# [R] Inverse Student t-value

JLucke at ria.buffalo.edu JLucke at ria.buffalo.edu
Tue Sep 30 21:39:42 CEST 2014

```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 <geomodelers at gmail.com>
Sent by: r-help-bounces at r-project.org
09/30/2014 02:45 PM

To
Duncan Murdoch <murdoch.duncan at gmail.com>,
cc
"r-help at r-project.org" <r-help at 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.duncan at 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.duncan at gmail.com
>> <mailto:murdoch.duncan at 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.duncan at gmail.com <mailto:murdoch.duncan at gmail.com>
>>         <mailto:murdoch.duncan at gmail.com
>>         <mailto:murdoch.duncan at gmail.com>>> wrote:
>>
>>             On 30/09/2014 1:31 PM, Andre wrote:
>>
>>
>>                 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?
>>
>>
>>
>>             That number looks pretty far off the true value. Have you
>>         got a
>>
>>             abs(qt(0.0000408831/2, df=1221)), but you'll get 4.117.
>>
>>             Duncan Murdoch
>>
>>
>>
>>
>>
>>
>

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