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Re: correlation coefficient and confidence level [message #87503 is a reply to message #87501] Sun, 09 February 2014 18:35 Go to previous messageGo to previous message
David Fanning is currently offline  David Fanning
Messages: 11724
Registered: August 2001
Senior Member
sid writes:

> I tried idl routines correlate and coyote's cgscatter2d, but both doesnt give, confidence level for the correlation coefficient.
> Then I tried r_correlate, which gives significance level, but I guess significance level is different from confidence level.
> So I have no idea how to do this.

The first article that appears when I use Google to search "confidence
correlation coefficient" is this article:

http://www2.sas.com/proceedings/sugi31/170-31.pdf

Low and behold, there is code in there that calculates the confidence
level of the correlation coefficient! Lucky! But, you know, sometimes it
happens. :-)

Simply translating the SAS code to IDL (I'm pretty sure you could have
done this, if I managed it), I get this:

n = 101
data_1 = cgDemoData(1)+ RandomU(-3L, n) * 10
data_2 = cgDemoData(1)+ RandomU(-5L, n) * 10
cgScatter2D, data_1, data_2

rho = Correlate(data_1, data_2)
fisherTransform = 0.5*(alog(1+rho) - alog(1-rho))
sigmaz = 1.0 / Sqrt(n-3)
l_95 = fisherTransform - (1.96 * sigmaz)
h_95 = fisherTransform + (1.96 * sigmaz)

lo95 = (exp(2*l_95)-1)/(exp(2*l_95)+1)
hi95 = (exp(2*h_95)-1)/(exp(2*h_95)+1)
Print, 'Low 95% Confidence Level: ', lo95
Print, 'High 95% Confidence Level: ', hi95
END

For a sanity check, I used another page from my Google search to find a
confidence level calculator. I plugged my numbers in and they matched
more or less:

http://vassarstats.net/rho.html?

I spent about 45 minutes on this, if you feel like you want to make a
contribution to the work.

Cheers,

David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.idlcoyote.com/
Sepore ma de ni thue. ("Perhaps thou speakest truth.")

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