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 - Alternative Hypothesis: Ha: Male factory workers have a higher salary than female factory workers. Null Hypothesis: H0: There is no relationship between height and shoe size.
Scribbr
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null & Alternative Hypotheses | Definitions, Templates & Examples
January 24, 2025 - 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. Example: Population on trialThink of a statistical test as being like a legal trial.
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, 2021Why can we not accept the null hypothesis if p>=0.95 but we can accept the alternative hypothesis if p<=0.05?
Um. I think you're thinking about P-values incorrectly. If P > 0.05 then you fail to reject the null hypothesis. Frequentest statistics are based on the assumptions of refutationism. This assumes that you can only prove things WRONG by providing refuting evidence. The null hypothesis is the hypothesis that there is NO effect, so your typical statistical tests seek to refute them. More on reddit.com
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March 10, 2015How would I test the null hypothesis using the "brms" package in R?
For null hypothesis testing, you need the model then h1 <- hypothesis(model, "Predictor = 0") Alternatively, you can calculate the posterior probability that each of your coefficients is above zero with mean(posterior_samples(model, "^b") > 0) In either case, you have to fit the model first with brm(formula, data) (maybe you did this?) More on reddit.com
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August 3, 2017ELI5 what is the null hypothesis and can you give me some simple examples?
More or less, the null hypothesis is a hypothesis that states there wasn't anything important discovered in observation. If it's a two-group trial and control study, the null hypothesis is generally "the trial group is no different".
If the study is testing a medication, the null hypothesis is "it doesn't do anything".
If the study is comparing gender differences in some mental task, the null hypothesis is "there isn't a difference".
More on reddit.com 13
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November 24, 2021What are some problems with the null hypothesis?
One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.
simplypsychology.org
simplypsychology.org › research methodology › what is the null hypothesis & when do you reject the null hypothesis
What Is The Null Hypothesis & When To Reject It
What is the difference between a null hypothesis and an alternative hypothesis?
The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.
It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.
It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.
simplypsychology.org
simplypsychology.org › research methodology › what is the null hypothesis & when do you reject the null hypothesis
What Is The Null Hypothesis & When To Reject It
Why can a null hypothesis not be accepted?
We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.
We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.
Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.
If the p-value is greater than the significance level, then you fail to reject the null hypothesis.
We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.
Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.
If the p-value is greater than the significance level, then you fail to reject the null hypothesis.
simplypsychology.org
simplypsychology.org › research methodology › what is the null hypothesis & when do you reject the null hypothesis
What Is The Null Hypothesis & When To Reject It
Videos
Examples of null and alternative hypotheses (video)
14:38
Writing the Null and Alternate Hypothesis in Statistics - YouTube
14:41
Hypothesis Testing and The Null Hypothesis - YouTube
04:33
What is a Null Hypothesis? (4 Minute Easy Explanation) - YouTube
01:58
Null hypothesis explained - YouTube
ThoughtCo
thoughtco.com › null-hypothesis-examples-609097
How to Formulate a Null Hypothesis (With Examples)
May 7, 2024 - It's essentially the opposite of the null hypothesis because it assumes the claim in question is true. For the first item in the table above, for example, an alternative hypothesis might be "Age does have an effect on mathematical ability."
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Null Hypothesis: What Is It and How Is It Used in Investing?
May 8, 2025 - We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis. ... Example A: Students in the school don’t score an average of seven out of 10 in exams.
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 - Important: Another crucial consideration is that, generally, the researcher is trying to reject the null hypothesis. Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.
Pressbooks
ecampusontario.pressbooks.pub › introstats › chapter › 8-2-null-and-alternative-hypotheses
8.2 Null and Alternative Hypotheses – Introduction to Statistics
September 1, 2022 - The null hypothesis is a claim that a population parameter equals some value. For example, [latex]H_0: \mu=5[/latex].
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.
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.
Lumen Learning
courses.lumenlearning.com › introstats1 › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses | Introduction to Statistics
We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H0: p __ 0.40 Ha: p __ 0.40 ... In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.
Simply Psychology
simplypsychology.org › research methodology › what is the null hypothesis & when do you reject the null hypothesis
What Is The Null Hypothesis & When To Reject It
July 31, 2023 - If the data collected from the random sample is not statistically significance, then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.
GeeksforGeeks
geeksforgeeks.org › mathematics › null-hypothesis
Null Hypothesis | Meaning, Symbol, Formula, Test & Alternate Hypothesis - GeeksforGeeks
August 6, 2025 - Conversely, the alternative hypothesis ... occur or by random chance. ... Example 1: A researcher claims that the average time students spend on homework is 2 hours per night....
BYJUS
byjus.com › maths › null-hypothesis
Null Hypothesis Definition
April 25, 2022 - For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis.
Scribd
scribd.com › document › 494845048 › Null-Hypothesis-Examples-docx
Null Hypothesis Examples | PDF | Null Hypothesis | Hypothesis
It states that a treatment or independent variable has no effect on the dependent variable. Examples of null hypotheses include "Age has no effect on mathematical ability" and "Taking aspirin daily does not affect heart attack risk."
YouTube
youtube.com › watch
What's a null hypothesis? // How to write a null hypothesis - YouTube
One way to say this is: A null hypothesis is a statement that says how the independent variable would have no effect on the dependent variable. Watch the vid...
Published February 11, 2025
Optimizely
optimizely.com › optimization-glossary › null-hypothesis
What is a null hypothesis? - Optimizely
June 10, 2025 - Here the null hypothesis assumes both colors have identical conversion rates. While educators could test "there is no difference in average test scores between students using the new teaching method versus the traditional method." These examples highlight why the null hypothesis framework is essential for data-driven decision-making.
Laerd Statistics
statistics.laerd.com › statistical-guides › hypothesis-testing-3.php
Hypothesis Testing - Significance levels and rejecting or accepting the null hypothesis
The null hypothesis is essentially ... it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference)....
Statistics How To
statisticshowto.com › home › probability and statistics topics index › hypothesis testing › support or reject the null hypothesis in easy steps
Support or Reject the Null Hypothesis in Easy Steps - Statistics How To
October 6, 2024 - In many statistical tests, the main goal is to either support or reject the null hypothesis. This means that we’re either going to keep the original hypothesis in place, or we’re not. For example, if your null hypothesis is that grass grows more than one inch per day, but an experiment shows it grows less than one inch per day, then you can throw out (reject) the null hypothesis.
ABPI Schools
abpischools.org.uk › topics › statistics › the-null-hypothesis-and-the-p-value
The null hypothesis and the p-value
For example, if you were investigating the effect that short bursts of exercise have on heart rate, your null hypothesis would state ‘Short bursts of exercise will have no effect on heart rate’.
Statology
statology.org › home › how to write a null hypothesis (5 examples)
How to Write a Null Hypothesis (5 Examples)
March 10, 2021 - Here is how to write the null and alternative hypotheses for this scenario: H0: p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%) HA: μ < 0.30 (the true proportion of citizens who support the law is less than 30%) Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance
Pressbooks
pressbooks-dev.oer.hawaii.edu › introductorystatistics › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses – Introductory Statistics
July 19, 2013 - Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0. 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.