On Fri, 22 Sep 2000, Paul C. Smith wrote:
> Linda -
> It looks as though a couple of people responded, but missed the point that
> you already knew that the deviations themselves add to zero (I assume that's
> why you indicated that it's the absolute value of the deviations your
> student proposed using instead). Here's my understanding - mostly
> assumptions on my part...
>
> The average absolute deviation is a perfectly good descriptive statistic.
> Were that all we needed, that's likely what we'd use. However, as I'm sure
> you know, the standard deviation (and not the average deviation) appears in
> most of the inferential methods involving means. We use the SD as our
> descriptive statistic simply because there's no point in learning two
> separate equally useful descriptive statistics, and the SD is the one we're
> going to wind up using for other purposes anyway.
I agree with Paul, but I'd like to take his explanation one step
further. His point is that while the SD and AD are both good
choices for descriptive stats, the SD wins hands down for
inferential. But why is it better for inferential? It seems it's
because mathematicians hate working with absolute values. They're
a real pain in the fanny (sorry, Britain, Australia, Ireland, and
the West Indies) when they try to derive things. You can do all
sorts of wonderful things, mathematical derivation-wise, and
especially in relation to the normal distribution, with the SD
but not with the AD. The algebra's apparently just too tough with
the AD and its intractable absolute values.
(I have a wonderful proof of this but unfortunately the margin is
too small to contain it).
-Stephen
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Stephen Black, Ph.D. tel: (819) 822-9600 ext 2470
Department of Psychology fax: (819) 822-9661
Bishop's University e-mail: [EMAIL PROTECTED]
Lennoxville, QC
J1M 1Z7
Canada Department web page at http://www.ubishops.ca/ccc/div/soc/psy
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