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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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Re: determining differences between intercepts after regression***From:*Jeph Herrin <jeph.herrin@yale.edu>

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