how do you state the alternative hypothesis

Reject the Null or Accept the Alternative? Semantics of Statistical Hypothesis Testing

If you are conducting a quantitative study for your dissertation, it is likely you have created a set of hypotheses to accompany your research questions. It is also likely that you have constructed your hypotheses in the “null/alternative” format. In this format, each research question has both a null hypothesis and an alternative hypothesis associated with it.

Let’s say, for example, that you were conducting a study with the following research question: “is there a difference in the IQs of arts majors and science majors?” The null hypothesis would state that there is no difference between the variables that you are testing (e.g., “there is no difference in the IQs of arts majors and science majors”). The alternative hypothesis would state that there is a difference (e.g., “there is a difference in the IQs of arts majors and science majors”). Typically, the researcher constructs these hypotheses with the expectation (based on the literature and theories in their field of study) that their findings will contradict the null hypothesis, and in turn support the alternative hypothesis. For instance, in our IQ example we may expect to see a difference between arts majors and science majors. Generally, it is difficult to justify conducting a study if you have no reason to believe that differences or relationships exist between your variables. Thus, studies are set up to provide evidence that the null hypothesis is “wrong,” and that the alternative hypothesis is “correct.”

Discover How We Assist to Edit Your Dissertation Chapters

Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.

• Bring dissertation editing expertise to chapters 1-5 in timely manner.
• Track all changes, then work with you to bring about scholarly writing.
• Ongoing support to address committee feedback, reducing revisions.

Setting up the null and alternative hypotheses is usually a pretty simple task. However, students often run into trouble when they finish their analysis and must present their results using the “null/alternative” language. Confusion may arise over what words to use and how statements should be phrased. For your dissertation, some of this may come down to your reviewers’ preferences. However, below are some basic guidelines you may follow.

First, let’s assume you ran your analysis and your results were significant (e.g., arts majors and science majors had different IQ levels). In this case, it is generally appropriate to say “the null hypothesis was rejected” because you found evidence against the null hypothesis. This statement is often sufficient, but sometimes reviewers want you to go further and also make a statement about the alternative hypothesis. In this case, you could say “the alternative hypothesis was supported.” Personally, I would avoid saying “the alternative hypothesis was accepted ” because this implies that you have proven the alternative hypothesis to be true. Generally, one study cannot “prove” anything, but it can provide evidence for (or against) a hypothesis. Additionally, the concept of challenging or “falsifying” a hypothesis is stronger than “proving” a hypothesis (for more in-depth discussion on this philosophy of science see Popper, 1959). Again, it is worth noting that your reviewers may have different preferences on the exact language to use here.

Now let’s consider the flip side and assume your results were not significant (e.g., there was no significant difference in IQ between arts majors and science majors). Here you could say “the null hypothesis was not rejected” or “failed to reject the null hypothesis” because you did not find evidence against the null hypothesis. You should NOT say “the null hypothesis was accepted .” Your study is not designed to “prove” the null hypothesis (or the alternative hypothesis, for that matter). Rather, your study is designed to challenge or “reject” the null hypothesis. People often compare this idea in statistical hypothesis testing to how verdicts are made in criminal court cases. If the prosecution does not have strong enough evidence that the defendant committed the crime, the defendant is judged as “not guilty” rather than as “innocent.” In other words, the court can provide evidence of guilt, but it cannot prove innocence. In the same way, a statistical test cannot prove the null hypothesis, but it can provide evidence against it. As for the alternative hypothesis, it may be appropriate to say “the alternative hypothesis was not supported” but you should avoid saying “the alternative hypothesis was rejected .” Once again, this is because your study is designed to reject the null hypothesis, not to reject the alternative hypothesis.

These are just some general tips to help guide the writing of your statistical findings. However, always defer to the requirements of your reviewers and your school when in doubt.

Popper, K. (1959). The logic of scientific discovery . London: Hutchinson.

Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

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 about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

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 .

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 adecision. 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 (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.

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

H a : More than 30% 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%. 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 ≠ 0.25

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 : 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

• H 0 : μ = 66
• H a : μ ≠ 66

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 : 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

• H 0 : μ ≥ 45
• H a : μ < 45

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 ≤ 0.066

H a : p > 0.066

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 (=, ≠, ≥, <, ≤, >) 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

Concept Review

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 (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, 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.

• OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

Alternative hypothesis

by Marco Taboga , PhD

In a statistical test, observed data is used to decide whether or not to reject a restriction on the data-generating probability distribution.

The assumption that the restriction is true is called null hypothesis , while the statement that the restriction is not true is called alternative hypothesis.

A correct specification of the alternative hypothesis is essential to decide between one-tailed and two-tailed tests.

Table of contents

Mathematical setting

Choice between one-tailed and two-tailed tests, the critical region, the interpretation of the rejection, the interpretation must be coherent with the alternative hypothesis.

• Power function

Accepting the alternative

More details, keep reading the glossary.

In order to fully understand the concept of alternative hypothesis, we need to remember the essential elements of a statistical inference problem:

we observe a sample drawn from an unknown probability distribution;

in principle, any valid probability distribution could have generated the sample;

however, we usually place some a priori restrictions on the set of possible data-generating distributions;

A couple of simple examples follow.

When we conduct a statistical test, we formulate a null hypothesis as a restriction on the statistical model.

The alternative hypothesis is

The alternative hypothesis is used to decide whether a test should be one-tailed or two-tailed.

The null hypothesis is rejected if the test statistic falls within a critical region that has been chosen by the statistician.

The critical region is a set of values that may comprise:

only the left tail of the distribution or only the right tail (one-tailed test);

both the left and the right tail (two-tailed test).

The choice of the critical region depends on the alternative hypothesis. Let us see why.

The interpretation is different depending on the tail of the distribution in which the test statistic falls.

The choice between a one-tailed or a two-tailed test needs to be done in such a way that the interpretation of a rejection is always coherent with the alternative hypothesis.

When we deal with the power function of a test, the term "alternative hypothesis" has a special meaning.

We conclude with a caveat about the interpretation of the outcome of a test of hypothesis.

The interpretation of a rejection of the null is controversial.

According to some statisticians, rejecting the null is equivalent to accepting the alternative.

However, others deem that rejecting the null does not necessarily imply accepting the alternative. In fact, it is possible to think of situations in which both hypotheses can be rejected. Let us see why.

According to the conceptual framework illustrated by the images above, there are three possibilities:

the null is true;

the alternative is true;

neither the null nor the alternative is true because the true data-generating distribution has been excluded from the statistical model (we say that the model is mis-specified).

If we are in case 3, accepting the alternative after a rejection of the null is an incorrect decision. Moreover, a second test in which the alternative becomes the new null may lead us to another rejection.

You can find more details about the alternative hypothesis in the lecture on Hypothesis testing .

Previous entry: Almost sure

Next entry: Binomial coefficient

How to cite

Please cite as:

Taboga, Marco (2021). "Alternative hypothesis", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/alternative-hypothesis.

Most of the learning materials found on this website are now available in a traditional textbook format.

• Maximum likelihood
• Binomial distribution
• Beta distribution
• Convergence in probability
• Delta method
• Exponential distribution
• Chi-square distribution
• Set estimation
• Wishart distribution
• Mathematical tools
• Fundamentals of probability
• Probability distributions
• Asymptotic theory
• Fundamentals of statistics
• About Statlect
• Cookies, privacy and terms of use
• Precision matrix
• Loss function
• Integrable variable
• Critical value
• To enhance your privacy,
• we removed the social buttons,
• but don't forget to share .

Statistics Resources

• Excel - Tutorials
• Basic Probability Rules
• Single Event Probability
• Complement Rule
• Intersections & Unions
• Compound Events
• Levels of Measurement
• Independent and Dependent Variables
• Entering Data
• Central Tendency
• Data and Tests
• Displaying Data
• Discussing Statistics In-text
• SEM and Confidence Intervals
• Two-Way Frequency Tables
• Empirical Rule
• Finding Probability
• Accessing SPSS
• Chart and Graphs
• Frequency Table and Distribution
• Descriptive Statistics
• Converting Raw Scores to Z-Scores
• Converting Z-scores to t-scores
• Split File/Split Output
• Sampling Methods
• Partial Eta Squared
• Downloading and Installing G*Power: Windows/PC
• Correlation
• Testing Parametric Assumptions
• One-Way ANOVA
• Two-Way ANOVA
• Repeated Measures ANOVA
• Goodness-of-Fit
• Test of Association
• Pearson's r
• Point Biserial
• Mediation and Moderation
• Simple Linear Regression
• Multiple Linear Regression
• Binomial Logistic Regression
• Multinomial Logistic Regression
• Independent Samples T-test
• Dependent Samples T-test
• Testing Assumptions
• T-tests using SPSS
• T-Test Practice
• Predictive Analytics This link opens in a new window
• Quantitative Research Questions
• Null & Alternative Hypotheses
• One-Tail vs. Two-Tail
• Alpha & Beta
• Associated Probability
• Decision Rule
• Statement of Conclusion
• Statistics Group Sessions

ASC Chat Hours

ASC Chat is usually available at the following times ( Pacific Time):

If there is not a coach on duty, submit your question via one of the below methods:

  928-440-1325

  Ask a Coach

  [email protected]

Search our FAQs on the Academic Success Center's  Ask a Coach   page.

Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.

In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.

• Null Hypothesis (H 0 ) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.”  This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change.
• Alternative Hypothesis (H a ) – This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. This is your answer to your research question.

Null Hypothesis:   H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis :  H a : Male factory workers have a higher salary than female factory workers.

Null Hypothesis :  H 0 : There is no relationship between height and shoe size. Alternative Hypothesis :  H a : There is a positive relationship between height and shoe size.

Null Hypothesis :  H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis :  H a : The quality of a brick mason’s work is influenced by on-the-job experience.

Was this resource helpful?

• << Previous: Hypothesis Testing
• Next: One-Tail vs. Two-Tail >>
• Last Updated: Oct 3, 2024 5:13 PM
• URL: https://resources.nu.edu/statsresources

Alternate Hypothesis in Statistics: What is it?

What is the alternate hypothesis.

• The status quo (null) hypothesis (H 0 ),
• The research (alternate) hypothesis (H a or H 1 ).

• Null hypothesis : President re-elected with 5 percent majority
• Alternate hypothesis: President re-elected with 1-2 percent majority.

Stating the alternate hypothesis

• If you want to support a claim, make it the alternative hypothesis.
• If you do not wish to support a claim, make it the null hypothesis.
• H 0 : μ < 1000
• H 1 : μ ≥ 1000 (your claim)
• H 0 : μ ≥ 1200
• Ha: u < 1200.

Alternate Hypothesis Examples

• 9 Hypothesis Tests
• Hypothesis Testing Memo

Comments are closed.

• Science, Tech, Math ›
• Statistics ›
• Inferential Statistics ›

Null Hypothesis and Alternative Hypothesis

• Inferential Statistics
• Statistics Tutorials
• Probability & Games
• Descriptive Statistics
• Applications Of Statistics
• Math Tutorials
• Pre Algebra & Algebra
• Exponential Decay
• Worksheets By Grade
• Ph.D., Mathematics, Purdue University
• M.S., Mathematics, Purdue University
• B.A., Mathematics, Physics, and Chemistry, Anderson University

Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.

How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.

The Null Hypothesis

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .

The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.

If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.

For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.

If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.

The Alternative Hypothesis

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”

If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.

The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.

• Null hypothesis: “ x is equal to y .” Alternative hypothesis “ x is not equal to y .”
• Null hypothesis: “ x is at least y .” Alternative hypothesis “ x is less than y .”
• Null hypothesis: “ x is at most y .” Alternative hypothesis “ x is greater than y .”
• What 'Fail to Reject' Means in a Hypothesis Test
• Type I and Type II Errors in Statistics
• An Example of a Hypothesis Test
• The Runs Test for Random Sequences
• An Example of Chi-Square Test for a Multinomial Experiment
• The Difference Between Type I and Type II Errors in Hypothesis Testing
• What Level of Alpha Determines Statistical Significance?
• What Is the Difference Between Alpha and P-Values?
• What Is ANOVA?
• How to Find Critical Values with a Chi-Square Table
• Example of a Permutation Test
• Degrees of Freedom for Independence of Variables in Two-Way Table
• Example of an ANOVA Calculation
• How to Find Degrees of Freedom in Statistics
• How to Construct a Confidence Interval for a Population Proportion
• Degrees of Freedom in Statistics and Mathematics

About the null and alternative hypotheses

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

One-sided and two-sided hypotheses

Examples of two-sided and one-sided hypotheses.

• Minitab.com
• License Portal
• Cookie Settings

You are now leaving support.minitab.com.

Click Continue to proceed to:

Null and Alternative Hypothesis: Research Guidelines

• Icon Calendar 17 June 2024
• Icon Page 2753 words
• Icon Clock 13 min read

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.

To Learn More, Read Relevant Articles

SAT Essay Examples With Explanations and Recommendations

• Icon Calendar 29 July 2020
• Icon Page 3990 words

How to Cite Lecture Notes in APA: Basic Guidelines

• Icon Calendar 27 July 2020
• Icon Page 2390 words

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

Size: 188 KB

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.

Text prompt

• Instructive
• Professional

10 Examples of Public speaking

20 Examples of Gas lighting

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice .

Neag School of Education

Educational Research Basics by Del Siegle

Null and alternative hypotheses.

Converting research questions to hypothesis is a simple task. Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists between the groups (experiment study) and you have the alternative hypothesis. Write the statement such that a relationship does not exist or a difference does not exist and you have the null hypothesis. You can reverse the process if you have a hypothesis and wish to write a research question.

When you are comparing two groups, the groups are the independent variable. When you are testing whether something affects something else, the cause is the independent variable. The independent variable is the one you manipulate.

Teachers given higher pay will have more positive attitudes toward children than teachers given lower pay. The first step is to ask yourself “Are there two or more groups being compared?” The answer is “Yes.” What are the groups? Teachers who are given higher pay and teachers who are given lower pay. The independent variable is teacher pay. The dependent variable (the outcome) is attitude towards school.

You could also approach is another way. “Is something causing something else?” The answer is “Yes.”  What is causing what? Teacher pay is causing attitude towards school. Therefore, teacher pay is the independent variable (cause) and attitude towards school is the dependent variable (outcome).

By tradition, we try to disprove (reject) the null hypothesis. We can never prove a null hypothesis, because it is impossible to prove something does not exist. We can disprove something does not exist by finding an example of it. Therefore, in research we try to disprove the null hypothesis. When we do find that a relationship (or difference) exists then we reject the null and accept the alternative. If we do not find that a relationship (or difference) exists, we fail to reject the null hypothesis (and go with it). We never say we accept the null hypothesis because it is never possible to prove something does not exist. That is why we say that we failed to reject the null hypothesis, rather than we accepted it.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

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: 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.

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 (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 9.1

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ .30 H a : More than 30% 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%. 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: 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 less than five years to graduate from college, on the average. The null and alternative hypotheses are: 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

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 ≤ 0.066 H a : p > 0.066

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 (=, ≠, ≥, <, ≤, >) 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.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/introductory-statistics-2e/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Introductory Statistics 2e
• Publication date: Dec 13, 2023
• Location: Houston, Texas
• Book URL: https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
• Section URL: https://openstax.org/books/introductory-statistics-2e/pages/9-1-null-and-alternative-hypotheses

© Jul 18, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

• Alternative vs Null Hypothesis: Pros, Cons, Uses & Examples

All research starts with a problem that needs to be solved. From this problem, hypotheses are developed to provide the researcher with a clear statement of the problem.

To understand alternative hypotheses also known as alternate hypotheses, you must first understand what the hypothesis is .

When you hear the word hypothesis it means the accurate explanations in relation to a set of facts that can be analyzed when studied, using some specific method of research.

There are primarily two types of hypothesis which are null hypothesis and alternative hypothesis.

When you think about the word “null” what should come to mind is something that can not change, what you expect is what you get, unlike alternate hypotheses which can change.

Now, the research problems or questions which could be in the form of null hypothesis or alternative hypothesis are expressed as the relationship that exists between two or more variables. The process for this states that the questions should be what expresses the relationship between two variables that can be measured.

Both null hypotheses and alternative hypotheses are used by statisticians and researchers to conduct research in various industries or fields such as mathematics, psychology, science, medicine, and technology.

We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.

What is an Alternative Hypothesis?

Alternative hypothesis simply put is another viable option to the null hypothesis. It means looking for a substantial change or option that can allow you to reject the null hypothesis.

It is an opposing theory to a null hypothesis.

If you develop a null hypothesis, you make an informed guess on whether a thing is true or whether there is a relationship between that thing and another variable. An alternate hypothesis will always take an opposite stand against a null hypothesis. So if according to a null hypothesis something is correct to an alternate hypothesis that same thing will be incorrect.

For example, let’s assume that you develop a null hypothesis that states “I”m going to be $500 richer” the alternate hypothesis will be “I’m going to get $500 or be richer”

When you are trying to disprove a null hypothesis, that is when you test an alternate hypothesis. If there is enough data to back up the alternative hypothesis then you can dispose of the null hypothesis. 

Get Answers: What is Empirical Research Study? [Examples & Method]

What is a Null Hypothesis?

The null hypothesis is best explained as the statement showing that no relationship exists between two variables that are being considered or that two groups are not related. As we have earlier established, a hypothesis is an assumed statement that has not been proven with sufficient data that could serve as a piece of evidence. 

The null hypothesis is now the statement that a researcher or an investigator wants to disprove. The null hypothesis is capable of being tested, being verifiable, and also capable of being rejected.

For example, if you want to conduct a study that will compare the relationship between project A and project B if the study is based on the assumption that both projects are of equal standard, the assumption is referred to as the null hypothesis.

This is because the null hypothesis should be specific at all times.

Learn: Hypothesis Testing in Research: Definition, Procedure, Uses, Limitations + Examples

Advantages of the Alternative Hypothesis 

• Alternative hypothesis gives a researcher specific clarifications on the research questions or problems .
• It provides a study with the direction that can be used to collect data and obtain results of interest by the researcher.
• An alternative hypothesis is always selected before commencing the studies which gives the researcher the opportunity to prove that the restatement is backed up by evidence and not just from the researcher’s ideas or values.
• Another good thing about alternative hypotheses is that it provides the opportunity to discover new theories that a researcher can use to disprove an existing theory that may not have been backed up by evidence .
• An alternate hypothesis is also useful to prove that there is a relationship between two selected variables and the outcomes of the conducted study are relevant.

Principles of the Alternative Hypothesis

• Alternative hypotheses will be accepted if the amount of data that is gone is insignificant within the significance level. This means that the null hypothesis will be rejected.
• Another principle of the alternative hypothesis is that the data gathered from random samples go through a statistical tool that analyzes the effect of the amount of data leaving the null hypothesis.

For the curious: Sampling Bias: Definition, Types + [Examples]

Purpose of the Null Hypothesis 

Here are the purposes of the null hypothesis in an experiment or study:

• The primary purpose of a null hypothesis is to disprove an assumption.
• Null hypotheses can help to further progress a theory in some scientific cases.
• You can also use a null hypothesis to ascertain how consistent the outcomes of multiple studies are.

Principle of the Null Hypothesis 

Now, these are the principles of the null hypothesis:

1. The primary principle of the null hypothesis is to prove that the assumed statement is true. This is done by collecting data and analyzing in the study , what chance the collected data has in the random sample.

2. If the collected data does not meet the expectation of the null hypothesis, it is determined that the data lacks sufficient evidence to back up the null hypothesis therefore the null hypothesis statement is rejected.

Just as in the case of the alternative hypothesis the collected data in a null hypothesis is analyzed using some statistical tools that are made to measure the extent to which data left the null hypothesis.

The process will determine whether the data that left the null hypothesis is larger than a set value. If the data collected from the random sample is enough to serve as evidence to prove the null hypothesis then the null hypothesis will be accepted as true. And also defined that it has no relationship with other variables .

Learn About: Research Reports: Definition, Types + [Writing Guide]

Types of Alternative Hypothesis (Advantages of Each and When to Use)

There are four types of alternative hypotheses, and we will briefly discuss them below.

• One-tailed directional: For one of the sampling distributions one tail, this type of alternative hypothesis focuses on the rejected part only.
• Two-tailed directional: In an alternative hypothesis, a two-tailed directional focus on the two parts or directions that were rejected in the sampling distribution.
• Point: Point is another alternate hypothesis. It occurs in hypothesis testing when the sample population in the alternate hypothesis has been completely defined in a distribution. If there are no known parameters, the hypothesis will serve no interest. They are, however, important to the foundation of the statistical inferences.
• Non-directional: In an alternate hypothesis, a non-directional does not focus on the two directions of rejection. The only focus of the nondirectional alternative hypothesis is to prove that the null hypothesis is incorrect.

Read: Type I vs Type II Errors: Definition, Examples & Prevention

Difference between Null Hypothesis and Alternative Hypothesis 

We are going to look at the differences between the alternate hypothesis and the null hypothesis based on these six factors which are:

• Mathematical expression
• Observation
• Acceptance criteria
• The difference in Mathematical expression

Null hypothesis is followed by an ‘equals to’ (=) sign. While the Alternative hypothesis is followed by these three signs; 

• The difference in how they are observed

In the null hypothesis, it is believed that the results that are observed are as a result of chance. While In the alternative hypothesis, it is believed that the observed results are the outcome of some real causes.

• Differences in results

The result of the null hypothesis always shows that there have been no changes in statements or opinions. While the result of the alternative hypothesis shows that there have been significant changes in statements and opinions.

• Differences in Acceptance criteria

If the p-value in a null hypothesis is greater than the significance level, then the null hypothesis is accepted.

If the p-value in an alternate hypothesis is smaller than the significance level, then the alternative hypothesis is accepted.

• Differences in importance

The null hypothesis accepts true existing theories and also if there has been consistency in multiple experiments of similar hypotheses.

The alternative hypothesis establishes whether a relationship exists between two variables, and the result will then lead to new improved theories.

Read: T-testing: Definition, Formula & Interpretations

Examples of an Alternative Hypothesis and Null Hypothesis

Here are some examples of the alternative hypothesis:.

A researcher assumes that a bridge’s bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be:

For the null hypothesis H0: µ= 10 tons

For the alternate hypothesis Ha: µ>10 tons

In another study being conducted, the researcher wants to find out whether there is a noticeable difference or change in a patient’s heart arrest medicine and the patient’s heart condition.

For the alternate hypothesis: The hypothesis is that there might indeed be a relationship between the new medicine and the frequency or chances of heart arrest in a patient.

Here are the examples of the null hypothesis

The hypothesis from example 2 in the alternate hypothesis implies that the use of one specific medicine can reduce the frequency and chances of heart arrest.

For the null hypothesis: The hypothesis will be that the use of that particular medicine cannot reduce the chance and frequency of heart arrest in a patient.

An alternate hypothesis states that the random exam scores are collected from both men and women. But are the scores of the two groups (men and women) the same or are they different?

For the null hypothesis: The hypothesis will state that the calculated mean of the men’s exam score is equal to the exam score of the women.

This is represented as

H0= The null hypothesis

µ1= The calculated mean score of men

µ2= The calculated mean score of women

Read: What is Empirical Research Study? [Examples & Method]

• Can you reject an alternative hypothesis?

It is quite inappropriate to say or report that an alternate hypothesis was rejected. It is much better to use the phrase “the alternate hypothesis was rather not supported”.

The reason behind this use of words is that only the null hypothesis is designed to be rejected in a study. The alternative hypothesis is designed to prove the null hypothesis incorrect, to introduce new facts that can disprove the null hypothesis but it is not designed to be rejected.

It can either be accepted or not supported.

• How do you identify alternative hypotheses?

A researcher can use this formula to identify the alternate hypothesis in a study or experiment.

H0 and Ha are in contrast.

Therefore, if Ho has:

Equal to (=)

Greater than or equal to (≥)

Less than or equal to (≤)

And then Ha has:

Not equal (≠) 

Greater than (>) or less than (

Less than ( )

If in a study, α ≤ p-value, then the researcher should not reject H0.

If in a study, α > p-value, then the researcher should reject H0.

α is preconceived. The value of α is determined even before the hypothesis test is conducted. While the p-value is derived from the calculation in the data.

• Which is better in formulating hypotheses of your study alternative or null?

The study a researcher wants to conduct will determine what hypothesis should be developed. However, the researcher should keep in mind what the purpose of the null and alternative two hypotheses are while developing the study hypothesis. So while the null hypothesis will accept existing theories that it found to be true or correct, and measure the consistency of multiple experiments, alternative hypotheses will find the relationship that exists (if any) between two phenomena and may lead to the development of a new and improved theory.

In this article, it has been clearly defined the relationship that exists between the null hypothesis and the alternative hypothesis. While the null hypothesis is always an assumption that needs to be proven with evidence for it to be accepted, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved. 

Researchers should note that for every null hypothesis, one or more alternate hypotheses can be developed.

Connect to Formplus, Get Started Now - It's Free!

• acceptance criteria
• alternate hypotheses
• alternative hypothesis
• alternative hypothesis types
• alternative vs null hypothesis
• null hypothese
• busayo.longe

You may also like:

Hypothesis Testing: Definition, Uses, Limitations + Examples

The process of research validation involves testing and it is in this context that we will explore hypothesis testing.

Acceptance Sampling: Meaning, Examples, When to Use

In this post, we will discuss extensively what acceptance sampling is and when it is applied.

Type I vs Type II Errors: Causes, Examples & Prevention

This article will discuss the two different types of errors in hypothesis testing and how you can prevent them from occurring in your research

Extrapolation in Statistical Research: Definition, Examples, Types, Applications

In this article we’ll look at the different types and characteristics of extrapolation, plus how it contrasts to interpolation.

Formplus - For Seamless Data Collection

Collect data the right way with a versatile data collection tool. try formplus and transform your work productivity today..