alternative assumption to the null hypothesis
Wikipedia
en.wikipedia.org › wiki › Alternative_hypothesis
Alternative hypothesis - Wikipedia
October 6, 2025 - Hypotheses are formulated to compare in a statistical hypothesis test. In the domain of inferential statistics, two rival hypotheses can be compared by explanatory power and predictive power. The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data.
National University
resources.nu.edu › statsresources › hypothesis
Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
October 27, 2025 - Null Hypothesis: H0: There is no relationship between height and shoe size. Alternative Hypothesis: Ha: There is a positive relationship between height and shoe size.
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, 2021I don't understand the reasoning behind alternative hypothesis and how a "=" or "<" or ">" H1 is able to shape the experiment
The alternative determines what test statistics are in your rejection region. Equivalently, what values of the test statistic count as "at least as extreme" for the purpose of computing p-values. In some cases it might impact what the most powerful test is, or whether there even is one (but I don't think in any case you'd be likely to encounter). when the reason of the experiment is just to reject H0? I don't know that I would agree that's what experiments are for Ok, then we prove H0 is wrong. How does it support H1? I mean, the real u could be like u = 2311. You would only tend to use the simple alternative under a few possible circumstances. For example: There were only two realistic possibilities. ("If it's not this value most people in this area think it is, this other theory is the only one that makes any sense at all, because otherwise we'd have seen a, b and c already, which means that "4" would be the value under the alternative"). It doesn't happen much in the social sciences but I have seen this in the 'hard' sciences. I saw one in astronomy just recently, where there were only two competing theories that were seen as having any realistic chance of being right; a more common/ conventional one and a less popular competing theory (that would have overturned a number of other accepted ideas as well and require a lot more new research to figure out what was going on). Each corresponded to a particular, specific value for a parameter. The person I saw talking about it did discuss whether the alternative should be more general but the equality alternative was actually the one considered in the paper that was discussed. 2. There's only one alternative you would care to reject the null for. Again, not common in the social sciences. More on reddit.com
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July 10, 2024Why do we need alternative hypothesis? - Cross Validated
When we do testing we end up with two outcomes. 1) We reject null hypothesis 2) We fail to reject null hypothesis. We do not talk about accepting alternative hypotheses. If we do not talk about More on stats.stackexchange.com
Alternative Asgard Death Hypothesis
We all hate the ending of SG-1. The Asgard suicide idea was terrible for the whole franchise We do? I never hated it and usually on this sub I don't see people hating the finale. At least not for that reason. Is it something that gets a lot of hate in Stargate communities outside of Reddit? More on reddit.com
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December 10, 2015Can the alternative hypothesis be proven?
No, it can’t be proven definitively. In hypothesis testing, we can reject the null hypothesis, which gives statistical support for the alternative hypothesis, but it is not absolute proof.
allen.in
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Alternative Hypothesis: Definition, Formulas & Applications
When do you accept an alternative hypothesis?
You accept (more precisely, support) the alternative hypothesis when statistical tests show that the null hypothesis is unlikely to be true, based on a chosen significance level (like 0.05).
allen.in
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Alternative Hypothesis: Definition, Formulas & Applications
What is an alternative hypothesis in simple terms?
The alternative hypothesis is a statement that suggests there is a real effect or difference in a population. It is what researchers aim to support through data analysis.
allen.in
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Alternative Hypothesis: Definition, Formulas & Applications
Videos
Examples of null and alternative hypotheses (video)
09:50
Alternative Hypotheses: Main Ideas!!! - 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
Scribbr
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null & Alternative Hypotheses | Definitions, Templates & Examples
January 24, 2025 - A null hypothesis claims that there is no effect in the population, while an alternative hypothesis claims that there is an effect.
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?
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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.
GeeksforGeeks
geeksforgeeks.org › mathematics › alternative-hypothesis-definition-types-and-examples
Alternative Hypothesis: Definition, Types and Examples - GeeksforGeeks
August 30, 2025 - (simple hypothesis). An Alternative Hypothesis is a claim or a complement to the null hypothesis. If the null hypothesis predicts a statement to be true, the Alternative Hypothesis predicts it to be false.
Texas Gateway
texasgateway.org › resource › 91-null-and-alternative-hypotheses
9.1 Null and Alternative Hypotheses | Texas Gateway
H0—The null hypothesis: It is 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. Ha—The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC6785820
An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors - PMC
In statistical terms, this belief or assumption is known as a hypothesis. 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 ...
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.
ALLEN
allen.in › home › jee maths › alternative hypothesis
Alternative Hypothesis: Definition, Formulas & Applications
June 8, 2025 - The alternative hypothesis is a key concept in statistical hypothesis testing. It proposes that there is a significant effect or difference in a population, challenging the assumption made by the null hypothesis. Researchers aim to find evidence supporting the alternative hypothesis to validate ...
Reddit
reddit.com › r/askstatistics › i don't understand the reasoning behind alternative hypothesis and how a "=" or "<" or ">" h1 is able to shape the experiment
r/AskStatistics on Reddit: I don't understand the reasoning behind alternative hypothesis and how a "=" or "<" or ">" H1 is able to shape the experiment
July 10, 2024 -
I understand the null hypothesis and how we can prove it wrong, but at least in my textbook I do not find it clear how the alternative hypothesis work.
It says things like: for an experiment we have the H0: u = 3 and the H1: u = 4.
Ok, then we prove H0 is wrong. How does it support H1? I mean, the real u could be like u = 2311. And we would be dealing with both hypothesis being useless.
Also, why should we change our experiments when H0: u = 3 and H1: u < 3, or H1: u < 2, or H1: u > 3, when the reason of the experiment is just to reject H0?
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EDIT: (For clarification, based on some of the other comments) For introductory texts of hypothesis testing, the null and alternative hypotheses are usually complementary, covering all possibilities. For example, H0: u =3 , H1: u ≠ 3. H0: u < 3, H1: u ≥ 3. EDIT: As mentioned in the comment, it's possible to compare two simple hypotheses as the null and alternative hypotheses. However, I suspect the confusion from OP is not from this kind of example, but from, for example, the kind of diagram OP mentioned in the comments, ( Diagram , which, I imagine, is about explaining false negative and false positive errors.)
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The alternative determines what test statistics are in your rejection region. Equivalently, what values of the test statistic count as "at least as extreme" for the purpose of computing p-values. In some cases it might impact what the most powerful test is, or whether there even is one (but I don't think in any case you'd be likely to encounter). when the reason of the experiment is just to reject H0? I don't know that I would agree that's what experiments are for Ok, then we prove H0 is wrong. How does it support H1? I mean, the real u could be like u = 2311. You would only tend to use the simple alternative under a few possible circumstances. For example: There were only two realistic possibilities. ("If it's not this value most people in this area think it is, this other theory is the only one that makes any sense at all, because otherwise we'd have seen a, b and c already, which means that "4" would be the value under the alternative"). It doesn't happen much in the social sciences but I have seen this in the 'hard' sciences. I saw one in astronomy just recently, where there were only two competing theories that were seen as having any realistic chance of being right; a more common/ conventional one and a less popular competing theory (that would have overturned a number of other accepted ideas as well and require a lot more new research to figure out what was going on). Each corresponded to a particular, specific value for a parameter. The person I saw talking about it did discuss whether the alternative should be more general but the equality alternative was actually the one considered in the paper that was discussed. 2. There's only one alternative you would care to reject the null for. Again, not common in the social sciences.
Statistics By Jim
statisticsbyjim.com › home › alternative hypothesis
Alternative hypothesis - Statistics By Jim
February 25, 2017 - The alternative hypothesis is one of two hypotheses in a hypothesis test. The alternative states a population parameter does not equal a specified value.
Quora
quora.com › What-is-an-alternative-hypothesis-in-quantitative-research
What is an alternative hypothesis in quantitative research? - Quora
Answer (1 of 3): In simple words, the Alternative Hypothesis is what you want to prove. Then, H0 is the status quo, what happens without the intervention or the event you are looking for.
CliffsNotes
cliffsnotes.com › home › biology
Biol350lecture0709-10-25-hypothesis-testing2student (pdf) - CliffsNotes
October 28, 2025 - Null hypothesis H 0 : Pea plants from parents heterozygous for round seeds, should have round and wrinkled seeds in a ratio of 3:1.
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There was, historically, disagreement about whether an alternative hypothesis was necessary. Let me explain this point of disagreement by considering the opinions of Fisher and Neyman, within the context of frequentist statistics, and a Bayesian answer.
Fisher - We do not need an alternative hypothesis; we can simply test a null hypothesis using a goodness-of-fit test. The outcome is a $p$-value, providing a measure of evidence for the null hypothesis.
Neyman - We must perform a hypothesis test between a null and an alternative. The test is such that it would result in type-1 errors at a fixed, pre-specified rate, $\alpha$. The outcome is a decision - to reject or not reject the null hypothesis at the level $\alpha$.
We need an alternative from a decision theoretic perspective - we are making a choice between two courses of action - and because we should report the power of the test $$ 1 - p\left(\textrm{Accept $H_0$} \, \middle|\, H_1\right) $$ We should seek the most powerful tests possible to have the best chance of rejecting $H_0$ when the alternative is true.
To satisfy both these points, the alternative hypothesis cannot be the vague 'not $H_0$' one.
Bayesian - We must consider at least two models and update their relative plausibility with data. With only a single model, we simple have $$ p(H_0) = 1 $$ no matter what data we collect. To make calculations in this framework, the alternative hypothesis (or model as it would be known in this context) cannot be the ill-defined 'not $H_0$' one. I call it ill-defined since we cannot write the model $p(\text{data}|\text{not }H_0)$.
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I will focus on "If we do not talk about accepting alternative hypothesis, why do we need to have alternative hypothesis at all?"
Because it helps us to choose a meaningful test statistic and design our study to have high power---a high chance of rejecting the null when the alternative is true. Without an alternative, we have no concept of power.
Imagine we only have a null hypothesis and no alternative. Then there's no guidance on how to choose a test statistic that will have high power. All we can say is, "Reject the null whenever you observe a test statistic whose value is unlikely under the null." We can pick something arbitrary: we could draw Uniform(0,1) random numbers and reject the null when they are below 0.05. This happens under the null "rarely," no more than 5% of the time---yet it's also just as rare when the null is false. So this is technically a statistical test, but it's meaningless as evidence for or against anything.
Instead, usually we have some scientifically-plausible alternative hypothesis ("There is a positive difference in outcomes between the treatment and control groups in my experiment"). We'd like to defend it against potential critics who would bring up the null hypothesis as devil's advocates ("I'm not convinced yet---maybe your treatment actually hurts, or has no effect at all, and any apparent difference in the data is due only to sampling variation").
With these 2 hypotheses in mind, now we can setup up a powerful test, by choosing a test statistic whose typical values under the alternative are unlikely under the null. (A positive 2-sample t-statistic far from 0 would be unsurprising if the alternative is true, but surprising if the null is true.) Then we figure out the test statistic's sampling distribution under the null, so we can calculate p-values---and interpret them. When we observe a test statistic that's unlikely under the null, especially if the study design, sample size, etc. were chosen to have high power, this provides some evidence for the alternative.
So, why don't we talk about "accepting" the alternative hypothesis? Because even a high-powered study doesn't provide completely rigorous proof that the null is wrong. It's still a kind of evidence, but weaker than some other kinds of evidence.
Indeed
indeed.com › career guide › career development › what is an alternative hypothesis? (definition and examples)
What Is an Alternative Hypothesis? (Definition and Examples) | Indeed.com
August 16, 2024 - An alternative hypothesis is an opposing theory to the null hypothesis. For example, if the null hypothesis predicts something to be true, the alternative hypothesis predicts it to be false.
BYJUS
byjus.com › maths › alternative-hypothesis
Difference Between Null and Alternative Hypothesis
August 28, 2019 - In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption.
Wolfram MathWorld
mathworld.wolfram.com › AlternativeHypothesis.html
Alternative Hypothesis -- from Wolfram MathWorld
June 4, 2004 - The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the result of a real effect (with some amount of chance variation superposed).
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.
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.
6 Sigma
6sigma.us › articles › understanding and applying alternative hypothesis in six sigma
Understanding and Applying Alternative Hypothesis in Six Sigma - SixSigma.us
February 26, 2025 - In Six Sigma projects, this hypothesis typically proposes that a process improvement or change has created a measurable effect. The alternative hypothesis definition stands in direct opposition to the null hypothesis, which assumes no significant change has occurred.