h1 hypothesis example

Null and Alternative Hypothesis: Research Guidelines

• Icon Calendar 17 June 2024
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When undertaking a qualitative or quantitative research project, researchers must first formulate a research question, from which they develop their theories. By definition, an assumption is a prediction that a researcher makes about an actual research question and can either be affirmative or negative. In this case, writing a research question has three main components: variables (independent and dependent), a population sample, and the relation between these variables. To find null and alternative hypotheses, scholars identify a specific research question, determine the variables involved, and state H0 as no effect or difference and H1 or Ha as a significant effect or difference. When the prediction contradicts the research question, it is referred to as a null assumption. In short, an initial theory is a statement that implies there is no relationship between independent and dependent variables. Hence, researchers need to learn how to write a good null and alternative hypothesis to present quality studies.

General Aspects

Students with qualitative or quantitative research assignments must learn how to formulate and write good research questions and proposition statements. In essence, hypothesis testing is a statistical method used to determine if there is enough evidence to reject an initial theory and support an alternative assumption based on sample data. By definition, a research proposition is an assumption or prediction that a scholar makes before undertaking an experimental investigation. Basically, academic standards require such a prediction to be a precise and testable statement, meaning that researchers must prove or disapprove of it in the course of their assignment and provide alternatives if possible. In this case, the main components of a typical research assumption are variables (independent and dependent), a population sample, and the relation between these variables. To formulate a null hypothesis (H0) in quantitative research, researchers state there is no effect or difference between variables (e.g., µ1 = µ2), and, for an alternative hypothesis (H1 or Ha), they posit there is a significant effect or difference (e.g., µ1 ≠ µ2). Therefore, a research proposition is a prediction that scholars write about the relationship between two or more variables. In turn, a standard research inquiry is a particular process that seeks to answer a specific research question and, in the process, test a particular theory by confirming or disapproving it.

Types of Hypotheses

There are several types of hypotheses, including null, alternative, directional, and non-directional assumptions. Basically, a directional hypothesis is a prediction of how an independent variable affects a dependent variable. In contrast, a non-directional hypothesis predicts that an independent variable influences a dependent variable but does not specify how. Regardless of the type, all propositions are about predicting the relationship between independent and dependent variables. To write H0 (null assumption) and H1 or Ha (alternative prediction), researchers clearly state H0 as a central assumption of no effect or no difference (e.g., µ1 = µ2) and H1 or Ha as a secondary assumption of a significant effect or difference (e.g., µ1 ≠ µ2).

What Is a Null Hypothesis (H0) and Its Purpose

According to its definition, a null hypothesis is a foundational statement in statistical testing that posits there is no significant effect, relationship, or difference between groups or variables within a given study. In simple words, a null hypothesis, usually symbolized as “H0,” is a statement that contradicts an actual research theory (Watt & Collins, 2019). The main purpose of writing a null hypothesis is to provide a basis for comparison, allowing researchers to determine whether there is sufficient evidence to reject this assumption in favor of an alternative theory, which suggests a real effect or relationship. As such, it is a negative statement, indicating that there is no relationship or connection between independent and dependent variables (Harrison et al., 2020). By starting with a null proposition, researchers can also employ various statistical tests to evaluate an entire data, ensuring the objectivity of findings and minimizing their bias. The process helps to ensure the validity of scientific research, minimizing the likelihood of drawing incorrect conclusions from the data collected. Moreover, by testing an initial theory, researchers can determine whether the inquiry results are due to the chance or the effect of manipulating a dependent variable (McNulty, 2022). In most instances, a null assumption corresponds with an alternative theory, a positive statement that covers a relationship that exists between independent and dependent variables. Finally, it is highly recommended that researchers should write an alternative assumption first before a null proposition.

What Is an Alternative Hypothesis (H1 or Ha) and Its Purpose

According to its definition and opposite to a null assumption, an alternative hypothesis in research is another statement in statistical testing that suggests there is a significant effect, relationship, or difference between groups or variables in a given study. Basically, this statement contrasts with what a null theory posits, which asserts that no such effect or relationship exists (Baker, 2021). The main purpose of writing an alternative hypothesis is to guide researchers in testing and validating new theories or effects and determine whether the observed data can provide evidence against a null proposition. The process involves comparing observed results to what would be expected under a null assumption. When statistical tests provide enough evidence to reject an initial postulation, an alternative theory becomes true, indicating that the observed effect or relationship is likely real and not due to random variation (Jawlik, 2016). By framing their research around an alternative hypothesis, scientists can focus their investigations on discovering meaningful effects and relationships, thereby advancing knowledge and understanding in their study fields. Hence, writing good null and alternative hypotheses is important because they provide a structured framework for statistical testing, allowing researchers to objectively evaluate evidence and draw conclusions about the presence of significant effects or relationships in an entire data.

Null vs. Alternative Hypothesis Formats

Steps on how to write a good null and alternative hypothesis.

• Identify a Specific Research Question: Start with clearly defining a particular problem or phenomenon you want to study.
• Determine Key Variables: Identify independent and dependent variables involved in your study.
• State a Specific Null Hypothesis (H0): Formulate a concrete statement that suggests no effect, no difference, or no relationship between your variables. This is usually a statement of equality (e.g., µ1 = µ2).
• State a Clear Alternative Hypothesis (H1 or Ha): Formulate another statement that suggests a significant effect, difference, or relationship between your variables. This is usually a statement of inequality (e.g., µ1 ≠ µ2, µ1 > µ2, or µ1 < µ2).
• Means: H0: µ1 = µ2 vs. H1: µ1 ≠ µ2
• Proportions: H0: p1 = p2 vs. H1: p1 ≠ p2
• One-tailed test: If you are testing for a specific direction of effect (e.g., H1: µ1 > µ2).
• Two-tailed test: If you are testing for any difference, regardless of direction (e.g., H1: µ1 ≠ µ2).
• Consult Literature: Review existing research to see how similar or alternative theories have been formulated. This can provide guidance and ensure your expectations are aligned with standard practices in your field.
• Write in Simple Terms: Ensure both null and alternative theories are stated clearly and concisely, making them easy to understand.
• Review and Refine: Double-check your propositions for clarity and correctness. Make sure they are mutually exclusive and collectively exhaustive, covering all possible outcomes.
• Seek Feedback: Discuss your approaches with peers or advisors to ensure they are logical, relevant, and testable. Adjust as necessary based on their input.

Note: A null hypothesis is a specific statement assuming no effect or difference, while other hypotheses refer to general statements that include writing null and alternative hypotheses and proposing possible outcomes to be tested.

Written Examples of Research Questions With H0 and H1 Hypotheses

Before developing any study proposition, a researcher must formulate a specific research question. In this case, a research hypothesis is a broad, testable statement about the expected relationship between variables, while a statistical hypothesis specifically refers to writing null and alternative hypotheses used in statistical testing to validate or refute an initial study assumption (O’Donnell et al., 2023). Then, the next step is to transform this study question into a negative statement that claims the lack of a relationship between independent and dependent variables. Alternatively, researchers can change the question into a positive statement that includes a relationship that exists between the variables. In turn, this latter statement becomes an alternative hypothesis and is symbolized as H1 or Ha. Hence, some of the examples of research questions and hull and alternative hypotheses are as follows:

Research Question (RQ) 1: Do physical exercises help individuals to age gracefully?

• A Null Hypothesis (H0): Physical exercises are not a guarantee for graceful old age.
• An Alternative Hypothesis (H1): Engaging in physical exercises enables individuals to remain healthy and active into old age.

RQ 2: What are the implications of therapeutic interventions in the fight against substance abuse?

• H0: Therapeutic interventions are of no help in the fight against substance abuse.
• H1: Exposing individuals with substance abuse disorders to therapeutic interventions helps to control and even stop their addictions.

RQ 3: How do sexual orientation and gender identity affect the experiences of late adolescents in foster care?

• H0: Sexual orientation and gender identity have no effects on the experiences of late adolescents in foster care.
• H1: The reality of stereotypes in society makes sexual orientation and gender identity factors complicate the experiences of late adolescents in foster care.

RQ 4: Does income inequality contribute to crime in high-density urban areas?

• H0: There is no correlation between income inequality and incidences of crime in high-density urban areas.
• H1: The high crime rates in high-density urban areas are due to the incidence of income inequality in those areas.

RQ 5: Does placement in foster care impact individuals’ mental health?

• H0: There is no correlation between being in foster care and having mental health problems.
• H1: Individuals placed in foster care experience anxiety and depression at one point in their life.

RQ 6: Do assistive devices and technologies lessen the mobility challenges of older adults with a stroke?

• H0: Assistive devices and technologies do not provide any assistance to the mobility of older adults diagnosed with a stroke.
• H1: Assistive devices and technologies enhance the mobility of older adults diagnosed with a stroke.

RQ 7: Does race identity undermine classroom participation?

• H0: There is no correlation between racial identity and the ability to participate in classroom learning.
• H1: Students from racial minorities are not as active as white students in classroom participation.

RQ 8: Do high school grades determine future success?

• H0: There is no correlation between how one performs in high school and their success level in life.
• H1: Attaining high grades in high school positions one for greater success in the future personal and professional lives.

RQ 9: Does critical thinking predict academic achievement?

• H0: There is no correlation between critical thinking and academic achievement.
• H1: Being a critical thinker is a pathway to academic success.

RQ 10: What benefits does group therapy provide to victims of domestic violence?

• H0: Group therapy does not help victims of domestic violence because individuals prefer to hide rather than expose their shame.
• H1: Group therapy provides domestic violence victims with a platform to share their hurt and connect with others with similar experiences.

Symbols and Signs in Writing

Common Mistakes

• Ambiguity in Theories: Writing vague or unclear null and alternative assumptions.
• Directional vs. Non-Directional Confusion: Confusing one-tailed (directional) and two-tailed (non-directional) claims.
• Using Sample Statistics: Stating initial and alternative propositions in terms of sample statistics instead of population parameters.
• Overlapping Assumptions: Creating null and alternative statements that are not mutually exclusive.
• Testing Multiple Variables: Including multiple variables or conditions in a single theory.
• Misinterpreting a Null Proposition: Assuming an initial statement is what you want to prove.
• Incorrect Symbols and Signs: Using incorrect or inconsistent symbols and signs for writing null and alternative propositions.
• Ignoring Context: Writing initial and alternative theories that are not relevant to an assigned research question or context.
• Not Testable Hypotheses: Formulating null and alternative statements that are not testable with the available data or methods.
• Confusing Null and Alternative Hypotheses: Swapping the roles of null and alternative assumptions.

The formulation of research questions in qualitative and quantitative assignments helps students to develop a specific theory for their experiments. In this case, learning how to write a good null and alternative hypothesis helps students and researchers to make their research relevant. Basically, the difference between a null and alternative hypothesis is that the former contradicts an entire research question, while the latter affirms it. In short, an initial proposition is a negative statement relative to a particular research question, and an alternative theory is a positive assumption. Moreover, it is important to note that developing a null hypothesis at the beginning of the assignment is for prediction purposes. As such, the research work must answer a specific research question and confirm or disapprove of an initial proposition. Hence, some of the tips that students and researchers need to know when developing any theory include:

• Formulate a research question that specifies the relationship between an independent variable and a dependent variable.
• Develop an alternative assumption that says a relationship exists between the variables.
• Develop a null proposition that says a relationship does not exist between the variables.
• Conduct an experiment to answer a research question under analysis, which allows the confirmation of a disapproval of a null theory or considering alternative options.

Baker, L. (2021). Hypothesis testing: How to choose the correct test (Getting started with statistics) . Chi-Squared Innovations.

Harrison, A. J., McErlain-Naylor, S. A., Bradshaw, E. J., Dai, B., Nunome, H., Hughes, G. T. G., Kong, P. W., Vanwanseele, B., Vilas-Boas, J. P., & Fong, D. T. (2020). Recommendations for statistical analysis involving null hypothesis significance testing. Sports Biomechanics , 19 (5), 561–568. https://doi.org/10.1080/14763141.2020.1782555

Jawlik, A. (2016). Statistics from A to Z: Confusing concepts clarified . John Wiley & Sons, Inc.

McNulty, R. (2022). A logical analysis of null hypothesis significance testing using popular terminology. BMC Medical Research Methodology , 22 (1), 1–9. https://doi.org/10.1186/s12874-022-01696-5

O’Donnell, C. T., Fielding-Singh, V., & Vanneman, M. W. (2023). The art of the null hypothesis — Considerations for study design and scientific reporting. Journal of Cardiothoracic and Vascular Anesthesia , 37 (6), 867–869. https://doi.org/10.1053/j.jvca.2023.02.026

Watt, R., & Collins, E. (2019). Null hypothesis testing . SAGE Publications Ltd.

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Alternative Hypothesis

Ai generator.

Diving deep into the realm of scientific research, the alternative hypothesis plays a pivotal role in steering investigations. It stands contrary to the null hypothesis , providing a different perspective or direction. This essential component often sets the foundation for groundbreaking discoveries. If you’re keen on understanding this concept further, our collection of alternative hypothesis statement examples, combined with a thorough writing guide and insightful tips, will serve as your comprehensive roadmap.

What is an Alternative hypothesis?

An alternative hypothesis is a statement used in statistical testing that indicates the presence of an effect, relationship, or difference. It stands in direct contrast to the null hypothesis, which posits that there is no effect or relationship. The alternative causual hypothesis provides a specific direction to the research and can be directional (e.g., one value is greater than another) or non-directional (e.g., two values are not equal).

What is an example of an Alternative hypothesis statement?

If a researcher is studying the effect of a new teaching method on student performance, the null hypothesis might be: “The new teaching method has no effect on student performance.” An example of an alternative hypothesis could be:

Directional: “Students exposed to the new teaching method will perform better than those who were not.” Non-directional: “Student performance will be different for those exposed to the new teaching method compared to those who were not.”

100 Alternative Hypothesis Statement Examples

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The alternative hypothesis symbolizes a statement of what a statistical hypothesis test is set to establish. Often contrasted with a null hypothesis, it indicates the expected direction of the tested relation. Dive into these varied thesis statement examples showcasing the core essence of alternative hypotheses.

• Smoking and Cancer : Smoking is positively related to lung cancer incidence.
• Diet and Weight Loss : The Atkins diet results in more weight loss than a conventional diet.
• Medication Efficiency : Drug A is more effective than Drug B in treating migraines.
• Exercise Duration : Engaging in physical activity for more than 30 minutes daily reduces depression symptoms.
• Class Size and Learning : Smaller class sizes lead to higher student test scores.
• Sugar Intake : Consuming more than 50 grams of sugar daily increases the risk of diabetes.
• Vitamin C and Cold : Vitamin C intake reduces the duration of the common cold.
• Sleep Duration : Sleeping less than 6 hours results in decreased cognitive function.
• Training Methods : Method X training increases employee productivity more than Method Y.
• Pollution Levels : Higher levels of industrial activity correlate with increased air pollution.
• Stress and Disease : Chronic stress has a positive relationship with heart diseases.
• Alcohol and Reaction Time : Alcohol consumption slows down reaction time.
• Meditation and Blood Pressure : Regular meditation lowers blood pressure.
• Organic Food : Consuming organic food leads to better gut health.
• Advertising : Increased advertising results in higher sales figures.
• Salary and Job Satisfaction : A higher salary correlates with job satisfaction.
• Age and Memory : As age increases, short-term memory retention decreases.
• Temperature and Aggression : Higher temperatures are associated with increased aggressive behavior.
• Social Media : Spending more than 2 hours on social media daily increases feelings of loneliness.
• Music and Concentration : Listening to classical music improves concentration during studies. …
• Recycling Habits : Communities with mandatory recycling policies have higher recycling rates.
• Urban Areas : Living in urban areas increases the likelihood of asthma.
• Pets and Loneliness : Owning a pet decreases feelings of loneliness.
• Reading Habits : Reading more than 3 books a month correlates with increased empathy.
• Green Spaces : Having access to green spaces reduces stress levels.
• Vaccination : Vaccination reduces the incidence of specific diseases.
• Chocolate and Mood : Consuming chocolate elevates mood.
• Remote Work : Working remotely improves overall work satisfaction.
• Financial Literacy : Financial literacy education reduces personal debt.
• Mindfulness and Anxiety : Practicing mindfulness decreases symptoms of anxiety. …
• Dietary Fiber : Higher dietary fiber intake is associated with lower risks of bowel cancer.
• Travel and Creativity : People who travel frequently are more creative.
• Education Level and Income : Individuals with higher education levels earn more income.
• Technology Adoption : People who receive technology training adapt to new devices faster.
• Parental Involvement and Academic Performance : Increased parental involvement enhances students’ academic performance.
• Exercise Frequency and Heart Health : Exercising at least five times a week improves heart health.
• Gender and Leadership Roles : Men are more likely to hold leadership positions in corporate settings.
• Social Support and Mental Health : Strong social support networks reduce the risk of depression.
• Quality of Sleep and Productivity : Better sleep quality leads to higher productivity levels.
• High-Fat Diet and Cholesterol Levels : A high-fat diet increases cholesterol levels.
• Caffeine Intake and Alertness : Higher caffeine intake enhances alertness and cognitive function.
• Online Shopping Habits : People who frequently shop online spend more money than in-store shoppers. …
• Education and Political Views : Higher education levels are associated with more liberal political views.
• Gender and Risk-Taking Behavior : Men are more likely to engage in risky behaviors.
• Temperature and Ice Cream Sales : Higher temperatures increase ice cream sales.
• Artificial Sweeteners and Weight Loss : Consuming products with artificial sweeteners aids in weight loss.
• Exercise and Stress Reduction : Regular exercise reduces stress levels.
• Music Genres and Mood : Listening to upbeat music improves mood.
• Online Learning and Engagement : Online learners are more engaged in virtual classroom discussions.
• Personality Traits and Job Performance : Extroverted individuals perform better in sales roles.
• Environmental Awareness and Recycling : Higher environmental awareness leads to more recycling practices.
• Social Media Usage and Self-Esteem : Excessive social media usage correlates with lower self-esteem. …
• Sleep Deprivation and Reaction Time : Sleep-deprived individuals have slower reaction times.
• Breakfast Consumption and Metabolism : Eating breakfast kickstarts metabolism for the day.
• Leadership Style and Employee Satisfaction : Transformational leadership style increases employee job satisfaction.
• Bilingualism and Cognitive Abilities : Bilingual individuals possess enhanced cognitive abilities.
• Video Game Playing and Aggression : Playing violent video games increases aggressive behavior.
• Hydration and Cognitive Function : Staying hydrated improves cognitive function.
• Parental Support and Academic Achievement : Supportive parenting leads to higher academic achievement.
• Workplace Flexibility and Work-Life Balance : Jobs with flexible schedules enhance work-life balance.
• Digital Learning and Knowledge Retention : Digital learning methods improve long-term knowledge retention.
• Art Exposure and Creativity : Exposure to various forms of art fosters creative thinking.
• Solar Energy Adoption and Utility Bills : Homes with solar energy systems experience lower utility bills.
• Parental Involvement and Student Behavior : Increased parental involvement reduces student behavioral issues.
• Team Diversity and Creativity : Diverse teams generate more creative solutions.
• Social Media Marketing and Brand Awareness : Social media marketing boosts brand awareness more than traditional methods.
• Morning Routine and Productivity : Following a structured morning routine enhances overall productivity.
• Music Training and Cognitive Development : Music training improves cognitive abilities in children.
• Employee Training and Job Satisfaction : Comprehensive employee training programs lead to higher job satisfaction.
• Eating Before Bed and Sleep Quality : Consuming heavy meals before bed negatively affects sleep quality.
• Financial Incentives and Employee Performance : Offering financial incentives increases employee performance.
• Parental Attachment and Emotional Well-being : Strong parental attachment fosters better emotional well-being in children.
• Social Interaction and Mental Well-being : Frequent social interaction correlates with improved mental health.
• Education and Crime Rates : Higher education levels result in lower crime rates within communities.
• Diet and Acne : A diet high in dairy products exacerbates acne.
• Leadership Style and Employee Motivation : Autocratic leadership style hampers employee motivation.
• Urban Green Spaces and Stress Reduction : Access to urban green spaces lowers stress levels.
• Sleep Duration and Athletic Performance : Adequate sleep duration enhances athletic performance.
• Financial Literacy and Investment Success : Individuals with high financial literacy make more successful investments.
• Team Collaboration and Project Success : Effective team collaboration leads to more successful project outcomes.
• Media Exposure and Body Image : Increased media exposure contributes to negative body image perceptions.
• Gender Representation and Film Success : Movies with more balanced gender representation achieve higher box office success. …
• Meditation and Anxiety Reduction : Regular meditation practice reduces symptoms of anxiety.
• Cognitive Training and Memory Enhancement : Cognitive training programs improve memory retention.
• Positive Affirmations and Self-Confidence : Repeating positive affirmations enhances self-confidence.
• Physical Fitness and Longevity : Being physically fit is linked to increased lifespan.
• Parental Guidance and Online Safety : Strong parental guidance promotes responsible online behavior in children.
• Artificial Intelligence and Job Displacement : Increased AI integration leads to more job displacement.
• Public Transportation Usage and Air Quality : Increased public transportation usage improves air quality in cities.
• Social Support and Addiction Recovery : Strong social support networks aid in addiction recovery.
• Gender Diversity and Company Performance : Companies with diverse gender representation outperform others.
• Mindfulness Meditation and Pain Management : Mindfulness meditation reduces perception of pain.
• Music Therapy and Autism : Music therapy improves social interaction skills in children with autism.
• Social Media Usage and Academic Performance : Excessive social media usage negatively impacts academic performance.
• Employee Engagement and Organizational Success : Higher employee engagement leads to greater organizational success.
• Healthy Eating and Longevity : A diet rich in fruits and vegetables contributes to a longer lifespan.
• Gender Stereotypes and Career Choice : Gender stereotypes influence career choices among young adults.
• Environmental Conservation Efforts and Biodiversity : Increased conservation efforts positively affect biodiversity.
• Volunteerism and Personal Well-being : Engaging in volunteer activities enhances personal well-being.
• Artificial Intelligence and Customer Service : AI-driven customer service improves user satisfaction.

Alternative Hypothesis Statement Examples in Research

In alternative research hypothesis propel investigations beyond the null. Examples span diverse fields, revealing the direction researchers expect their findings to take.

• Effect of Music on Concentration : Listening to classical music enhances concentration during study.
• Green Tea and Weight Loss : Green tea consumption leads to more significant weight loss than water intake.
• Parental Involvement and Academic Achievement : Active parental involvement boosts student academic achievement.
• Social Media Usage and Self-Esteem : Frequent social media use correlates with lower self-esteem.

Alternative Hypothesis Statement Examples in Business Research

Business research thrives on alternative hypotheses. Dive into these business-oriented examples that challenge null assumptions.

• Marketing Campaign Impact : Marketing campaign A generates higher conversion rates than campaign B.
• Employee Training and Productivity : Comprehensive employee training enhances workplace productivity.
• Work-Life Balance and Employee Satisfaction : Improved work-life balance increases employee job satisfaction.
• Customer Service Channel Effectiveness : Online chat support results in higher customer satisfaction compared to phone support.
• Branding Influence on Purchase Intent : Strong brand presence leads to increased purchase intent.

Directional Alternative Hypothesis Statement Examples

Directional hypothesis add clarity to research expectations. Explore these examples that predict specific outcomes.

• Exercise Frequency and Heart Health : Engaging in physical activity five times a week improves heart health.

Alternative Hypothesis Statement Examples in Psychology

Psychological studies benefit from well-crafted alternative hypotheses. These psychology hypothesis examples delve into the realm of human behavior and cognition.

• Mindfulness Meditation and Anxiety Reduction : Regular mindfulness practice reduces symptoms of anxiety.

Alternative Null Hypothesis Statement Examples

Explore alternative null hypothesis —statements asserting the absence of specific effects or differences.

• Coffee Consumption and Weight Gain : Increased coffee consumption does not lead to weight gain.
• Smartphone Usage and Sleep Quality : Using smartphones before bed does not impact sleep quality.
• Music Genre and Study Performance : Studying with rock music does not affect academic performance.
• Green Spaces and Stress Reduction : Access to green spaces does not decrease stress levels.
• Team Diversity and Project Success : Team diversity does not influence project success rates.

Alternative Hypothesis Statement Examples in Medical Research

Medical research relies on robust alternative hypotheses to drive scientific inquiry. These examples explore hypotheses in the realm of healthcare.

• Exercise and Diabetes Prevention : Regular exercise decreases the risk of developing type 2 diabetes.
• Medication A and Blood Pressure Reduction : Medication A leads to greater reduction in blood pressure compared to medication B.
• Nutritional Intake and Heart Disease : Higher intake of fruits and vegetables lowers the risk of heart disease.
• Stress Reduction Techniques and Anxiety Levels : Practicing stress reduction techniques decreases anxiety levels.
• Alternative Medicine and Pain Management : Alternative medicine therapies alleviate chronic pain more effectively than traditional treatments.

Alternative Hypothesis Statement Examples in Education Research

Education research thrives on alternative hypotheses to investigate innovative approaches. Explore examples that challenge conventional notions.

• Technology Integration and Student Engagement : Integrating technology enhances student engagement in the classroom.
• Project-Based Learning and Knowledge Retention : Project-based learning improves long-term knowledge retention.
• Teacher Professional Development and Student Performance : Effective teacher professional development positively impacts student academic performance.
• Inclusive Classroom Environment and Learning Outcomes : Inclusive classrooms lead to better learning outcomes for diverse students.
• Feedback Frequency and Writing Improvement : Frequent feedback results in greater improvement in student writing skills.

These examples showcase the pivotal role of alternative hypotheses across various disciplines, serving as the driving force behind scientific exploration and advancement.

What is the Alternative Hypothesis Formula?

The alternative hypothesis, denoted as “Ha” or “H1,” represents the assertion researchers aim to support through evidence. It stands in contrast to the null hypothesis (Ho), which suggests no effect or relationship. The formula for the alternative hypothesis varies based on the nature of the study:

• Directional Hypothesis : For studies with an expected direction, the formula takes the form of a prediction. For instance, “The new drug increases patient recovery rates.”
• Non-Directional Hypothesis : For exploratory studies, the formula reflects the possibility of any difference or effect. For example, “There is a difference in recovery rates between the two drugs.”

How do you start an Alternative Hypothesis?

Starting an alternative simple hypothesis involves framing a clear research statement that highlights the anticipated effect, relationship, or difference. To begin:

• Identify the Research Question: Determine the specific aspect you intend to explore or compare.
• Formulate a Hypothesis: Craft a statement that directly addresses the expected outcome.
• Include Variables: Introduce the relevant variables and their predicted connection.
• Be Clear and Specific: Ensure the alternative hypothesis is concise and unambiguous.

Is the Alternative Hypothesis a Claim or Statement?

The alternative hypothesis is both a claim and a statement. It claims that there is a measurable effect, relationship, or difference in the variables being studied. It is also a statement that researchers work to validate through evidence.

How do you write an Alternative Hypothesis Statement? – Step by Step Guide

Creating a robust alternative hypothesis statement involves structured steps:

• Identify Variables : Clearly define the independent and dependent variables in your study.
• State Expected Effect : Express the anticipated impact, relationship, or difference between variables.
• Be Precise : Use specific language to convey the exact nature of the expected outcome.
• Include Direction (if applicable) : If your hypothesis is directional, specify the expected direction.
• Avoid Ambiguity : Make sure your statement is clear and leaves no room for confusion.

Tips for Writing an Alternative Hypothesis Statement

• Be Specific : Clearly define the variables and the predicted relationship.
• Use Measurable Terms : Incorporate quantifiable terms to indicate the magnitude of the effect.
• Testability : Ensure the hypothesis can be tested empirically.
• Conciseness : Keep the statement concise and to the point.
• Alignment with Research Question : Ensure the hypothesis directly answers your research question.
• Avoid Value Judgments : Avoid value judgments or personal biases in the hypothesis.
• Review Literature : Consult existing literature to align your hypothesis with prior research.

Crafting a strong alternative hypothesis statement is essential for guiding your research and forming the basis for causual hypothesis testing. It directs the focus of your investigation and lays the foundation for drawing meaningful conclusions.

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Hypothesis Testing

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Hypothesis Testing Experiment Design Scientific hypotheses come in pairs: the research hypothesis (H1) that states the potential relationship between two variables or the potential differences between two groups, and the null hypothesis (H0), which states that there is no relationship between the two variables or no differences between two groups. Example: H1: The taller a person is, the longer their arms will be. H0: Height has no effect on arm length. H1: The grocery store is more crowded on Saturdays than on Sundays. H0: There is no difference in how many people buy groceries on Saturday vs. Sunday. We use the null hypothesis, because we can never truly prove something to be true, but we can prove something to be false, so if we falsify (or reject) the null hypothesis, we in turn support its opposite, the research hypothesis. For each of the following cases, give a potential null hypothesis to complete each pair. Remember, hypotheses need to be testable and falsifiable. For each pair, also identify the dependent and independent variables (think about what changing, or what differs between your treatments, and what measuring). H1: Using smaller font sizes increases reading comprehension. H0: There is no difference in font size on reading comprehension Dependent: reading comprehension Independent: font size H1: Children with higher IQ have higher anxiety levels than children with lower IQ. H0: There is no difference in anxiety levels in children with higher or lower IQs Dependent: anxiety levels Independent: IQ H1: Taking aspirin makes headaches feel better. H0: There is no difference in how headaches feel taking aspirin Dependent: how headaches feel Independent: aspirin Next, going to have you not only develop a hypothesis, but design an experiment to test it. You decide to inventory the birdhouses in your neighborhood as a school project. During this inventory, you locate a total of 34 birdhouses for Wrens only 14 of which are being used nesting birds. The others are currently unoccupied. You decide that you would like to know why some of the birdhouses are occupied and others are not. Background information: You already know the following about birds: The size of the entrance hole determines which species can fit inside the birdhouse. Each species of bird builds very stereotypical nests, so they may not nest inside a box that is too large or too small. Squirrels and other organisms can act as nest predators, eating the eggs or ba birds. Different birdhouse placement or design may influence whether predators can find and get inside a birdhouse. The temperature inside a birdhouse is important to the survival of the inside, and can be affected amount of construction materials, etc. Use this information to ask a question or pose a problem you want to solve about the nesting habits of wrens in your local birdhouses. Does the temperature of a birdhouse affect whether it is inhabited Wrens? Hypotheses: H1: If the birdhouse is hot, there will be less Wrens in that birdhouse. H0: There is no difference in temperature and the amount of Wrens in birdhouses. Variables: Dependent: the amount of Wrens Independent: temperature Is your dependent variable qualitative or quantitative? Quantitative Is your independent variable qualitative or quantitative? Quantitative How would you design an experiment with different treatment groups to test your hypothesis?

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Unlocking the Power of Advanced Statistical Methods in Clinical Trials

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Explaining hypothesis testing with real-world examples.

Hypothesis testing is a fundamental concept in statistics, particularly in the field of medical research. At StatisMed, we understand the importance of accurately analyzing data to draw meaningful conclusions. In this blog post, we get insights into explaining hypothesis testing with real-world examples and how it can be applied in medical settings.

Understanding Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), collecting data, performing statistical tests, and drawing conclusions based on the results.

Real-World Examples

• A pharmaceutical company wants to test a new drug’s effectiveness in lowering blood pressure compared to the current standard treatment. The null hypothesis states that there is no difference in blood pressure reduction between the two treatments, while the alternative hypothesis suggests that the new drug is more effective.
• Researches conducting a clinical trial to determine the efficacy of a new vaccine in preventing a specific disease. The null hypothesis posits that the vaccine does not provide any protection, while the alternative hypothesis proposes that the vaccine is effective.
• A medical team wants to compare the effectiveness of two treatments for a certain condition. By formulating null and alternative hypotheses, collecting data on patient outcomes, and performing statistical tests, they can determine which treatment is more effective.

Application in Medical Research

In the field of medical research, hypothesis testing plays a crucial role in evaluating new treatments, determining the effectiveness of interventions, and establishing evidence-based practices. By using statistical analysis services from StatisMed, medical professionals can ensure their research is conducted rigorously and ethically.

Hypothesis testing is a powerful tool that allows researchers to draw meaningful conclusions from data. By explaining hypothesis testing with real-world examples and applying them in real-world scenarios, medical professionals can make informed decisions about treatment options, interventions, and research outcomes. At StatisMed, we are committed to providing top-notch statistical analysis services to support evidence-based medical research. Contact us to learn more about how we can assist you in unlocking the potential of hypothesis testing in your research projects.

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• 1.6 - Hypothesis Testing

Another way to make statistical inferences about a population parameter such as the mean is to use hypothesis testing to make decisions about the parameter’s value. Suppose that we are interested in a particular value of the mean single-family home sale price, for example, a claim from a realtor that the mean sale price in this market is \(\$\)255,000. Does the information in our sample support this claim, or does it favor an alternative claim?

The rejection region method

To decide between two competing claims, we can conduct a hypothesis test as follows.

• Express the claim about a specific value for the population parameter of interest as a null hypothesis , denoted NH. [More traditional notation uses H0.] The null hypothesis needs to be in the form "parameter = some hypothesized value," for example, NH: E(Y) = 255. A frequently used legal analogy is that the null hypothesis is equivalent to a presumption of innocence in a trial before any evidence has been presented.
• Express the alternative claim as an alternative hypothesis , denoted AH. [More traditional notation uses Ha or H1.]. The alternative hypothesis can be in a lower-tail form, for example, AH: E(Y) < 255, or an upper-tail form, for example, AH: E(Y) > 255, or a two-tail form, for example, AH: E(Y) ≠ 255. The alternative hypothesis, also sometimes called the research hypothesis, is what we would like to demonstrate to be the case, and needs to be stated before looking at the data. To continue the legal analogy, the alternative hypothesis is guilt, and we will only reject the null hypothesis (innocence) if we favor the alternative hypothesis (guilt) beyond a reasonable doubt. To illustrate, we will presume for the home prices example that we have some reason to suspect that the mean sale price is higher than claimed by the realtor (perhaps a political organization is campaigning on the issue of high housing costs and has employed us to investigate whether sale prices are "too high" in this housing market). Thus, our upper-tail alternative hypothesis is AH: E(Y) > 255.
• Calculate a test statistic based on the assumption that the null hypothesis is true. For hypothesis tests for a univariate population mean the relevant test statistic is \[\text{t-statistic}=\frac{m_Y-\text{E}(Y)}{s_Y/\sqrt{n}},\] where \(m_Y\) is the sample mean, E(Y) is the value of the population mean in the null hypothesis, \(s_Y\) is the sample standard deviation, and n is the sample size.
• For an upper-tail test, a t-statistic that is positive and far from zero would then lead us to favor the alternative hypothesis (a t-statistic that was far from zero but negative would favor neither hypothesis and the test would be inconclusive).
• For a lower-tail test, a t-statistic that is negative and far from zero would then lead us to favor the alternative hypothesis (a t-statistic that was far from zero but positive would favor neither hypothesis and the test would be inconclusive).
• For a two-tail test, any t-statistic that is far from zero (positive or negative) would lead us to favor the alternative hypothesis.
• To decide how far from zero a t-statistic would have to be before we reject the null hypothesis in favor of the alternative, recall the legal analogy. To deliver a guilty verdict (the alternative hypothesis), the jury must establish guilt beyond a reasonable doubt. In other words, a jury rejects the presumption of innocence (the null hypothesis) only if there is compelling evidence of guilt. In statistical terms, compelling evidence of guilt is found only in the tails of the t-distribution density curve. For example, in conducting an upper-tail test, if the t-statistic is way out in the upper tail, then it seems unlikely that the null hypothesis could have been true—so we reject it in favor of the alternative. Otherwise, the t-statistic could well have arisen while the null hypothesis held true—so we do not reject it in favor of the alternative. How far out in the tail does the t-statistic have to be to favor the alternative hypothesis rather than the null? Here we must make a decision about how much evidence we will require before rejecting a null hypothesis. There is always a chance that we might mistakenly reject a null hypothesis when it is actually true (the equivalent of pronouncing an innocent defendant guilty). Often, this chance—called the significance level —will be set at 5%, but more stringent tests (such as in clinical trials of new pharmaceutical drugs) might set this at 1%, while less stringent tests (such as in sociological studies) might set this at 10%. For the sake of argument, we use 5% as a default value for hypothesis tests in this course (unless stated otherwise).
• For an upper-tail test, the critical value is the 95th percentile of the t-distribution with n−1 degrees of freedom; reject the null in favor of the alternative if the t-statistic is greater than this.
• For a lower-tail test, the critical value is the 5th percentile of the t-distribution with n−1 degrees of freedom; reject the null in favor of the alternative if the t-statistic is less than this.
• For a two-tail test, the two critical values are the 2.5th and the 97.5th percentiles of the t-distribution with n−1 degrees of freedom; reject the null in favor of the alternative if the t-statistic is less than the 2.5th percentile or greater than the 97.5th percentile.

It is best to lay out hypothesis tests in a series of steps, so for the house prices example:

• State null hypothesis: NH: E(Y) = 255.
• State alternative hypothesis: AH: E(Y) > 255.
• Calculate test statistic: t-statistic = \(m_Y−\text{E}(Y)/(s_Y/\sqrt{n})=(278.6033−255)/(53.8656/\sqrt{30})=2.40\).
• Set significance level: 5%.
• Look up critical value: The 95th percentile of the t-distribution with 29 degrees of freedom is 1.699; the rejection region is therefore any t-statistic greater than 1.699.
• Make decision: Since the t-statistic of 2.40 falls in the rejection region, we reject the null hypothesis in favor of the alternative.
• Interpret in the context of the situation: The 30 sample sale prices suggest that a population mean of \(\$\)255,000 seems implausible—the sample data favor a value greater than this (at a significance level of 5%).

The p-value method

An alternative way to conduct a hypothesis test is to again assume initially that the null hypothesis is true, but then to calculate the probability of observing a t-statistic as extreme as the one observed or even more extreme (in the direction that favors the alternative hypothesis). This is known as the p-value (sometimes also called the observed significance level):

• For an upper-tail test, the p-value is the area under the curve of the t-distribution (with n−1 degrees of freedom) to the right of the observed t-statistic.
• For a lower-tail test, the p-value is the area under the curve of the t-distribution (with n−1 degrees of freedom) to the left of the observed t-statistic.
• For a two-tail test, the p-value is the sum of the areas under the curve of the t-distribution (with n−1 degrees of freedom) beyond both the observed t-statistic and the negative of the observed t-statistic.

If the p-value is too "small," then this suggests that it seems unlikely that the null hypothesis could have been true—so we reject it in favor of the alternative. Otherwise, the t-statistic could well have arisen while the null hypothesis held true—so we do not reject it in favor of the alternative. Again, the significance level chosen tells us how small is small: If the p-value is less than the significance level, then reject the null in favor of the alternative; otherwise, do not reject it. For the home prices example:

• Look up p-value: The area to the right of the t-statistic (2.40) for the t-distribution with 29 degrees of freedom is less than 0.025 but greater than 0.01 (since the 97.5th percentile of this t-distribution is 2.045 and the 99th percentile is 2.462); thus the upper-tail p-value is between 0.01 and 0.025.
• Make decision: Since the p-value is between 0.01 and 0.025, it must be less than the significance level (0.05), so we reject the null hypothesis in favor of the alternative.

The following figure shows why the rejection region method and the p-value method will always lead to the same decision (since if the t-statistic is in the rejection region, then the p-value must be smaller than the significance level, and vice versa).

Why do we need two methods if they will always lead to the same decision? Well, when learning about hypothesis tests and becoming comfortable with their logic, many people find the rejection region method a little easier to apply. However, when we start to rely on statistical software for conducting hypothesis tests in later chapters of the book, we will find the p-value method easier to use. At this stage, when doing hypothesis test calculations by hand, it is helpful to use both the rejection region method and the p-value method to reinforce learning of the general concepts. This also provides a useful way to check our calculations since if we reach a different conclusion with each method we will know that we have made a mistake.

Lower-tail tests

Lower-tail tests work in a similar way to upper-tail tests, but all the calculations are performed in the negative (left-hand) tail of the t-distribution density curve; the following figure illustrates.

A lower-tail test would result in an inconclusive result for the home prices example (since the large, positive t-statistic means that the data favor neither the null hypothesis, NH: E(Y) = 255, nor the alternative hypothesis, AH: E(Y) < 255).

Two-tail tests

Two-tail tests work similarly, but we have to be careful to work with both tails of the t-distribution; the following figure illustrates.

For the home prices example, we might want to do a two-tail hypothesis test if we had no prior expectation about how large or small sale prices are, but just wanted to see whether or not the realtor's claim of \(\$\)255,000 was plausible. The steps involved are as follows.

• State alternative hypothesis: AH: E(Y) ≠ 255.
• critical value: The 97.5th percentile of the t-distribution with 29 degrees of freedom is 2.045; the rejection region is therefore any t-statistic greater than 2.045 or less than −2.045 (we need the 97.5th percentile in this case because this is a two-tail test, so we need half the significance level in each tail).
• p-value: The area to the right of the t-statistic (2.40) for the t-distribution with 29 degrees of freedom is less than 0.025 but greater than 0.01 (since the 97.5th percentile of this t-distribution is 2.045 and the 99th percentile is 2.462); thus the upper-tail area is between 0.01 and 0.025 and the two-tail p-value is twice as big as this, that is, between 0.02 and 0.05.
• Since the t-statistic of 2.40 falls in the rejection region, we reject the null hypothesis in favor of the alternative.
• Since the p-value is between 0.02 and 0.05, it must be less than the significance level (0.05), so we reject the null hypothesis in favor of the alternative.
• Interpret in the context of the situation: The 30 sample sale prices suggest that a population mean of $255,000 seems implausible—the sample data favor a value different from this (at a significance level of 5%).

Hypothesis test errors

When we introduced the significance level above, we saw that the person conducting the hypothesis test gets to choose this value. We now explore this notion a little more fully. Whenever we conduct a hypothesis test, either we reject the null hypothesis in favor of the alternative or we do not reject the null hypothesis. "Not rejecting" a null hypothesis isn't quite the same as "accepting" it. All we can say in such a situation is that we do not have enough evidence to reject the null—recall the legal analogy where defendants are not found "innocent" but rather are found "not guilty." Anyway, regardless of the precise terminology we use, we hope to reject the null when it really is false and to "fail to reject it" when it really is true. Anything else will result in a hypothesis test error. There are two types of error that can occur, as illustrated in the following table:

A type 1 error can occur if we reject the null hypothesis when it is really true—the probability of this happening is precisely the significance level. If we set the significance level lower, then we lessen the chance of a type 1 error occurring. Unfortunately, lowering the significance level increases the chance of a type 2 error occurring—when we fail to reject the null hypothesis but we should have rejected it because it was false. Thus, we need to make a trade-off and set the significance level low enough that type 1 errors have a low chance of happening, but not so low that we greatly increase the chance of a type 2 error happening. The default value of 5% tends to work reasonably well in many applications at balancing both goals. However, other factors also affect the chance of a type 2 error happening for a specific significance level. For example, the chance of a type 2 error tends to decrease the greater the sample size.

Start Here!

• Welcome to STAT 462!
• Search Course Materials
• 1.1 - Identifying and Summarizing Data
• 1.2 - Population Distributions
• 1.3 - Selecting Individuals at Random
• 1.4 - Random Sampling
• 1.5 - Interval Estimation
• 1.7 - Random Errors and Prediction
• Lesson 2: Simple Linear Regression (SLR) Model
• Lesson 3: SLR Evaluation
• Lesson 4: SLR Assumptions, Estimation & Prediction
• Lesson 5: Multiple Linear Regression (MLR) Model & Evaluation
• Lesson 6: MLR Assumptions, Estimation & Prediction
• Lesson 7: Transformations & Interactions
• Lesson 8: Categorical Predictors
• Lesson 9: Influential Points
• Lesson 10: Regression Pitfalls
• Lesson 11: Model Building
• Lesson 12: Logistic, Poisson & Nonlinear Regression
• Website for Applied Regression Modeling, 2nd edition
• Notation Used in this Course
• R Software Help
• Minitab Software Help

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