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

[Jeph Herrin <junk@spandrel.net>]

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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