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From |
Jeph Herrin <jeph.herrin@yale.edu> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 18 Feb 2009 17:04:46 -0500 |

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/

**Follow-Ups**:**Re: st: Re: determining differences between intercepts after regression***From:*Jeph Herrin <junk@spandrel.net>

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