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Null Hypothesis: Definition, Rejecting & Examples

By Jim Frost 6 Comments

What is a Null Hypothesis?

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.

• 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. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.

In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!

You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.

Related post : What is an Effect in Statistics?

Null Hypothesis Examples

Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.

After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.

Let’s see how you reject the null hypothesis and get to those more exciting findings!

When to Reject the Null Hypothesis

So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.

The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .

After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The p-value is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.

When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the p-value to your significance level .

Rejecting the Null Hypothesis

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!

When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .

Failing to Reject the Null Hypothesis

Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!

Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .

That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!

Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.

Related posts : How Hypothesis Tests Work and Interpreting P-values

How to Write a Null Hypothesis

The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.

Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics

Group Means

T-tests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.

For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group means are equal in the population: µ 1 = µ 2 , or µ 1 – µ 2 = 0
• Alternative Hypothesis H A : Group means are not equal in the population: µ 1 ≠ µ 2 , or µ 1 – µ 2 ≠ 0.

Group Proportions

Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.

For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group proportions are equal in the population: p 1 = p 2 .
• Alternative Hypothesis H A : Group proportions are not equal in the population: p 1 ≠ p 2 .

Correlation and Regression Coefficients

Some studies assess the relationship between two continuous variables rather than differences between groups.

In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.

For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.

• Null Hypothesis H 0 : The correlation in the population is zero: ρ = 0.
• Alternative Hypothesis H A : The correlation in the population is not zero: ρ ≠ 0.

For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.

The preceding examples are all for two-tailed hypothesis tests. To learn about one-tailed tests and how to write a null hypothesis for them, read my post One-Tailed vs. Two-Tailed Tests .

Related post : Understanding Correlation

Neyman, J; Pearson, E. S. (January 1, 1933).  On the Problem of the most Efficient Tests of Statistical Hypotheses .  Philosophical Transactions of the Royal Society A .  231  (694–706): 289–337.

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January 11, 2024 at 2:57 pm

Thanks for the reply.

January 10, 2024 at 1:23 pm

Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?

January 10, 2024 at 2:15 pm

Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.

Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.

With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.

So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).

For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.

I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!

February 20, 2022 at 9:26 pm

Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”

February 23, 2022 at 9:21 pm

Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a one-sided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.

It’s the alternative hypothesis that typically contains does not equal.

There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.

In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.

February 15, 2022 at 9:32 am

Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent

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Writing Null Hypotheses in Research and Statistics

Last Updated: January 17, 2024 Fact Checked

This article was co-authored by Joseph Quinones and by wikiHow staff writer, Jennifer Mueller, JD . Joseph Quinones is a High School Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 28,545 times.

Are you working on a research project and struggling with how to write a null hypothesis? Well, you've come to the right place! Start by recognizing that the basic definition of "null" is "none" or "zero"—that's your biggest clue as to what a null hypothesis should say. Keep reading to learn everything you need to know about the null hypothesis, including how it relates to your research question and your alternative hypothesis as well as how to use it in different types of studies.

Things You Should Know

• Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups.

• Adjust the format of your null hypothesis to match the statistical method you used to test it, such as using "mean" if you're comparing the mean between 2 groups.

What is a null hypothesis?

• Research hypothesis: States in plain language that there's no relationship between the 2 variables or there's no difference between the 2 groups being studied.
• Statistical hypothesis: States the predicted outcome of statistical analysis through a mathematical equation related to the statistical method you're using.

Examples of Null Hypotheses

Null Hypothesis vs. Alternative Hypothesis

• For example, your alternative hypothesis could state a positive correlation between 2 variables while your null hypothesis states there's no relationship. If there's a negative correlation, then both hypotheses are false.

• You need additional data or evidence to show that your alternative hypothesis is correct—proving the null hypothesis false is just the first step.
• In smaller studies, sometimes it's enough to show that there's some relationship and your hypothesis could be correct—you can leave the additional proof as an open question for other researchers to tackle.

How do I test a null hypothesis?

• Group means: Compare the mean of the variable in your sample with the mean of the variable in the general population. [6] X Research source
• Group proportions: Compare the proportion of the variable in your sample with the proportion of the variable in the general population. [7] X Research source
• Correlation: Correlation analysis looks at the relationship between 2 variables—specifically, whether they tend to happen together. [8] X Research source
• Regression: Regression analysis reveals the correlation between 2 variables while also controlling for the effect of other, interrelated variables. [9] X Research source

Templates for Null Hypotheses

• Research null hypothesis: There is no difference in the mean [dependent variable] between [group 1] and [group 2].

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

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

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

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Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones .

• ↑ https://online.stat.psu.edu/stat100/lesson/10/10.1
• ↑ https://online.stat.psu.edu/stat501/lesson/2/2.12
• ↑ https://support.minitab.com/en-us/minitab/21/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/null-and-alternative-hypotheses/
• ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5635437/
• ↑ https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing
• ↑ https://education.arcus.chop.edu/null-hypothesis-testing/
• ↑ https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions/bs704_hypothesistest-means-proportions_print.html

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Null Hypothesis Definition and Examples, How to State

What is the null hypothesis, how to state the null hypothesis, null hypothesis overview.

Why is it Called the “Null”?

The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify . It doesn’t mean that the statement is null (i.e. amounts to nothing) itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).

Why Do I need to Test it? Why not just prove an alternate one?

The short answer is, as a scientist, you are required to ; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.

• Null hypothesis : H 0 : The world is flat.
• Alternate hypothesis: The world is round.

Several scientists, including Copernicus , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong .

How to State the Null Hypothesis from a Word Problem

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis . Breaking your problem into a few small steps makes these problems much easier to handle.

Step 2: Convert the hypothesis to math . Remember that the average is sometimes written as μ.

H 1 : μ > 8.2

Broken down into (somewhat) English, that’s H 1 (The hypothesis): μ (the average) > (is greater than) 8.2

Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H 0 : μ ≤ 8.2

Broken down again into English, that’s H 0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

How to State the Null Hypothesis: Part Two

But what if the researcher doesn’t have any idea what will happen.

Example Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. 

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H 0 : μ = 8.2

Broken down into English, that’s H 0 (The null hypothesis): μ (the average) = (is equal to) 8.2

Step 2: Figure out the alternate hypothesis . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H 1 : μ ≠ 8.2

In English again, that’s H 1 (The  alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2

That’s How to State the Null Hypothesis!

Check out our Youtube channel for more stats tips!

Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.

Null Hypothesis Definition and Examples

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In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.

The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .

How to State a Null Hypothesis

There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.

For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.

The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."

This can be written mathematically as: H 1 : μ > 6

In this example, μ is the average.

Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:

H 0 : μ ≤ 6

The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:

H 0 : μ = 6

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 null hypothesis.

Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.

Why Test a Null Hypothesis?

You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.

For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.

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Null Hypothesis Examples

The null hypothesis (H 0 ) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment .

The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance. If the null hypothesis is rejected, then it’s strong evidence there is a true difference between test sets or that the independent variable affects the dependent variable.

• The null hypothesis is a nullifiable hypothesis. A researcher seeks to reject it because this result strongly indicates observed differences are real and not just due to chance.
• The null hypothesis may be accepted or rejected, but not proven. There is always a level of confidence in the outcome.

What Is the Null Hypothesis?

The null hypothesis is written as H 0 , which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1 . When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.

An experimenter tests the null hypothesis with a statistical analysis called a significance test. The significance test determines the likelihood that the results of the test are not due to chance. Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01). But, even if the confidence in the test is high, there is always a small chance the outcome is incorrect. This means you can’t prove a null hypothesis. It’s also a good reason why it’s important to repeat experiments.

Exact and Inexact Null Hypothesis

The most common type of null hypothesis assumes no difference between two samples or groups or no measurable effect of a treatment. This is the exact hypothesis . If you’re asked to state a null hypothesis for a science class, this is the one to write. It is the easiest type of hypothesis to test and is the only one accepted for certain types of analysis. Examples include:

There is no difference between two groups H 0 : μ 1  = μ 2 (where H 0  = the null hypothesis, μ 1  = the mean of population 1, and μ 2  = the mean of population 2)

Both groups have value of 100 (or any number or quality) H 0 : μ = 100

However, sometimes a researcher may test an inexact hypothesis . This type of hypothesis specifies ranges or intervals. Examples include:

Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time

There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105

An inexact hypothesis offers “directionality” about a phenomenon. For example, an exact hypothesis can indicate whether or not a treatment has an effect, while an inexact hypothesis can tell whether an effect is positive of negative. However, an inexact hypothesis may be harder to test and some scientists and statisticians disagree about whether it’s a true null hypothesis .

How to State the Null Hypothesis

To state the null hypothesis, first state what you expect the experiment to show. Then, rephrase the statement in a form that assumes there is no relationship between the variables or that a treatment has no effect.

Example: A researcher tests whether a new drug speeds recovery time from a certain disease. The average recovery time without treatment is 3 weeks.

• State the goal of the experiment: “I hope the average recovery time with the new drug will be less than 3 weeks.”
• Rephrase the hypothesis to assume the treatment has no effect: “If the drug doesn’t shorten recovery time, then the average time will be 3 weeks or longer.” Mathematically: H 0 : μ ≥ 3

This null hypothesis (inexact hypothesis) covers both the scenario in which the drug has no effect and the one in which the drugs makes the recovery time longer. The alternate hypothesis is that average recovery time will be less than three weeks:

H A : μ < 3

Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3

The danger of testing this hypothesis is that rejecting it only implies the drug affected recovery time (not whether it made it better or worse). This is because the alternate hypothesis is:

H A : μ ≠ 3 (which includes μ <3 and μ >3)

Even though the no-effect null hypothesis yields less information, it’s used because it’s easier to test using statistics. Basically, testing whether something is unchanged/changed is easier than trying to quantify the nature of the change.

Remember, a researcher hopes to reject the null hypothesis because this supports the alternate hypothesis. Also, be sure the null and alternate hypothesis cover all outcomes. Finally, remember a simple true/false, equal/unequal, yes/no exact hypothesis is easier to test than a more complex inexact hypothesis.

• Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007).  Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN  978-90-79418-01-5 .
• Cox, D. R. (2006).  Principles of Statistical Inference . Cambridge University Press. ISBN  978-0-521-68567-2 .
• Everitt, Brian (1998).  The Cambridge Dictionary of Statistics . Cambridge, UK New York: Cambridge University Press. ISBN 978-0521593465.
• Weiss, Neil A. (1999).  Introductory Statistics  (5th ed.). ISBN 9780201598773.

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Null Hypothesis

Definition of null hypothesis.

The null hypothesis is a statement that assumes there is no significant relationship or difference between two observed phenomena. It is typically denoted as H0 and is used in statistical hypothesis testing. The purpose of the null hypothesis is to serve as a baseline or default assumption, which is then tested against an alternative hypothesis to determine if there is evidence to support rejecting the null hypothesis.

Suppose a researcher wants to investigate whether there is a difference in test scores between students who receive tutoring and those who do not. The null hypothesis in this case would be that there is no difference in test scores between the two groups. In statistical terms, it would be stated as “the mean test scores of students who receive tutoring (μ1) is equal to the mean test scores of students who do not receive tutoring (μ2)”.

To test this null hypothesis, the researcher collects data on test scores from both groups and conducts a statistical analysis. If the analysis yields a significant result, it would suggest that there is evidence to reject the null hypothesis. On the other hand, if the result is not significant, it would indicate that there is not enough evidence to reject the null hypothesis, and the researcher would fail to find a difference in test scores between the groups.

Importance of Null Hypothesis

The null hypothesis is a fundamental component of hypothesis testing and statistical inference. It provides a basis for comparison and allows researchers to make conclusions based on the evidence at hand. By explicitly stating a null hypothesis, researchers can test their assumptions and determine whether there is a meaningful relationship or difference between variables. This helps to ensure that any observed effects or associations are not due to random chance or sampling error. Additionally, the concept of the null hypothesis fosters scientific rigor and encourages critical thinking in research.

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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.

Table of contents

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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• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis (H 0 ): There’s no effect in the population .
• Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and 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 (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question
• They both make claims about the population
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
• Alternative hypothesis (H A ): Independent variable affects dependent variable .

Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

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

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

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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 Null Hypothesis?

Null hypothesis symbol, formula of null hypothesis, types of null hypothesis, null hypothesis examples, principle of null hypothesis, how do you find null hypothesis, null hypothesis in statistics, null hypothesis and alternative hypothesis, null hypothesis and alternative hypothesis examples, null hypothesis – practice problems.

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.

Null Hypothesis Meaning

Null Hypothesis represents 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.

The 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.

• 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.

The null hypothesis is usually formulated to be tested against an alternative hypothesis (H 1 or H [Tex]\alpha [/Tex] ) which suggests that there is an effect, difference or relationship present in the population.

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.

In statistical hypothesis testing, researchers begin by stating the null hypothesis, often based on theoretical considerations or previous research. The null hypothesis is then tested against an alternative hypothesis (Ha), which represents the researcher’s claim or the hypothesis they seek to support.

The process of hypothesis testing involves collecting sample data and using statistical methods to assess the likelihood of observing the data if the null hypothesis were true. This assessment is typically done by calculating a test statistic, which measures the difference between the observed data and what would be expected under the null 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.

Difference Between Null Hypothesis and 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.

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.

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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.

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?

Summary – Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) and alternative hypothesis (H a ) are fundamental concepts in statistical hypothesis testing. The null hypothesis represents the default assumption, stating that there is no significant effect, difference, or relationship between variables. It serves as the baseline against which the alternative hypothesis is tested. In contrast, the alternative hypothesis represents the researcher’s hypothesis or the claim to be tested, suggesting that there is a significant effect, difference, or relationship between variables. The relationship between the null and alternative hypotheses is such that they are complementary, and statistical tests are conducted to determine whether the evidence from the data is strong enough to reject the null hypothesis in favor of the alternative hypothesis. This decision is based on the strength of the evidence and the chosen level of significance. Ultimately, the choice between the null and alternative hypotheses depends on the specific research question and the direction of the effect being investigated.

FAQs on Null Hypothesis

What does null hypothesis stands for.

The null hypothesis, denoted as H 0 ​, is a fundamental concept in statistics used for hypothesis testing. It represents the statement that there is no effect or no difference, and it is the hypothesis that the researcher typically aims to provide evidence against.

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.

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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What Is a Type I Error?

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Type 1 Error: Definition, False Positives, and Examples

Investopedia / Julie Bang

In statistical research, a type 1 error is when the null hypothesis is rejected, which incorrectly leads to the study stating that notable differences were found in the variables when actually there were no differences. Put simply, a type I error is a false positive result.

Making a type I error often can't be avoided because of the degree of uncertainty involved. A null hypothesis is established during hypothesis testing before a test begins. In some cases, a type I error assumes there's no cause-and-effect relationship between the tested item and the stimuli to trigger an outcome to the test.

Key Takeaways

• A type I error occurs during hypothesis testing when a null hypothesis is rejected, even though it is accurate and should not be rejected.
• Hypothesis testing is a testing process that uses sample data.
• The null hypothesis assumes no cause-and-effect relationship between the tested item and the stimuli applied during the test.
• A type I error is a false positive leading to an incorrect rejection of the null hypothesis.
• A false positive can occur if something other than the stimuli causes the outcome of the test.

How a Type I Error Works

Hypothesis testing is a testing process that uses sample data. The test is designed to provide evidence that the hypothesis or conjecture is supported by the data being tested. A null hypothesis is a belief that there is no statistical significance or effect between the two data sets, variables, or populations being considered in the hypothesis. A researcher would generally try to disprove the null hypothesis.

For example, let's say the null hypothesis states that an investment strategy doesn't perform any better than a market index like the S&P 500 . The researcher would take samples of data and test the historical performance of the investment strategy to determine if the strategy performed at a higher level than the S&P. If the test results show that the strategy performed at a higher rate than the index, the null hypothesis is rejected.

This condition is denoted as n=0. If the result seems to indicate that the stimuli applied to the test subject caused a reaction when the test is conducted, the null hypothesis stating that the stimuli do not affect the test subject then needs to be rejected.

A null hypothesis should ideally never be rejected if it's found to be true. It should always be rejected if it's found to be false. However, there are situations when errors can occur.

False Positive Type I Error

A type I error is also called a false positive result. This result leads to an incorrect rejection of the null hypothesis. It rejects an idea that shouldn't have been rejected in the first place.

Rejecting the null hypothesis under the assumption that there is no relationship between the test subject, the stimuli, and the outcome may sometimes be incorrect. If something other than the stimuli causes the outcome of the test, it can cause a false positive result.

Examples of Type I Errors

Let's look at a couple of hypothetical examples to show how type I errors occur.

Criminal Trials

Type I errors commonly occur in criminal trials, where juries are required to come up with a verdict of either innocent or guilty. In this case, the null hypothesis is that the person is innocent, while the alternative is guilty. A jury may come up with a type I error if the members find that the person is found guilty and is sent to jail, despite actually being innocent.

Medical Testing

In medical testing, a type I error would cause the appearance that a treatment for a disease has the effect of reducing the severity of the disease when, in fact, it does not. When a new medicine is being tested, the null hypothesis will be that the medicine does not affect the progression of the disease.

Let's say a lab is researching a new cancer drug . Their null hypothesis might be that the drug does not affect the growth rate of cancer cells.

After applying the drug to the cancer cells, the cancer cells stop growing. This would cause the researchers to reject their null hypothesis that the drug would have no effect. If the drug caused the growth stoppage, the conclusion to reject the null, in this case, would be correct.

However, if something else during the test caused the growth stoppage instead of the administered drug, this would be an example of an incorrect rejection of the null hypothesis (i.e., a type I error).

How Does a Type I Error Occur?

A type I error occurs when the null hypothesis, which is the belief that there is no statistical significance or effect between the data sets considered in the hypothesis, is mistakenly rejected. The type I error should never be rejected even though it's accurate. It is also known as a false positive result.

What Is the Difference Between a Type I and Type II Error?

Type I and type II errors occur during statistical hypothesis testing. While the type I error (a false positive) rejects a null hypothesis when it is, in fact, correct, the type II error (a false negative) fails to reject a false null hypothesis. For example, a type I error would convict someone of a crime when they are actually innocent. A type II error would acquit a guilty individual when they are guilty of a crime.

What Is a Null Hypothesis?

A null hypothesis occurs in statistical hypothesis testing. It states that no relationship exists between two data sets or populations. When a null hypothesis is accurate and rejected, the result is a false positive or a type I error. When it is false and fails to be rejected, a false negative occurs. This is also referred to as a type II error.

What's the Difference Between a Type I Error and a False Positive?

A type I error is often called a false positive. This occurs when the null hypothesis is rejected even though it's correct. The rejection takes place because of the assumption that there is no relationship between the data sets and the stimuli. As such, the outcome is assumed to be incorrect.

Hypothesis testing is a form of testing that uses data sets to either accept or determine a specific outcome using a null hypothesis. Although we often don't realize it, we use hypothesis testing in our everyday lives.

This comes in many areas, such as making investment decisions or deciding the fate of a person in a criminal trial. Sometimes, the result may be a type I error. This false positive is the incorrect rejection of the null hypothesis even when it is true.

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Null Hypothesis

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Making a certain class or laboratory experiment would require a good null hypothesis . You will be given variables to be used in your experiment and then you would be able to identify the relationship between the two. Every beginning of the experiment report would indicate your hypotheses. It is proven useful for it can be tested to prove if the result is considered false.

What is a Null Hypothesis?

A null hypothesis is used during experiments to prove that there is no difference in the relationship between the two variables. Every type of experiment would require you to make a null hypothesis. From the word itself “null” means zero or no value. If you want to practice making a good experiment report , consider providing a good null hypothesis. Null hypothesis is designed to be rejected if the alternative hypothesis is proven to be exact.

Null Hypothesis Examples in Research

1. medical research.

• Research Question: Does a new drug lower cholesterol levels more effectively than the current drug?
• Null Hypothesis (H0): The new drug has no effect on cholesterol levels compared to the current drug.
• Symbolic Form: H0: ?1 = ?2

2. Educational Research

• Research Question: Does the use of interactive technology improve student test scores?
• Null Hypothesis (H0): Interactive technology does not improve student test scores.

3. Business Research

• Research Question: Does a new marketing strategy increase sales?
• Null Hypothesis (H0): The new marketing strategy does not increase sales.

4. Psychological Research

• Research Question: Does cognitive-behavioral therapy reduce symptoms of anxiety more than standard therapy?
• Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce anxiety symptoms more than standard therapy.

5. Environmental Research

• Research Question: Does urbanization affect bird population diversity?
• Null Hypothesis (H0): Urbanization has no effect on bird population diversity.
• Symbolic Form: H0: ?urban = ?rural

6. Nutritional Research

• Research Question: Does a low-carb diet lead to more weight loss than a low-fat diet?
• Null Hypothesis (H0): A low-carb diet does not lead to more weight loss than a low-fat diet.

7. Economic Research

• Research Question: Does increasing the minimum wage reduce poverty levels?
• Null Hypothesis (H0): Increasing the minimum wage does not reduce poverty levels.
• Symbolic Form: H0: ?before = ?after

8. Sociological Research

• Research Question: Does social media usage affect teenagers’ self-esteem?
• Null Hypothesis (H0): Social media usage does not affect teenagers’ self-esteem.
• Symbolic Form: H0: ?users = ?non-users

9. Agricultural Research

• Research Question: Does the use of a new fertilizer increase crop yield?
• Null Hypothesis (H0): The new fertilizer does not increase crop yield.

10. Technological Research

• Research Question: Does a new software algorithm improve processing speed?
• Null Hypothesis (H0): The new software algorithm does not improve processing speed.
• Symbolic Form: H0: ?new = ?old

Null Hypothesis Examples in Psychology

1. effectiveness of therapy.

• Research Question: Does cognitive-behavioral therapy (CBT) reduce symptoms of depression more effectively than no treatment?
• Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce symptoms of depression more effectively than no treatment.
• Symbolic Form: H0: ?CBT = ?control

2. Impact of Sleep on Memory

• Research Question: Does sleep deprivation affect short-term memory performance?
• Null Hypothesis (H0): Sleep deprivation has no effect on short-term memory performance.
• Symbolic Form: H0: ?sleep_deprived = ?non_sleep_deprived

3. Influence of Color on Mood

• Research Question: Does the color of a room affect individuals’ mood?
• Null Hypothesis (H0): The color of a room does not affect individuals’ mood.
• Symbolic Form: H0: ?color1 = ?color2 = ?color3

4. Social Media and Self-Esteem

• Research Question: Does the frequency of social media use affect teenagers’ self-esteem?
• Null Hypothesis (H0): The frequency of social media use does not affect teenagers’ self-esteem.
• Symbolic Form: H0: ?high_use = ?low_use

5. Mindfulness and Stress Reduction

• Research Question: Does mindfulness meditation reduce stress levels in college students?
• Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels in college students.
• Symbolic Form: H0: ?mindfulness = ?control

6. Parenting Styles and Academic Performance

• Research Question: Does authoritative parenting style affect children’s academic performance?
• Null Hypothesis (H0): Authoritative parenting style does not affect children’s academic performance.
• Symbolic Form: H0: ?authoritative = ?other_styles

7. Impact of Exercise on Anxiety

• Research Question: Does regular exercise reduce anxiety levels in adults?
• Null Hypothesis (H0): Regular exercise does not reduce anxiety levels in adults.
• Symbolic Form: H0: ?exercise = ?no_exercise

8. Gender Differences in Risk-Taking Behavior

• Research Question: Are there differences in risk-taking behavior between males and females?
• Null Hypothesis (H0): There are no differences in risk-taking behavior between males and females.
• Symbolic Form: H0: ?males = ?females

9. Impact of Music on Concentration

• Research Question: Does listening to music while studying affect concentration levels?
• Null Hypothesis (H0): Listening to music while studying does not affect concentration levels.
• Symbolic Form: H0: ?music = ?no_music

10. Effect of Group Therapy on Social Skills

• Research Question: Does group therapy improve social skills in individuals with social anxiety?
• Null Hypothesis (H0): Group therapy does not improve social skills in individuals with social anxiety.
• Symbolic Form: H0: ?group_therapy = ?no_therapy

Null Hypothesis Examples in Biology

1. effect of fertilizers on plant growth.

• Research Question: Does a new fertilizer improve plant growth compared to no fertilizer?
• Null Hypothesis (H0): The new fertilizer does not improve plant growth compared to no fertilizer.
• Symbolic Form: H0: ?fertilizer = ?no_fertilizer

2. Antibiotic Effectiveness on Bacteria

• Research Question: Does a new antibiotic reduce bacterial growth more effectively than an existing antibiotic?
• Null Hypothesis (H0): The new antibiotic does not reduce bacterial growth more effectively than the existing antibiotic.
• Symbolic Form: H0: ?new_antibiotic = ?existing_antibiotic

3. Impact of Temperature on Enzyme Activity

• Research Question: Does temperature affect the activity of a specific enzyme?
• Null Hypothesis (H0): Temperature does not affect the activity of the specific enzyme.
• Symbolic Form: H0: Enzyme activity at temperature1 = Enzyme activity at temperature2

4. Genetic Influence on Trait Expression

• Research Question: Does a specific gene affect the expression of a particular trait in a plant species?
• Null Hypothesis (H0): The specific gene does not affect the expression of the particular trait in the plant species.
• Symbolic Form: H0: Trait expression with gene = Trait expression without gene

5. Effect of Light Intensity on Photosynthesis

• Research Question: Does light intensity affect the rate of photosynthesis in plants?
• Null Hypothesis (H0): Light intensity does not affect the rate of photosynthesis in plants.
• Symbolic Form: H0: Photosynthesis rate at light intensity1 = Photosynthesis rate at light intensity2

6. Impact of Diet on Animal Growth

• Research Question: Does a high-protein diet affect the growth rate of animals?
• Null Hypothesis (H0): A high-protein diet does not affect the growth rate of animals.
• Symbolic Form: H0: Growth rate on high-protein diet = Growth rate on normal diet

7. Effect of Pollution on Aquatic Life

• Research Question: Does water pollution affect the survival rate of fish in a lake?
• Null Hypothesis (H0): Water pollution does not affect the survival rate of fish in a lake.
• Symbolic Form: H0: Fish survival in polluted water = Fish survival in non-polluted water

8. Impact of Caffeine on Heart Rate in Daphnia

• Research Question: Does caffeine affect the heart rate of Daphnia (water fleas)?
• Null Hypothesis (H0): Caffeine does not affect the heart rate of Daphnia.
• Symbolic Form: H0: Heart rate with caffeine = Heart rate without caffeine

9. Influence of Soil pH on Plant Germination

• Research Question: Does soil pH affect the germination rate of seeds?
• Null Hypothesis (H0): Soil pH does not affect the germination rate of seeds.
• Symbolic Form: H0: Germination rate at pH1 = Germination rate at pH2

10. Effect of Salinity on Aquatic Plant Growth

• Research Question: Does salinity affect the growth of aquatic plants?
• Null Hypothesis (H0): Salinity does not affect the growth of aquatic plants.
• Symbolic Form: H0: Plant growth in saline water = Plant growth in freshwater

Null Hypothesis Examples in Business

1. effect of marketing campaign on sales.

• Research Question: Does a new marketing campaign increase product sales?
• Null Hypothesis (H0): The new marketing campaign does not increase product sales.
• Symbolic Form: H0: ?campaign = ?no_campaign

2. Impact of Training Programs on Employee Productivity

• Research Question: Do training programs improve employee productivity?
• Null Hypothesis (H0): Training programs do not improve employee productivity.
• Symbolic Form: H0: ?trained = ?untrained

3. Influence of Price Changes on Demand

• Research Question: Do price changes affect the demand for a product?
• Null Hypothesis (H0): Price changes do not affect the demand for the product.
• Symbolic Form: H0: ?price_change = ?no_price_change

4. Customer Satisfaction and Service Quality

• Research Question: Does improving service quality increase customer satisfaction?
• Null Hypothesis (H0): Improving service quality does not increase customer satisfaction.
• Symbolic Form: H0: ?improved_service = ?standard_service

5. Effect of Employee Benefits on Retention Rates

• Research Question: Do enhanced employee benefits reduce turnover rates?
• Null Hypothesis (H0): Enhanced employee benefits do not reduce turnover rates.
• Symbolic Form: H0: ?enhanced_benefits = ?standard_benefits

6. Impact of Social Media Presence on Brand Awareness

• Research Question: Does an active social media presence increase brand awareness?
• Null Hypothesis (H0): An active social media presence does not increase brand awareness.
• Symbolic Form: H0: ?active_social_media = ?inactive_social_media

7. Influence of Store Layout on Customer Purchases

• Research Question: Does store layout affect customer purchasing behavior?
• Null Hypothesis (H0): Store layout does not affect customer purchasing behavior.
• Symbolic Form: H0: ?layout1 = ?layout2

8. Online Advertising and Website Traffic

• Research Question: Does online advertising increase website traffic?
• Null Hypothesis (H0): Online advertising does not increase website traffic.
• Symbolic Form: H0: ?ads = ?no_ads

9. Effect of Product Packaging on Sales

• Research Question: Does new product packaging design increase sales?
• Null Hypothesis (H0): The new product packaging design does not increase sales.
• Symbolic Form: H0: ?new_packaging = ?old_packaging

10. Influence of Remote Work on Employee Performance

• Research Question: Does remote work affect employee performance?
• Null Hypothesis (H0): Remote work does not affect employee performance.
• Symbolic Form: H0: ?remote_work = ?office_work

Null Hypothesis Examples in Statistics

1. comparing means.

• Research Question: Is there a difference in average test scores between two groups of students?
• Null Hypothesis (H0): There is no difference in the average test scores between the two groups.

2. Proportions

• Research Question: Is the proportion of defective products the same in two different production lines?
• Null Hypothesis (H0): The proportion of defective products is the same in both production lines.
• Symbolic Form: H0: p1 = p2

3. Regression Analysis

• Research Question: Is there a relationship between years of experience and salary?
• Null Hypothesis (H0): There is no relationship between years of experience and salary.
• Symbolic Form: H0: ? = 0 (where ? is the regression coefficient)

4. ANOVA (Analysis of Variance)

• Research Question: Are the means of three or more groups equal?
• Null Hypothesis (H0): The means of all groups are equal.
• Symbolic Form: H0: ?1 = ?2 = ?3 = … = ?k

5. Chi-Square Test for Independence

• Research Question: Are gender and voting preference independent?
• Null Hypothesis (H0): Gender and voting preference are independent.
• Symbolic Form: H0: There is no association between gender and voting preference.

6. Time Series Analysis

• Research Question: Does a time series exhibit a trend over time?
• Null Hypothesis (H0): There is no trend in the time series data over time.
• Symbolic Form: H0: The time series has no significant trend component.

7. Hypothesis Testing for Variance

• Research Question: Is the variance in test scores different between two classes?
• Null Hypothesis (H0): The variances in test scores are equal between the two classes.
• Symbolic Form: H0: ?1² = ?2²

8. Correlation Analysis

• Research Question: Is there a correlation between two variables, such as height and weight?
• Null Hypothesis (H0): There is no correlation between the two variables.
• Symbolic Form: H0: ? = 0 (where ? is the correlation coefficient)

9. Two-Sample t-Test

• Research Question: Do two samples have the same mean?
• Null Hypothesis (H0): The two samples have the same mean.

10. One-Sample t-Test

• Research Question: Does the sample mean differ from a known population mean?
• Null Hypothesis (H0): The sample mean is equal to the population mean.
• Symbolic Form: H0: ? = ?0

Real life Examples of Null Hypothesis

1. medical studies.

• Research Question: Does a new medication lower blood pressure more effectively than the current medication?
• Null Hypothesis (H0): The new medication does not lower blood pressure more effectively than the current medication.
• Example: A clinical trial compares blood pressure readings between patients taking the new medication and those taking the current medication.

2. Education

• Research Question: Does a new teaching method improve student test scores?
• Null Hypothesis (H0): The new teaching method does not improve student test scores.
• Example: An educational study compares test scores of students taught using the new method versus those taught using traditional methods.

3. Business

• Research Question: Does a new advertising campaign increase product sales?
• Null Hypothesis (H0): The new advertising campaign does not increase product sales.
• Example: A company runs the new campaign and compares sales data before and after the campaign.

4. Public Health

• Research Question: Does a smoking cessation program reduce the smoking rate in a community?
• Null Hypothesis (H0): The smoking cessation program does not reduce the smoking rate in the community.
• Example: Public health officials analyze smoking rates before and after implementing the program.

5. Environmental Science

• Research Question: Does the introduction of a specific fish species affect the biodiversity of a lake?
• Null Hypothesis (H0): The introduction of the specific fish species does not affect the biodiversity of the lake.
• Example: Environmental scientists monitor biodiversity levels before and after introducing the fish species.

6. Economics

• Research Question: Does raising the minimum wage reduce poverty levels?
• Null Hypothesis (H0): Raising the minimum wage does not reduce poverty levels.
• Example: Economists compare poverty rates in regions with and without recent minimum wage increases.

7. Psychology

• Research Question: Does mindfulness meditation reduce stress levels among college students?
• Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels among college students.
• Example: A study measures stress levels before and after a mindfulness meditation program in a group of students.

8. Agriculture

• Example: Farmers apply the new fertilizer to one field and a standard fertilizer to another and compare the yields.

9. Technology

• Research Question: Does a new software update improve the speed of a computer program?
• Null Hypothesis (H0): The new software update does not improve the speed of the computer program.
• Example: Software engineers measure the program’s speed before and after applying the update.

10. Marketing

• Research Question: Does personalized email marketing increase customer engagement?
• Null Hypothesis (H0): Personalized email marketing does not increase customer engagement.
• Example: A company sends personalized emails to one group and generic emails to another, then compares engagement rates.

More Null Hypothesis Examples & Samples in PDF

1. null hypothesis significance test example.

2. Sample Null Hypothesis Example

3. Critical Assessment of Null Hypothesis Example

4. Confidence Levels for Null Hypotheses Example

5. Interpreting Failure to Reject A Null Hypothesis Example

6. Simple Null Hypothesis Example

7. Basic Neurology Null Hypothesis Example

8. Null Research Hypothesis in DOC

Purpose of Null Hypothesis

The null hypothesis is a fundamental concept in statistics and scientific research . It serves several critical purposes in the process of hypothesis testing, guiding researchers in drawing meaningful conclusions from their data. Below are the primary purposes of the null hypothesis:

1. Baseline for Comparison

The null hypothesis provides a baseline or a default position that indicates no effect, no difference, or no relationship between variables. It is the statement that researchers aim to test against an alternative hypothesis. By starting with the assumption that there is no effect, researchers can objectively assess whether the data provide enough evidence to support the alternative hypothesis.

2. Eliminates Bias

By assuming no effect or no difference, the null hypothesis helps eliminate bias in research. Researchers approach their study without preconceived notions about the outcome, ensuring that the results are based on the data collected rather than personal beliefs or expectations.

3. Framework for Statistical Testing

The null hypothesis provides a structured framework for conducting statistical tests. It is essential for calculating p-values and test statistics, which determine whether the observed data are significantly different from what would be expected under the null hypothesis. This framework allows for a standardized approach to testing hypotheses across various fields of study.

4. Facilitates Decision Making

The null hypothesis facilitates decision-making in research by providing clear criteria for accepting or rejecting it. If the data provide sufficient evidence to reject the null hypothesis, researchers can conclude that there is a statistically significant effect or difference. This decision-making process is critical in advancing scientific knowledge and understanding.

5. Controls Type I and Type II Errors

The null hypothesis plays a crucial role in controlling Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis is incorrectly rejected (a false positive), while a Type II error happens when the null hypothesis is incorrectly accepted (a false negative). By defining the null hypothesis, researchers can set significance levels (e.g., alpha level) to manage the risk of these errors.

When is the Null Hypothesis Rejected?

Rejecting the null hypothesis is a critical step in the process of hypothesis testing. The decision to reject the null hypothesis is based on statistical evidence derived from the data collected in a study. Below are the key factors that determine when the null hypothesis is rejected:

The p-value is a measure of the probability that the observed data (or something more extreme) would occur if the null hypothesis were true. The null hypothesis is rejected if the p-value is less than or equal to the predetermined significance level (?).

• Significance Level (?): This is the threshold set by the researcher, commonly 0.05 (5%). If the p-value ? 0.05, the null hypothesis is rejected.
• If a p-value of 0.03 is obtained and the significance level is 0.05, the null hypothesis is rejected.

2. Test Statistic

The test statistic is a standardized value calculated from sample data during a hypothesis test. It measures the degree to which the sample data differ from the null hypothesis. The decision to reject the null hypothesis depends on whether the test statistic falls within the critical region.

• Critical Region: This is determined by the significance level and the distribution of the test statistic (e.g., Z-distribution, t-distribution).
• In a two-tailed test with ? = 0.05, the critical region for a Z-test might be Z < -1.96 or Z > 1.96. If the test statistic is 2.10, the null hypothesis is rejected.

3. Confidence Intervals

Confidence intervals provide a range of values that are likely to contain the population parameter. If the confidence interval does not include the value specified by the null hypothesis, the null hypothesis is rejected.

• If a 95% confidence interval for the mean difference between two groups is (2.5, 5.0) and the null hypothesis states that the mean difference is 0, the null hypothesis is rejected.

4. Effect Size

Effect size measures the magnitude of the difference between groups or the strength of a relationship between variables. While not a direct criterion for rejecting the null hypothesis, a substantial effect size can support the decision to reject the null hypothesis when combined with a significant p-value.

Null Hypothesis vs. Alternative Hypothesis

How to Write a Null Hypothesis

Writing a null hypothesis is a crucial step in designing a scientific study or experiment. The null hypothesis (H0) serves as a starting point for statistical testing and represents a statement of no effect or no difference. Here’s a step-by-step guide on how to write a null hypothesis:

1. Identify the Research Question

Start by clearly defining the research question you want to investigate. Understand what you are testing and what you expect to find.

• Example Research Question: Does a new medication reduce blood pressure more effectively than an existing medication?

2. Determine the Variables

Identify the independent and dependent variables in your study.

• Independent Variable: The variable that is manipulated or categorized (e.g., type of medication).
• Dependent Variable: The variable that is measured or observed (e.g., blood pressure).

3. State the Null Hypothesis Clearly

The null hypothesis should assert that there is no effect, no difference, or no relationship between the variables. It is usually written as a statement of equality or no change.

• Format: “There is no [effect/difference/relationship] in [dependent variable] between [independent variable groups].”
• Example: “There is no difference in blood pressure reduction between the new medication and the existing medication.”

4. Use Proper Symbols and Notation

In formal scientific writing, use symbols and proper notation to represent the null hypothesis.

• Here, ?1 represents the mean blood pressure reduction for the new medication, and ?2 represents the mean blood pressure reduction for the existing medication.

Why is the null hypothesis important?

The null hypothesis is crucial as it provides a baseline for comparison and allows researchers to test the significance of their findings.

How do you state a null hypothesis?

A null hypothesis is stated as no effect or no difference, typically in the form “There is no [effect/difference] between [groups/variables].”

What is the alternative hypothesis?

The alternative hypothesis (H1) suggests that there is an effect or difference between variables, opposing the null hypothesis.

What does it mean to reject the null hypothesis?

Rejecting the null hypothesis means the data provides sufficient evidence to support the alternative hypothesis, indicating a significant effect or difference.

What is a p-value?

A p-value measures the probability that the observed data would occur if the null hypothesis were true. Low p-values indicate strong evidence against the null hypothesis.

What is a Type I error?

A Type I error occurs when the null hypothesis is incorrectly rejected, meaning a false positive result is concluded.

What is a Type II error?

A Type II error happens when the null hypothesis is incorrectly accepted, meaning a false negative result is concluded.

How do you choose a significance level (?)?

The significance level, often set at 0.05, is chosen based on the acceptable risk of making a Type I error in the context of the study.

Can the null hypothesis be proven true?

No, the null hypothesis can only be rejected or not rejected. Failing to reject it does not prove it true, only that there is not enough evidence against it.

What is the role of sample size in hypothesis testing?

Larger sample sizes increase the test’s power, reducing the risk of Type II errors and making it easier to detect a true effect.

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