R help - Jul 2010 - Chi-square distribution probability density function:

Hi to all I found
an formular of an **
***p-Value Calculator for the Chi-Square test*
*http://www.danielsoper.com/statcalc/calc11.aspx*
*with the formula*
*http://www.danielsoper.com/statkb/topic11.aspx*
*what's the gamma function of this formula in r?*
*df=5*
*ch2=25.50878*
*the following code does not give the result  <0.001 for the values above *
*p= ((0.5^(df/2))/gamma(df))*(ch2^((df/2)-1))* (2.718281828459^(-ch2/2))  
or is there any other error?

Regards Knut
***

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On Jul 21, 2010, at 6:52 AM, Knut Krueger wrote:
> Hi to all I found
> an formular of an **
> ***p-Value Calculator for the Chi-Square test*
> *http://www.danielsoper.com/statcalc/calc11.aspx*
> *with the formula*
> *http://www.danielsoper.com/statkb/topic11.aspx*
> *what's the gamma function of this formula in r?*
> *df=5*
> *ch2=25.50878*
> *the following code does not give the result  <0.001 for the values  
> above *
> *p= ((0.5^(df/2))/gamma(df))*(ch2^((df/2)-1))* (2.718281828459^(- 
> ch2/2))
> or is there any other error?
Check your implementation of that formula. You made an error in the  
gamma argument.

See also:

?Chisquare
?gamma
-- 

David Winsemius, MD
West Hartford, CT

On Jul 21, 2010, at 12:36 PM, Knut Krueger wrote:
> David Winsemius schrieb:
>>
>>
>> On Jul 21, 2010, at 6:52 AM, Knut Krueger wrote:
>>
>>> Hi to all I found
>>> an formular of an **
>>> ***p-Value Calculator for the Chi-Square test*
>>> *http://www.danielsoper.com/statcalc/calc11.aspx*
>>> *with the formula*
>>> <http://www.danielsoper.com/statkb/topic11.aspx>
>>> *what's the gamma function of this formula in r?*
>>> *df=5*
>>> *ch2=25.50878*
>>> *the following code does not give the result  <0.001 for the  
>>> values above *
>>> *p= ((0.5^(df/2))/gamma(df))*(ch2^((df/2)-1))* (2.718281828459^(- 
>>> ch2/2))
>>> or is there any other error?
>>
>> Check your implementation of that formula. You made an error in the  
>> gamma argument.
>>
> Sorry a copy and paste error but gamma(df/2) does not solve the  
> problem
> I am not able to get the implementation of the function working :-(
>
>> See also:
>>
>> ?Chisquare
>> ?gamma
>
> there is also a different result using this function from the helpf  
> files and the function
> /f_n(x) = 1 / (2^(n/2) Gamma(n/2)) x^(n/2-1) e^(-x/2)
That is (perhaps) because you are confusing a density function with a  
cumulative probability function. The expression above should give the  
same result as a (proper) R transcription of the formula on the page  
you offered above and should be what dchisq referenced on the ? 
Chisquare page returns as well.

Sure enough...
 > dchisq(25.50878, 5)
[1] 4.951e-05
 > p= ((0.5^(df/2))/gamma(df/2))*(ch2^((df/2)-1))* (2.718281828459^(- 
ch2/2))
 > p
[1] 4.951e-05

  Those formulae only differ in how they use grouping of the constant  
terms. (In R the function is gamma, not Gamma.) You should be able to  
get the P(X^2|x>25.508, df=5) from an integration of that function.
>
> Knut
>
> /
David Winsemius, MD
West Hartford, CT

David Winsemius schrieb:
>
>
> And exactly why did you think I offered
>
> ?Chisquare
I was completely on the wrong way, and tried to find a solution with the 
formula instead to substitute the formula.

So I tried to implement pchisq into the formula - and of course I got 
wrong values ...

Thank's Knut

On Jul 21, 2010, at 1:18 PM, Knut Krueger wrote:
> David Winsemius schrieb:
>>
>>
>> And exactly why did you think I offered
>>
>> ?Chisquare
> I was completely on the wrong way, and tried to find a solution with  
> the formula instead to substitute the formula.
>
> So I tried to implement pchisq into the formula - and of course I  
> got wrong values ...
 > p <- function(x) ((0.5^(5/2))/gamma(5/2))*(x^((5/2)-1))*  
(2.718281828459^(-x/2))
 > integrate(p, 25.508, Inf)
0.0001111 with absolute error < 2.7e-05

Check result>>>>

 > pchisq(25.508,5)
[1] 0.9999
 > 1-pchisq(25.508,5)
[1] 0.0001111
>
> Thank's Knut
David Winsemius, MD
West Hartford, CT