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Re: st: ratios first or last?


From   Ronan Conroy <rconroy@rcsi.ie>
To   "statalist hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: ratios first or last?
Date   Mon, 24 Nov 2003 10:06:54 -0000

on 23/11/2003 01:27, David Airey at david.airey@vanderbilt.edu wrote:

> Recently I was surprised to find a difference between two methods of
> calculating a ratio during an experiment. Each animal has two measures
> taken repeatedly over time. The ratio is of the two measures. I could
> take the ratio at each time point, and then average the ratios to get
> my animal ratio. Alternatively, I could average each of the two
> measures and then form a ratio of the two averages, again getting my
> animal ratio. The second method consistently gets a higher ratio than
> the first method. Why would this occur? The second method is standard
> in my literature base.

The method of taking an average at each time point gives each time point
equal weighting in the final calculation.

Summing all time points allows time points to affect the sum in proportion
to the absolute measured value. It is equivalent to an area under the curve
where the time points are equally spaced.

Still, the way you describe it, there is no stated rationale for either
method. Summarising measurements really does require a knowledge of what
construct is being measured by the data. In other words, it is the
scientific meaning of the data that dictate the appropriate method of
summarising the data.

So, in the end, it's a science question, rather than a statistical one in
the narrow sense.

Ronan M Conroy (rconroy@rcsi.ie)
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland
+353 1 402 2431 (fax 2764)

--------------------
Ugh - what's that bitter taste in my coffee?
www.maketradefair.org

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