# Re: st: RE: correlated data

 From sjsamuels@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: RE: correlated data Date Tue, 1 Sep 2009 13:35:31 -0500

```Why didn't people respond?  Perhaps, because your question was
confused, and you gave too little information.

"how close (do they differ significantly?"

These two questions are not the same, so your purpose is not clear.
Is it to find if one or more of the alternatives is close enough to
the standard to replace it?  If so, the problem is one of
equivalence-testing, supplemented with confidence intervals.

If you really just want to ask if the new methods differ from the
standard, you could do a pairwise multivariate hypothesis test that
the three algorithms differ from the standard; this would take into
account the correlation,  but I don't see that this is useful on two
counts: 1) a difference of one method would be masked by similarity of
the other two; 2) ultimately you probably want a separate assessment
for each of the three methods.

If you want to know "how differnt", I would do the three pair-wise
equivalence tests. However, confidence intervals might be equally
informative.  I would also not correct for multiple-comparisons, but
again that depends on the purpose of your analysis.

More: you are not clear whether each algorithm uses the same
measurement information or whether the algorithms independently
re-measure the scans.  If the algorithms use the same measurement
information, but differ mathematically, then a priori, they will give
different results, no statistical inference necessary.

If the algorithms do independently re-measure the scans, then you
might find point comparisons of the original measurements useful.   If
the measurements are not automatic, but there is room for operator or
other variation (such as in placing the scanned images, calibration),
then the experiment should probably have included replication of the
the methods on random, blinded, presentations of the same scans.

I suspect that the pairwise plots (method vs method) will give you
the best information.  You could have perfect monotone, but
non-linear, association, for example.

Ultimately, the number of scans will determine the precision of any
estimates of difference.

-Steve

On Tue, Sep 1, 2009 at 7:28 AM, Nick Cox<n.j.cox@durham.ac.uk> wrote:
> You asked the same question on 23 August:
>
> <http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist
> .0908/Author/article-1091.html>
>
> and received two quick but brief replies.
>
> Before repeating a question like this, it is usually best to think: Why
> did I not get a detailed reply? Was my question not clear enough? Does
> the list lack experts in this field? Should I rephrase the question? See
> also
>
>
> It is also best to explain why any replies you got do not help.
>
> I don't know the answer, but I do note that list members are often more
> questions.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Nikolaos Pandis
>
> We have a set of 3-D images constructed from cat scans, and we are
> measuring volumes defined by certain anatomical points on the 3-D
> images.
>
> The reconstruction/measuring technique is performed using 3 new types of
> software and their results will be compared with the results of
> validated/reference technique.
>
> The same reconstructions/cat scans are used for all techniques.
>
> The objective is to see how close (do they differ significantly?) the
> volume values recorded by each technique are to the values recorded by
> the reference technique.
>
> I was thinking along the lines of regression with the volume(continuous)
> variable as the dependent variable and technique as the categorical
> dependent variable with 4 levels. The reference level would be the the
> standard/validated method.
>
> However, how would I account for the fact that the data is correlated
> since all measurements for the 4 methods are taken from the same
> reconstructions/scans?
>
> *
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>

--
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
845-246-0774

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```