how to develop a null hypothesis

Statistics Made Easy

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

Published by Zach

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 22,880 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.

$\mu _{1}=\mu _{2}$

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?

A null hypothesis states that there's no relationship between 2 variables.

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

Step 1 Null hypotheses and alternative hypotheses are mutually exclusive.

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.

Step 2 Proving the null hypothesis false is a precursor to proving the alternative.

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?

Use statistical methods on collected data to test the 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].

$\mu _{1}+\mu _{2}=0$

Research null hypothesis: The proportion of [dependent variable] in [group 1] and [group 2] is the same.

$p_{1}=p_{2}$

Research null hypothesis: There is no correlation between [independent variable] and [dependent variable] in the population.

$\rho =0$

Research null hypothesis: There is no relationship between [independent variable] and [dependent variable] in the population.

$\beta =0$

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Expert Interview

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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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9.1 Null and Alternative Hypotheses

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

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

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

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

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

Mathematical Symbols Used in H 0 and H a :

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

Example 9.1

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

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

Example 9.2

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

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

H 0 : μ __ 66
H a : μ __ 66

Example 9.3

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

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

H 0 : μ __ 45
H a : μ __ 45

Example 9.4

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

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

H 0 : p __ 0.40
H a : p __ 0.40

Collaborative Exercise

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

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a or H 1 ).
Collect data in a way designed to test the hypothesis.
Perform an appropriate statistical test .
Decide whether to reject or fail to reject your null hypothesis.
Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

an estimate of the difference in average height between the two groups.
a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

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.

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).

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.

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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ($H_0$) and an alternative hypothesis ($H_a$).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

At this point we can write hypotheses for a single mean ($\mu$), paired means($\mu_d$), a single proportion ($p$), the difference between two independent means ($\mu_1-\mu_2$), the difference between two proportions ($p_1-p_2$), a simple linear regression slope ($\beta$), and a correlation ($\rho$).
The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., $\mu_0$ and $p_0$). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., $p$ and $\mu$). The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

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How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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Video transcript

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter , ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

Example 4: Burger Weights

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

How to Perform a Normality Test in Excel (Step-by-Step)

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Null Hypothesis Examples

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The null hypothesis —which assumes that there is no meaningful relationship between two variables—may be the most valuable hypothesis for the scientific method because it is the easiest to test using a statistical analysis. This means you can support your hypothesis with a high level of confidence. Testing the null hypothesis can tell you whether your results are due to the effect of manipulating the dependent variable or due to chance.

What Is the Null Hypothesis?

The null hypothesis states there is no relationship between the measured phenomenon (the dependent variable) and the independent variable . You do not need to believe that the null hypothesis is true to test it. On the contrary, you will likely suspect that there is a relationship between a set of variables. One way to prove that this is the case is to reject the null hypothesis. Rejecting a hypothesis does not mean an experiment was "bad" or that it didn't produce results. In fact, it is often one of the first steps toward further inquiry.

To distinguish it from other hypotheses, the null hypothesis is written as H 0 (which is read as “H-nought,” "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95 percent or 99 percent is common. Keep in mind, even if the confidence level is high, there is still a small chance the null hypothesis is not true, perhaps because the experimenter did not account for a critical factor or because of chance. This is one reason why it's important to repeat experiments.

Examples of the Null Hypothesis

To write a null hypothesis, first start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect. Write your hypothesis in a way that reflects this.

What Is a Hypothesis? (Science)
What 'Fail to Reject' Means in a Hypothesis Test
What Are the Elements of a Good Hypothesis?
Scientific Method Vocabulary Terms
Null Hypothesis Definition and Examples
Definition of a Hypothesis
Six Steps of the Scientific Method
Understanding Simple vs Controlled Experiments
Hypothesis Test for the Difference of Two Population Proportions
What Is the Difference Between Alpha and P-Values?
Null Hypothesis and Alternative Hypothesis
What Are Examples of a Hypothesis?
Hypothesis Test Example
How to Conduct a Hypothesis Test
What Is a P-Value?
The Difference Between Type I and Type II Errors in Hypothesis Testing

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7.3: The Research Hypothesis and the Null Hypothesis

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Michelle Oja
Taft College

Hypotheses are predictions of expected findings.

The Research Hypothesis

A research hypothesis is a mathematical way of stating a research question. A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean. The last one gives the research hypothesis a direction. In other words, a research hypothesis should include:

The name of the groups being compared. This is sometimes considered the IV.
What was measured. This is the DV.
Which group are we predicting will have the higher mean.

There are two types of research hypotheses related to sample means and population means: Directional Research Hypotheses and Non-Directional Research Hypotheses

Directional Research Hypothesis

If we expect our obtained sample mean to be above or below the other group's mean (the population mean, for example), we have a directional hypothesis. There are two options:

Symbol: $ \displaystyle \bar{X} > \mu $
(The mean of the sample is greater than than the mean of the population.)
Symbol: $ \displaystyle \bar{X} < \mu $
(The mean of the sample is less than than mean of the population.)

Example $\PageIndex{1}$

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework. What’s a directional hypothesis for how scoring higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend more time on their homework than the population of junior high students.

Answer in Symbols: $ \displaystyle \bar{X} > \mu $

Non-Directional Research Hypothesis

A non-directional hypothesis states that the means will be different, but does not specify which will be higher. In reality, there is rarely a situation in which we actually don't want one group to be higher than the other, so we will focus on directional research hypotheses. There is only one option for a non-directional research hypothesis: "The sample mean differs from the population mean." These types of research hypotheses don’t give a direction, the hypothesis doesn’t say which will be higher or lower.

A non-directional research hypothesis in symbols should look like this: $ \displaystyle \bar{X} \neq \mu $ (The mean of the sample is not equal to the mean of the population).

Exercise $\PageIndex{1}$

What’s a non-directional hypothesis for how scoring higher on growth mindset higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework (Blackwell, Trzesniewski, & Dweck, 2007)? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend a different amount of time on their homework than the population of junior high students.

Answer in Symbols: $ \displaystyle \bar{X} \neq \mu $

See how a non-directional research hypothesis doesn't really make sense? The big issue is not if the two groups differ, but if one group seems to improve what was measured (if having a growth mindset leads to more time spent on math homework). This textbook will only use directional research hypotheses because researchers almost always have a predicted direction (meaning that we almost always know which group we think will score higher).

The Null Hypothesis

The hypothesis that an apparent effect is due to chance is called the null hypothesis, written $H_0$ (“H-naught”). We usually test this through comparing an experimental group to a comparison (control) group. This null hypothesis can be written as:

\[\mathrm{H}_{0}: \bar{X} = \mu \nonumber \]

For most of this textbook, the null hypothesis is that the means of the two groups are similar. Much later, the null hypothesis will be that there is no relationship between the two groups. Either way, remember that a null hypothesis is always saying that nothing is different.

This is where descriptive statistics diverge from inferential statistics. We know what the value of $\overline{\mathrm{X}}$ is – it’s not a mystery or a question, it is what we observed from the sample. What we are using inferential statistics to do is infer whether this sample's descriptive statistics probably represents the population's descriptive statistics. This is the null hypothesis, that the two groups are similar.

Keep in mind that the null hypothesis is typically the opposite of the research hypothesis. A research hypothesis for the ESP example is that those in my sample who say that they have ESP would get more correct answers than the population would get correct, while the null hypothesis is that the average number correct for the two groups will be similar.

In general, the null hypothesis is the idea that nothing is going on: there is no effect of our treatment, no relation between our variables, and no difference in our sample mean from what we expected about the population mean. This is always our baseline starting assumption, and it is what we seek to reject. If we are trying to treat depression, we want to find a difference in average symptoms between our treatment and control groups. If we are trying to predict job performance, we want to find a relation between conscientiousness and evaluation scores. However, until we have evidence against it, we must use the null hypothesis as our starting point.

In sum, the null hypothesis is always : There is no difference between the groups’ means OR There is no relationship between the variables .

In the next chapter, the null hypothesis is that there’s no difference between the sample mean and population mean. In other words:

There is no mean difference between the sample and population.
The mean of the sample is the same as the mean of a specific population.
$\mathrm{H}_{0}: \bar{X} = \mu \nonumber $
We expect our sample’s mean to be same as the population mean.

Exercise $\PageIndex{2}$

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework. What’s the null hypothesis for scoring higher on growth mindset (compared to the population of junior high students) and how long students spent on their homework? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend a similar amount of time on their homework as the population of junior high students.

Answer in Symbols: $ \bar{X} = \mu $

Contributors and Attributions

Foster et al. (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)

Dr. MO ( Taft College )

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Null Hypothesis

Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

What Is a Null Hypothesis?

Symbol of Null Hypothesis

Formula of null hypothesis, types of null hypothesis, principle of null hypothesis, how do you find null hypothesis, what is a null hypothesis.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

Definition of Null Hypothesis

Null Hypothesis represent a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 , asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

Null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there’s no significant difference in variances between groups or populations.

Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there’s no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.

Examples of Null Hypothesis

Medicine: Null Hypothesis: “No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo.”
Education: Null Hypothesis: “There’s no significant variation in test scores between students using a new teaching method and those using traditional teaching.”
Economics: Null Hypothesis: “There’s no significant change in consumer spending pre- and post-implementation of a new taxation policy.”
Environmental Science: Null Hypothesis: “There’s no substantial difference in pollution levels before and after a water treatment plant’s establishment.”

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

$\alpha$

Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Null Hypothesis and Alternative Hypothesis

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

Null Hypothesis vs Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Example of Alternative and Null Hypothesis

Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”

Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

Also, Check

Solved Examples on Null Hypothesis

Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.

Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.

Example 2: A company asserts that the error rate in its production process is less than 1%.

Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.

Null Hypothesis – Practice Problems

Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?

Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?

Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?

Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?

Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?

Null Hypothesis – Frequently Asked Questions

How to form a null hypothesis.

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.

What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

Is it Possible to Prove the Null Hypothesis?

No, statistical testing aims to either reject or fail to reject the null hypothesis based on evidence from sample data. It does not prove the null hypothesis to be true.

What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

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Null hypothesis

Null hypothesis n., plural: null hypotheses [nʌl haɪˈpɒθɪsɪs] Definition: a hypothesis that is valid or presumed true until invalidated by a statistical test

Table of Contents

Null Hypothesis Definition

Null hypothesis is defined as “the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact”.

More formally, we can define a null hypothesis as “a statistical theory suggesting that no statistical relationship exists between given observed variables” .

In biology , the null hypothesis is used to nullify or reject a common belief. The researcher carries out the research which is aimed at rejecting the commonly accepted belief.

What Is a Null Hypothesis?

A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. It needs and requires more experiments and testing for confirmation. There are two possibilities that by doing more experiments and testing, a hypothesis can be false or true. It means it can either prove wrong or true (Blackwelder, 1982).

For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment for almost a month. She watered some plants with mineral water and some with distilled water.

In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis. In the above example of plants, the null hypothesis is:

There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.

Usually, an investigator tries to prove the null hypothesis wrong and tries to explain a relation and association between the two variables.

An opposite and reverse of the null hypothesis are known as the alternate hypothesis . In the example of plants the alternate hypothesis is:

There are statistical relationships among the forms of water that are given to plants for growth and nourishment.

The example below shows the difference between null vs alternative hypotheses:

Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.

Copernicus and many other scientists try to prove the null hypothesis wrong and false. By their experiments and testing, they make people believe that alternate hypotheses are correct and true. If they do not prove the null hypothesis experimentally wrong then people will not believe them and never consider the alternative hypothesis true and correct.

The alternative and null hypothesis for Susie’s assumption is:

Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and nourishment of these two plants.
Alternative Hypothesis: If one plant is watered with distilled water and the other with mineral water, then the plant with mineral water shows better growth and nourishment.

The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.

Most people consider the null hypothesis true and correct. Scientists work and perform different experiments and do a variety of research so that they can prove the null hypothesis wrong or nullify it. For this purpose, they design an alternate hypothesis that they think is correct or true. The null hypothesis symbol is H 0 (it is read as H null or H zero ).

Why is it named the “Null”?

The name null is given to this hypothesis to clarify and explain that the scientists are working to prove it false i.e. to nullify the hypothesis. Sometimes it confuses the readers; they might misunderstand it and think that statement has nothing. It is blank but, actually, it is not. It is more appropriate and suitable to call it a nullifiable hypothesis instead of the null hypothesis.

Why do we need to assess it? Why not just verify an alternate one?

In science, the scientific method is used. It involves a series of different steps. Scientists perform these steps so that a hypothesis can be proved false or true. Scientists do this to confirm that there will be any limitation or inadequacy in the new hypothesis. Experiments are done by considering both alternative and null hypotheses, which makes the research safe. It gives a negative as well as a bad impact on research if a null hypothesis is not included or a part of the study. It seems like you are not taking your research seriously and not concerned about it and just want to impose your results as correct and true if the null hypothesis is not a part of the study.

Development of the Null

In statistics, firstly it is necessary to design alternate and null hypotheses from the given problem. Splitting the problem into small steps makes the pathway towards the solution easier and less challenging. how to write a null hypothesis?

Writing a null hypothesis consists of two steps:

Firstly, initiate by asking a question.
Secondly, restate the question in such a way that it seems there are no relationships among the variables.

In other words, assume in such a way that the treatment does not have any effect.

The usual recovery duration after knee surgery is considered almost 8 weeks.

A researcher thinks that the recovery period may get elongated if patients go to a physiotherapist for rehabilitation twice per week, instead of thrice per week, i.e. recovery duration reduces if the patient goes three times for rehabilitation instead of two times.

Step 1: Look for the problem in the hypothesis. The hypothesis either be a word or can be a statement. In the above example the hypothesis is:

“The expected recovery period in knee rehabilitation is more than 8 weeks”

Step 2: Make a mathematical statement from the hypothesis. Averages can also be represented as μ, thus the null hypothesis formula will be.

In the above equation, the hypothesis is equivalent to H1, the average is denoted by μ and > that the average is greater than eight.

Step 3: Explain what will come up if the hypothesis does not come right i.e., the rehabilitation period may not proceed more than 08 weeks.

There are two options: either the recovery will be less than or equal to 8 weeks.

H 0 : μ ≤ 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ and ≤ represents that the average is less than or equal to eight.

What will happen if the scientist does not have any knowledge about the outcome?

Problem: An investigator investigates the post-operative impact and influence of radical exercise on patients who have operative procedures of the knee. The chances are either the exercise will improve the recovery or will make it worse. The usual time for recovery is 8 weeks.

Step 1: Make a null hypothesis i.e. the exercise does not show any effect and the recovery time remains almost 8 weeks.

H 0 : μ = 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ, and the equal sign (=) shows that the average is equal to eight.

Step 2: Make the alternate hypothesis which is the reverse of the null hypothesis. Particularly what will happen if treatment (exercise) makes an impact?

In the above equation, the alternate hypothesis is equivalent to H1, the average is denoted by μ and not equal sign (≠) represents that the average is not equal to eight.

Significance Tests

To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population. The data can be in different forms like in means or proportions. It can either be the difference of proportions and means or any odd ratio.

The following table will explain the symbols:

P-value is the chief statistical final result of the significance test of the null hypothesis.

P-value = Pr(data or data more extreme | H 0 true)
| = “given”
Pr = probability
H 0 = the null hypothesis

The first stage of Null Hypothesis Significance Testing (NHST) is to form an alternate and null hypothesis. By this, the research question can be briefly explained.

Null Hypothesis = no effect of treatment, no difference, no association Alternative Hypothesis = effective treatment, difference, association

When to reject the null hypothesis?

Researchers will reject the null hypothesis if it is proven wrong after experimentation. Researchers accept null hypothesis to be true and correct until it is proven wrong or false. On the other hand, the researchers try to strengthen the alternate hypothesis. The binomial test is performed on a sample and after that, a series of tests were performed (Frick, 1995).

Step 1: Evaluate and read the research question carefully and consciously and make a null hypothesis. Verify the sample that supports the binomial proportion. If there is no difference then find out the value of the binomial parameter.

Show the null hypothesis as:

H 0 :p= the value of p if H 0 is true

To find out how much it varies from the proposed data and the value of the null hypothesis, calculate the sample proportion.

Step 2: In test statistics, find the binomial test that comes under the null hypothesis. The test must be based on precise and thorough probabilities. Also make a list of pmf that apply, when the null hypothesis proves true and correct.

When H 0 is true, X~b(n, p)

N = size of the sample

P = assume value if H 0 proves true.

Step 3: Find out the value of P. P-value is the probability of data that is under observation.

Rise or increase in the P value = Pr(X ≥ x)

X = observed number of successes

P value = Pr(X ≤ x).

Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.

Sample proportion
The direction of difference (either increases or decreases)

Perceived Problems With the Null Hypothesis

Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis. Statistical tests of the null hypothesis are reasonably not strong. There is randomization about significance. (Gill, 1999) The main issue with the testing of the null hypothesis is that they all are wrong or false on a ground basis.

There is another problem with the a-level . This is an ignored but also a well-known problem. The value of a-level is without a theoretical basis and thus there is randomization in conventional values, most commonly 0.q, 0.5, or 0.01. If a fixed value of a is used, it will result in the formation of two categories (significant and non-significant) The issue of a randomized rejection or non-rejection is also present when there is a practical matter which is the strong point of the evidence related to a scientific matter.

The P-value has the foremost importance in the testing of null hypothesis but as an inferential tool and for interpretation, it has a problem. The P-value is the probability of getting a test statistic at least as extreme as the observed one.

The main point about the definition is: Observed results are not based on a-value

Moreover, the evidence against the null hypothesis was overstated due to unobserved results. A-value has importance more than just being a statement. It is a precise statement about the evidence from the observed results or data. Similarly, researchers found that P-values are objectionable. They do not prefer null hypotheses in testing. It is also clear that the P-value is strictly dependent on the null hypothesis. It is computer-based statistics. In some precise experiments, the null hypothesis statistics and actual sampling distribution are closely related but this does not become possible in observational studies.

Some researchers pointed out that the P-value is depending on the sample size. If the true and exact difference is small, a null hypothesis even of a large sample may get rejected. This shows the difference between biological importance and statistical significance. (Killeen, 2005)

Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected. If the size of simple is infinity and the null hypothesis is proved true there are still chances of Type I error. That is the reason this approach or method is not considered consistent and reliable. There is also another problem that the exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.

Null Hypothesis Examples

Here are some examples:

Example 1: Hypotheses with One Sample of One Categorical Variable

Among all the population of humans, almost 10% of people prefer to do their task with their left hand i.e. left-handed. Let suppose, a researcher in the Penn States says that the population of students at the College of Arts and Architecture is mostly left-handed as compared to the general population of humans in general public society. In this case, there is only a sample and there is a comparison among the known population values to the population proportion of sample value.

Research Question: Do artists more expected to be left-handed as compared to the common population persons in society?
Response Variable: Sorting the student into two categories. One category has left-handed persons and the other category have right-handed persons.
Form Null Hypothesis: Arts and Architecture college students are no more predicted to be lefty as compared to the common population persons in society (Lefty students of Arts and Architecture college population is 10% or p= 0.10)

Example 2: Hypotheses with One Sample of One Measurement Variable

A generic brand of antihistamine Diphenhydramine making medicine in the form of a capsule, having a 50mg dose. The maker of the medicines is concerned that the machine has come out of calibration and is not making more capsules with the suitable and appropriate dose.

Research Question: Does the statistical data recommended about the mean and average dosage of the population differ from 50mg?
Response Variable: Chemical assay used to find the appropriate dosage of the active ingredient.
Null Hypothesis: Usually, the 50mg dosage of capsules of this trade name (population average and means dosage =50 mg).

Example 3: Hypotheses with Two Samples of One Categorical Variable

Several people choose vegetarian meals on a daily basis. Typically, the researcher thought that females like vegetarian meals more than males.

Research Question: Does the data recommend that females (women) prefer vegetarian meals more than males (men) regularly?
Response Variable: Cataloguing the persons into vegetarian and non-vegetarian categories. Grouping Variable: Gender
Null Hypothesis: Gender is not linked to those who like vegetarian meals. (Population percent of women who eat vegetarian meals regularly = population percent of men who eat vegetarian meals regularly or p women = p men).

Example 4: Hypotheses with Two Samples of One Measurement Variable

Nowadays obesity and being overweight is one of the major and dangerous health issues. Research is performed to confirm that a low carbohydrates diet leads to faster weight loss than a low-fat diet.

Research Question: Does the given data recommend that usually, a low-carbohydrate diet helps in losing weight faster as compared to a low-fat diet?
Response Variable: Weight loss (pounds)
Explanatory Variable: Form of diet either low carbohydrate or low fat
Null Hypothesis: There is no significant difference when comparing the mean loss of weight of people using a low carbohydrate diet to people using a diet having low fat. (population means loss of weight on a low carbohydrate diet = population means loss of weight on a diet containing low fat).

Example 5: Hypotheses about the relationship between Two Categorical Variables

A case-control study was performed. The study contains nonsmokers, stroke patients, and controls. The subjects are of the same occupation and age and the question was asked if someone at their home or close surrounding smokes?

Research Question: Did second-hand smoke enhance the chances of stroke?
Variables: There are 02 diverse categories of variables. (Controls and stroke patients) (whether the smoker lives in the same house). The chances of having a stroke will be increased if a person is living with a smoker.
Null Hypothesis: There is no significant relationship between a passive smoker and stroke or brain attack. (odds ratio between stroke and the passive smoker is equal to 1).

Example 6: Hypotheses about the relationship between Two Measurement Variables

A financial expert observes that there is somehow a positive and effective relationship between the variation in stock rate price and the quantity of stock bought by non-management employees

Response variable- Regular alteration in price
Explanatory Variable- Stock bought by non-management employees
Null Hypothesis: The association and relationship between the regular stock price alteration ($) and the daily stock-buying by non-management employees ($) = 0.

Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

Research Question: Is the relation between the bill paid in a restaurant and the tip given to the waiter, is linear? Is this relation different for dining and family restaurants?
Explanatory Variable- total bill amount
Response Variable- the amount of tip
Null Hypothesis: The relationship and association between the total bill quantity at a family or dining restaurant and the tip, is the same.

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Blackwelder, W. C. (1982). “Proving the null hypothesis” in clinical trials. Controlled Clinical Trials , 3(4), 345–353.
Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138.
Gill, J. (1999). The insignificance of null hypothesis significance testing. Political Research Quarterly , 52(3), 647–674.
Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16(5), 345–353.

Last updated on June 16th, 2022

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Research Hypothesis In Psychology: Types, & Examples

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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What Is a Null Hypothesis?

How a null hypothesis works, the alternative hypothesis, examples of a null hypothesis.

Null Hypothesis and Investments
Null Hypothesis FAQs
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Null Hypothesis: What Is It and How Is It Used in Investing?

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H 0 .

The null hypothesis, also known as the conjecture, is used in quantitative analysis to test theories about markets, investing strategies, or economies to decide if an idea is true or false.

Key Takeaways

A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
The alternative hypothesis proposes that there is a difference.
Hypothesis testing provides a method to reject a null hypothesis within a certain confidence level.
If you can reject the null hypothesis, it provides support for the alternative hypothesis.
Null hypothesis testing is the basis of the principle of falsification in science.

Investopedia / Alex Dos Diaz

A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process. For example, a gambler may be interested in whether a game of chance is fair. If it is fair, then the expected earnings per play come to zero for both players. If the game is not fair, then the expected earnings are positive for one player and negative for the other. To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, then tests the null hypothesis that the expected earnings are not different from zero.

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the sample data are near zero, then the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and zero is explainable by chance alone.

The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.

Analysts look to reject the null hypothesis because doing so is a strong conclusion. This requires strong evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that factors other than chance may be at work but may not be strong enough for the statistical test to detect them.

A null hypothesis can only be rejected, not proven.

An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H1).

For the above examples, the alternative hypothesis would be:

Students score an average that is not equal to seven.
The mean annual return of the mutual fund is not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

Here is a simple example: A school principal claims that students in her school score an average of seven out of 10 in exams. The null hypothesis is that the population mean is 7.0. To test this null hypothesis, we record marks of, say, 30 students (sample) from the entire student population of the school (say 300) and calculate the mean of that sample.

We can then compare the (calculated) sample mean to the (hypothesized) population mean of 7.0 and attempt to reject the null hypothesis. (The null hypothesis here—that the population mean is 7.0—cannot be proved using the sample data. It can only be rejected.)

Take another example: The annual return of a particular mutual fund is claimed to be 8%. Assume that a mutual fund has been in existence for 20 years. The null hypothesis is that the mean return is 8% for the mutual fund. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.

For the above examples, null hypotheses are:

Example A : Students in the school score an average of seven out of 10 in exams.
Example B: Mean annual return of the mutual fund is 8% per year.

For the purposes of determining whether to reject the null hypothesis, the null hypothesis (abbreviated H 0 ) is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0). Then, if the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be “explainable by chance alone,” being within the range that is determined by chance alone.

How Null Hypothesis Testing Is Used in Investments

As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock . The null hypothesis states that there is no difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.

Refuting the null hypothesis would require showing statistical significance, which can be found by a variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.

One tool that can determine the statistical significance of the results is the p-value. A p-value represents the probability that a difference as large or larger than the observed difference between the two average returns could occur solely by chance.

A p-value that is less than or equal to 0.05 often indicates whether there is evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns (the p-value is less than or equal to 0.05), she can then reject the null hypothesis and conclude the alternative hypothesis.

How Is the Null Hypothesis Identified?

The analyst or researcher establishes a null hypothesis based on the research question or problem that they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?) the null hypothesis could be H 0 : X = 0. If the question is instead, is X the same as Y, the H0 would be X = Y. If it is that the effect of X on Y is positive, H0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.

How Is Null Hypothesis Used in Finance?

In finance, a null hypothesis is used in quantitative analysis. A null hypothesis tests the premise of an investing strategy, the markets, or an economy to determine if it is true or false. For instance, an analyst may want to see if two stocks, ABC and XYZ, are closely correlated. The null hypothesis would be ABC ≠ XYZ.

How Are Statistical Hypotheses Tested?

Statistical hypotheses are tested by a four-step process . The first step is for the analyst to state the two hypotheses so that only one can be right. The next step is to formulate an analysis plan, which outlines how the data will be evaluated. The third step is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

What Is an Alternative Hypothesis?

An alternative hypothesis is a direct contradiction of a null hypothesis. This means that if one of the two hypotheses is true, the other is false.

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Pages 4–7.

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Page 4.

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Page 7.

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How to Write a Null Hypothesis (5 Examples)
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.
Null & Alternative Hypotheses
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 ...
How to Write a Null Hypothesis (with Examples and Templates)
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.
Null Hypothesis: Definition, Rejecting & Examples
When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H 0 or H A.. Null Hypothesis H 0: No effect exists in the population.; Alternative Hypothesis H A: The effect exists in the population.; In every study or experiment, researchers assess an effect or relationship.
9.1: Null and Alternative Hypotheses
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.
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.
Null Hypothesis Definition and Examples, How to State
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.
Null and Alternative Hypotheses
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
How to Write a Strong Hypothesis
6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a.
Hypothesis Testing
Step 1: State your null and alternate hypothesis. After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o) and alternate (H a) hypothesis so that you can test it mathematically.. The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables.
5.2
Alternative Hypothesis. The statement that there is some difference in the population (s), denoted as H a or H 1. When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.
How to Write a Strong Hypothesis
Step 5: Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
Examples of null and alternative hypotheses
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
What Is The Null Hypothesis & When To Reject It
A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis. Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.
How to Write a Null Hypothesis (5 Examples)
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.
Null Hypothesis Definition and Examples
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
Examples of the Null Hypothesis
The null hypothesis—which assumes that there is no meaningful relationship between two variables—may be the most valuable hypothesis for the scientific method because it is the easiest to test using a statistical analysis. This means you can support your hypothesis with a high level of confidence. Testing the null hypothesis can tell you whether your results are due to the effect of ...
7.3: The Research Hypothesis and the Null Hypothesis
The Research Hypothesis. A research hypothesis is a mathematical way of stating a research question. A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean. The last one gives the research hypothesis a direction. In other words, a research hypothesis ...
Null Hypothesis
Null hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. Learn more about Null Hypothesis, its formula, symbol and example in this article ... Develop the null hypothesis to ...
Null hypothesis
Biology definition: A null hypothesis is an assumption or proposition where an observed difference between two samples of a statistical population is purely accidental and not due to systematic causes. It is the hypothesis to be investigated through statistical hypothesis testing so that when refuted indicates that the alternative hypothesis is true. . Thus, a null hypothesis is a hypothesis ...
Research Hypothesis In Psychology: Types, & Examples
The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. ... write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional ...
Null Hypothesis: What Is It and How Is It Used in Investing?
Null Hypothesis: A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. The null hypothesis attempts to ...

How to Write a Null Hypothesis (5 Examples)

Example 1: Weight of Turtles

Example 2: Height of Males

Example 3: Graduation Rates

Example 4: Burger Weights

Example 5: Citizen Support

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Variables in hypotheses

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Step 2: Do some preliminary research

Step 3: Formulate your hypothesis

Step 4: Refine your hypothesis

Step 5: Phrase your hypothesis in three ways

Step 6. Write a null hypothesis

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How to Write a Null Hypothesis (5 Examples)

Example 1: Weight of Turtles

Example 2: Height of Males

Example 3: Graduation Rates

Example 4: Burger Weights

Example 5: Citizen Support

Additional Resources

How to Perform a Normality Test in Excel (Step-by-Step)

Null Hypothesis Examples

What Is the Null Hypothesis?

Examples of the Null Hypothesis

7.3: The Research Hypothesis and the Null Hypothesis

The Research Hypothesis

Directional Research Hypothesis

Non-Directional Research Hypothesis

The Null Hypothesis

Contributors and Attributions

Null Hypothesis

Symbol of Null Hypothesis

Definition of Null Hypothesis

Mean Comparison (Two-sample t-test)

Proportion Comparison

Equality in Variance (F-test in ANOVA)

Independence (Chi-square Test of Independence):