Talk:Student's t-distribution

message: The mgf diverges, a note has been made in the summary table. WT
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This page contains special entities (characters) that cannot be displayed on many browsers. See Maxwell's equations for a way to fix this. David 21:17 Oct 15, 2002 (UTC)
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As of the beginning of 2003, there is a much better way to fix that problem, and this page now (in displayed math, as opposed to symbols embedded in lines of text) takes advantage of that advance. Michael Hardy 01:14 Feb 9, 2003 (UTC)
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There is a possible error in the PDF, compared to for example:
http://www.wolframalpha.com/input/?i=t+distribution
or my statistics text book
---  —Preceding unsigned comment added by 77.75.167.74 (talk) 13:36, 23 January 2010 (UTC)
thread_title:  Miscellany 

message: ijil l on our sample variance S2? AxelBoldt 07:58 Feb 9, 2003 (UTC)
:I agree with AxelBoldt - the n subscript is confusing. I prefer n-1 or no subscript. The n subscript is usually used when you want to highlight the fact you divided by n instead of n-1 when calculating the sample variance. It's especially confusing if you are trying to cross refrence the Wikipedia article on variance - extract from that article follows:
::s_n^2 = \frac 1n \sum_{i=1}^n \left(y_i - \overline{y} \right)^ 2 = \left(\frac{1}{n} \sum_{i=1}^{n}y_i^2\right) - \overline{y}^2,
:and
::s^2 = \frac{1}{n-1} \sum_{i=1}^n\left(y_i - \overline{y} \right)^ 2 = \frac{1}{n-1}\sum_{i=1}^n y_i^2 - \frac{n}{n-1} \overline{y}^2,
:Both are referred to as sample variance. Most advanced electronic calculators can calculate both s_n^2 and s^2at the press of a button, in which case that button is usually labeled \sigma^2 or \sigma_n^2 for s_n^2 and \sigma_{n-1}^2 for s^2. 
--Jconnolly 02:20, 27 February 2007 (UTC)
replies: text: I just did a few minor edits to fr:Loi de Student.  My feeble grasp of French is such that I would not attempt more than very minor edits.  Please note that in TeX you don't need to write ">=".  I was identified in the edit history only by the IP number 128.101.152.68. Michael Hardy 19:48, 19 October 2005 (UTC)

text: Those denote the digamma function and Beta function, respectively. --MarkSweep✍ 23:49, 23 October 2005 (UTC)
thread_title:  Should we put an index ''n'' 

message: Mark, I have to disagree with you reverting my change in the table. First, we simply can't put a formula in an article that uses non-defined items. So that links to the definition of psi and B have to appear some place or the other. I'll thus revert the change.
If you really think that these can't be in the table, then I engage to move them to some other part of the article rather than deleting them outright. If you wish to do this I draw you attention on two points: putting that in the article's body will make the expression less straightforward for a reader, and will force you to add a "see text for definitons of psi and B" note in the table, which will hardly take less room than the links themselves. Second, if this table is intended as a summary, then it should be self-sufficient to the greatest extent possible, which for me speaks in favor of putting links to the two functions inside the table... ThorinMuglindir 08:22, 28 October 2005 (UTC)
thread_title: Definition of <math>\psi</math> and <math>B</math>

message: OK, the table was not as grossly wrong as I thought, but it was badly explained.  I will replace it with a further edited version. Michael Hardy 00:46, 8 November 2005 (UTC)
replies: text: 10\pm1.37218 \frac{\sqrt{2}}{\sqrt{11}}=[9.41490,10.58510]
But in case of a double sided confidence interval it should change from 90% to 80% if one still uses the value r for the 90% one sided confidence interval. Please revise this.
137.132.3.12 14:14, 3 May 2006 (UTC)
thread_title: Table

message: Hi, 
The cdb function stated in the summary table uses the Function F_1 that I couldn't find a definition for anywhere in the article. Thanks for any explanation - Maybe someone knows what the cdb should look like.
Thanks, --ISee 13:13, 2 February 2006 (UTC)
replies: text: I added the link to the hypergeometric function.Pdbailey 20:32, 20 April 2006 (UTC)
thread_title:  Missing definition of F_1 in table 

message: I'm not entirely sure, but isn't the expected mean only defined for degrees of freedom > 1? Student's w/one DoF is supposed to be equivalent to standard Cauchy, which definitely has undefined mean.
I would update the page (it's only a minor edit) if I were more sure about my math. Pcastine 18:06, 30 March 2006 (UTC)
thread_title:  Expected Mean 

message: The edits by user:129.137.87.25 that I just reverted don't make sense.
* The central limit theorem is not in fact involved in the way it said, because it was given that the random variables involved were already normally distributed, and moreover, if one did use the central limit theorem, one would have to speak of convergence to the normal distribution, rather than of being exactly normally distributed.
* One should not use the same symbol, the lower-case t, to refer both to the random variable and to the argument to the density function.
Michael Hardy 01:40, 3 April 2006 (UTC)
thread_title: reasons for my recent reversion

message: It would be very useful to explain the alternate form of the t-table such as the one found here. If my memory serves me correctly it is based on the population standard deviation rather than the stadard deviation. I think it is okay to not address the tables that use the residual (alpha) as that can be easily figured out. But the table presented here and these other tables are not obvious.--Nick Y. 23:25, 11 June 2006 (UTC)
replies: text: Your memory serves you very badly in this case.  The table you cite is 2-sided, as opposed to the 1-sided table given here.  The population-versus-sample issue has nothing at all to do with it.  The explanation is essentially here in this article, where it talks about 1-sided versus 2-sided, but the explanation is missing from the page you cite. Michael Hardy 23:41, 11 June 2006 (UTC)
thread_title: Alternate forms of the t-table

message: user:193.11.239.45 put the following comment into the article; I've deleted it from there and pasted it here:
::Comment: We are novices but strongly belive that the value of v is wrong, it should be 0,879 which corresponds to v=10 and 80% in the table above. /Emil and Christian
I don't understand which "v" is being referred to. Michael Hardy 18:36, 20 September 2006 (UTC)
thread_title: comment moved from article

message: On 24 September 2007, user 141.212.137.29 performed the following change (under the header 'Confidence intervals derived from Student's t-distribution':	
:\overline{X}_n\pm A\frac{S_n}{\sqrt{n}}
is a 90-percent confidence interval for μ
He changed it to:
:\overline{X}_n\pm A\frac{S_n}{\sqrt{n}}
is a 95-percent confidence interval for μ.
I think that the old version was correct, however, I'm not sure. Can anyone respond on this? Basten 09:35, 11 October 2007 (UTC)
thread_title:  Confidence interval: 80% or 90% 

message: Since this page refers to the famous work of Abramowitz and Stegun, I went ahead and replaced the citation of A&S in this article's reference list with a template invocation. The template was originally created by User:William Ackerman and explained at  because Abramowitz and Stegun are cited so often in the physics pages. A sample invocation is . This expands into a cite of chapter 26, where the number 26 is clickable so that it opens up page 985 of the online version of A&S.  In this case I had to replace the original '26.7' with '26' because the template won't take decimal points in the chapter field. If this bothers you, revert the change. Up till now the template has always used without subst. EdJohnston 16:20, 17 November 2006 (UTC)
replies: text: Thanks for the references!  I didn't know there was an online copy of Abramowitz!  That will sure come in handy for lots of things, not just editing this page!  And a link to the original work by Gosset -- that's great!  I still see some problems with this article;  I hope you and Chris53516 will stick around and help work them out.  I'll probably make some more comments and/or changes soon.  --Coppertwig 03:23, 18 November 2006 (UTC)
thread_title:  Used Template:Abramowitz_Stegun_ref to make the A&S reference clickable 

message: The last item in our external links section is a paper by William T. Shaw which concerns drawing random samples from what he calls the univariate 'T' distribution, when working in a multivariate setting. This paper seems rather esoteric for the current article, and the non-standard usage of capital 'T' could be confusing.  The Shaw paper is not explicitly mentioned in the text of the article and no reference to its subject matter is made. If no-one objects I'll remove this paper from the reference list. EdJohnston 06:02, 18 November 2006 (UTC)
thread_title:  Remove external link to Shaw's paper about the capital-T statistic? 

message: (I thought I had already made this comment but don't see it;  I must have forgotten to click "save changes".) Re the (large) table in the section "Table of selected values":  I would like to have clear explanations in the article of the definitions of the three types of quantities in the table:  the integers along the left, the percentages along the top, and the numbers in the main body of the table.  Note that one of the problems I see is that it's not clear whether the \nu in the corner refers to the numbers along the left or to the percentages along the top.  I suggest something like the following.  Please critique.  I would put this just below the table:
The number at the beginning of each row in the table above is \nu which has been defined above as n-1.  The percentage along the top is 100\%(1 - \alpha).  The numbers in the main body of the table are t_{\alpha,\nu}.  If a quantity T is distributed as a Student's t distribution with \nu degrees of freedom, then there is a probability 1 - \alpha that T will be less than t_{\alpha,\nu}. 
--Coppertwig 23:52, 18 November 2006 (UTC)
replies: text: That seems less clear to me than the present explanation. Perhaps it will help to specify which entry is intended? Septentrionalis 00:25, 19 November 2006 (UTC)
replies: text: Sorry;  I don't understand what you mean by  "which entry is intended" and I don't know what part of the article you're referring to by "the present explanation".  Maybe you mean the example shown immediately above the table?  An example is fine, but I would like to see also a concise definition that applies to all elements of the table and that someone can refer to, in order to get the meaning of the table, without having to work through an example again. An example is not a substitute for a definition. --Coppertwig 03:58, 19 November 2006 (UTC)
thread_title:  Clear definitions of the quantities in the table 

message: I think the intro might need to be reworded slightly, since the t-statistic was actually first defined by R.A.Fisher in a paper of 1924.  The quantity whose distribution was discussed by Student was 'z', where t = z sqrt(n-1) is the relation between the old and new definitions. This 'z' was not the one we use nowadays with the normal distribution. The external link to 'Earliest known uses...' makes this evident. When time permits I'd like to make a try at rewording the opening paragraph, and will offer it here on the Talk page for discussion. Also I think it's NOT desirable to capitalize 't', which happens further down on the page. Regular statistics books don't do that. Moreover I think Student DID NOT wrote the formula that is attributed to him in the article where t is related to the gamma function. He was not a mathematician, but Fisher was.
Here is the actual quote from the 'Earliest known uses of some of the words of mathematics' web site which makes clear that Student did not call it 't':
:In his 1908 paper, "The Probable Error of a Mean", Biometrika, 6, 1-25 Gosset introduced the statistic, z, for testing hypotheses on the mean of the normal distribution. Gosset used the divisor n, not the modern (n - 1), when he estimated  and his z is proportional to the modern t with t = z sqrt (n - 1). Fisher introduced the t form because it fitted in with his theory of degrees of freedom (q.v.). Fisher used the t symbol and described Student's distribution (and others based on the normal distribution) and the role of degrees of freedom in "On a Distribution Yielding the Error Functions of Several well Known Statistics", Proceedings of the International Congress of Mathematics, Toronto, 2, 805-813. Although the paper was presented in 1924, it was not published until 1928 (Tankard, page 103; David, 1995). According to the OED2, the letter t was chosen arbitrarily. A new symbol suited Fisher for he was already using z for a statistic of his own (see entry for F). -- EdJohnston 21:24, 20 November 2006 (UTC)
replies: text: If you've got the references for it, change the article and cite your sources. – Chris53516 (Talk) 21:31, 20 November 2006 (UTC)

text: Perhaps not an earth-shaking issue, but the first version of this article, as created in 2002, got the terminology and the attribution correct. Somewhere along the way Student morphed into Fisher. Another issue with the article is that the term 'statistic' never gets defined, so the presentation seems incomplete. For modern readers it is most natural to describe Student's t-distribution as the distribution of the t-statistic, even though Student did not use that terminology. (Fisher introduced the term 'statistic' in 1922). I think that only minor rewording would be enough to make this clear. EdJohnston 06:34, 21 November 2006 (UTC)
thread_title:  Student did not actually present the t-statistic in 1908 

message: The t-table is incorrect, every value should be moved horizontally to the left one box. —The preceding unsigned comment was added by 134.10.2.125 (talk) 
Yep, I agree. It's incorrect.
72.142.195.237 00:55, 17 July 2007 (UTC)
thread_title: t-table

message: I have just fixed a t-pdf function in the info-box, that was different from the t-pdf function in the text. They were both correct in essence, but the difference is confusing.
This is the formula in the text:
:f(t) = \frac{\Gamma((\nu+1)/2)}{\sqrt{\nu\pi\,}\,\Gamma(\nu/2)} (1+t^2/\nu)^{-(\nu+1)/2}
This is the one I fixed:
:f(t) = \frac{\Gamma((\nu+1)/2)}{\sqrt{\nu\pi\,}\,\Gamma(\nu/2)\,(1+t^2/\nu)^{(\nu+1)/2}}
Note the (-) sign in the exponent of the first function.
Dyaka 05:46, 14 March 2007 (UTC)
replies: text: The pdf function in the text was not different from the one in the info-box; only the notation was different (just barely).  There was certainly nothing "incorrect" in either (unless both were incorrect, in which case they still are---I'll look closely later). Michael Hardy 18:34, 14 March 2007 (UTC)
replies: text: Yes, bad title, but I changed one of the formulas to avoid confusion. Dyaka 04:15, 22 March 2007 (UTC)
thread_title:  Incorrect pdf Formula 

message: can anyone add the definition of t?
Jfermiller 17:25, 13 May 2007 (UTC)
thread_title:  what does "t" stand for? 

message: when v>2, the variance is defined which is v/(v-2), how to standardize it to one? Is this its pdf: :f(t) = \frac{\Gamma((\nu+1)/2)}{\sqrt{(\nu-2)\pi\,}\,\Gamma(\nu/2)} (1+t^2/(\nu-2))^{-(\nu+1)/2} I hope someone can verify this and put it in the article. Jackzhp 15:05, 13 July 2007 (UTC)
replies: text: Change scale on t. I trust this is covered under Normalization. Septentrionalis PMAnderson 15:37, 13 July 2007 (UTC)
replies: text:  Normalization is a disambiguation page with lots of entries: normalization in metallurgy, normalization in sociology, text normalization, maybe even normalization of diplomatic relations.  Try normalizing constant. Michael Hardy 01:40, 17 July 2007 (UTC)
thread_title: standardization

message: I spent hours to figure out why the p-value equation has a 2 on the denominator. And finally get to the conclusion that the p-value here is a single-sided/single-tailed p-value while the A(t|v) is a double-sided/double-tailed probability. I would argue a cumulative distribution integrated from negative infinity is much closer to the convention. Or at least use that to introduce the two-sided A(t|v). And the sentence "For the statistic t, with ν degrees of freedom, A(t | ν) is the probability that t would be less than the observed value if the two means were the same" made it even more confusing because the sentence assumed t to be positive and did not give a definition of t. I assumed t was the same as the T in the previous sections, but it actually is its absolute value.
I also argue a two-sided p-value is the "default" for many people, like in this article:  (in PDF). An absolute value "t" counting for both side used, why would you make the p-value single-sided???  —Preceding unsigned comment added by 128.227.105.227 (talk) 23:19, 27 September 2007 (UTC)
thread_title:  p-value and  A(t | ν) ambiguous 

message: I've edited the page to try to explain the relation between A(t|nu) and f(t).  As noted above, it still needs t defined.  This is actually done on the "Student t test" page, so it could do with a reference.
The whole business about using the absolute value of t for the test based on A(t|nu) is still untidy,
not helped by absence of discussion that 1-A(t|nu) is two-sided probability.  But I don't have time for more.
Also see Abramowitz and Stegun for definition of A(t|nu) and condition on relation to beta function.
JohnPhysicist. Sorry, no Wikipedia account (or I've forgotten its name)77.99.31.195 21:58, 4 November 2007 (UTC)
thread_title:  A(t|nu) discussion not very enlightening 

message: Am I mistaken or is there an error in the example given of how to use the values from the table under "Table of Selected Values"?  The text says the following:
:For example, given a sample with a sample variance 2 and sample mean of 10, taken from a sample set of 11 (10 degrees of freedom), using the formula
:
::\overline{X}_n\pm A\frac{S_n}{\sqrt{n}}.
:
:We can determine that at 90% confidence, we have a true mean lying below
:
::10+1.37218 \frac{\sqrt{2}}{\sqrt{11}}=10.58510.
But when I look at the table, the value (A) for 90% with 10 degrees of freedom should be 1.812, not 1.37218.  The 1.372 value appears to correspond to 80%, not 90%.
I'm certainly not an expert in this area, so it's possible I'm misunderstanding something.. Am I reading the table wrong, or is this example using the wrong number? -- Foogod (talk) 00:21, 22 November 2007 (UTC)
replies: text: Yes, the table is wrong, the T value quoted in the text is correct excapt for the other example. I've checked the T values using a calculator and also Mathematica, and it turnes out that the percentages are wrong: 80% should be 90%, 90% should be 95% etc. Count Iblis (talk) 17:59, 29 November 2007 (UTC)
replies: text: Aha.. Thank you, that answers another question I was rather confused about (namely, if it is a one-tailed probability table, then shouldn't the 50% numbers, by definition, all be 0?)  That table makes more sense now.. -- Foogod 01:41, 4 December 2007 (UTC)
thread_title:  Error in example after table? 

message: The listed probablities (first row of table) were wrong, I've corrected it. I suggest that we all check that it is correct and also check every single critical T value that islisted to make sure they are all correct. Count Iblis (talk) 19:00, 29 November 2007 (UTC)
replies: text: This may partly be my responsibility - many apologies. I was trying to patch up some IP edits made on 14th November. When restoring the column headings I looked at (contrary to the article statements and original version prior to the IP edit) a two-sided distribution reference. Apologies again - second math error I've made in the past few weeks, on a small number of edits so my percentage rate is quite appalling. Asperal 20:11, 29 November 2007 (UTC)
thread_title:  Corrected error in table. 

message: 
The introduction and the section "Why use the student's t-distribution?" are excellent but the rest of the article is difficult to understand. 69.140.159.215 (talk) 12:57, 12 January 2008 (UTC)
replies: text: That's not really a compelling reason to tag this article.  --C S (talk) 06:29, 14 August 2008 (UTC)
thread_title:  please explain the formulas 

message: I just want to comment here that there is a mismatch between student t values and the confidence interval values.  For sure the values under 97.5 % are the 95 % confidence interval student t's.  These table headings should be corrected.  Thanks.  —Preceding unsigned comment added by Julescarlson (talk • contribs) 05:03, 29 February 2008 (UTC)
thread_title: Table of Student t's 

message: Is k in the leading diagrams actually \nu that appears in the info box?  It would be helpful if the notation matched. --Michael C. Price talk 12:12, 21 January 2009 (UTC)
thread_title: K or nu?

message: I deleted this statement:
: 
: For \nu = 30 the t-distribution is almost the same as the normal distribution.
: 
I have a suspicion as to the origin of this statement: A rule of thumb sometimes says sample sizes of 30 or more are enough to justify using a normal approximation for the distribution of a sum or an average, based on the central limit theorem.  So extremely confused students try to apply that to this situation—an altogether different thing.  It is profoundly appalling that someone could be that confused, but it really can happen—I've seen it.
: 
Software in front of me is giving the 90th percentile of Student's distribution with 30 degrees of freedom as 1.3104, and that of the normal distribution as 1.2816. Michael Hardy (talk) 13:00, 13 March 2009 (UTC)
thread_title:  Misleading statement deleted 

message: I am curious as to why there is no mention of the more general t distribution. I understand that when doing t-tests everything is rescaled N(0,1) but shouldn't the more general distribution be mentioned here anyway, where Z~N(mu,sigma^2). MATThematical (talk) 21:08, 7 February 2010 (UTC)
replies: text: This point is partly met by the article Noncentral t-distribution, which is mentioned in the "characterization" section. Melcombe (talk) 12:20, 8 February 2010 (UTC)
replies: text: I added it a few months back; it's the "three-parameter version". Benwing (talk) 16:37, 3 November 2010 (UTC)
thread_title: More general version

message: There appears to be an error in the formula for finding P value from the T value, section: probability density.  Specifically in the "for even degrees of freedom" part. 
For \nu even,
: \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} =  \frac{(\nu -1)(\nu -3)\cdots 5 \cdot 3} {2\sqrt{\nu}(\nu -2)(\nu -4)\cdots 4 \cdot 2\,}. 
The pi mysteriously disappears in the right hand side of the formula.  Compare with the 'for odd' formula immediately below.  I didn't feel confident enough editing it myself, since the syntax for writing formulas looked complex.
Jktejik (talk) 04:04, 3 January 2011 (UTC)
replies: text: I can't see anything wrong here. The Gamma function for half-integer argument involves a factor of √π. See the formulae about half way through the Gamma function#General section. Qwfp (talk) 10:02, 3 January 2011 (UTC)
thread_title:  typo in formula? 

message: I think it depends on what "My preferences>Appearance>Math" you have set for wikipedia. In mine, I have "HTML if very simple or else PNG"
* <math>\nu/math> = \nu looks very good to me in a subtitle
* the character "ν" renders as nearly a bold "v" to me, which is why I changed it to <math>\nu/math>
* A third option is & nu ; = ν which also renders as nearly a bold "v" to me
I forgot all of this and just assumed that the original editor had made a less-than-optimum choice. We should figure out a way that is preference independent. PAR (talk) 12:17, 26 July 2011 (UTC)
replies: text: This seems partly solved, but the point was that maths in section titles does not work well in terms of the appearance in the contents list, which here just appeared at a section number followed by blank. I don't think the options selected matter for this. The present version looks OK, but it may be worth thinking of making this material into a table, or possibly just joining the lines together to take up less page space. For others, this discussion relates to the subsection headed "Special cases". Melcombe (talk) 08:56, 27 July 2011 (UTC)
thread_title:  math in subtitle 

message: In section "Integral of Student's probability density function and p-value" the last formula is wrong. 
The same error can be found in a number of papers on the Web, but this does not make the formula more true. 
I have verified it against R package, with the ppoint 7.5 and v=3 for example (the difference on the third place behind decimal point: true value is .997..., the formula yeals .994...). The correct one is that on Wolfram's page 
Please change it accodingly.
217.67.210.18 (talk) 13:27, 24 August 2011 (UTC)
replies: text: Formula now changed, with citation. Melcombe (talk) 16:44, 25 August 2011 (UTC)
thread_title:  An error in a formula relating t-student to incomplete beta 

message: For example   variance ∞ for 1 < \nu ≤ 2, otherwise undefined
Do these apply for real degrees of freedom as well as integer values?
Paul A Bristow (talk) 17:07, 31 July 2012 (UTC)
thread_title:  Please can anyone provide a source for the equations for moments when df is small? 

message: Someone created a section labeled "Definition", right after the lead section, that said this:
==== begin excerpt ====
The  textbook definition of Student's t-distribution can be understood as  follows:
: 
==== end excerpt ====
How can any sensible person not be offended?  No attempt was made to say what "t values" are, nor to say that this is intended to apply to i.i.d. samples from a normally distributed population.  One should presume the author of the book is innocent and got quoted out of context, but no one could read the quote above without that context and then somehow know what it means.  This article is what should provide that context; only those who already know what the t-distribution is would know that already. Michael Hardy (talk) 14:00, 13 November 2011 (UTC)
thread_title:  Offensive so-called "definition" 

message: How can any sensible person not be offended?  No attempt was made to say what "t values" are, nor to say that this is intended to apply to i.i.d. samples from a normally distributed population.  One should presume the author of the book is innocent and got quoted out of context, but no one could read the quote above without that context and then somehow know what it means.  This article is what should provide that context; only those who already know what the t-distribution is would know that already. Michael Hardy (talk) 14:00, 13 November 2011 (UTC)
thread_title:  end excerpt 

message: In the expression for entropy the beta term is shown as B(nu/2, 1/2). But in Katz et al Multivariate T Distributions and Their Applications, the term in the multivariate case is shown as B(p/2, nu/2) (so B(1/2, nu/2) in single variate case. Is it a mistake in the article here?  — Preceding unsigned comment added by Analyticposterior (talk • contribs) 09:57, 11 April 2013 (UTC)
replies: text: B is symmetric in its arguments. Melcombe (talk) 14:06, 11 April 2013 (UTC)
thread_title:  Question about entropy expression 

message: In the introduction, the article states now:
:"... then the t-distribution (for n-1) can be defined as the distribution of the location of the true mean, relative to the sample mean and divided by the sample standard deviation... In this way the t-distribution can be used to estimate how likely it is that the true mean lies in any given range."
Is this right? It seems like nonsense to me. Isn't it backwards? I would say it gives the distribution of the location of the sample mean, relative to the true mean, etc.
Steven J Haker (talk) 20:48, 19 October 2013 (UTC)
replies: text: (true mean - sample mean)/(sample standard deviation) is the negative of (sample mean - true mean)/(sample standard deviation), and the t distribution is symmetrical, so taken literally, the statements are equivalent.  You're right that the statement in the article could be misleading in that it suggests that the true mean varies relative to the sample mean when the random process by itself is the other way around.  On the other hand, it's effective in suggesting to a beginning reader how the t distribution might be relevant to its purpose of making inferences about the true mean, even though neither frequentist nor Bayesian inference actually works in this exact way. Hashproduct (talk) 02:45, 2 October 2014 (UTC)
thread_title: Distribution of the True Mean?

message: In the section on moments, it is claimed that the even moments of order greater than ν are infinite and only the odd moments do not exist.  This is incorrect.  Every reference in mathematical statistics I've ever used (including Billingsley, and Rao's Linear Statistical Inference) has the same condition on expectations:
E{g(X)} exists if and only if E{|g(X)|} < ∞.
The expectation in this case is not finite, and therefore does not exist.  It is not a matter of 0/0 vs 1/0: claiming it is in the article simply obfuscates the matter.
A central T random variable has moments of all order up to int(ν-1).  Higher order moments do not exist.
128.123.198.241 (talk) 23:38, 15 November 2013 (UTC)
thread_title:  Undefined expectation versus infinite expectation versus non-existent expecations 

message: The logend colors in the example CDF do not match the colors of the curve.
(It seems that the colors of the curves are the same as those in the PDF, but the legend colors are different).
The CDF graph should be reproduced with the correct colors.
07:39, 23 February 2014 (UTC)
thread_title:  Minor comment: legend of CDF graph 

message: Looking at the first 7 pages given by Google for "student distribution" (skipping Wikipedia and YouTube) I observe that 6 of them do not speak explicitly about a family (of distributions), but just of a distribution depending on parameter(s). Only one of the 7 ("mathworks") says "The Student's t distribution is a family of curves depending on a single parameter ν (the degrees of freedom)." Maybe it is better not to mention the "family" in the lead (but do mention it later). For now I see in our article "Student's t-distribution (or simply the t-distribution) is the continuous probability distributions that arise..."; quite terrible. Boris Tsirelson (talk) 15:31, 22 November 2014 (UTC)
thread_title:  Subject-verb agreement 

message: In the section on the probability density function, there are two equations.  
One shows a calculation when v is even, and the other shows a calculation when v is odd.  Each shows a numerator series and a denominator series.   At the right end of each series is a multiplication.  The multiplications need to be further explained, as they are not self-evident in the contexts of the series’.  Since those are described as implementations of the Beta function, there is a disconnect between the Beta function formulae as described on this page, and the Beta function formulae described on the Beta function page that is linked here. By that I mean, I am not seeing these two formulas on the Beta function page.
If we substitute either the fourth or fifth formulae into the first formula, then the returned value will become zero once the numerator, v-n becomes zero.  — Preceding unsigned comment added by Statguy1 (talk • contribs) 03:12, 17 February 2015 (UTC)
thread_title: Probability Density Function

message: Hello fellow Wikipedians,
I have just added archive links to  on Student's t-distribution. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive https://web.archive.org/20150430193238/http://wwwmaths.anu.edu.au/research.reports/srr/95/044/ to http://wwwmaths.anu.edu.au/research.reports/srr/95/044/
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thread_title:  External links modified 

message: WHy do the plots show the same spreading (in terms of std errror or std uncertainty = standard deviation / sqrt(n))? If n is high, the student's t function should be much more narrow than the normal distribution, since the application of student's t is to find the confidence interval of the median value rather than the actual measurements. Mange01 (talk) 11:44, 10 October 2017 (UTC)
replies: text: No. The variance of the Student distribution is \frac{\nu}{\nu-2}; for large \nu it is close to 1. Boris Tsirelson (talk) 14:07, 10 October 2017 (UTC)
replies: text: Of course but we are talking about two different variances: The variance of the data points and the variance of their mean value. Mange01 (talk) 21:48, 9 November 2017 (UTC)
replies: text: True. And the plots are made for the Student distribution "as is". Do you want to see other plots, for the appropriately scaled distribution? These would be more relevant to "Student's t-test" article. Boris Tsirelson (talk) 07:38, 10 November 2017 (UTC)
thread_title:  Plots should show lower spreading for higher n 

message: :The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 
The result of the move request was: not moved (non-admin closure)  Bada Kaji (talk • श्रीमान् गम्भीर) 12:17, 31 August 2021 (UTC)
replies: text: It's not as ubiquitous as you might think. Just scanning the titles in the citation lists for these articles, "t distribution" vs. "t-distribution" = 2:2, "t test" vs. "t-test" = 4:2, "F distribution" vs. "F-distribution" = 3:2, "z distribution" vs. "z-distribution" = 1:0. In Matrix t-distribution = 1:0. Multivariate t-distribution = 3:0. Noncentral F-distribution = 1:1. In no case is the hyphenated version more popular. In 5 of 7 cases, the unhyphenated version is more popular. Some of the cited sources hyphenate within phrases like "Student's t", "Matrix t", "Multivariate t", "Noncentral F" and "Fischer's z", as these are compound modifiers of the word that follows them in these titles"distribution" or "test" they identify the type of distribution or the type of test. In only one of the seven cases (F-distribution) is the title using a single unmodified letter as the prefix. Arguably, that one should be moved to use a compound modifier also, as it may be better described as the Snedecor F distribution. Also arguably, if we want to include a punctuation mark in the multi-word prefixed ones, it should be an en dash, as per MOS:SUFFIXDASH, as in "", although I don't think that would realy be desirable. —⁠ ⁠BarrelProof (talk) 16:06, 24 August 2021 (UTC)
replies: text: Evidence given above. —⁠ ⁠BarrelProof (talk) 16:59, 24 August 2021 (UTC)
thread_title:  Requested move 24 August 2021 

message: In the definition of the density function is f(t) used. But the y label in the plots of the density functions says "P(x)".  — Preceding unsigned comment added by Sigbert (talk • contribs) 15:44, 28 October 2023 (UTC)
thread_title:  Plot labels wrong?