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- Null and Alternative Hypotheses | Definitions & Examples
Null & Alternative Hypotheses | Definitions, Templates & Examples
Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :
- Null hypothesis ( H 0 ): There’s no effect in the population .
- Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.
Table of contents
Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.
The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:
- The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
- The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .
You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.
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The null hypothesis is the claim that there’s no effect in the population.
If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.
Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.
Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).
You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.
Examples of null hypotheses
The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.
| ( ) | ||
| Does tooth flossing affect the number of cavities? | Tooth flossing has on the number of cavities. | test: The mean number of cavities per person does not differ between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ = µ . |
| Does the amount of text highlighted in the textbook affect exam scores? | The amount of text highlighted in the textbook has on exam scores. | : There is no relationship between the amount of text highlighted and exam scores in the population; β = 0. |
| Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression.* | test: The proportion of people with depression in the daily-meditation group ( ) is greater than or equal to the no-meditation group ( ) in the population; ≥ . |
*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .
The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.
Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.
The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.
Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.
Examples of alternative hypotheses
The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.
| Does tooth flossing affect the number of cavities? | Tooth flossing has an on the number of cavities. | test: The mean number of cavities per person differs between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ ≠ µ . |
| Does the amount of text highlighted in a textbook affect exam scores? | The amount of text highlighted in the textbook has an on exam scores. | : There is a relationship between the amount of text highlighted and exam scores in the population; β ≠ 0. |
| Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression. | test: The proportion of people with depression in the daily-meditation group ( ) is less than the no-meditation group ( ) in the population; < . |
Null and alternative hypotheses are similar in some ways:
- They’re both answers to the research question.
- They both make claims about the population.
- They’re both evaluated by statistical tests.
However, there are important differences between the two types of hypotheses, summarized in the following table.
| A claim that there is in the population. | A claim that there is in the population. | |
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| Equality symbol (=, ≥, or ≤) | Inequality symbol (≠, <, or >) | |
| Rejected | Supported | |
| Failed to reject | Not supported |
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To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.
General template sentences
The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:
Does independent variable affect dependent variable ?
- Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
- Alternative hypothesis ( H a ): Independent variable affects dependent variable.
Test-specific template sentences
Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.
| ( ) | ||
| test
with two groups | The mean dependent variable does not differ between group 1 (µ ) and group 2 (µ ) in the population; µ = µ . | The mean dependent variable differs between group 1 (µ ) and group 2 (µ ) in the population; µ ≠ µ . |
| with three groups | The mean dependent variable does not differ between group 1 (µ ), group 2 (µ ), and group 3 (µ ) in the population; µ = µ = µ . | The mean dependent variable of group 1 (µ ), group 2 (µ ), and group 3 (µ ) are not all equal in the population. |
| There is no correlation between independent variable and dependent variable in the population; ρ = 0. | There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0. | |
| There is no relationship between independent variable and dependent variable in the population; β = 0. | There is a relationship between independent variable and dependent variable in the population; β ≠ 0. | |
| Two-proportions test | The dependent variable expressed as a proportion does not differ between group 1 ( ) and group 2 ( ) in the population; = . | The dependent variable expressed as a proportion differs between group 1 ( ) and group 2 ( ) in the population; ≠ . |
Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
- Normal distribution
- Descriptive statistics
- Measures of central tendency
- Correlation coefficient
Methodology
- Cluster sampling
- Stratified sampling
- Types of interviews
- Cohort study
- Thematic analysis
Research bias
- Implicit bias
- Cognitive bias
- Survivorship bias
- Availability heuristic
- Nonresponse bias
- Regression to the mean
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).
A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).
A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.
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Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved August 21, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/
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Title Page Setup
A title page is required for all APA Style papers. There are both student and professional versions of the title page. Students should use the student version of the title page unless their instructor or institution has requested they use the professional version. APA provides a student title page guide (PDF, 199KB) to assist students in creating their title pages.
Student title page
The student title page includes the paper title, author names (the byline), author affiliation, course number and name for which the paper is being submitted, instructor name, assignment due date, and page number, as shown in this example.
Title page setup is covered in the seventh edition APA Style manuals in the Publication Manual Section 2.3 and the Concise Guide Section 1.6
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- Student Title Page Guide (PDF, 263KB)
- Student Paper Setup Guide (PDF, 3MB)
Student papers do not include a running head unless requested by the instructor or institution.
Follow the guidelines described next to format each element of the student title page.
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| Paper title | Place the title three to four lines down from the top of the title page. Center it and type it in bold font. Capitalize of the title. Place the main title and any subtitle on separate double-spaced lines if desired. There is no maximum length for titles; however, keep titles focused and include key terms. |
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| Author names | Place one double-spaced blank line between the paper title and the author names. Center author names on their own line. If there are two authors, use the word “and” between authors; if there are three or more authors, place a comma between author names and use the word “and” before the final author name. | Cecily J. Sinclair and Adam Gonzaga |
| Author affiliation | For a student paper, the affiliation is the institution where the student attends school. Include both the name of any department and the name of the college, university, or other institution, separated by a comma. Center the affiliation on the next double-spaced line after the author name(s). | Department of Psychology, University of Georgia |
| Course number and name | Provide the course number as shown on instructional materials, followed by a colon and the course name. Center the course number and name on the next double-spaced line after the author affiliation. | PSY 201: Introduction to Psychology |
| Instructor name | Provide the name of the instructor for the course using the format shown on instructional materials. Center the instructor name on the next double-spaced line after the course number and name. | Dr. Rowan J. Estes |
| Assignment due date | Provide the due date for the assignment. Center the due date on the next double-spaced line after the instructor name. Use the date format commonly used in your country. | October 18, 2020 |
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| Use the page number 1 on the title page. Use the automatic page-numbering function of your word processing program to insert page numbers in the top right corner of the page header. | 1 |
Professional title page
The professional title page includes the paper title, author names (the byline), author affiliation(s), author note, running head, and page number, as shown in the following example.
Follow the guidelines described next to format each element of the professional title page.
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| Paper title | Place the title three to four lines down from the top of the title page. Center it and type it in bold font. Capitalize of the title. Place the main title and any subtitle on separate double-spaced lines if desired. There is no maximum length for titles; however, keep titles focused and include key terms. |
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| Author names
| Place one double-spaced blank line between the paper title and the author names. Center author names on their own line. If there are two authors, use the word “and” between authors; if there are three or more authors, place a comma between author names and use the word “and” before the final author name. | Francesca Humboldt |
| When different authors have different affiliations, use superscript numerals after author names to connect the names to the appropriate affiliation(s). If all authors have the same affiliation, superscript numerals are not used (see Section 2.3 of the for more on how to set up bylines and affiliations). | Tracy Reuter , Arielle Borovsky , and Casey Lew-Williams | |
| Author affiliation
| For a professional paper, the affiliation is the institution at which the research was conducted. Include both the name of any department and the name of the college, university, or other institution, separated by a comma. Center the affiliation on the next double-spaced line after the author names; when there are multiple affiliations, center each affiliation on its own line.
| Department of Nursing, Morrigan University |
| When different authors have different affiliations, use superscript numerals before affiliations to connect the affiliations to the appropriate author(s). Do not use superscript numerals if all authors share the same affiliations (see Section 2.3 of the for more). | Department of Psychology, Princeton University | |
| Author note | Place the author note in the bottom half of the title page. Center and bold the label “Author Note.” Align the paragraphs of the author note to the left. For further information on the contents of the author note, see Section 2.7 of the . | n/a |
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| The running head appears in all-capital letters in the page header of all pages, including the title page. Align the running head to the left margin. Do not use the label “Running head:” before the running head. | Prediction errors support children’s word learning |
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| Use the page number 1 on the title page. Use the automatic page-numbering function of your word processing program to insert page numbers in the top right corner of the page header. | 1 |
IMAGES
COMMENTS
Find sample papers formatted in seventh edition APA Style for different paper types and purposes. Download Word files to use as templates and edit them as needed for your own papers.
Indent the first line of every paragraph of text 0.5 in. using the tab key or the paragraph-formatting function of your word-processing program. Page numbers: Put a page number in the top right corner of every page, including the title page or cover page, which is page 1. Student papers do not require a running head on any page.
This checklist corresponds to the writing and formatting guidelines described in full in the Publication Manual of the American Psychological Association (7th ed.). Refer to the following chapters for specific information: paper elements and format in Chapter 2. writing style and grammar in Chapter 4. bias-free language in Chapter 5.
Media Files: APA Sample Student Paper , APA Sample Professional Paper This resource is enhanced by Acrobat PDF files. Download the free Acrobat Reader. Note: The APA Publication Manual, 7 th Edition specifies different formatting conventions for student and professional papers (i.e., papers written for credit in a course and papers intended for scholarly publication).
In this sample paper, we've put four blank lines above the title. Commented [AF3]: Authors' names are written below the title, with one double-spaced blank line between them. Names should be written as follows: First name, middle initial(s), last name. Commented [AF4]: Authors' affiliations follow immediately after their names.
Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question.
Basic guidelines for formatting the reference list at the end of a standard APA research paper Author/Authors Rules for handling works by a single author or multiple authors that apply to all APA-style references in your reference list, regardless of the type of work (book, article, electronic resource, etc.)
APA 7th Edition Template. Download this 7th-edition template, and use it to format your APA-style Research Paper. Simply download and save a new copy of the document and paste the contents of your paper into the appropriate fields within the template. This version of the template includes the ABSTRACT page.
APA Citation Style: A Sample. Student's Name. Department's name, University of Hawai'i - West O'ahu. PSY 250: Social Psychology. Instructor's name. October 23, 2020. The due date for the assignment should be here. The title should be centered, bolded, and 3-4 lines below the top of the page. Authors' names are written below the title ...
Throughout your paper, you need to apply the following APA format guidelines: Set page margins to 1 inch on all sides. Double-space all text, including headings. Indent the first line of every paragraph 0.5 inches. Use an accessible font (e.g., Times New Roman 12pt., Arial 11pt., or Georgia 11pt.).
Margins. APA specifies 1-inch margins all around (top, bottom, left, right). Pagination. Use your word processor's header function to put page numbers in the upper-right-hand corner one inch from the right-hand edge of the page. Start with the title page and go all the way through.
p values. There are two ways to report p values. One way is to use the alpha level (the a priori criterion for the probablility of falsely rejecting your null hypothesis), which is typically .05 or .01. Example: F(1, 24) = 44.4, p < .01. You may also report the exact p value (the a posteriori probability that the result that you obtained, or ...
your well-defined hypothesis, i.e. the over-arching, guiding principle upon which your research was based (Chen et. al., 2010). No heading is used for the introduction (APA, 2020). Writing in APA style requires attention to format, APA writing style, bias-free writing, author citation, and references which are all covered in this paper.
ading (see box below)This paper describes some basic parts of writing in. PA style 7th Edi. student writing, useof language, in-text citations, the references page, a. d titles and fi. ures. This paper alsoprovides examples of specific changes that are required by. itations, frustrat.
Reporting Research Results in APA Style | Tips & Examples. Published on December 21, 2020 by Pritha Bhandari.Revised on January 17, 2024. The results section of a quantitative research paper is where you summarize your data and report the findings of any relevant statistical analyses.. The APA manual provides rigorous guidelines for what to report in quantitative research papers in the fields ...
Papers usually end with a concluding section, often called the "Discussion.". The Discussion is your opportunity to evaluate and interpret the results of your study or paper, draw inferences and conclusions from it, and communicate its contributions to science and/or society. Use the present tense when writing the Discussion section.
The main heading of "Methods" should be centered, boldfaced, and capitalized. Subheadings within this section are left-aligned, boldfaced, and in title case. You can also add lower level headings within these subsections, as long as they follow APA heading styles. To structure your methods section, you can use the subheadings of ...
APA (American Psychological Association) style is most commonly used to cite sources within the social sciences. This resource, revised according to the 6th edition, second printing of the APA manual, offers examples for the general format of APA research papers, in-text citations, endnotes/footnotes, and the reference page. For more information, please consult the Publication Manual of the ...
Common Reference Examples in APA Style 7th ed. More than 100 reference examples and their corresponding in-text citations are presented in the Publication Manual. Examples of the most common kinds of works that writers cite are provided on this page for your ease of use. Note that print and electronic works have the same foundation; look for ...
APA Style 7th edition APA citation examples Citing sources ... Hypothesis testing example. You want to test whether there is a relationship between gender and height. Based on your knowledge of human physiology, you formulate a hypothesis that men are, on average, taller than women. ...
Keywords Format. More information on how to write and format an abstract and keywords can be found in the Publication Manual of the American Psychological Association (7th ed.) Sections 2.9 to 2.10 and in the Concise Guide to APA Style (7th ed.) Section 1.10. SOURCE: American Psychological Association. (2020).
This document provides a template for a psychology lab report following APA style guidelines. It includes sections for the title page, abstract, introduction, method, results, discussion, and references. The introduction provides background on the topic and states the aims and hypotheses. The method describes the participants, materials, and procedures. The results section presents data in ...
APA Style 7th edition ... As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis. Examples of alternative hypotheses. The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own. Research question: Alternative hypothesis (H a)
This guide contains examples of common types of APA Style references. Section numbers indicate where to find the examples in the Publication Manual of the American Psychological Association (7th ed.). More information on references and reference examples are in Chapters 9 and 10 of the Publication Manual as well as the Concise Guide to APA ...
Format. Example. Paper title. Place the title three to four lines down from the top of the title page. Center it and type it in bold font. Capitalize major words of the title. Place the main title and any subtitle on separate double-spaced lines if desired. There is no maximum length for titles; however, keep titles focused and include key terms.