Talk:Null hypothesis

message: Seeing as how this is based on a scientific, or at least scholarly topic, I believe this needs references. I'm (I hope appropriately) adding the "Not Verified" tag, so hopefully someone will come through  and add references so the poor, confused beginning stats students (myself included) can know this is more than the ramblings of a demented mind. Having had experience using the subject matter, even reading this straight from a textbook can make one crazy. Garnet avi 10:41, 5 September 2006 (UTC)
thread_title:  References 

message: I believe this suffers from too much negation, yes the hypothesis is negation and yes we talk about rejecting it, but somewhere it would help to have an affirmative. - just my 2 cents.72.202.213.206 (talk) 23:44, 28 April 2016 (UTC)
replies: text: I agree. This is unreadable. Behaviour of sets of data indeed! Nonsense. Can someone with scientific authority define it here please and just delete the rest of this garbage?  —Preceding unsigned comment added by 90.179.192.118 (talk) 19:02, 5 October 2009 (UTC)
thread_title:  ?? 

message: "For example, if we want to compare the test scores of two random samples of men and women, a null hypothesis would be that the mean score of the male population was the same as the mean score of the female population, and therefore there is no significant statistical difference between them:"
This is wrong, the two samples can have the the same mean and be statistically totally different (e.g. differ in variance).
84.147.219.67 15:56, 26 June 2006 (UTC)
replies: text: I made some changes:  I deleted "and therefore there is no significant statistical difference between them:", because it is redundant and arguably incorrect.  I also added a few words to the part about assuming they're drawn from the same population, to say that this means they have the same variance and shape of distribution too.  I deleted the equation with mu1 - mu0 = 0 because it was out of context IMO given the sentence that was just before it, and because it is practically the same as the previous equation mu1 = mu0.  Sorry I forgot again to put an "edit summary".  Coppertwig 00:14, 5 November 2006 (UTC)

text: Wikipedia articles should not have phrases like "we want" per MOS:SOCRATIC. ~TPW 16:30, 15 February 2023 (UTC)
thread_title:  example conclusion 

message: After a statistical test (say, determining p-values), one can only reject or not reject the Null Hypothesis. Accepting the alternative hypothesis is wrong because there is always a probability that you are incorrectly accepting or rejecting (alpha and beta; type I and type II error). --70.111.218.254 02:03, 22 November 2006 (UTC)
replies: text: Ditto to MarkSJ. The correct language around null hypothesis testing is to reject or not reject. It cannot be accepted even in principle. That is the language found in textbooks on the subject, such as this one which says on page 291: "The null hypothesis cannot be 'accepted'; at most, a researcher can state that he/she found no reason to reject it." Dan Kuck (talk) 20:04, 11 September 2020 (UTC)
thread_title:  Accept, reject, do not reject Null Hypothesis 

message: This article appears to be a little confused at the moment — I would appreciate a little discussion before I make some changes. In particular...
"if the null hypothesis is that sample A is drawn from a population whose mean is lower than the mean of the population from which sample B is drawn, the alternative hypothesis is that sample A comes from a population with a higher mean than the population from which sample B is drawn, which can be tested with a one-tailed test."
I believe this to be misleading. A null hypothesis is a statement of no effect — by definition it has no directionality. There is a very good reason for this: null hypothesis testing works by first assuming the null hypothesis to be true, and then calculating how often we would expect to see results as extreme as those observed even when the null hypothesis is true. That is, we are trying to find out how often the observed results would be obtained by chance.
It is only possible to do this when we have a well-defined null hypothesis — e.g. when it states that one mean is equal to another mean, or when a mean is equal to a defined value. It would not be possible to calculate our test statistic if our null hypothesis merely said, "Mean one is less than mean two", and indeed this would not be a null hypothesis.
I think the confusion arises in the case of a one-tailed test. Take, for example, an experiment investigating the height of men and women in a class. We might wish to test the hypothesis "that men are taller than women". In this case our hypotheses are as follows:
* Null: That men and women are of equal height.
* Experimental: That men are taller (have greater height) than women.
In this case, we have defined our experimental hypothesis in a one-tailed form. The question many people ask is, "But what if women are taller than men? Surely neither of our hypotheses addresses this?". The confusion then lies in whether or not the null hypothesis should incorporate this possibility. To the very best of my knowledge, it should not: the null hypothesis remains a statement of no effect.
The reason for this is that we are looking to see whether there is evidence to support the specific experimental hypothesis that we have postulated. If we find our results to be non-significant, this tells us that we do not have sufficient evidence to accept our specific experimental hypothesis. If it turns out that we're interested in a difference that we find in the other direction, well that suggests that we should have proposed a two-tailed hypothesis in the first place. Indeed, I would argue that it is very rare indeed that a one-tailed hypothesis is appropriate: we are almost always interested in results in the other direction from that predicted.
Does this sound sensible? If so, then I will modify the article accordingly, and will add some relevant citations!
-- Sjb90 16:34, 15 May 2007 (UTC)
replies: text: OK, I will start making some changes to this later. This has been quite a complicated issue to resolve, and has involved going back to the paper that first defined the term 'null hypothesis'. Full discussion can be found on Lindsay658's talk page. -- Sjb90 11:06, 18 May 2007 (UTC)
thread_title:  Formulation of null hypotheses 

message: I noticed the request to simplify (above), and had the idea of inserting something into the lede that would relate this idea to a proof by contradiction.  For example, "This is similar to the idea of a proof by contradiction, but instead of a definite proof, experimental data is used to show that the null hypothesis is very unlikely to be true.".  I'm not entirely sure if that wording is clear enough, or perhaps there's some imprecision; suggestions? —AySz88\^-^ 22:48, 13 March 2008 (UTC)
thread_title:  Analogy to proof by contradiction 

message: The language used in this article  is extremely unclear and vague if not outright confusing. Will someone familiar with the subject please edit it, making sure that the text and subject matter have flow? This is a very badly compiled text so far. The exact definition for the null hypothesis seems to have been forgotten initially, and vague examples are presented to illustrate an undefined term. Thanks
=== Hypothesis Testing Definition ===
I came to this page trying to understand the concept. Maybe somebody more learned than I can make the following statement more readily accessible to the layman...
"Hypothesis testing works by collecting data and measuring how probable the data are, assuming the null hypothesis is true."  —Preceding unsigned comment added by Jdownie (talk • contribs) 12:19, 14 October 2010 (UTC)
thread_title:  Rewrite this page please 

message: I came to this page trying to understand the concept. Maybe somebody more learned than I can make the following statement more readily accessible to the layman...
"Hypothesis testing works by collecting data and measuring how probable the data are, assuming the null hypothesis is true."  —Preceding unsigned comment added by Jdownie (talk • contribs) 12:19, 14 October 2010 (UTC)
thread_title:  Hypothesis Testing Definition 

message: I think that the last but one sentence is unclear and the last one is wrong. Therefore, I suggest that the end of the initial paragraph:
:It is possible for an experiment to fail to reject the null hypothesis. The null hypothesis is never accepted as suspicion always remains over its validity. Failing to reject H0 allows for alternative hypotheses to be developed and tested.
to be changed into this:
:It is possible for an experiment to fail to reject the null hypothesis. This does not prove H0 in any way, it only means that it can not be rejected. The best one can do to substantiate H0 is to consider all reasonable alternative hypotheses and reject them.
--Pot (talk) 17:26, 27 January 2009 (UTC)
replies: text: I just now rewrote the sentence in question, before seeing your similar comments here... AnonMoos (talk) 10:22, 18 February 2009 (UTC)
replies: text: I think the version above is more clear.  What do you think about putting the above one instead of the new one you wrote? --Pot (talk) 12:04, 18 February 2009 (UTC)
replies: text: The version above is not good. It almost says to try as many alternative models as possible ...and if enough alternatives are tried one can then always reject the null hypothesis, unless of course some effort is put into taking proper account of having done the multiple tests. In any case, some of these ideas should more properly be stated in the article on hypothesis testing. Melcombe (talk) 13:10, 18 February 2009 (UTC)
replies: text: There was a problem with the wording "the null hypothesis is never accepted"; this may be correct according to some definitions of technical terminology, but it would fail to convey much useful meaning to those who aren't already knowledgeable.  Your revisions are OK on this point... AnonMoos (talk) 15:27, 18 February 2009 (UTC)
thread_title:  The initial paragraph 

message: I suggest that H0 be used in place of H0. Same for H1 and similar ones in the article. This is not a variable, so probably its name should not be slanted. --Pot (talk) 16:15, 28 January 2009 (UTC)
thread_title:  ''H''<sub>0</sub> or H<sub>0</sub>? 

message: The way to make it make sense is to use examples.  Concrete examples.  Not, buried three sections deep, but should be the main focus of the intro.
You don't teach by starting with abstractions; you give concrete examples first, and let the mind generalize the abstraction after seeing multiple examples.  Human minds are great at figuring out abstractions from concrete examples.  Example: you statisticians, long ago, were shown simple statistics examples.  Then you learned the general rules later.  Now, you are so full of abstractions, it's hard to think in concrete terms anymore.  You've already done that thinking and understood the generalization - the abstraction.  I still don't understand what the null hypothesis is, cuz I haven't seen good examples yet.
Like, that example titled "Example" sucks.  It's not an example, it's more cloudy abstractions.  The first sentence is full of abstractions, each of which has multiple possible concrete meanings:
    "Given the test scores of two random samples, one of men and one of women, does one group differ from the other?"
"test": you mean the SATs?  Testing batteries?  Testing if the soup is too hot?
"two random samples": 
* I walked out into the field with my shovel, and at two places I picked at random, I dug some sod into my plastic bags, and took them back to the lab.  
* I got a random number generator, and I wrote a program to sample 100 times and save them all into a file.  Then I did that twice.
"men" and "women": are you talking about ALL men and women in the world, in general?  Just the ones in this classroom?
"does one group differ from the other?": well of course!  They're completely different people!  There isn't one person who's in both groups.
"one/other group": are you talking about group of random samples?  or group of people?  Or group of scores?
Abstractions are confusing if you can't read the mind of the author.
==== A better example of an example ====
To make something concrete, describe it in 'meat space'.  Give people names.  Describe objects you could touch with your hands or see with your eyes.  Plug in specific numbers and names of things.  Then people can relate, and understand what you're talking about.  Like this:
Natasha is a chemistry teacher, and her classroom has 20 students, 10 male and 10 female.  She gave a chemistry test to all of the students.  
try 1: She calculated the average scores of the men, and of the women.  Are the averages the same?
try 2: Most of the scores clustered around 70%.  How many of the men scored below 70%?  Is that the same as the number of women [who scored below 70%]?  How about the scores of men vs women above 70%?
try 3: There were 5 questions, therefore 6 possible scores.  Natasha made a table with 6 columns, for each possible score.  On the top row, she wrote numbers for how many men got each score.  In the second row, how many women got that score.  Do the two rows have the same numbers at the same places?
those 3 tries are me trying to understand what Null Hypothesis is all about.  Pick one that's educational and adapt it.  Then, make another example, again concrete, but a pretty different situation, where there's still a null hypothesis.  Then, the reader can make the connection, what's similar about Null Hypothesis in two different situations.
Amber breeds cats, she has 17 cats.  They all descended from a pair of Siamese cats, years ago.  She's worried that one or more might have rabies, but she's also heard that Siamese cats can't get rabies.  She brings them to the vet to be tested.  Her null hypothesis is that none of them have rabies.  [yeah i still don't know what that means].   But, if they all have rabies, that's a Worst Case hypothesis.  Or, if just one of them has rabies, that's an Abelian Hypothesis.  If half of them have rabies, that's a Cartesian Hypothesis.  [i'm really making this up.]
See what I'm talking about?  You can see and touch a cat, or a person named Amber or Natasha.  Or a table on a piece of paper.  Everybody's taken a chemistry test.  Rabies is a disease that maybe cats have, that everybody's heard of - better than saying 'some disease'.  70% is a plausible score that a student could have.  People know what a vet is, many have brought their pets there.  Stick to concrete objects in your examples.  
And, now you can step back and see how I've educated you: instead of waving my hands around, describing the general properties of an example, I nailed down specifics, I wrote you two concrete examples of examples (as best i could).  If I hadn't, you'd still be writing hazy, abstract examples.  And, I plugged in real concrete concepts in the examples of examples I wrote, to show you how it's done.  Then, after those examples of examples, I wrote a paragraph (just above) that described the abstractions that you can remember the next time you have to write an example in a really different situation: concrete (which is an abstract word), objects (way abstract), person (there's 8 billion of them, I picked out two), Everybody, People.
Now, somebody who understands null hypotheses needs to make concrete examples that actually illustrate the concepts instead of me feeling around in the dark.
OsamaBinLogin (talk) 10:02, 11 December 2021 (UTC)
replies: text: OsamaBinLogin, I'm not used to Wikipedia articles where a whole section on examples is a thing. Are you satisfied with the examples currently in the article? GBFEE (talk) 20:48, 15 January 2022 (UTC)
thread_title:  How to Write Examples 

message: To make something concrete, describe it in 'meat space'.  Give people names.  Describe objects you could touch with your hands or see with your eyes.  Plug in specific numbers and names of things.  Then people can relate, and understand what you're talking about.  Like this:
Natasha is a chemistry teacher, and her classroom has 20 students, 10 male and 10 female.  She gave a chemistry test to all of the students.  
try 1: She calculated the average scores of the men, and of the women.  Are the averages the same?
try 2: Most of the scores clustered around 70%.  How many of the men scored below 70%?  Is that the same as the number of women [who scored below 70%]?  How about the scores of men vs women above 70%?
try 3: There were 5 questions, therefore 6 possible scores.  Natasha made a table with 6 columns, for each possible score.  On the top row, she wrote numbers for how many men got each score.  In the second row, how many women got that score.  Do the two rows have the same numbers at the same places?
those 3 tries are me trying to understand what Null Hypothesis is all about.  Pick one that's educational and adapt it.  Then, make another example, again concrete, but a pretty different situation, where there's still a null hypothesis.  Then, the reader can make the connection, what's similar about Null Hypothesis in two different situations.
Amber breeds cats, she has 17 cats.  They all descended from a pair of Siamese cats, years ago.  She's worried that one or more might have rabies, but she's also heard that Siamese cats can't get rabies.  She brings them to the vet to be tested.  Her null hypothesis is that none of them have rabies.  [yeah i still don't know what that means].   But, if they all have rabies, that's a Worst Case hypothesis.  Or, if just one of them has rabies, that's an Abelian Hypothesis.  If half of them have rabies, that's a Cartesian Hypothesis.  [i'm really making this up.]
See what I'm talking about?  You can see and touch a cat, or a person named Amber or Natasha.  Or a table on a piece of paper.  Everybody's taken a chemistry test.  Rabies is a disease that maybe cats have, that everybody's heard of - better than saying 'some disease'.  70% is a plausible score that a student could have.  People know what a vet is, many have brought their pets there.  Stick to concrete objects in your examples.  
And, now you can step back and see how I've educated you: instead of waving my hands around, describing the general properties of an example, I nailed down specifics, I wrote you two concrete examples of examples (as best i could).  If I hadn't, you'd still be writing hazy, abstract examples.  And, I plugged in real concrete concepts in the examples of examples I wrote, to show you how it's done.  Then, after those examples of examples, I wrote a paragraph (just above) that described the abstractions that you can remember the next time you have to write an example in a really different situation: concrete (which is an abstract word), objects (way abstract), person (there's 8 billion of them, I picked out two), Everybody, People.
Now, somebody who understands null hypotheses needs to make concrete examples that actually illustrate the concepts instead of me feeling around in the dark.
OsamaBinLogin (talk) 10:02, 11 December 2021 (UTC)
replies: text: OsamaBinLogin, I'm not used to Wikipedia articles where a whole section on examples is a thing. Are you satisfied with the examples currently in the article? GBFEE (talk) 20:48, 15 January 2022 (UTC)
thread_title:  A better example of an example 

message: Made a bunch of changes. Hope you like them. Lfstevens (talk) 21:21, 7 June 2010 (UTC)
thread_title:  Copy-edits 

message: went from a steady 1 to 3k traffic, to 143k today, thanks to this XKCD cartoon.Mercurywoodrose (talk) 17:20, 30 April 2011 (UTC)
thread_title: Jump in readership

message: i come across the terms composite and also compound for a hypothesis that allows for more than one distribution. Is there a preference, or are both common terms? Nijdam (talk) 20:48, 15 October 2011 (UTC)
replies: text: Are you confusing composite hypotheses with compound distributions? By "more than one distribution" do you mean "more than one family of distributions" ...  a composite hypothesis includes "more than one distribution" in the sense of "more than one distribution having different parameter values within the same family of distributions". I have not seen "compound hypothesis" ... it is none of my 3 stats dictionaries.  Melcombe (talk) 12:34, 17 October 2011 (UTC)
replies: text: A coarse and simple tool that will often allow you to determine the relative usage of a term is at . Formerly it gave the numbers of each usage; now it only indicates the "victor" in the "battle" (and, for a more detailed word count you would need to go to Google itself for each of the two terms). The observation that "even some reputable statistical articles use the term "compound"" is irrelevant, and producing that fact as evidence is a flawed argument; just because some people call koalas "bears", does not change the fact that they are marsupials. Also, the general term for the incorrect usage of a word or expression is catachresis; and it certainly seems that any individual applying the term compound hypothesis is using the expression catachrestically.Lindsay658 (talk) 21:37, 17 October 2011 (UTC)
replies: text: Fine with me, I just asked. Nijdam (talk) 22:40, 18 October 2011 (UTC)
thread_title:  Composite and/or compound 

message: The article currently states:
:However, formulating the null hypothesis before collecting data rejects a true null hypothesis only a small percent of the time.
Surely, if taken literally, this violates causality: the collected data cannot be affected by when the formulation was made.  Perhaps this should be reworded: You should think about what the hell you're doing before you start taking data?  linas (talk) 21:26, 10 April 2012 (UTC)
replies: text: I have rephrased this. I guess the point being attempted was related to Testing hypotheses suggested by the data and I have now linked this in. Melcombe (talk) 09:20, 13 April 2012 (UTC)
thread_title:  Causality violation? 

message: In the "Principle" section, the following sentence is confusing to the statistical layman:
"If the data-set is very unlikely, defined as belonging to a set of data that only rarely will be observed (usually in less than either 5% of the time or 1% of the time), the experimenter rejects the null hypothesis concluding it (probably) is false."
What does this mean?  Here is my best guess, based on the prose around the sentence in question.  If my null hypothesis is true, then I expect certain observations to be rare, and appear 1% to 5% of the time.  If I get a dataset in which these rarely-expected results are common, then that rejects the null hypothisis.
Is that correct?  If so, what is the definition of "common"?  If I expect rare events 1% to 5% of the time, what percentage of rare events do I need for a data-set to be "very unlikely"?
I don't consider myself sufficiently expert to edit this page.  I do feel qualified enough to point out when the prose is confusing to those of us who are not expert statisticians.  I'd like to ask if those with the proper expertise might consider rewriting or expanding the sentence quoted above.  I think the topic is important, and worthy of prose that the lay person can understand.
Thanks!
Coachjpg (talk) 13:02, 8 May 2012 (UTC)
replies: text: No, not quite correct. It is not the observations (meaning individual observations) that need to be rare, but the overall set of observations (taken all together) that needs to be rare. In practice this concept is simplified in that the overall set of observations is reduced to the observed value of a test statistic and it is the rareness of occurence of more extreme values of the test statistic that is ued to judge rareness. Inherent in the definition of the particular test statistic used is a particular way of defining the particular type of divergence from the null hypothesis that is being looked for. The "rareness" needs to be considered as a whole for the whole collection of observations ... what proportion of new sets of observations would produce more extreme vlaues of the test statistic. Melcombe (talk) 15:45, 8 May 2012 (UTC)
replies: text: I have attempted a rephrasing of the paragraph. Is it any better? Much more detail is/should be found in statistical hypothesis testing, and the text in the present article needs to be limited so as not to duplicate too much material. Melcombe (talk) 16:15, 8 May 2012 (UTC)
thread_title:  Please clarify re. "very unlikely" 

message: I'm going to insert a section discussing the null hypothesis and parapsychology from psychologist James Alcock (whose page I'm rewriting). I think his paper clearly clarifies what the null hypothesis is which will help readers better understand this oncept.  http://www.imprint.co.uk/pdf/Alcock-editorial.pdf Sgerbic (talk) 15:19, 9 June 2012 (UTC)
thread_title:  James Alcock on the null hypothesis 

message: I'm not sure whether the term "point hypothesis" is a regular notion in statistics. At least is the description in the article not very clear. Nijdam (talk) 10:21, 12 June 2012 (UTC)
thread_title:  Point hypothesis 

message: The first sentence in this doesn't follow most other wiki arts on things, in that it is hard to see what it gets at! It should explain it in far easier terms too. Stats on wiki is pretty hard to get comapred to most subjects!  — Preceding unsigned comment added by 137.43.182.225 (talk) 13:20, 5 December 2012 (UTC)
thread_title: Stats on wikip

message: There is not enough citation in this article, and some of the citations do not come from academic sources. I am particularly concerned about the lead remark that "there is no relationship between two measured phenomena." Additionally, the lead makes it sound like the null hypothesis is central to scientific research, when in fact, it has been criticized. 
The introduction has a few remarks that appear more like opinion, that is unjustified from academic literature in statistics.
Moving further into the article there is a lack of citation. Thelema418 (talk) 07:59, 10 December 2013 (UTC)
thread_title:  Marked article for much needed editing 

message: "This is analogous to a criminal trial, in which the defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree)."
Can someone with legal expertise confirm whether 'beyond reasonable doubt' is analogous to 'to a statistically significant degree'. My layman's understanding is that any evidence which contradicts proof of guilt means a verdict of not guilty must be returned? So statistical significance is certainly applied (as in genetic fingerprinting for example) but the overall burden of proof requires more (I would hope so anyway). Btljs (talk) 11:34, 24 November 2016 (UTC)
replies: text: One of the mistakes in that is that law does never decide innocents, it will only decide if someone is guilty, or not guilty for the accusations. That is why in court you need to decide the exact accusations you are going to make, as one can't go use "He must be guilty for something, as no one is innocent" and hence as you can't be sued twice for the same crime, you need to be sure that you pick the ones that you can provide evidence. That is why "....is assumed to be innocent...." is totally false, as it is suppose to be ".....is assumed not guilty until proven guilty....". Everyone questioning that, should watch the movie "Twelve Angry Man" to understand the "reasonable doubt" scenario in a good way. You can have a very heavy evidences about something, but as you pile all up, you might come up a scenario where each individual evidence shows together a pattern that there is a reasonable doubt. Why you never want to go for the court with a huge list of claims because they can together stack up to be reasonable doubt it is all false. Providing just one claim and evidence for that can be far stronger case than making multiple claims with multiple evidences as it is more difficult to challenge one strong case than multiple ones. 91.156.175.137 (talk)  —Preceding undated comment added 08:22, 24 September 2020 (UTC)
thread_title:  Criminal trial analogy 

message: The following Wikimedia Commons file used on this page has been nominated for deletion:
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Participate in the deletion discussion at the . —Community Tech bot (talk) 12:53, 1 September 2018 (UTC)
thread_title:  A Commons file used on this page has been nominated for deletion 

message: “that” is being used as a conjunction however there is no verb in the following subordinate clause: 
that a quantity of interest being larger or equal to zero AND smaller or equal to zero. Bscip (talk) 15:05, 20 December 2020 (UTC)
thread_title:  Sentence does not make sense: 

message: Null hypothesis has way more articles linking to it than Exclusion of the null hypothesis. Also, the word "exclusion" is only used 1 time in this article. Any objections to moving? –Novem Linguae (talk) 10:55, 4 August 2021 (UTC)
thread_title:  Move to [[Null hypothesis]]? 

message: . Doug Weller talk 13:37, 23 August 2021 (UTC)
thread_title:  "How the strange idea of ‘statistical significance’ was born" - it's a critique