----- Original Message -----
From: Gene Gallagher > Here is an error that is subtle, but very
common. The statistical
> test (multiple regression) was applied perfectly, but the
> statistical inference was wrong.
> My first reference to this type of error is in the classic,
> but highly controversial, ecology treatise by Andrewartha & Birch
> (1954): The distribution and abundance of animals, p. 580.
>
> These Australian ecologists wanted to show that animal
> populations aren't controlled by density-dependent factors like
> competition or predation. They regress 14 years of thrip (an
> insect) abundance vs weather variables. They considered weather a
> density-independent factor (mortality from a storm or a hot day
> isn't directly related to animal density).
> They conclude, "...altogether, 78 per cent of the variance
> <in thrip maximal abundance> was explained by four quantities which
> were calculated entirely from meteorological records. This left
> virtually no chance of finding any other systematic cause for
> variation, because 22 per cent is a rather small residium to
> be left as due to random sampling errors.
> All the variation in maximal numbers from year to year may therefore
> be attributed to causes that are not related to density: not only
> did we not find a "density-dependent factor," but we also showed
that
> there was no room for one."
Also, as both weather and population data tend to be
autocorrelated,
simple regression would tend to overestimate the significance of
correlation (though not the correlation itself), by imputing more
degrees of freedom than genuinely present.
-Robert Dawson
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