# RE: st: Testing equality of means with correlated samples?

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: Testing equality of means with correlated samples? Date Thu, 28 Apr 2005 12:18:20 -0500

```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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```