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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

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Published by Nicolas at January 16th, 2024 , Revised On January 23, 2024

How To Write A Hypotheses – Guide For Students

The word “hypothesis” might conjure up images of scientists in white coats, but crafting a solid hypothesis is a crucial skill for students in any field. Whether you are analyzing Shakespeare’s sonnets or conducting a science experiment, a well-defined research hypothesis sets the stage for your dissertation or thesis and fuels your investigation. 

Table of Contents

Writing a hypothesis is a crucial step in the research process. A hypothesis serves as the foundation of your research paper because it guides the direction of your study and provides a clear framework for investigation. But how to write a hypothesis? This blog will help you craft one. Let’s get started.

What Is A Hypothesis

A hypothesis is a clear and testable thesis statement or prediction that serves as the foundation of a research study. It is formulated based on existing knowledge, observations, and theoretical frameworks. 

A hypothesis articulates the researcher’s expectations regarding the relationship between variables in a study.

Hypothesis Example

Students exposed to multimedia-enhanced teaching methods will demonstrate higher retention of information compared to those taught using traditional methods.

The formulation of a hypothesis is crucial for guiding the research process and providing a clear direction for data collection and analysis. A well-crafted research hypothesis not only makes the research purpose explicit but also sets the stage for drawing meaningful conclusions from the study’s findings.

What Is A Null Hypothesis And Alternative Hypothesis

There are two main types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha). 

The null hypothesis posits that there is no significant effect or relationship, while the alternative hypothesis suggests the presence of a significant effect or relationship.

For example, in a study investigating the effect of a new drug on blood pressure, the null hypothesis might state that there is no difference in blood pressure between the control group (not receiving the drug) and the experimental group (receiving the drug). The alternative hypothesis, on the other hand, would propose that there is a significant difference in blood pressure between the two groups.

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How To Write A Good Research Hypothesis

Writing a hypothesis involves a systematic process that guides your research and provides a clear and testable statement about the expected relationship between variables. Go through the MLA vs. APA guidelines before writing. Here are the steps to help you how to write a hypothesis:

Step 1: Identify The Research Topic

Clearly define the research topic or question that you want to investigate. Ensure that your research question is specific and focused, providing a clear direction for your study.

Step 2: Conduct A Literature Review

Review existing literature related to your research topic. A thorough literature review helps you understand what is already known in the field, identify gaps, and build a foundation for formulating your hypothesis.

Step 3: Define Variables

Identify the variables involved in your study. The independent variable is the factor you manipulate, and the dependent variable is the one you measure. Clearly define the characteristics or conditions you are studying.

Step 4: Establish The Relationship

Determine the expected relationship between the independent and dependent variables. Will a change in the independent variable lead to a change in the dependent variable? Specify whether you anticipate a positive, negative, or no relationship.

Step 5: Formulate The Null Hypothesis (H0)

The null hypothesis represents the default position, suggesting that there is no significant effect or relationship between the variables you are studying. It serves as the baseline to be tested against. The null hypothesis is often denoted as H0.

Step 6: Formulate The Alternative Hypothesis (H1 or Ha)

The alternative hypothesis articulates the researcher’s expectation about the existence of a significant effect or relationship. It is what you aim to support with your research paper . The alternative hypothesis is denoted as H1 or Ha.

For example, if your research topic is about the effect of a new fertilizer on plant growth:

• Null Hypothesis (H0): There is no significant difference in plant growth between plants treated with the traditional fertilizer and those treated with the new fertilizer.
• Alternative Hypothesis (H1): There is a significant difference in plant growth between plants treated with the traditional fertilizer and those treated with the new fertilizer.

Step 7: Ensure Testability And Specificity

Confirm that your research hypothesis is testable and can be empirically investigated. Ensure that it is specific, providing a clear and measurable statement that can be validated or refuted through data collection and analysis.

Hypothesis Examples

What makes a good hypothesis.

• Clear Statement: A hypothesis should be stated clearly and precisely. It should be easily understandable and convey the expected relationship between variables.
• Testability: A hypothesis must be testable through empirical observation or experimentation. This means that there should be a feasible way to collect data and assess whether the expected relationship holds true.
• Specificity: The research hypothesis should be specific in terms of the variables involved and the nature of the expected relationship. Vague or ambiguous hypotheses can lead to unclear research outcomes.
• Measurability: Variables in a hypothesis should be measurable, meaning they can be quantified or observed objectively. This ensures that the research can be conducted with precision.
• Falsifiability: A good research hypothesis should be falsifiable, meaning there should be a possibility of proving it wrong. This concept is fundamental to the scientific method, as hypotheses that cannot be tested or disproven lack scientific validity.

Frequently Asked Questions

How to write a hypothesis.

• Clearly state the research question.
• Identify the variables involved.
• Formulate a clear and testable prediction.
• Use specific and measurable terms.
• Align the hypothesis with the research question.
• Distinguish between the null hypothesis (no effect) and alternative hypothesis (expected effect).
• Ensure the hypothesis is falsifiable and subject to empirical testing.

How to write a hypothesis for a lab?

• Identify the purpose of the lab.
• Clearly state the relationship between variables.
• Use concise language and specific terms.
• Make the hypothesis testable through experimentation.
• Align with the lab’s objectives.
• Include an if-then statement to express the expected outcome.
• Ensure clarity and relevance to the experimental setup.

What Is A Null Hypothesis?

A null hypothesis is a statement suggesting no effect or relationship between variables in a research study. It serves as the default assumption, stating that any observed differences or effects are due to chance. Researchers aim to reject the null hypothesis based on statistical evidence to support their alternative hypothesis.

How to write a null hypothesis?

• State there is no effect, difference, or relationship between variables.
• Use clear and specific language.
• Frame it in a testable manner.
• Align with the research question.
• Specify parameters for statistical testing.
• Consider it as the default assumption to be tested and potentially rejected in favour of the alternative hypothesis.

What is the p-value of a hypothesis test?

The p-value in a hypothesis test represents the probability of obtaining observed results, or more extreme ones, if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis, often leading to its rejection. Common significance thresholds include 0.05 or 0.01.

How to write a hypothesis in science?

• Clearly state the research question
• Identify the variables and their relationship.
• Formulate a testable and falsifiable prediction.
• Use specific, measurable terms.
• Distinguish between the null and alternative hypotheses.
• Ensure clarity and relevance to the scientific investigation.

How to write a hypothesis for a research proposal?

• Clearly define the research question.
• Identify variables and their expected relationship.
• Formulate a specific, testable hypothesis.
• Align the hypothesis with the proposal’s objectives.
• Clearly articulate the null hypothesis.
• Use concise language and measurable terms.
• Ensure the hypothesis aligns with the proposed research methodology.

How to write a good hypothesis psychology?

• Formulate a specific and testable prediction.
• Use precise and measurable terms.
• Align the hypothesis with psychological theories.
• Articulate the null hypothesis.
• Ensure the hypothesis guides empirical testing in psychological research.

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How to Write a Hypothesis – Steps & Tips

Published by Alaxendra Bets at August 14th, 2021 , Revised On October 26, 2023

What is a Research Hypothesis?

You can test a research statement with the help of experimental or theoretical research, known as a hypothesis.

If you want to find out the similarities, differences, and relationships between variables, you must write a testable hypothesis before compiling the data, performing analysis, and generating results to complete.

The data analysis and findings will help you test the hypothesis and see whether it is true or false. Here is all you need to know about how to write a hypothesis for a  dissertation .

Research Hypothesis Definition

Not sure what the meaning of the research hypothesis is?

A research hypothesis predicts an answer to the research question  based on existing theoretical knowledge or experimental data.

Some studies may have multiple hypothesis statements depending on the research question(s).  A research hypothesis must be based on formulas, facts, and theories. It should be testable by data analysis, observations, experiments, or other scientific methodologies that can refute or support the statement.

Variables in Hypothesis

Developing a hypothesis is easy. Most research studies have two or more variables in the hypothesis, particularly studies involving correlational and experimental research. The researcher can control or change the independent variable(s) while measuring and observing the independent variable(s).

“How long a student sleeps affects test scores.”

In the above statement, the dependent variable is the test score, while the independent variable is the length of time spent in sleep. Developing a hypothesis will be easy if you know your research’s dependent and independent variables.

Once you have developed a thesis statement, questions such as how to write a hypothesis for the dissertation and how to test a research hypothesis become pretty straightforward.

Looking for dissertation help?

Researchprospect to the rescue then.

We have expert writers on our team who are skilled at helping students with quantitative dissertations across a variety of STEM disciplines. Guaranteeing 100% satisfaction!

Step-by-Step Guide on How to Write a Hypothesis

Here are the steps involved in how to write a hypothesis for a dissertation.

Step 1: Start with a Research Question

• Begin by asking a specific question about a topic of interest.
• This question should be clear, concise, and researchable.

Example: Does exposure to sunlight affect plant growth?

Step 2: Do Preliminary Research

• Before formulating a hypothesis, conduct background research to understand existing knowledge on the topic.
• Familiarise yourself with prior studies, theories, or observations related to the research question.

Step 3: Define Variables

• Independent Variable (IV): The factor that you change or manipulate in an experiment.
• Dependent Variable (DV): The factor that you measure.

Example: IV: Amount of sunlight exposure (e.g., 2 hours/day, 4 hours/day, 8 hours/day) DV: Plant growth (e.g., height in centimetres)

Step 4: Formulate the Hypothesis

• A hypothesis is a statement that predicts the relationship between variables.
• It is often written as an “if-then” statement.

Example: If plants receive more sunlight, then they will grow taller.

Step 5: Ensure it is Testable

A good hypothesis is empirically testable. This means you should be able to design an experiment or observation to test its validity.

Example: You can set up an experiment where plants are exposed to varying amounts of sunlight and then measure their growth over a period of time.

Step 6: Consider Potential Confounding Variables

• Confounding variables are factors other than the independent variable that might affect the outcome.
• It is important to identify these to ensure that they do not skew your results.

Example: Soil quality, water frequency, or type of plant can all affect growth. Consider keeping these constant in your experiment.

Step 7: Write the Null Hypothesis

• The null hypothesis is a statement that there is no effect or no relationship between the variables.
• It is what you aim to disprove or reject through your research.

Example: There is no difference in plant growth regardless of the amount of sunlight exposure.

Step 8: Test your Hypothesis

Design an experiment or conduct observations to test your hypothesis.

Example: Grow three sets of plants: one set exposed to 2 hours of sunlight daily, another exposed to 4 hours, and a third exposed to 8 hours. Measure and compare their growth after a set period.

Step 9: Analyse the Results

After testing, review your data to determine if it supports your hypothesis.

Step 10: Draw Conclusions

• Based on your findings, determine whether you can accept or reject the hypothesis.
• Remember, even if you reject your hypothesis, it’s a valuable result. It can guide future research and refine questions.

Three Ways to Phrase a Hypothesis

Try to use “if”… and “then”… to identify the variables. The independent variable should be present in the first part of the hypothesis, while the dependent variable will form the second part of the statement. Consider understanding the below research hypothesis example to create a specific, clear, and concise research hypothesis;

If an obese lady starts attending Zomba fitness classes, her health will improve.

In academic research, you can write the predicted variable relationship directly because most research studies correlate terms.

The number of Zomba fitness classes attended by the obese lady has a positive effect on health.

If your research compares two groups, then you can develop a hypothesis statement on their differences.

An obese lady who attended most Zumba fitness classes will have better health than those who attended a few.

How to Write a Null Hypothesis

If a statistical analysis is involved in your research, then you must create a null hypothesis. If you find any relationship between the variables, then the null hypothesis will be the default position that there is no relationship between them. H0 is the symbol for the null hypothesis, while the hypothesis is represented as H1. The null hypothesis will also answer your question, “How to test the research hypothesis in the dissertation.”

H0: The number of Zumba fitness classes attended by the obese lady does not affect her health.

H1: The number of Zumba fitness classes attended by obese lady positively affects health.

Also see:  Your Dissertation in Education

Hypothesis Examples

Research Question: Does the amount of sunlight a plant receives affect its growth? Hypothesis: Plants that receive more sunlight will grow taller than plants that receive less sunlight.

Research Question: Do students who eat breakfast perform better in school exams than those who don’t? Hypothesis: Students who eat a morning breakfast will score higher on school exams compared to students who skip breakfast.

Research Question: Does listening to music while studying impact a student’s ability to retain information? Hypothesis 1 (Directional): Students who listen to music while studying will retain less information than those who study in silence. Hypothesis 2 (Non-directional): There will be a difference in information retention between students who listen to music while studying and those who study in silence.

How can ResearchProspect Help?

If you are unsure about how to rest a research hypothesis in a dissertation or simply unsure about how to develop a hypothesis for your research, then you can take advantage of our dissertation services which cover every tiny aspect of a dissertation project you might need help with including but not limited to setting up a hypothesis and research questions,  help with individual chapters ,  full dissertation writing ,  statistical analysis , and much more.

Frequently Asked Questions

What are the 5 rules for writing a good hypothesis.

• Clear Statement: State a clear relationship between variables.
• Testable: Ensure it can be investigated and measured.
• Specific: Avoid vague terms, be precise in predictions.
• Falsifiable: Design to allow potential disproof.
• Relevant: Address research question and align with existing knowledge.

What is a hypothesis in simple words?

A hypothesis is an educated guess or prediction about something that can be tested. It is a statement that suggests a possible explanation for an event or phenomenon based on prior knowledge or observation. Scientists use hypotheses as a starting point for experiments to discover if they are true or false.

What is the hypothesis and examples?

A hypothesis is a testable prediction or explanation for an observation or phenomenon. For example, if plants are given sunlight, then they will grow. In this case, the hypothesis suggests that sunlight has a positive effect on plant growth. It can be tested by experimenting with plants in varying light conditions.

What is the hypothesis in research definition?

A hypothesis in research is a clear, testable statement predicting the possible outcome of a study based on prior knowledge and observation. It serves as the foundation for conducting experiments or investigations. Researchers test the validity of the hypothesis to draw conclusions and advance knowledge in a particular field.

Why is it called a hypothesis?

The term “hypothesis” originates from the Greek word “hypothesis,” which means “base” or “foundation.” It’s used to describe a foundational statement or proposition that can be tested. In scientific contexts, it denotes a tentative explanation for a phenomenon, serving as a starting point for investigation or experimentation.

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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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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

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.

On This Page:

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.

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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

\(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

\(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.

\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

• \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
• \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.

• \(H_{0}: \mu \_ 66\)
• \(H_{a}: \mu \_ 66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

• \(H_{0}: \mu \geq 5\)
• \(H_{a}: \mu < 5\)

Exercise \(\PageIndex{3}\)

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• \(H_{0}: \mu \_ 45\)
• \(H_{a}: \mu \_ 45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.

• \(H_{0}: p \_ 0.40\)
• \(H_{a}: p \_ 0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

• Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
• Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

Writing a Strong Hypothesis Statement

All good theses begins with a good thesis question. However, all great theses begins with a great hypothesis statement. One of the most important steps for writing a thesis is to create a strong hypothesis statement. 

What is a hypothesis statement?

A hypothesis statement must be testable. If it cannot be tested, then there is no research to be done.

Simply put, a hypothesis statement posits the relationship between two or more variables. It is a prediction of what you think will happen in a research study. A hypothesis statement must be testable. If it cannot be tested, then there is no research to be done. If your thesis question is whether wildfires have effects on the weather, “wildfires create tornadoes” would be your hypothesis. However, a hypothesis needs to have several key elements in order to meet the criteria for a good hypothesis.

In this article, we will learn about what distinguishes a weak hypothesis from a strong one. We will also learn how to phrase your thesis question and frame your variables so that you are able to write a strong hypothesis statement and great thesis.

What is a hypothesis?

A hypothesis statement posits, or considers, a relationship between two variables.

As we mentioned above, a hypothesis statement posits or considers a relationship between two variables. In our hypothesis statement example above, the two variables are wildfires and tornadoes, and our assumed relationship between the two is a causal one (wildfires cause tornadoes). It is clear from our example above what we will be investigating: the relationship between wildfires and tornadoes.

A strong hypothesis statement should be:

• A prediction of the relationship between two or more variables

A hypothesis is not just a blind guess. It should build upon existing theories and knowledge . Tornadoes are often observed near wildfires once the fires reach a certain size. In addition, tornadoes are not a normal weather event in many areas; they have been spotted together with wildfires. This existing knowledge has informed the formulation of our hypothesis.

Depending on the thesis question, your research paper might have multiple hypothesis statements. What is important is that your hypothesis statement or statements are testable through data analysis, observation, experiments, or other methodologies.

Formulating your hypothesis

One of the best ways to form a hypothesis is to think about “if...then” statements.

Now that we know what a hypothesis statement is, let’s walk through how to formulate a strong one. First, you will need a thesis question. Your thesis question should be narrow in scope, answerable, and focused. Once you have your thesis question, it is time to start thinking about your hypothesis statement. You will need to clearly identify the variables involved before you can begin thinking about their relationship.

One of the best ways to form a hypothesis is to think about “if...then” statements . This can also help you easily identify the variables you are working with and refine your hypothesis statement. Let’s take a few examples.

If teenagers are given comprehensive sex education, there will be fewer teen pregnancies .

In this example, the independent variable is whether or not teenagers receive comprehensive sex education (the cause), and the dependent variable is the number of teen pregnancies (the effect).

If a cat is fed a vegan diet, it will die .

Here, our independent variable is the diet of the cat (the cause), and the dependent variable is the cat’s health (the thing impacted by the cause).

If children drink 8oz of milk per day, they will grow taller than children who do not drink any milk .

What are the variables in this hypothesis? If you identified drinking milk as the independent variable and growth as the dependent variable, you are correct. This is because we are guessing that drinking milk causes increased growth in the height of children.

Refining your hypothesis

Do not be afraid to refine your hypothesis throughout the process of formulation.

Do not be afraid to refine your hypothesis throughout the process of formulation. A strong hypothesis statement is clear, testable, and involves a prediction. While “testable” means verifiable or falsifiable, it also means that you are able to perform the necessary experiments without violating any ethical standards. Perhaps once you think about the ethics of possibly harming some cats by testing a vegan diet on them you might abandon the idea of that experiment altogether. However, if you think it is really important to research the relationship between a cat’s diet and a cat’s health, perhaps you could refine your hypothesis to something like this:

If 50% of a cat’s meals are vegan, the cat will not be able to meet its nutritional needs .

Another feature of a strong hypothesis statement is that it can easily be tested with the resources that you have readily available. While it might not be feasible to measure the growth of a cohort of children throughout their whole lives, you may be able to do so for a year. Then, you can adjust your hypothesis to something like this:

I f children aged 8 drink 8oz of milk per day for one year, they will grow taller during that year than children who do not drink any milk .

As you work to narrow down and refine your hypothesis to reflect a realistic potential research scope, don’t be afraid to talk to your supervisor about any concerns or questions you might have about what is truly possible to research. 

What makes a hypothesis weak?

We noted above that a strong hypothesis statement is clear, is a prediction of a relationship between two or more variables, and is testable. We also clarified that statements, which are too general or specific are not strong hypotheses. We have looked at some examples of hypotheses that meet the criteria for a strong hypothesis, but before we go any further, let’s look at weak or bad hypothesis statement examples so that you can really see the difference.

Bad hypothesis 1: Diabetes is caused by witchcraft .

While this is fun to think about, it cannot be tested or proven one way or the other with clear evidence, data analysis, or experiments. This bad hypothesis fails to meet the testability requirement.

Bad hypothesis 2: If I change the amount of food I eat, my energy levels will change .

This is quite vague. Am I increasing or decreasing my food intake? What do I expect exactly will happen to my energy levels and why? How am I defining energy level? This bad hypothesis statement fails the clarity requirement.

Bad hypothesis 3: Japanese food is disgusting because Japanese people don’t like tourists .

This hypothesis is unclear about the posited relationship between variables. Are we positing the relationship between the deliciousness of Japanese food and the desire for tourists to visit? or the relationship between the deliciousness of Japanese food and the amount that Japanese people like tourists? There is also the problematic subjectivity of the assessment that Japanese food is “disgusting.” The problems are numerous.

The null hypothesis and the alternative hypothesis

The null hypothesis, quite simply, posits that there is no relationship between the variables.

What is the null hypothesis?

The hypothesis posits a relationship between two or more variables. The null hypothesis, quite simply, posits that there is no relationship between the variables. It is often indicated as H 0 , which is read as “h-oh” or “h-null.” The alternative hypothesis is the opposite of the null hypothesis as it posits that there is some relationship between the variables. The alternative hypothesis is written as H a or H 1 .

Let’s take our previous hypothesis statement examples discussed at the start and look at their corresponding null hypothesis.

H a : If teenagers are given comprehensive sex education, there will be fewer teen pregnancies .

H 0 : If teenagers are given comprehensive sex education, there will be no change in the number of teen pregnancies .

The null hypothesis assumes that comprehensive sex education will not affect how many teenagers get pregnant. It should be carefully noted that the null hypothesis is not always the opposite of the alternative hypothesis. For example:

If teenagers are given comprehensive sex education, there will be more teen pregnancies .

These are opposing statements that assume an opposite relationship between the variables: comprehensive sex education increases or decreases the number of teen pregnancies. In fact, these are both alternative hypotheses. This is because they both still assume that there is a relationship between the variables . In other words, both hypothesis statements assume that there is some kind of relationship between sex education and teen pregnancy rates. The alternative hypothesis is also the researcher’s actual predicted outcome, which is why calling it “alternative” can be confusing! However, you can think of it this way: our default assumption is the null hypothesis, and so any possible relationship is an alternative to the default.

Step-by-step sample hypothesis statements

Now that we’ve covered what makes a hypothesis statement strong, how to go about formulating a hypothesis statement, refining your hypothesis statement, and the null hypothesis, let’s put it all together with some examples. The table below shows a breakdown of how we can take a thesis question, identify the variables, create a null hypothesis, and finally create a strong alternative hypothesis.

Once you have formulated a solid thesis question and written a strong hypothesis statement, you are ready to begin your thesis in earnest. Check out our site for more tips on writing a great thesis and information on thesis proofreading and editing services.

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Review Checklist

Start with a clear thesis question

Think about “if-then” statements to identify your variables and the relationship between them

Create a null hypothesis

Formulate an alternative hypothesis using the variables you have identified

Make sure your hypothesis clearly posits a relationship between variables

Make sure your hypothesis is testable considering your available time and resources

What makes a hypothesis strong? +

A hypothesis is strong when it is testable, clear, and identifies a potential relationship between two or more variables.

What makes a hypothesis weak? +

A hypothesis is weak when it is too specific or too general, or does not identify a clear relationship between two or more variables.

What is the null hypothesis? +

The null hypothesis posits that the variables you have identified have no relationship.

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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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?

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. 

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

Key Terms of Hypothesis Testing

• 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:

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.

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.

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

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

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,

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.

• 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:

• 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:

• i,j are the rows and columns index respectively.

Real life Hypothesis Testing example

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 Hypothesis Testing

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,

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.

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

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 ( ): No effect or difference exists. Alternative Hypothesis ( ): An effect or difference exists. Significance Level ( ): 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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