Andre For the last time, there is NO simple rational approximation to the quantiles of the t-distribution.
From R help, qt = TINV is based on Hill, G. W. (1970) Algorithm 396: Student's t-quantiles. Communications of the ACM, 13(10), 619–620. And Hill, G. W. (1981) Remark on Algorithm 396, ACM Transactions on Mathematical Software, 7, 250–1. Both of these articles can be googled and the source code obtained from the ACM. (I have done it.) The code uses a rational approximation to the inverse for which you can compute values by hand. Then you can see why we use qt(). :-) Joe Andre <geomodel...@gmail.com> 10/02/2014 07:27 AM To jlu...@ria.buffalo.edu, cc Duncan Murdoch <murdoch.dun...@gmail.com>, "r-help@r-project.org" <r-help@r-project.org>, r-help-boun...@r-project.org Subject Re: [R] Inverse Student t-value Dear All, The manual formula mean that how to calculate that value by hand for TINV(0.0000408831, 1221) and the resulted is 4.0891672 Appreciate your help in advance. Cheers! On Wed, Oct 1, 2014 at 9:15 PM, <jlu...@ria.buffalo.edu> wrote: What do you mean by a "manual" formula? Andre <geomodel...@gmail.com> 09/30/2014 11:54 PM To jlu...@ria.buffalo.edu, cc Duncan Murdoch <murdoch.dun...@gmail.com>, "r-help@r-project.org" < r-help@r-project.org>, r-help-boun...@r-project.org Subject Re: [R] Inverse Student t-value Hi JLucke, Maybe the old excel function. TINV and T.INV.2T is same function for T wo-Tailed Inverse of the student`s t-distribution but T.INV use for Left-Tailed inverse of the Student's t-distribution and can be use for Inverse of the student`s t-distribution. I know automatic or functions any software but I just need a manual formula or compute formula (TINV or T.INV.2T) step by step presented by math for calculate until resulted. Thanks in advance. Cheers! On Wed, Oct 1, 2014 at 2:39 AM, <jlu...@ria.buffalo.edu> wrote: The website has your answer. The t-distribution is a regularized incomplete beta function. The incomplete beta function is given by R's pbeta function. You regularize it with R's beta function. Then you use R's uniroot function to find the inverse. Good homework problem. Andre <geomodel...@gmail.com> Sent by: r-help-boun...@r-project.org 09/30/2014 02:45 PM To Duncan Murdoch <murdoch.dun...@gmail.com>, cc "r-help@r-project.org" <r-help@r-project.org> Subject Re: [R] Inverse Student t-value Hi Duncan, Let me explain again, I just need a manual expression for inverse student t value. You could go to web page http://www.danielsoper.com/statcalc3/calc.aspx?id=10 That's inverse student t value calculator. Do you know a manual expression use it. Cheers! On Wednesday, October 1, 2014, Duncan Murdoch <murdoch.dun...@gmail.com> wrote: > On 30/09/2014 2:26 PM, Andre wrote: > >> Hi Duncan, >> >> Actually, I am trying trace the formula for the "Critical value of Z" and >> manual formula is =(I7-1)/SQRT(I7)*SQRT((TINV(0. >> 05/I7,I7-2))^2/(I7-2+TINV(0.05/I7,I7-2))) >> >> So, I got new problem for TINV formula. I just need a manual equation for >> TINV. >> > > Sorry, can't help. I'm not sure I understand what you want, but if it's a > simple formula for quantiles of the t distribution, it doesn't exist. > > Duncan Murdoch > > >> Hope solve this problem. >> >> Cheers! >> >> >> On Wed, Oct 1, 2014 at 1:20 AM, Duncan Murdoch < murdoch.dun...@gmail.com >> <mailto:murdoch.dun...@gmail.com>> wrote: >> >> On 30/09/2014 2:11 PM, Andre wrote: >> >> Hi Duncan, >> >> No, that's correct. Actually, I have data set below; >> >> >> Then it seems Excel is worse than I would have expected. I >> confirmed R's value in two other pieces of software, >> OpenOffice and some software I wrote a long time ago based on an >> algorithm published in 1977 in Applied Statistics. (They are >> probably all using the same algorithm. I wonder what Excel is doing?) >> >> N= 1223 >> alpha= 0.05 >> >> Then >> probability= 0.05/1223=0.0000408831 >> degree of freedom= 1223-2= 1221 >> >> So, TINV(0.0000408831,1221) returns 4.0891672 >> >> >> Could you show me more detail a manual equation. I really >> appreciate it if you may give more detail. >> >> >> I already gave you the expression: abs(qt(0.0000408831/2, >> df=1221)). For more detail, I suppose you could look at the help >> page for the qt function, using help("qt"). >> >> Duncan Murdoch >> >> >> Cheers! >> >> >> On Wed, Oct 1, 2014 at 1:01 AM, Duncan Murdoch >> <murdoch.dun...@gmail.com <mailto:murdoch.dun...@gmail.com> >> <mailto:murdoch.dun...@gmail.com >> <mailto:murdoch.dun...@gmail.com >>> wrote: >> >> On 30/09/2014 1:31 PM, Andre wrote: >> >> Dear Sir/Madam, >> >> I am trying to use calculation for two-tailed inverse >> of the >> student`s >> t-distribution function presented by Excel functions like >> =TINV(probability, deg_freedom). >> >> For instance: The Excel function >> =TINV(0.0000408831,1221) = returns >> 4.0891672. >> >> Would you like to show me a manual calculation for this? >> >> Appreciate your helps in advance. >> >> >> That number looks pretty far off the true value. Have you >> got a >> typo in your example? >> >> You can compute the answer to your question as >> abs(qt(0.0000408831/2, df=1221)), but you'll get 4.117. >> >> Duncan Murdoch >> >> >> >> >> >> > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
