Re: Fwd: Correlational Example Involving COVID-19 Useful for Classes

Posted by Bruce Weaver on Oct 25, 2020; 2:55pm
URL: http://spssx-discussion.165.s1.nabble.com/Correlational-Example-Involving-COVID-19-Useful-for-Classes-tp5739871p5739888.html

Mike wrote
> Thanks for bringing up the correlation between chocolate consumption (CC)
> and the number
> of Nobel Laureates (#NL); I remember when it first came out.  However,
> although the correlation
> is between group/aggregate values, I think that this is a better example
> of spurious correlation
> than an ecological correlation.  

Fair point.  

> --- snip ---
> My understanding of ecological correlation/inference (also known as the
> ecological fallacy) is
> that statistics and relationships based on aggregate/grouped data do not
> necessarily reflect
> the statistics or relationships based on individual level data (or
> whatever the lowest unit of analysis
> is; in the social sciences, this would usually be the person level).  The
> Wikipedia entry on the
> Ecological Fallacy (see: https://en.wikipedia.org/wiki/Ecological_fallacy
> ) is consistent with
> this view

Agreed.  Ditto for the atomistic fallacy, except for the reversed direction
(i.e., associations at the level of individuals do not necessarily match
associations between the same variables at the aggregate level).  


> but I think Simpson's Paradox presents the fallacy most directly (see:
> https://en.wikipedia.org/wiki/Ecological_fallacy#Simpson's_paradox ).

Hmm. You're going to have to explain this one to me.  Simpson's Paradox is
often illustrated with examples where there appears to be no association
between X and Y, but when one "controls" for Z, the X-Y association becomes
apparent.  As this article suggests, it is an example of suppression, or
negative confounding, as epidemiologists might call it:

https://link.springer.com/article/10.1186/s12982-019-0087-0

See the example in Table 1.  

Perhaps what you're suggesting is that to get the correct estimate of the
X-Y association, one must compute estimates within each stratum of the
confounder, and then a pooled estimate of those within-stratum estimates
(rather than pooling the data across strata)?  I don't see that as being the
same thing as computing the association between aggregate measures of X and
Y, though.  

--- snip the rest ---




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Bruce Weaver
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