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Re: st: test for trend from table data?


From   "R. Allan Reese" <R.A.Reese@gri.hull.ac.uk>
To   Stata distribution list <statalist@hsphsun2.harvard.edu>
Subject   Re: st: test for trend from table data?
Date   Mon, 16 Jun 2003 14:59:46 +0100 (BST)

On Mon, 16 Jun 2003, Copeland, Laurel wrote:

> A pharmacist asked me if I could do a test for trend over time from this
> table:
>
> Year	Pharm	Clin  Total  Ratio
> 1997	400	44      444   4:1
> 1998	221	54      275   4:1
> 1999	187	69      256   3:1
> 2000	123	63      186   2:1
> 2001	74	42      116   3:2
> 2002	145	149     294   1:1

Without prejudice (meaning you can't sue me for defamation) I would worry
that what is expected is a mathematical sledgehammer to crush an answer
without worrying too much about the figures.  There are techniques: to
those that have been mentioned, I'll add a runs test as it has least
assumptions.

But look at the data and consider the meaning. The annual totals vary by
4:1, and almost triple between 2001 to 2002.  Unless the number of
treatments varied similarly - as might be the case if this relates to an
epidemic disease - then there is a very strange mechanism for reporting
adverse effects, with a very high variance.  A trend test might come out
as significant, but another view might be that the 1997 total for
pharmacists was an outlier, and some new factor entered the system in
2002.

I'd worry about any "trend" claimed from a time series of 6 observations
as a statistical result.  The term might be purely descriptive, but
calling it a trend invites the use of a forecasting model.  The outcome is
seen on a regular basis in the behaviour of stockmarket investors.

R. Allan Reese                       Email: r.a.reese@gri.hull.ac.uk

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