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

 From "Martin Weiss" To Subject Re: st: Re: determining differences between intercepts after regression Date Wed, 18 Feb 2009 23:26:01 +0100

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Thank you very much, that is much clearer than browsing through those articles from the insect research magazines...
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HTH
Martin
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----- Original Message ----- From: "Jeph Herrin" <junk@spandrel.net>
```To: <statalist@hsphsun2.harvard.edu>
Sent: Wednesday, February 18, 2009 11:06 PM
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Subject: Re: st: Re: determining differences between intercepts after regression
```

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```Martin Weiss wrote:
>

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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