[R] p value for joint probability

[Mike Marchywka]

> Date: Tue, 1 Feb 2011 12:10:31 -0800
> From: NordlDJ at dshs.wa.gov
> To: r-help at r-project.org
> Subject: Re: [R] p value for joint probability
>
> > -----Original Message-----
> > From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> > project.org] On Behalf Of moleps
> > Sent: Tuesday, February 01, 2011 11:32 AM
> > To: Peter Ehlers
> > Cc: r-help at r-project.org
> > Subject: Re: [R] p value for joint probability
> >
> >
> > My terminology is probably way off. I´ll try again in plain english.
> >
> > I´d like to generate a scatter plot of r1 & r2 and color code each
> > pair according to the probability of observing the pair given that the
> > two samples (r1 & r2) are drawn from two independent normal
> > distributions.
> >
> > rr<-data.frame(r1=-rnorm(1000,10,5),r2=-rnorm(1000,220,5))
> >
> > with(rr,plot(r1,r2))
> >
> > Best,
> > //M
>>
>
> And the answer is the same as Peter gave below. The theoretical probability of a specific pair of numbers occurring in your example is zero. So, I will ask Peter's question differently (although his question was a good one). What is your interest in doing these plots? What are you trying to understand? Are you just trying to learn how do this "joint probability" plot for use on data where there is a non-zero probability of pairs of numbers occurring? Equiring minds would like to know. :-)

Empirically of course, the probability is not zero since it did happen :) As with the folks
surprised about floating point equality compares, there is some integration over the
quantization interval. So in fact the probabiliyt of measuring what was measured is
an integral over the floating point difference between the two closest numbers. Presumably
however you want an answer unrelated to the fp properties. 


>
> Dan
>
> Daniel J. Nordlund
> Washington State Department of Social and Health Services
> Planning, Performance, and Accountability
> Research and Data Analysis Division
> Olympia, WA 98504-5204
>