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Re: st: positive interaction - negative covariance


From   andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: positive interaction - negative covariance
Date   Mon, 25 Feb 2013 00:20:58 +0100

Dear Nick, Maarten and David,

Many thanks for clarifying the point that if the terms using
interactions are not significant at conventional levels, the
interaction can't be regarded as well established.
And thank you for the references. I will read them.

To Nick:
Actually I use Stata 11 (sorry, I thought it was not relevant for my question).
I plotted the marginal effect of X on Y for Z=0 and Z=1.
The marginal effect is always positive. The confidence intervals are
above the zero-line when Z=0, while the lower CI (slightly) crosses
the zero-libe when Z=1.


Many thanks.

Andrea

2013/2/23 David Hoaglin <dchoaglin@gmail.com>:
> The problems that arise from trying to compare confidence intervals
> are more general.  They arise in situations where the estimates are
> independent.  Thus, the covariance in the sampling distribution of b1
> and b3 is not the real issue.
>
> To assess the difference between two estimates, it is usually a
> mistake to compare their confidence intervals.  The correct approach
> is to form the appropriate confidence interval for the difference and
> ask whether that confidence interval includes zero.  I often encounter
> people who think that they can determine whether two estimates (e.g.,
> the means of two independent samples) are different by checking
> whether the two confidence intervals overlap.  They are simply wrong.
> The article by Schenker and Gentleman (2001) explains.  (I said
> "usually" above to exclude intervals that are constructed specifically
> for use in assessing the significance of pairwise comparisons.)
>
> David Hoaglin
>
> Nathaniel Schenker and Jane F. Gentleman, On judging the significance
> of differences by examining the overlap between confidence intervals.
> The American Statistician 2001; 55(3):182-186.
>
> On Sat, Feb 23, 2013 at 10:50 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
>>>>>>> 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
>
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