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Re: st: Testing equality of means with correlated samples?


From   Berk Sensoy <berksensoy@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Testing equality of means with correlated samples?
Date   Thu, 28 Apr 2005 13:32:07 -0500

Thanks to everyone for your replies.  The samples are bhat*x from a
regression y = a + bx, where the regression residuals are correlated. 
So I have two regressions

y1 = a1 + b1*x1
y2 = a2 + b2*x2

In each regression the residuals are correlated along a known
dimension, so I can use the appropriate cluster option.

The problem is I don't know the right test for mean(b1hat*x1) = mean(b2hat*x2).

Thanks!!


On 4/28/05, FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)
<alan.h.feiveson@nasa.gov> wrote:
> Berk  -
> 
> Following Joseph's question - you don't say what sort of correlation you
> have - equicorrelated within each sample?, AR? or what? If you actually knew
> the covariance matrix within each sample and assumed normality, you could
> transform to independent observations and do a t-test.
> 
> Al Feiveson
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Joseph Coveney
> Sent: Thursday, April 28, 2005 12:51 AM
> To: Statalist
> Subject: Re: st: Testing equality of means with correlated samples?
> 
> Berk Sensoy wrote:
> 
> I would like to test whether the mean of variable A is equal to that
> of variable B.  Observations are correlated, however.  The
> observations of A are all potentially correlated with each other, and
> the same is true for B.  There is no correlation between A and B.
> 
> Because of this structure, I believe the standard t-test for equality
> of means will give a p-value that is way too low, because it assumes
> the samples are distributed iid.
> 
> Anyone know how to do this (in Stata)?
> 
> ----------------------------------------------------------------------------
> 
> I'm missing something here.  With a t-test, observations of variable A are,
> say, 3, 1, 4, 2 and 5.  The concept of correlation wouldn't seem to apply to
> such an unordered series of numbers as this.  Likewise, for variable B with,
> say, 4, 6, 3, 5 and 2, as values.
> 
> Are you saying that there are several *clusters* of values for each of
> variables A and B, and the values within the clusters are more similar than
> between the clusters, as if the assignment to treatment group were by
> clusters?  If so, and if you can identify the clusters, then perhaps you can
> use Jeph Herrin's -clttest-.  (-findit cltest- or -findit clttest-)
> 
> Joseph Coveney
> 
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