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Re: st: positive interaction - negative covariance


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: positive interaction - negative covariance
Date   Sat, 23 Feb 2013 16:50:47 +0100

>>>>> Thank you for clarifying the point. Indeed, if I compare the
>>>>> confidence interval of b1 to the confidence interval of (b1+b3), they
>>>>> are not statistically different. Is it the same? In a book I read, the
>>>>> authors make this comparison.

That is a common mistake. If you want to know whether the two curves
are equal you must look at the interaction term (b3), not whether the
confidence intervals of both curves (b1 and b1 + b3) overlap. The
latter ignores the covariance in the sampling distribution of both
parameters, and is thus wrong. See for example:

Andrew Gelman and Hal Stern (2006) "The Difference Between
`Significant' and `Not Significant' is not Itself Statistically
Significant" The American Statistician, 60(4):328--331.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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