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) – ... the topic. This is your answer to your research question. ... Null Hypothesis: H0: There is no difference in the salary of factory workers based on gender....
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, 2021Eli5: What is a null hypothesis and how do type 1 and type 2 errors work.
The null hypothesis, in statistics, is the idea that there is no significant difference between two populations. If, for example, you're testing whether your company's fancy new insect killing chemical is more effective than the competition, you might run some tests in two groups: one using a reference chemical (or nothing at all), and one using your new one. The null hypothesis is "This chemical is no more effective than what was used in the other group." The alternative hypothesis is that it is more effective. "Type I" and "Type II" errors can be thought of a lot easier by their colloquial names: "false positive" and "false negative." The false positive is where you erroneously believe your chemical is more effective (when it actually isn't), and the false negative is where you erroneously believe your chemical is not more effective (when it actually is). In statistics, these errors occur due to improperly selected cutoff values (how are we judging effectiveness) and confidences (how many tests are we doing). More on reddit.com
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July 3, 2021[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, 2023ELI5 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 23, 2021What’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 & Alternative Hypotheses | Definitions, Templates & 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.
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Null & Alternative Hypotheses | Definitions, Templates & Examples
What symbols are used to represent null hypotheses?
The null hypothesis is often abbreviated as H0. When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
scribbr.com
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Null & Alternative Hypotheses | Definitions, Templates & Examples
Videos
14:52
Null and Alternate Hypothesis - Statistical Hypothesis Testing ...
Examples of null and alternative hypotheses (video)
04:29
What's a null hypothesis? // How to write a null hypothesis - YouTube
14:38
Writing the Null and Alternate Hypothesis in Statistics - YouTube
14:41
Hypothesis Testing and The Null Hypothesis - YouTube
Hypothesis Testing EXPLAINED
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Null Hypothesis: What Is It and How Is It Used in Investing?
May 8, 2025 - Example B: The mean annual return of the mutual fund is not 8% per year. For the purposes of determining whether to reject the null hypothesis (abbreviated H0), said hypothesis is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0).
ThoughtCo
thoughtco.com › null-hypothesis-examples-609097
How to Formulate a Null Hypothesis (With Examples)
May 7, 2024 - For the first item in the table above, for example, an alternative hypothesis might be "Age does have an effect on mathematical ability." In hypothesis testing, the null hypothesis assumes no relationship between two variables, providing a baseline for statistical analysis.
Statistics By Jim
statisticsbyjim.com › home › blog › null hypothesis: definition, rejecting & examples
Null Hypothesis: Definition, Rejecting & Examples - Statistics By Jim
November 7, 2022 - 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.
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.
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 ...
Optimizely
optimizely.com › optimization-glossary › null-hypothesis
What is a null hypothesis? - Optimizely
June 10, 2025 - These examples highlight why the null hypothesis framework is essential for data-driven decision-making. In business contexts, particularly A/B testing and conversion optimization, it prevents teams from implementing changes based on random data fluctuations. By requiring statistical evidence to reject the null hypothesis, organizations make more reliable decisions about product changes, marketing strategies, and user experience improvements while preventing costly mistakes from pursuing changes that only appear beneficial due to chance.
PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC6785820
An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors - PMC
For superiority studies, the alternate ... example, in the ABLE study, we start by stating the null hypothesis—there is no difference in mortality between groups receiving fresh RBCs and standard-issue RBCs....
Corporate Finance Institute
corporatefinanceinstitute.com › home › resources › null hypothesis
Null Hypothesis - Overview, How It Works, Example
November 21, 2023 - For example, a null hypothesis statement can be “the rate of plant growth is not affected by sunlight.” It can be tested by measuring the growth of plants in the presence of sunlight and comparing this with the growth of plants in the absence ...
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)
Test statistic value: z = 48 · Test Procedures for Normal Populations with Known Variances · Null hypothesis: H0: µ1 – µ2 = Δ0 · Alternative Hypothesis Rejection Region for Level α Test · Ha: µ1 – µ2 > Δ0 z ≥zα (upper-tailed) Ha: µ1 – µ2 < Δ0 z ≤– zα (lower-tailed) Ha: µ1 – µ2 ≠ Δ0 either z ≥zα/2 or z ≤– zα/2(two- · tailed) 49 · Example 1 ·
Brookbush Institute
brookbushinstitute.com › home › glossary › null hypothesis
Null Hypothesis - Brookbush Institute
Together, these contributions laid the foundation for most of the statistical tools used in frequentist inference—t-tests, ANOVA, confidence intervals, etc.—all of which rely on assuming the null hypothesis is true to estimate sampling distributions and make valid probabilistic conclusions. ... Misuse #1: Failing to reject the null does not equal proof of the opposite. For example, a study that finds no correlation between an anterior pelvic tilt and hip pain does not mean that posture and pain are not correlated.
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].
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.
BYJUS
byjus.com › maths › null-hypothesis
Null Hypothesis Definition
April 25, 2022 - In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It ...
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-700.html
Finding and Using Health Statistics
The null (H0) and alternative (Ha) ... and the class average score on the math exam. ... In the null hypothesis, there is no difference between the observed mean (µ) and the claimed value (75)....
Penn State Statistics
online.stat.psu.edu › stat100 › Lesson10
10 Hypothesis Testing – STAT 100 | Statistical Concepts and Reasoning
The probability of heads when a penny is spun is really p = 0.5. ... Alternative Hypothesis: The probability of heads when a penny is spun is really p < 0.5. A statistical hypothesis test is designed to answer the question: “Does the Null Hypothesis provide a reasonable explanation of the data?”
Statistics LibreTexts
stats.libretexts.org › campus bookshelves › las positas college › math 40: statistics and probability › 8: hypothesis testing with one sample › 8.1: steps in hypothesis testing
8.1.1: Null and Alternative Hypotheses - Statistics LibreTexts
August 8, 2020 - This can often be considered the status quo and as a result if you cannot accept the null it requires some action. \(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\).
Statsig
statsig.com › perspectives › null-hypothesis-guide-experimentation
What is a null hypothesis? A guide for experimentation
February 25, 2025 - H₀ states there's no improvement, while H₁ suggests there's a positive effect. If your p-value is less than α (say, 0.05), you have statistical grounds to reject H₀ and conclude the new method makes a difference. ... Type I error (false positive): Rejecting a true null hypothesis.
Wikipedia
en.wikipedia.org › wiki › Null_hypothesis
Null hypothesis - Wikipedia
3 weeks ago - If the hypothesis summarizes a ... set of data. Example: If a study of last year's weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather reports from any other year....