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Subject: Re: Old bug in corrcoef not yet fixed
Date: Thu, 8 Jan 2009 02:35:03 +0000 (UTC)
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"Pasco Alquim" <pasquimm@yahoo.com> wrote in message <gk3k0q$hko$1@fred.mathworks.com>...
> Help info of corrcoef says that
> 
> % 'alpha' A number between 0 and 1 to specify a confidence
> % level of 100*(1-ALPHA)%. Default is 0.05 for 95%
> % confidence intervals.
> 
> However, the 'alpha' value is simply ignored (as far back as in R13)
> e.g
> Sorry for the repetition but I forgot one very important thin in the subject - the BUG word
> 
> xy = rand(10,2);
> [r,p]=corrcoef(xy)
> 
> r =
>     1.0000 0.3724
>     0.3724 1.0000
> p =
> 
>     1.0000 0.2892
>     0.2892 1.0000
> 
> 
> [r,p]=corrcoef(xy,'alpha',0.5);
> r =
>     1.0000 0.3724
>     0.3724 1.0000
> p =
>     1.0000 0.2892
>     0.2892 1.0000

  As I understand it, the confidence level set with the 'alpha' parameter is used in computing the confidence interval bounds, 'rlo' and 'rup', returned in the third and fourth output values of 'corrcoef':

 [r,p,rlo,rup] = corrcoef(...)

It has nothing to do with the 'r' and 'p' values returned.  In particular the 'p' values, which are based on a statistical normality assumption about the data, do not involve a confidence level setting.  To quote Mathworks' documentation, "Each p-value is the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero."  You don't need a confidence level to make such a probability assessment, just a reference to an assumed probability distribution.

  To show any differences between the default 'alpha' value .05 and the .5 value you entered, you would have to display these confidence interval bounds.  Do you detect any effect there?

Roger Stafford