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


From   Jeph Herrin <junk@spandrel.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: determining differences between intercepts after regression
Date   Thu, 19 Feb 2009 08:59:41 -0500

Interesting. I reposted this because I had accidentally
sent this copy from an email address that isn't (and never
has been) subscribed to statalist. But it came through
anyway  - 12 hours later. Go figure.

Jeph Herrin wrote:
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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