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
Scribbr
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Null and Alternative Hypotheses | Definitions & Examples
January 24, 2025 - The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started. *Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p1 = p2. The alternative ...
National University
resources.nu.edu › statsresources › hypothesis
Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
October 27, 2025 - Alternative Hypothesis: Ha: There is a positive relationship between height and shoe size. Null Hypothesis: H0: Experience on the job has no impact on the quality of a brick mason’s work.
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
From the beginning of the most ... hypothesis is the "first step" of any good experiment and subsequent analysis. Now that I have been venturing into more complex courses and topics, I see this exercise still being performed. I have always perceived the proposal of the null v. alternative as a teachable example of how to ... More on stats.stackexchange.com
Null vs. Alternative Hypothesis
A null hypothesis represents the status quo. Ie a manufacturer claims that their baseball weighs 50grams. So our null is that the mean weight is 50grams. An alternative is a departure from that null. I think the manufacturer is lying. So the alternative is that the mean weight is not 50 grams. I'm not claiming to know what the mean weight actually is, only that it's significantly different from 50 grams.
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January 4, 2018Did you find the idea of a null hypothesis to be confusing when you were first learning statistics? If you did, then what did you find confusing about it?
Yes. If you didn't find the idea of the null hypothesis confusing, you didn't understand it.
There's an article by Gigerenzer called "Mindless Statstics" here: http://library.mpib-berlin.mpg.de/ft/gg/GG_Mindless_2004.pdf where he talks about this. The problem is that hypothesis testing, as we think of it, is a mash up of two (or three) very different ways of thinking about what p-values mean. (The three are Fisher, Neyman-Pearson, and Bayes). These people had arguments that went on for decades about these things, and now we act like those differences don't exist. The notion of a type I error doesn't make sense under Fisher's approach. Under Neyman-Pearson's approach, a p-value is greater than 0.05, or it's not. You don't report p=0.035. So you can't report exact p-values, and talk about type I and type II errors, and be logically consistent. But we try.
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July 28, 2013What 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.
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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.
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Null and Alternative Hypotheses | Definitions & Examples
Videos
Examples of null and alternative hypotheses (video)
06:52
Hypothesis Testing - Null and Alternative Hypotheses - YouTube
03:49
Null and alternative hypotheses with Lindsey Leach - YouTube
14:38
Writing the Null and Alternate Hypothesis in Statistics - YouTube
04:35
Null Hypothesis Vs Alternative Hypothesis (Easy Explanation) - YouTube
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 - For example, the Obama administration and the Bush administration, as we have data on both. Alright, let’s get out of politics and get into hypotheses. Here’s a simple topic that CAN be tested. According to Glassdoor (the popular salary information website), the mean data scientist salary in the US is 113,000 dollars. So, we want to test if their estimate is correct. There are two hypotheses that are made: the null hypothesis, denoted H0, and the alternative hypothesis, denoted H1or HA.
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.
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 - Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.
Pressbooks
ecampusontario.pressbooks.pub › introstats › chapter › 8-2-null-and-alternative-hypotheses
8.2 Null and Alternative Hypotheses – Introduction to Statistics
September 1, 2022 - On a state driver's test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. State the null and alternative hypotheses. ... In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.
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 - Your null hypothesis (H0): the program had no effect on sales revenue. Your alternative hypothesis (Ha): the program increased sales revenue.
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
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Null Hypothesis: What Is It and How Is It Used in Investing?
May 8, 2025 - Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?), the null hypothesis could be H0: X = 0.
Duke University
www2.stat.duke.edu › courses › Fall11 › sta10 › STA10lecture21.pdf pdf
Hypothesis Testing – Examples and Case Studies
Alternative hypothesis: Fewer than 0.50, or 50%, of the population · would answer yes to this question. The majority do not think Clinton ... Step 2. Collect and summarize data into a test statistic. Sample proportion is: 233/518 = 0.45. The standard deviation = (0.50) × (1 – 0.50) = 0.022. ... Copyright ©2005 Brooks/Cole, a division of Thomson Learning, Inc. ... Step 3. Determine the p-value. Recall the alternative hypothesis was one-sided.
Lumen Learning
courses.lumenlearning.com › introstats1 › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses | Introduction to Statistics
This practice is acceptable because we only make the decision to reject or not reject the null hypothesis. H0: No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 · Ha: More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30 · A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
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...
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 ... (the treatments are equal). For 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....
GeeksforGeeks
geeksforgeeks.org › mathematics › alternative-hypothesis-definition-types-and-examples
Alternative Hypothesis: Definition, Types and Examples - GeeksforGeeks
August 30, 2025 - Null Hypothesis (H0): Independent variable does not affect dependent variable. Alternative Hypothesis (Ha): Independent variable affects dependent variable. Various examples of Alternative Hypothesis includes:
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)
Null hypothesis: H0: µ = µ0 · Test statistic value: Alternative Hypothesis · Rejection Region for a Level α · Test · 24 · CI vs. Hypotheses · Rejection regions have a lot in common with confidence intervals. Source: shex.org · 25 · CI vs. Hypotheses · Example: The Brinell scale is a measure of how hard a ·
Outlier
articles.outlier.org › null-vs-alternative-hypothesis
Null vs. Alternative Hypothesis [Overview] | Outlier
April 28, 2023 - One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the ...
Simply Psychology
simplypsychology.org › research methodology › research hypothesis in psychology: types, & examples
Research Hypothesis In Psychology: Types, & Examples
December 13, 2023 - Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following: The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon. The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon.
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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
For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and ...