Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. Answer from stat_daddy on reddit.com
National University
resources.nu.edu › statsresources › hypothesis
Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
October 27, 2025 - They work as a complementary pair, each stating that the other is wrong. Null Hypothesis (H0) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.” This hypothesis states that there is no difference between groups or no relationship between variables.
Scribbr
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null and Alternative Hypotheses | Definitions & Examples
January 24, 2025 - On the other hand, if you fail to reject the null hypothesis, then you can say that the alternative hypothesis is not supported. Never say that you’ve proven or disproven a hypothesis. 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 >).
Null hypothesis and Alternative Hypothesis
Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. More on reddit.com
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January 5, 2021Null vs Alternative hypothesis in practice - Cross Validated
The thread at stats.stackexcha... and attempt to characterize them. Please check it out. $\endgroup$ ... $\begingroup$ It’s so common to test a null hypothesis of no effect against an alternative of some effect that it’s kind of a slang to leave that implicit. (Whether or not this is good for the field or science in general is a different ... More on stats.stackexchange.com
Question about choosing null vs alternative hypotheses in hypothesis testing
Mostly yes. It depends a bit on the discipline (field) and purpose, but you usually pick as H0 the thing you want to reject (demonstrate implausible). So for a drug, H0 is that it doesn’t work. Your examples are less clear cut, but they also show that it’s sometimes tricky to formulate the hypotheses and the test. Sometimes there is no “correct” formulation. Just varying levels of appropriateness. And the whole practice on null-based testing has been heavily criticized for decades (again, depends on the problem). More on reddit.com
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February 6, 2023[Q] Question about choosing null and alternative hypotheses
The null is ALWAYS the opposite of what you want to prove. It is related to modus tollens. If A then B and Not B therefore not A. More on reddit.com
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March 26, 2023What are null and alternative hypotheses?
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.
scribbr.com
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Null and Alternative Hypotheses | Definitions & Examples
What’s the difference between a research hypothesis and a statistical hypothesis?
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.
scribbr.com
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Null and Alternative Hypotheses | Definitions & Examples
What is hypothesis testing?
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.
scribbr.com
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null and Alternative Hypotheses | Definitions & Examples
Videos
Examples of null and alternative hypotheses (video)
03:49
Null and alternative hypotheses with Lindsey Leach - YouTube
06:52
Hypothesis Testing - Null and Alternative Hypotheses - YouTube
14:38
Writing the Null and Alternate Hypothesis in Statistics - YouTube
04:35
Null Hypothesis Vs Alternative Hypothesis (Easy Explanation) - YouTube
Null hypothesis vs alternative hypothesis #math #mathematics #mathtok #teacher #teachersoftiktok #maths #statistics | TikTok
365 Data Science
365datascience.com › blog › tutorials › statistics tutorials › hypothesis testing: null hypothesis and alternative hypothesis
Null Hypothesis and Alternative Hypothesis – 365 Data Science
September 19, 2025 - The null hypothesis would be: The mean data scientist salary is 113,000 dollars. While the alternative: The mean data scientist salary is not 113,000 dollars. Author's note: If you're interested in a data scientist career, check out our articles Data Scientist Career Path, 5 Business Basics for Data Scientists, Data Science Interview Questions, and 15 Data Science Consulting Companies Hiring Now.
Reddit
reddit.com › r/askstatistics › null hypothesis and alternative hypothesis
r/AskStatistics on Reddit: Null hypothesis and Alternative Hypothesis
January 5, 2021 -
Hey! Can someone explain to me in simple terms the definition of null hypothesis? If u can use an example it would be great! Also if we reject the null hypothesis does it mean that the alternative hypothesis is true?
Top answer 1 of 4
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Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics.
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The null hypothesis (Ho) signifies no change. The alternative hypothesis (Ha) signifies a change. If we reject the null, we have evidence for the alternative hypothesis. This doesn’t mean that it’s true just that within this study, we have evidence to support the alternative hypothesis. If we fail to reject the null (we don’t use the word accept) then there is not enough evidence supporting the alternative hypothesis. Example: I’m wondering if smoking impacts lung function using a spirometry test that measures forced exploratory volume per second (FEV1). Ho: There is no difference in FEV1 between smokers vs non smokers Ha: There is a difference in FEV1 between smokers and non smokers. Rejecting or failing to reject the null aka Ho will involve more steps than just analyzing the mean FEV1 between the two groups, so let’s stop here before we get into more hypothesis testing.
Statistics LibreTexts
stats.libretexts.org › campus bookshelves › los angeles city college › introductory statistics › 9: hypothesis testing with one sample
9.2: Null and Alternative Hypotheses - Statistics LibreTexts
July 29, 2023 - They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. \(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related.
Pressbooks
ecampusontario.pressbooks.pub › introstats › chapter › 8-2-null-and-alternative-hypotheses
8.2 Null and Alternative Hypotheses – Introduction to Statistics
September 1, 2022 - A hypothesis test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints and only one of these hypotheses is true.
Tallahassee State College
tsc.fl.edu › media › divisions › learning-commons › resources-by-subject › math › statistics › The-Null-and-the-Alternative-Hypotheses.pdf pdf
The Null and the Alternative Hypotheses
more than or less than 50%. The Null and Alternative Hypotheses looks like: H0: p = 0.5 (This is ... They want to test what proportion of the parts do not meet the specifications. Since they claim · that the proportion is less than 2%, the symbol for the Alternative Hypothesis will be <. As is the
Medium
medium.com › @andersongimino › differences-between-the-null-and-alternative-hypotheses-6b2e794543f6
Differences between the null and alternative hypotheses | by Anderson Gimino | Medium
July 14, 2023 - The null hypothesis assumes that the status quo hasn’t changed. The alternative hypothesis suggests a new possibility or different explanation. Let’s check out some examples to get a better idea of how to write the null and alternative hypotheses for different scenarios:
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Null Hypothesis: What Is It and How Is It Used in Investing?
May 8, 2025 - A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process. The alternative hypothesis proposes that there is a difference.
Duke University
www2.stat.duke.edu › courses › Fall11 › sta10 › STA10lecture21.pdf pdf
Hypothesis Testing – Examples and Case Studies
• If really no difference between dieting and exercise as fat · loss methods, would see such an extreme result only 3% of ... Copyright ©2005 Brooks/Cole, a division of Thomson Learning, Inc. ... Copyright ©2005 Brooks/Cole, a division of Thomson Learning, Inc. ... Step 1. Determine the null and alternative hypotheses. Null hypothesis: There is no clear winning opinion on this issue;
Lumen Learning
courses.lumenlearning.com › introstats1 › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses | Introduction to Statistics
H0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt. Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.
Pressbooks
pressbooks-dev.oer.hawaii.edu › introductorystatistics › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses – Introductory Statistics
July 19, 2013 - H0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt. Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.
Quora
quora.com › What-are-some-examples-of-null-hypothesis-and-its-corresponding-alternative-hypothesis
What are some examples of null hypothesis and its corresponding alternative hypothesis? - Quora
Answer (1 of 3): These are statistical terms and are used only for statistical analysis. In statistics there is the population and there are the samples. The population is an idealized group of every example in every place through all of time. Say we are going to compare healing times of intrame...
Outlier
articles.outlier.org › null-vs-alternative-hypothesis
Null vs. Alternative Hypothesis [Overview] | Outlier
April 28, 2023 - In medical studies, where scientists ... the alternative hypothesis represents the hypothesis that the treatment does have an effect, while the null hypothesis represents the assumption that the treatment has no effect...
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC6785820
An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors - PMC
Counterintuitively, what the researcher believes in (or is trying to prove) is called the “alternate” hypothesis, and the opposite is called the “null” hypothesis; every study has a null hypothesis and an alternate hypothesis. For superiority studies, the alternate hypothesis states ...
GeeksforGeeks
geeksforgeeks.org › mathematics › alternative-hypothesis-definition-types-and-examples
Alternative Hypothesis: Definition, Types and Examples - GeeksforGeeks
August 30, 2025 - We see that the null hypothesis assumes no relationship between the variables whereas an alternative hypothesis proposes a significant relation between variables. An alternative theory is the one tested by the researcher and if the researcher ...
Applied Mathematics
colorado.edu › amath › sites › default › files › attached-files › lesson9_hyptests.pdf pdf
9 Hypothesis Tests (Ch 9.1-9.3, 9.5-9.9)
Thus when using a significance level of .05, the null · hypothesis is rejected in roughly 4.5% of these 10,000 · tests. If we continued to generate samples and carry out the test · for each sample at significance level .05, in the long run 5% of the P-values would be in the first class interval. 39 · Distribution of p-values · A histogram of the P-values when we simulate under an alternative ·
Simply Psychology
simplypsychology.org › research methodology › research hypothesis in psychology: types, & examples
Research Hypothesis In Psychology: Types, & Examples
December 13, 2023 - It’s what researchers aim to support or demonstrate through their study. The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other).
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Your question starts out as if the statistical null and alternative hypotheses are what you are interested in, but the penultimate sentence makes me think that you might be more interested in the difference between scientific and statistical hypotheses.
Statistical hypotheses can only be those that are expressible within a statistical model. They typically concern values of parameters within the statistical model. Scientific hypotheses almost invariably concern the real world, and they often do not directly translate into the much more limited universe of the chosen statistical model. Few introductory stats books spend any real time considering what constitutes a statistical model (it can be very complicated) and the trivial examples used have scientific hypotheses so simple that the distinction between model and real-world hypotheses is blurry.
I have written an extensive account of hypothesis and significance testing that includes several sections dealing with the distinction between scientific and statistical hypotheses, as well as the dangers that might come from assuming a match between the statistical model and the real-world scientific concerns: A Reckless Guide to P-values
So, to answer your explicit questions:
• No, statisticians do not always use null and alternative hypotheses. Many statistical methods do not require them.
• It is common practice in some disciplines (and maybe some schools of statistics) to specify the null and alternative hypothesis when a hypothesis test is being used. However, you should note that a hypotheses test requires an explicit alternative for the planning stage (e.g. for sample size determination) but once the data are in hand that alternative is no longer relevant. Many times the post-data alternative can be no more than 'not the null'.
• I'm not sure of the mental heuristic thing, but it does seem possible to me that the beginner courses omit so much detail in the service of simplicity that the word 'hypothesis' loses its already vague meaning.
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You wrote
the declaration of a null and alternative hypothesis is the "first step" of any good experiment and subsequent analysis.
Well, you did put quotes around first step, but I'd say the first step in an experiment is figuring out what you want to figure out.
As to "subsequent analysis", it might even be that the subsequent analysis does not involve testing a hypothesis! Maybe you just want to estimate a parameter. Personally, I think tests are overused.
Often, you know in advance that the null is false and you just want to see what is actually going on.
Laerd Statistics
statistics.laerd.com › statistical-guides › hypothesis-testing-3.php
Hypothesis Testing - Significance levels and rejecting or accepting the null hypothesis
In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis).