Re: st: Re: determining differences between intercepts after regression

["Martin Weiss" <martin.weiss1@gmx.de>]

<>

Thank you very much, that is much clearer than browsing through those 
articles from the insect research magazines...


HTH
Martin
_______________________
----- Original Message ----- 
From: "Jeph Herrin" <junk@spandrel.net>
To: <statalist@hsphsun2.harvard.edu>
Sent: Wednesday, February 18, 2009 11:06 PM
Subject: Re: st: Re: determining differences between intercepts after 
regression


> Martin Weiss wrote:
> >
> > Please explain!
>
>
> Take the simple but illustrative case where X & Y are
> independent, and have the same standard deviation SDx=SDy.
> Since they are independent,
>
>  var(X-Y)=var(X)+var(Y)
>          = 2*SD^2
> hence
>
>  sd(X-Y)= sqrt(2)*SD = ~ 1.414SD
>
> so the CI for X-Y is going to be 1.414 times
> as wide as the CI for X or Y, not twice as wide.
> As long as the difference between X and Y is somewhere
> between 1.414 and 2, the CIs will overlap but the CI of
> the difference will not include zero.
>
> To wit, suppose mean(CI) for X is 0(-1,1) and for
> Y is 1.5(0.5,2.5). They overlap, but the mean(CI)
> of X-Y is going to be 1.5(1.5-1.41,1.5+1.41),
> or 1.5(0.09,2.91). So the difference is significantly
> different from zero, even though they CIs overlap.
>
> HTH,
> Jeph
>
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