Python Implementation of Case B

import scipy.stats as stats import math import numpy as np # Given data sample_data = np . array ( [ 205 , 198 , 210 , 190 , 215 , 205 , 200 , 192 , 198 , 205 , 198 , 202 , 208 , 200 , 205 , 198 , 205 , 210 , 192 , 205 , 198 , 205 , 210 , 192 , 205 ]) population_std_dev = 5 population_mean = 200 sample_size = len ( sample_data ) # Step 1: Define the Hypotheses # Null Hypothesis (H0): The average cholesterol level in a population is 200 mg/dL. # Alternate Hypothesis (H1): The average cholesterol level in a population is different from 200 mg/dL. # Step 2: Define the Significance Level alpha = 0.05 # Two-tailed test # Critical values for a significance level of 0.05 (two-tailed) critical_value_left = stats . norm . ppf ( alpha / 2 ) critical_value_right = - critical_value_left # Step 3: Compute the test statistic sample_mean = sample_data . mean () z_score = ( sample_mean - population_mean ) / \ ( population_std_dev / math . sqrt ( sample_size )) # Step 4: Result # Check if the absolute value of the test statistic is greater than the critical values if abs ( z_score ) > max ( abs ( critical_value_left ), abs ( critical_value_right )): print ( "Reject the null hypothesis." ) print ( "There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL." ) else : print ( "Fail to reject the null hypothesis." ) print ( "There is not enough evidence to conclude that the average cholesterol level in the population is different from 200 mg/dL." )

Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.

## Limitations of Hypothesis Testing

- Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
- The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
- Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

## Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

## 2.What are the 4 components of hypothesis testing?

Null Hypothesis ( [Tex]H_o [/Tex] ): No effect or difference exists. Alternative Hypothesis ( [Tex]H_1 [/Tex] ): An effect or difference exists. Significance Level ( [Tex]\alpha [/Tex] ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

## 3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

## 4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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## What Is the Function of the Hypothesis?

## Types of Observation in the Scientific Method

Hypotheses are the questions scientists ask as they use the scientific method to understand the world. People use the process of formulating then attempting to disprove a hypothesis in their everyday lives as well. The function of the hypothesis is to give structure to the process of understanding how the world works.

## Identification

A hypothesis is an educated guess, based on the probability of an outcome. Scientists formulate hypotheses after they understand all the current research on their subject. Hypotheses specify the relationship between at least two variables, and are testable. For a hypothesis to function properly, other scientists must be able to reproduce the results that prove or disprove it. Two types of hypotheses exist: a descriptive hypothesis asks a question, and a directional hypothesis makes a statement.

## Scientific Method

The scientific method is the process by which hypotheses function. Scientists use the scientific method to, over time, form an accurate picture of the world. The scientific method attempts to remove the scientist's bias from the research. The four parts of the scientific method are observation and description, formulation of a hypothesis, use of the hypothesis for prediction and performance of testing of the hypothesis. Scientists use the scientific method to disprove hypotheses, rather than prove them. It they cannot be disproved, the hypotheses over time become accepted theories.

## Experiments

The most important function hypotheses perform is providing the framework for testing and experimentation. Scientists formulate a hypothesis, or ask a question, about a certain phenomenon and how it relates to other aspects of the world. Then they devise ways to try to disprove their theory as to the answer. For instance, if a scientist made a hypothesis that what goes up must come down, he would test it by throwing many items in the air to see if they do come down. Because scientists cannot test every single possible item for this theory, hypotheses are never proven. However, after many scientists have experimented with the hypothesis, it becomes accepted scientific theory.

## Formulating Hypotheses

Scientists make a hypothesis by comparing the phenomenon being studied to another phenomenon. For instance, in the real world, a person might decide that her house is cold because a window is open. She would test this theory by checking the windows. If the windows are closed, then that hypothesis is proven false, and another is formed when the person decides that her house is probably cold because the furnace isn't working properly. The process of forming and disproving hypotheses continues until a person makes a hypothesis that cannot be disproved.

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## How Important Is Scientific Evidence?

- Richmond University; What Is a Good Hypothesis?; Daniel Palazzolo, Ph.D., et al.
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Shaunta Alburger has been a professional writer for 15 years. She's worked on staff at both major Las Vegas newspapers, as well as a rural Nevada weekly. Her first novel was published in 2014.

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## Table of Contents

In today’s data-driven world, decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

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## What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life -

- A teacher assumes that 60% of his college's students come from lower-middle-class families.
- A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

## Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

- Here, x̅ is the sample mean,
- μ0 is the population mean,
- σ is the standard deviation,
- n is the sample size.

## How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

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## Null Hypothesis and Alternative Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average.

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

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## Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

## Steps in Hypothesis Testing

Hypothesis testing is a statistical method to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here’s a breakdown of the typical steps involved in hypothesis testing:

## Formulate Hypotheses

- Null Hypothesis (H0): This hypothesis states that there is no effect or difference, and it is the hypothesis you attempt to reject with your test.
- Alternative Hypothesis (H1 or Ha): This hypothesis is what you might believe to be true or hope to prove true. It is usually considered the opposite of the null hypothesis.

## Choose the Significance Level (α)

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. Common choices for α are 0.05 (5%), 0.01 (1%), and 0.10 (10%).

## Select the Appropriate Test

Choose a statistical test based on the type of data and the hypothesis. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis. The selection depends on data type, distribution, sample size, and whether the hypothesis is one-tailed or two-tailed.

## Collect Data

Gather the data that will be analyzed in the test. This data should be representative of the population to infer conclusions accurately.

## Calculate the Test Statistic

Based on the collected data and the chosen test, calculate a test statistic that reflects how much the observed data deviates from the null hypothesis.

## Determine the p-value

The p-value is the probability of observing test results at least as extreme as the results observed, assuming the null hypothesis is correct. It helps determine the strength of the evidence against the null hypothesis.

## Make a Decision

Compare the p-value to the chosen significance level:

- If the p-value ≤ α: Reject the null hypothesis, suggesting sufficient evidence in the data supports the alternative hypothesis.
- If the p-value > α: Do not reject the null hypothesis, suggesting insufficient evidence to support the alternative hypothesis.

## Report the Results

Present the findings from the hypothesis test, including the test statistic, p-value, and the conclusion about the hypotheses.

## Perform Post-hoc Analysis (if necessary)

Depending on the results and the study design, further analysis may be needed to explore the data more deeply or to address multiple comparisons if several hypotheses were tested simultaneously.

## Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

## Chi-Square

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

## Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

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## Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

## One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

## Become a Data Scientist With Real-World Experience

## Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

- The null hypothesis is (H0 <= 90) or less change.
- A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

## Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

## Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true].

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

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## Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

- It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
- Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
- Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
- Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

## Learn All The Tricks Of The BI Trade

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore the Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

## 1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

## 2. What is H0 and H1 in statistics?

In statistics, H0 and H1 represent the null and alternative hypotheses. The null hypothesis, H0, is the default assumption that no effect or difference exists between groups or conditions. The alternative hypothesis, H1, is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data.

## 3. What is a simple hypothesis with an example?

A simple hypothesis is a specific statement predicting a single relationship between two variables. It posits a direct and uncomplicated outcome. For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here, the hypothesis suggests a direct relationship between the amount of sunlight (independent variable) and the growth rate of sunflowers (dependent variable), with no additional variables considered.

## 4. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

- Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
- Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
- Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

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## Nuclear Theory

Title: application of the shift-invert lanczos algorithm to a non-equilibrium green function for transport problems.

Abstract: Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function.

Comments: | 8 pages, 4 figures, 1 table |

Subjects: | Nuclear Theory (nucl-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech); Chemical Physics (physics.chem-ph) |

Report number: | KUNS-3011 |

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## Non-Fermi-liquid behavior of the t − J model in the strange metal phase: U ( 1 ) gauge theory consistent with local constraints

Long liang, yue yu, and xi luo, phys. rev. b 110 , 075125 – published 12 august 2024.

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- INTRODUCTION
- CONSISTENT U ( 1 ) GAUGE THEORY FOR THE t − J …
- PERTURBATION THEORY
- ONE-ELECTRON GREEN'S FUNCTION AND…
- RESPONSES TO THE EXTERNAL ELECTRIC AND…
- CONCLUSIONS AND DISCUSSIONS
- ACKNOWLEDGMENTS

In the slave particle representation with U ( 1 ) gauge symmetry, local constraints on physical states characterized by various mean field solutions belong to Dirac's second-class ones. Although constrained systems are extensively investigated, realistic methods to solve the gauge theory problem with second-class constraints are yet to be developed. We formulate a Becchi-Rouet-Stora-Tyutin (BRST) quantization theory, called consistent U ( 1 ) gauge theory, that is consistent with both first- and second-class local constraints for strongly correlated condensed matter systems. In our consistent U ( 1 ) gauge theory, the redundant gauge degrees of freedom are removed by proper gauge fixing conditions while the constraints are exactly retained and the gauge invariance is guaranteed by the BRST symmetry. Furthermore, the gauge fixing conditions endow the gauge field with dynamics. This turns the strongly correlated electron model into a weakly coupled slave boson model, so most of the system's physical properties can be calculated by the conventional quantum many-body perturbation method. We focus on the property of the strange metal phase in the t − J model. The electron momentum distribution and the spectral function are calculated, and the non-Fermi-liquid behavior agrees with the angle-resolved photoemission spectroscopy measurements for cuprate materials. We also study the electromagnetic responses of the strange metal state. The observed non-Fermi-liquid anomalies are captured by our calculations. Especially, we find that the Hall resistivity decreases as temperature increases, and the sign of the Hall resistivity varies from negative to positive when the dopant concentration varies from optimal doping to underdoping in the strange metal regime.

- Received 27 February 2024
- Accepted 1 August 2024

DOI: https://doi.org/10.1103/PhysRevB.110.075125

©2024 American Physical Society

## Physics Subject Headings (PhySH)

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- Physical Systems

## Authors & Affiliations

- 1 Department of Physics, Institute of Solid State Physics and Center for Computational Sciences, Sichuan Normal University , Chengdu, Sichuan 610066, China
- 2 Department of Physics, Fudan University , Shanghai 200433, China
- 3 College of Science, University of Shanghai for Science and Technology , Shanghai 200093, China
- * Contact author: [email protected]
- † Contact author: [email protected]

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The Feynman diagrams for the free one-particle Green's functions of (a) f σ , (b) h , (c) δ a μ = ( δ λ , δ a a ) . ξ f ( h ) k = k 2 2 m f ( h ) − μ f ( h ) .

The Feynman diagrams for the three-point vertex.

The Feynman diagrams for the four-point vertex.

The electron Green's function is constructed from the full Green's functions of holon and spinon, and a full vertex correction, which are represented by thick lines and black circles. The second to the fourth lines represent the self-energy corrections of holons and spinons up to g 2 order. The fourth line represents the vertex correction up to g 2 order. The ellipsis ( ⋯ ) represents higher-order terms. The Green's function of δ λ is indicated by the dotted line, while the wavy line indicates that of δ a b .

The Feynman diagrams of the g 4 order with k a k b -dependent contributions.

The electron spectral function without gauge fluctuations at T = 200 K > T * .

The electron spectral function for different momentum and frequency. Solid line: holon self-energy is neglected. Dashed line: both spinon and holon self-energies are neglected.

The electron spectral function for different momentum and frequency. Solid line: with gauge fluctuations. Dashed line: without gauge fluctuations.

Dependence of temperature and dopant concentration on Hall resistivity. We choose q = ( 0.01 , 0.01 ) in Eqs. ( 64 ) and ( 65 ).

The Feynman diagrams for the anomalous Green's functions of (a) G ( 0 ) , (b) F ( 0 ) † , and (c) F ( 0 ) .

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## ENTJ: The Commander (Extraverted, Intuitive, Thinking, Judging)

Assertiveness and confidence are hallmarks of the ENTJ personality type

- Characteristics
- Cognitive Functions
- Personal Relationships
- Career Paths

## Tips for Interacting With ENTJs

- Next in Myers-Briggs Type Indicator Guide ENTP Personality Type (Extroverted, Intuitive, Thinking, Perceiving)

Personality is what makes us unique, but according to the Myers-Briggs Type Indicator (MBTI), our personalities tend to fall into one of 16 distinct "types." Each of these types is identified by a four-letter acronym describing key personality traits. For the ENTJ personality type, these letters stand for extraverted, intuitive, thinking, and judging. People with this personality type are often described as assertive, confident, and outspoken.

Sometimes referred to as the "Commander," ENTJs tend to be great with people. They have a knack for envisioning the future and place a lot of emphasis on abstract ideas when they are making decisions. You might recognize them as the natural leaders who love to plan ahead.

The MBTI is one of the most popular personality assessments. It was developed by Isabel Myers and her mother, Katherine Briggs, and is based on Carl Jung's theory of personality types .

## At a Glance

ENTJs are extraverts, which means they are outgoing and gain energy by spending time around others. They thrive in social situations and naturally tend to take charge when decisions need to be made. They are confident and self-assured but sometimes struggle with being a little impatient or stubborn. Understanding how these traits appear in your own personality can give you insights in how your personality affects your career, relationships, and happiness.

## Characteristics of the ENTJ Personality Type

According to psychologist David Keirsey, the ENTJ type is quite rare, accounting for a mere 2% of the population. They typically share a number of different strengths and weaknesses.

## ENTJs Have Many Strengths...

Like other personality types, ENTJs have a number of important strengths:

- Great with people : People with this personality type enjoy spending time with other people. They have strong verbal skills, and interacting with others helps them feel energized.
- Future-focused : ENTJ types prefer to think about the future, and they enjoy thinking about abstract ideas. When making decisions , ENTJs place a greater emphasis on objective and logical information.
- Great at planning : ENTJs are planners. Making decisions and having a schedule or course of action planned out gives them a sense of predictability and control.
- Highly rational : They are highly rational, good at spotting problems, and excel at taking charge. These tendencies make them natural leaders who are focused on efficiently solving problems.

## ...But They Also Have Some Weaknesses

Like other personality types, ENTJs also have traits that can be challenges at times:

- Trouble focusing on details : Because they are so focused on the future, they often lose sight of what's happening in the here and now. While they love abstract concepts, they tend to feel bored if they have to focus on a lot of concrete, detailed information.
- Tend to ignore other people's emotions : Personal feelings and the emotions of others tend not to factor much into their choices. ENTJs are not necessarily good with emotions, but that does not mean they are intentionally cruel.
- Tend to hide their own feelings : They are prone to hiding their own emotions and sentimentality, viewing it as a weakness that should not be made known to others.

Strong leadership skills

Self-assured

Well-organized

Good at making decisions

Assertive and outspoken

Strong communication skills

Insensitive

## Understanding the Cognitive Functions of ENTJs

Based upon the Jungian personality theory, the MBTI suggests that personality is composed of several different cognitive functions. These functions can be focused primarily outward (extraverted) or inward (introverted).

Each function relates to how people perceive the world and make decisions.:

- The dominant function is the most prominent aspect of personality, while the auxiliary function plays a supporting role.
- The tertiary function has a weaker influence but can become more apparent when a person is under stress.
- The inferior function is primarily unconscious and is often a point of weakness. Developing this aspect can help people form a more balanced personality.

## Dominant: Extraverted Thinking (Te)

This is an ENTJ preferred function and is expressed through the way they make decisions and judgments.

ENTJs tend to speak first without listening, making snap judgments before really taking in all the information about a situation.

While they tend to make snap judgments, they are also very rational and objective. They are focused on imposing order and standards on the world around them. Setting measurable goals is important.

## Auxiliary: Introverted Intuition (Ni)

The auxiliary function helps balance a person's personality. Using the dominant function all the time would lead to a one-dimensional personality. The dominant function does act as the primary driver of personality, but the auxiliary function is there to offer support.

People with this personality type are future-focused and always consider the possibilities when approaching a decision.

ENTJs are forward-thinking and are not afraid of change. They trust their instincts, although they tend to regret jumping to conclusions so quickly.

## Tertiary: Extraverted Sensing

The tertiary function in personality acts as a background support, although it is less prominent that the dominant and auxiliary functions.

This cognitive function gives ENTJs an appetite for adventure. They enjoy novel experiences and may sometimes engage in thrill-seeking behaviors.

Because of their outward sensory focus, they also have an appreciation for beautiful things in life. They often enjoy surrounding themselves with things that they find attractive or interesting.

## Inferior: Introverted Feeling

The inferior function is the weakest part of your personality. That means that it is frequently one of your biggest challenges. Introverted feeling is centered on internal feelings and values.

Emotions can be difficult area for ENTJs, and they often lack an understanding of how this part of their personality contributes to their decision-making process.

When this aspect of personality is weak, ENTJs may feel uncomfortable or awkward in settings where an emotional response is required.

## ENTJs You Might Know

- Franklin D. Roosevelt, U.S. President
- Bill Gates, Microsoft founder
- Vince Lombardi, football coach
- Carl Sagan, astronomer
- Lex Luthor, Superman character

## Personal Relationships With ENTJs

Since ENTJs are extraverts , they gain energy from socializing (unlike introverts , who expend energy in social situations). They love having passionate and lively conversations and debates. In some cases, other people can feel intimidated by the ENTJs confidence and strong verbal skills. When they have a good idea, people with this personality type feel compelled to share their point of view with others.

Despite their verbal abilities, ENTJs are not always good at understanding other people's emotions.

Expressing emotions can be difficult for them at times, and their tendency to get into debates can make them seem aggressive, argumentative, and confrontational. People can overcome this problem by making a conscious effort to think about how other people might be feeling.

They may struggle to understand or get along with more sensitive personality types. While they are extroverts, they are not emotionally expressive and other people may see them as insensitive.

## Subtypes: ENTJ-T vs. ENTJ-A

ENTJs can be further categorized as:

- ENTJ-T (the turbulent commander) —Seeks validation and attention; tends toward anger and jealousy; emotionally driven; more sensitive, sentimental, and affectionate than ENTJ-A
- ENTJ-A (the assertive commander) —Confident; assumes others' acceptance; less emotionally reactive; handles stress and negativity well

## Career Paths for ENTJs

Thanks to their comfort in the spotlight, ability to communicate, and a tendency to make quick decisions, ENTJs tend to naturally fall into leadership roles.

These individuals sometimes find themselves taking control of a group without really knowing how they came to be in such a position. Because of their love for structure and order, the ENTJ is also good at supervising and directing others and helping groups complete tasks and achieve goals. They can quickly see what needs to be accomplished, develop a plan of action, and assign roles to group members.

ENTJs do best in careers where there is a lot of structure, but plenty of room for variety. Jobs that allow them to meet and interact with lots of different people are ideal. People with this type bring a lot of desirable skills to the table, including excellent leadership and communication skills, a hard-working attitude, and an ability to plan for the future.

## Popular ENTJ Careers

- Human resources manager
- Company CEO or manager
- Software developer
- Business analyst
- Entrepreneur
- University professor

Knowing more about how to interact with an ENTJ can help keep your relationships running smoothly with fewer conflicts. How you respond to an ENTJ can depend on the nature of your relationship. For example, you would communicate with them differently if they are your partner versus a co-worker. Here are some tips that can help you navigate different types of ENTJ relationships:

## Friendships

ENTJ are social people and love engaging conversations. While they can seem argumentative and confrontational at times, just remember that this is part of their communication style. Try not to take it personally. They tend to have the easiest friendships with people who share their interests and views and may struggle to understand people who are very introverted, sensitive, or emotional.

Parents of ENTJ children should recognize that their child is independent and intellectually curious. You can help your child by allowing them to pursue their curiosity. Understand that your child will often need your reasoning explained to understand why certain rules need to be followed.

You can also help your child develop their emotional understanding by talking openly about feelings. Point out how people might feel about different experiences so that your ENTJ child can learn to better interpret both their own emotions and those of others.

## Relationships

An ENTJ partner can often seem quite dominating in a relationship. Because dealing with emotions does not come naturally to them, they may seem insensitive to their partner's feelings. It is important to remember that this does not mean that ENTJ’s don’t have feelings—they just need to feel completely comfortable in order to show their emotions.

They are very committed to making relationships work and are always looking for ways that they can improve their relationships. If you have an issue with your partner, be upfront and honest. Your partner would rather hear the truth than try to guess your feelings.

It's important to remember that while ENTJs share many common traits, each person is unique. That means that how their personality is expressed may vary.

Learning more about your own personality type can help you to better understand you strengths and weaknesses. In doing so, you'll be better prepared to maximize your strengths and cope with your challenges.

Myers IB, Kirby LK, Myers KD. Introduction to Myers-Briggs Type: A Guide to Understanding Your Results on the MBTI Assessment . 7th ed. Consulting Psychologists Press; 2015.

Keirsey D. Please understand me II: Temperament, character, intelligence . Prometheus Nemesis; 1998.

Myers & Briggs Foundation. MBTI basics .

Myers & Briggs Foundation. The processes of type dynamics .

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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## Food & Function

An untargeted metabolomics approach applied to the study of the bioavailability and metabolism of three different bioactive plant extracts in human blood samples..

Advances in the understanding of bioavailability and metabolism of bioactive compounds have been achieved primarily through targeted or semi-targeted metabolomics approaches using the hypothesis of potential metabolized compounds. The recent development of untargeted metabolomics approaches can present great advantages in this field, such as in the discovery of new metabolized compounds or to study the metabolism of compounds from multiple matrices simultaneously. Thus, this study proposes the use of an untargeted metabolomics strategy based on HPLC-ESI-QTOF-MS for the study of bioavailability and metabolism of bioactive compounds from different vegetal sources. Specifically, this study has been applied to plasma samples collected in an acute human intervention study using three matrices (Hibiscus sabdariffa, Silybum marianum and Theobroma cacao). This approach allowed the selection of those significant variables associated with exogenous metabolites derived from the consumption of bioactive compounds for their subsequent identification. As a result, 14, 25 and 3 potential metabolites associated with supplement intake were significantly detected in the plasma samples from volunteers who ingested the H. sabdariffa (HS), S. marianum (SM) and T. cacao (TC) extracts. Furthermore, relative Tmax values have been computed for each detected compound. The results highlight the potential of untargeted metabolomics for rapid and comprehensive analysis when working with a wide range of exogenous metabolites from different plant sources in biological samples.

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M. D. C. Villegas Aguilar, M. D. L. Luz Cádiz-Gurrea, M. Herranz López, E. Barrajón Catalán, D. Arráez-Román, Á. Fernández-Ochoa and A. Segura-Carretero, Food Funct. , 2024, Accepted Manuscript , DOI: 10.1039/D4FO01522C

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## Physical Review C

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## Shell structure and shape transition in odd- Z superheavy nuclei with proton numbers Z = 117 , 119: Insights from applying deformed relativistic Hartree-Bogoliubov theory in continuum

Y. x. zhang (张妍心), b. r. liu (刘博然), k. y. zhang (张开元), and j. m. yao (尧江明), phys. rev. c 110 , 024302 – published 6 august 2024.

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- INTRODUCTION
- THEORETICAL FRAMEWORK
- RESULTS AND DISCUSSION
- ACKNOWLEDGMENTS

We present a systematic study on the structural properties of odd- Z superheavy nuclei with proton numbers Z = 117 , 119 , and neutron numbers N increasing from N = 170 to the neutron dripline within the framework of axially deformed relativistic Hartree-Bogoliubov theory in continuum. The results are compared with those of even-even superheavy nuclei with proton numbers Z = 118 and 120. We analyze various bulk properties of their ground states, including binding energies, quadrupole deformations, root-mean-square radii, nucleon separation energies, and α -decay energies. The coexistence of competing prolate and oblate or spherical shapes leads to abrupt changes in both quadrupole deformations and charge radii as functions of neutron numbers. Compared to even-even nuclei, the odd-mass ones exhibit a more complicated transition picture, in which the quantum numbers of K π of the lowest-energy configuration may change with deformation. This may result in the change of angular momentum in the ground-state to ground-state α decay and thus quench the decay rate in odd-mass nuclei. Moreover, our results demonstrate a pronounced proton shell gap at Z = 120 , instead of Z = 114 , which is consistent with the predictions of most covariant density functional theories. Besides, large neutron shell gaps are found at N = 172 and N = 258 in the four isotopic chains, as well as at N = 184 in the light two isotopic chains with Z = 117 and Z = 118 , attributed to the nearly degenerate 3 d and 4 p spin-orbit doublet states due to the presence of bubble structure.

- Received 16 May 2024
- Accepted 19 July 2024

DOI: https://doi.org/10.1103/PhysRevC.110.024302

©2024 American Physical Society

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## Authors & Affiliations

- 1 School of Physics and Astronomy, Sun Yat-sen University , Zhuhai 519082, People's Republic of China
- 2 Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics , Mianyang, Sichuan 621900, People's Republic of China
- * Contact author: [email protected]

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The average binding energy per nucleon B / A (MeV) of the ground states of Z = 117 – 120 isotopes as a function of the neutron number from the DRHBc calculations using the PC-PK1 EDF, in comparison with the WS4 mass model [ 26 ]. In the DRHBc results, both odd- N and even- N nuclei are considered for Z = 118 , 120 isotopic chains, while only even- N nuclei are considered for Z = 117 , 119 isotopic chains.

The discrepancy of the total energies of the ground states of Z = 117 – 120 isotopes, (a) between the DRHBc and LDM6 model and (b) between the DRHBc and WS4 mass model.

The various terms ( 21 ) contributing to the average binding energies of Z = 117 isotopes in the LDM6 model, as a function of neutron number, where the total average binding energy is given by the cancellation of the volume term with other terms. The pairing term (about 0.04 MeV per nucleon) is too small to be seen in the figure. See text for details.

The quadruple deformation parameters β 20 ( t ) of the energy-minimal states in Z = 117 – 120 isotopes, as a function of the neutron number, from (a) the DRHBc calculation, in comparison with (b) the WS4 mass model.

The total energies of states in Z = 119 isotopes as a function of the intrinsic quadrupole deformation parameter β 20 ( t ) , where the neutron numbers are (a) N = 170 , 174 , 176 , 178 , (b) N = 184 – 206 , (c) N = 242 – 250 , and (d) N = 258 – 268 , respectively. All energies are normalized to their ground states (indicated with bullets), but with an additional energy shift of 1 MeV between two neighboring isotopes.

The total energies of states with K π = 7 / 2 − (red solid line) and 11 / 2 + (blue dotted line) in 119 365 as a function of the intrinsic quadrupole deformation parameter β 20 ( t ) . The energies of the lowest-energy states (magenta dashed-dotted line) at each quadrupole deformation are also plotted for comparison.

The quadrupole deformation parameters β 20 ( t ) of the first two lowest-energy minima states (indicated with filled red circles and open blue circles, respectively) in Z = 119 isotopes from the DRHBc calculations with PC-PK1, where the neutron numbers are (a) N = 184 – 206 , (b) N = 242 – 250 , and (c) N = 258 – 268 , respectively.

(a) The rms radii R n of neutrons and (b) charge radii R ch in the nuclei of the Z = 117 – 120 isotopic chains as a function of neutron number. The empirical formula R n = 1.141 N 1 / 3 [ 56 ] is also given for comparison.

Nilsson diagram for (a) protons and (b) neutrons in 120 304 as a function of the axial deformation parameter β 20 ( t ) . All single-particle energy levels are labeled with K π , where positive parity states are represented by solid lines and negative parity with dashed lines. The Fermi energies are indicated with black filled square.

The single-particle energy levels of (a) protons and (b) neutrons in the spherical states of Z = 120 isotopes as a function of neutron number. An evident discontinuity occurs at N = 258 , where pairing correlation between neutrons collapses.

Comparison of the two-proton shell gap Δ S 2 p ( sph . ) (blue solid lines) and the energy gap δ ε p (gray dashed lines) between two proton energy levels around Z = 120 as a function of neutron number.

The spin-orbit splitting of (a) neutrons and (b) protons in the spherical states of Z = 120 isotopes as a function of neutron number.

The L = 0 component ( 17 ) of the proton density in Z = 120 isotopes with neutron number (a) N = 170 – 186 and (b) N = 252 – 260 , respectively.

(a) The two-neutron separation energies S 2 n and (b) their differences Δ S 2 n in the Z = 117 – 120 isotopic chains as a function of neutron number. The results of calculations for the states restricted to have spherical shape are also plotted for comparison.

Same as Fig. 13 , but for neutrons.

The Q α values of the four isotopic chains with Z = 117 – 120 as a function of neutron number from the DRHBc calculations, in comparison with the results of WS4 model. The values of two neighboring isotopic chains are shifted by 4 MeV. The isotopes with only even neutron numbers are considered. (a) and (b) show the results of DRHBc calculations without and with the energy correction from the restoration of rotational symmetry, respectively. The data are taken from Refs. [ 12, 13 ].

The deviation Δ Q α of the α -decay energies by the LDM6 model from the DRHBc theory (without E rot ) for the Z = 119 , 120 isotopes as a function of neutron number.

The α -decay chains originating from the ground states of 119 293 , 295 , 297 from the DRHBc calculation. The lowest-energy state of each nucleus along the chain, together with the state with K π = 5 / 2 − , is shown. The black arrows indicate the favored α decays. The energy difference between two energy levels is given near each arrow. The possible energy levels in between are not concerned. All energies are in MeV. The superheavy nuclei that have already been produced by the Bk 249 + Ca 48 reaction [ 69 ] are indicated with light yellow. See main text for details.

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Figure 1. The average binding energy per nucleon B / A (MeV) of the ground states of Z = 117 - 120 isotopes as a function of the neutron number from the DRHBc calculations using the PC-PK1 EDF, in comparison with the WS4 mass model [].In the DRHBc results, both odd-N and even-N nuclei are considered for Z = 118, 120 isotopic chains, while only even-N nuclei are considered for Z = 117, 119 ...