# [R] Find the cutoff correlation value for Pearson correlation test

David Carlson dcarlson at tamu.edu
Fri Nov 15 16:41:51 CET 2013

```I haven't looked at fBasics::correlationTest, but cor.test uses
the t distribution to evaluate significance:

t = sqrt(df) * r/sqrt(1 - r^2)

where df=n-2

If you solve that for r, you get

r = t/sqrt(t^2+100-2)

If you choose t as qt(.975, df) for a two-tailed test at p<.05
you can plug in t and place your limits at +/- of that value. Eg
for 100 observations:

> t <- qt(.975, 98)
> t
 1.984467
> rlim <- t/sqrt(t^2+100-2)
> rlim
 0.1965512
> rs <- replicate(1000, cor(rnorm(100), rnorm(100)))
> hist(rs)
> abline(v=c(-rlim, rlim))

-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352

-----Original Message-----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Jim Lemon
Sent: Thursday, November 14, 2013 9:44 PM
To: jpm miao
Cc: r-help
Subject: Re: [R] Find the cutoff correlation value for Pearson
correlation test

On 11/15/2013 12:53 PM, jpm miao wrote:
> Hi,
>
>     I find a few Pearson correlation test functions like
>
>     fBasics::correlationTest or stats::cor.test
>
> which give the p-value of the test result. Is there a function
that
> calculate the cutoff correlation value for a specific p-value
, e.g., p =
> 0.05?
>
> I have a plot for the cross correlations between two time
series, and I
> would like to add a horizontal line that marks the
significance of the
> correlations.

Hi Miao,
Perhaps you could use the confidence interval.

Jim

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