# [R] How to increase precision to handle very low P-values

Duncan Murdoch murdoch.duncan at gmail.com
Wed Nov 23 20:06:58 CET 2011

```On 23/11/2011 11:16 AM, alonso_canada wrote:
> Hello, Rlisters
>
> I have to compute p-values that are on the tail of the distribution,
> P-values<  10^-20.
>
> However, my current implementations enable one to estimate P-values up to
> 10^-12, or so.
>
> A typical example is found below, where t is my critical value.

The p* functions (pnorm, etc.) generally have a "log" argument, so they
can return logs of probabilities.  Together with the "lower" argument,
they have a huge range.

To use them with integrate(), rescale them.  For example, to find the
integral of pnorm() from z=-32 to -30 you could do:

maxval <- pnorm(-30, log=TRUE)
scaled <- function(x) exp( pnorm(x, log=TRUE) - maxval )
scaledintegral <- integrate(scaled, lower=-32, upper=-30)
# Log of the result:
log(scaledintegral\$value) + maxval

(The answer is -457.7, so it is actually representable:  1.631957e-199.)

Duncan Murdoch

> ########### example - code adapted from Rassoc #######################
>
> rho01 = 0.5
> rho105 = 0.5
> rho005  = 0.5
> t = 8
> z = 2
>
> w0=(rho005-rho01*rho105)/(1-rho01^2)
> w1=(rho105-rho01*rho005)/(1-rho01^2)
>
>
>   fun1=function(t,z){
>   return(pnorm((t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
>   }
>   fun2=function(t,z){
>   return(pnorm(((t-w0*z)/w1-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
>   }
>   fun3=function(t,z){
>   return(pnorm((-t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
>   }
>
> asy=function(t){
> z1=2*integrate(function(z){fun1(t,z)},lower=0,upper=t*(1-w1)/w0,subdivisions=1000)\$value
> z2=2*integrate(function(z){fun2(t,z)},lower=t*(1-w1)/w0,upper=t,subdivisions=1000)\$value
> z3=-2*integrate(function(z){fun3(t,z)},lower=0,upper=t,subdivisions=500)\$value
> return(z1+z2+z3)
> }
>
> pvalue<-  1-asy(t)
> pvalue
>   ###########################################
>
> Using this script, my critical values can achieve values up to 7.5, or so.
> Above this cutoff my P-values show up as negative values. Why's that?
>
>
> Grateful for any tips.
>
> All the best,
>
> Alonso
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/How-to-increase-precision-to-handle-very-low-P-values-tp4100250p4100250.html
> Sent from the R help mailing list archive at Nabble.com.
>
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