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9.1: Null and Alternative Hypotheses
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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.
\(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
\(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove.
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.
\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
Example \(\PageIndex{1}\)
- \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
- \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)
Exercise \(\PageIndex{1}\)
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
- \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
- \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)
Example \(\PageIndex{2}\)
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
- \(H_{0}: \mu = 2.0\)
- \(H_{a}: \mu \neq 2.0\)
Exercise \(\PageIndex{2}\)
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.
- \(H_{0}: \mu \_ 66\)
- \(H_{a}: \mu \_ 66\)
- \(H_{0}: \mu = 66\)
- \(H_{a}: \mu \neq 66\)
Example \(\PageIndex{3}\)
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
- \(H_{0}: \mu \geq 5\)
- \(H_{a}: \mu < 5\)
Exercise \(\PageIndex{3}\)
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
- \(H_{0}: \mu \_ 45\)
- \(H_{a}: \mu \_ 45\)
- \(H_{0}: \mu \geq 45\)
- \(H_{a}: \mu < 45\)
Example \(\PageIndex{4}\)
In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
- \(H_{0}: p \leq 0.066\)
- \(H_{a}: p > 0.066\)
Exercise \(\PageIndex{4}\)
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.
- \(H_{0}: p \_ 0.40\)
- \(H_{a}: p \_ 0.40\)
- \(H_{0}: p = 0.40\)
- \(H_{a}: p > 0.40\)
COLLABORATIVE EXERCISE
Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:
- Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
- Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
- If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
- Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
Formula Review
\(H_{0}\) and \(H_{a}\) are contradictory.
- If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
- If\(\alpha > p\)-value, then reject \(H_{0}\).
\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References
Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .
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Methodology
- How to Write a Strong Hypothesis | Steps & Examples
How to Write a Strong Hypothesis | Steps & Examples
Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .
Example: Hypothesis
Daily apple consumption leads to fewer doctor’s visits.
Table of contents
What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Variables in hypotheses
Hypotheses propose a relationship between two or more types of variables .
- An independent variable is something the researcher changes or controls.
- A dependent variable is something the researcher observes and measures.
If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.
In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .
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Step 1. ask a question.
Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.
Step 2. Do some preliminary research
Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.
At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.
Step 3. Formulate your hypothesis
Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.
4. Refine your hypothesis
You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:
- The relevant variables
- The specific group being studied
- The predicted outcome of the experiment or analysis
5. Phrase your hypothesis in three ways
To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.
If you are comparing two groups, the hypothesis can state what difference you expect to find between them.
6. Write a null hypothesis
If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .
- H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
- H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.
If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.
- Sampling methods
- Simple random sampling
- Stratified sampling
- Cluster sampling
- Likert scales
- Reproducibility
Statistics
- Null hypothesis
- Statistical power
- Probability distribution
- Effect size
- Poisson distribution
Research bias
- Optimism bias
- Cognitive bias
- Implicit bias
- Hawthorne effect
- Anchoring bias
- Explicit bias
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
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9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.
H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.
Mathematical Symbols Used in H 0 and H a :
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
Example 9.1
H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.
Example 9.2
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
- H 0 : μ __ 66
- H a : μ __ 66
Example 9.3
We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
- H 0 : μ __ 45
- H a : μ __ 45
Example 9.4
An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066
On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
- H 0 : p __ 0.40
- H a : p __ 0.40
Collaborative Exercise
Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.
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Writing Null Hypotheses in Research and Statistics
Last Updated: January 17, 2024 Fact Checked
This article was co-authored by Joseph Quinones and by wikiHow staff writer, Jennifer Mueller, JD . Joseph Quinones is a High School Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 22,964 times.
Are you working on a research project and struggling with how to write a null hypothesis? Well, you've come to the right place! Start by recognizing that the basic definition of "null" is "none" or "zero"—that's your biggest clue as to what a null hypothesis should say. Keep reading to learn everything you need to know about the null hypothesis, including how it relates to your research question and your alternative hypothesis as well as how to use it in different types of studies.
Things You Should Know
- Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups.
- Adjust the format of your null hypothesis to match the statistical method you used to test it, such as using "mean" if you're comparing the mean between 2 groups.
What is a null hypothesis?
- Research hypothesis: States in plain language that there's no relationship between the 2 variables or there's no difference between the 2 groups being studied.
- Statistical hypothesis: States the predicted outcome of statistical analysis through a mathematical equation related to the statistical method you're using.
Examples of Null Hypotheses
Null Hypothesis vs. Alternative Hypothesis
- For example, your alternative hypothesis could state a positive correlation between 2 variables while your null hypothesis states there's no relationship. If there's a negative correlation, then both hypotheses are false.
- You need additional data or evidence to show that your alternative hypothesis is correct—proving the null hypothesis false is just the first step.
- In smaller studies, sometimes it's enough to show that there's some relationship and your hypothesis could be correct—you can leave the additional proof as an open question for other researchers to tackle.
How do I test a null hypothesis?
- Group means: Compare the mean of the variable in your sample with the mean of the variable in the general population. [6] X Research source
- Group proportions: Compare the proportion of the variable in your sample with the proportion of the variable in the general population. [7] X Research source
- Correlation: Correlation analysis looks at the relationship between 2 variables—specifically, whether they tend to happen together. [8] X Research source
- Regression: Regression analysis reveals the correlation between 2 variables while also controlling for the effect of other, interrelated variables. [9] X Research source
Templates for Null Hypotheses
- Research null hypothesis: There is no difference in the mean [dependent variable] between [group 1] and [group 2].
- Research null hypothesis: The proportion of [dependent variable] in [group 1] and [group 2] is the same.
- Research null hypothesis: There is no correlation between [independent variable] and [dependent variable] in the population.
- Research null hypothesis: There is no relationship between [independent variable] and [dependent variable] in the population.
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- ↑ https://online.stat.psu.edu/stat100/lesson/10/10.1
- ↑ https://online.stat.psu.edu/stat501/lesson/2/2.12
- ↑ https://support.minitab.com/en-us/minitab/21/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/null-and-alternative-hypotheses/
- ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5635437/
- ↑ https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing
- ↑ https://education.arcus.chop.edu/null-hypothesis-testing/
- ↑ https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions/bs704_hypothesistest-means-proportions_print.html
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Null Hypothesis
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Fisher, R. (1925). Statistical methods for research workers (1st ed.). Edinburgh: Oliver and Boyd.
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Gigerenzer, G. (2004). Mindless statistics. The Journal of Socio-Economics, 33 , 587–606.
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Hays, W. L. (1994). Statistics (5th ed.). Belmont: Wadsworth.
Neyman, J., & Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London, Series A, 231 , 289–337.
Szucs, D., & Ioannidis, J. P. A. (2016). When null hypothesis significance testing is unsuitable for research: A reassessment. bioRxiv . https://doi.org/10.1101/095570 .
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The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant.
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 ( H0) answers “No, there’s no effect in the population.”. The alternative hypothesis ( Ha) answers “Yes, there is an effect in the ...
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign.
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.
Null hypothesis. In scientific research, the null hypothesis (often denoted H0) [1] is the claim that the effect being studied does not exist. Note that the term "effect" here is not meant to imply a causative relationship. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or ...
Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”. Step 2: Convert the hypothesis to math.
6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a.
They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. H0, the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups. Write a statistical null hypothesis as a mathematical equation, such as. μ 1 = μ 2 {\displaystyle \mu _ {1}=\mu _ {2}} if you're comparing group means.
A hypothesis is a statement or explanation about the nature or causes of some phenomena of interest. In the process of scientific study, we can distinguish two forms of hypotheses. A research hypothesis poses the question of interest, and if well stated, will include the variables under study and the expected relationship between them.