http://spssx-discussion.165.s1.nabble.com/Correlational-Example-Involving-COVID-19-Useful-for-Classes-tp5739871p5739892.html
Thanks for the links, Mike. I see that I also have access to Simpson (1951)
that.
> >
> wrote:
>
>> > --- snip ---
>> > but I think Simpson's Paradox presents the fallacy most directly (see:
>> >
>>
https://urldefense.proofpoint.com/v2/url?u=https-3A__en.wikipedia.org_wiki_Ecological-5Ffallacy-23Simpson-27s-5Fparadox&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=A8kXUln5f-BYIUaapBvbXA&m=300e3cAU3FH4Wnoe4MY_n1Jmt3K-xsHo9cXm3y8sse0&s=sDi6eBkVmVauFo92kBooAiYs9NvPwMPBB0WifOkOGaY&e=>> ).
>>
>> 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://urldefense.proofpoint.com/v2/url?u=https-3A__link.springer.com_article_10.1186_s12982-2D019-2D0087-2D0&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=A8kXUln5f-BYIUaapBvbXA&m=300e3cAU3FH4Wnoe4MY_n1Jmt3K-xsHo9cXm3y8sse0&s=4zYrM0WEJGa9AyckGqWEStFDWkuDwpHt5FoH70LHtvQ&e=>>
>> See the example in Table 1.
>>
>
> A few points:
> (1) I think that the case you are referring to, i.e., no association
> between X and Y
> when Z is controlled for, is a special case of Simpson's paradox, that is,
> sometimes suppression may give rise to the Simpson's paradox but
> Simpson's paradox can still occur without suppression. More on this
> point shortly.
>
> (2) Please see the following article:
> Kievit, R., Frankenhuis W., Waldorp L., & Borsboom, D. (2013). Simpson's
> paradox in
> psychological science: a practical guide.Frontiers in Psychology, 4, 513.
>
> The article can be accessed at:
>
https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00513/full>
> The abstract to the article follows:
> The direction of an association at the population-level may be reversed
> within the subgroups
> comprising that population --- a striking observation called Simpson's
> paradox. When facing this
> pattern, psychologists often view it as anomalous. Here, we argue that
> Simpson's paradox is
> more common than conventionally thought, and typically results in
> incorrect
> interpretations --
> potentially with harmful consequences. We support this claim by reviewing
> results from cognitive
> neuroscience, behavior genetics, clinical psychology, personality
> psychology, educational psychology,
> intelligence research, and simulation studies. We show that Simpson's
> paradox is most likely to
> occur when inferences are drawn across different levels of explanation
> (e.g., from populations
> to subgroups, or subgroups to individuals). We propose a set of
> statistical
> markers indicative
> of the paradox, and offer psychometric solutions for dealing with the
> paradox when encountered --
> including a toolbox in R for detecting Simpson's paradox.
> *We show that explicit modeling of situations *
>
> *in which the paradox might occur not only prevents incorrect
> interpretations of data, but also *
> *results in a deeper understanding of what data tell us about the world.*
> NOTE: emphasis of the last sentence is added. Modeling the data pattern
> is
> important because
> of the next point.
>
> (3) On page 6 of the PDF for the article (scroll down on the webpage) the
> following quote
> appears:
>
> *A Survival Guide to Simpson's Paradox*
> We have shown that SP may occur in a wide variety of research designs,
> methods, and questions.
> As such, it would be useful to develop means to “control” or minimize the
> risk of SP occurring, much
> like we wish to control instances of other statistical problems.
>
> *Pearl (1999, 2000) has shown that(unfortunately) there is no single
> mathematical property that all instances of SP have in common,
> andtherefore, there will not be a single, correct rule for analyzing data
> so as to prevent cases of SP.*
> Based on graphical models, Pearl (2000) shows that conditioning on
> subgroups may sometimes be
> appropriate, but may sometimes increase spurious dependencies (see also
> Spellman et al., 2001).
> It appears that some cases are observationally equivalent, and only when
> it
> can be assumed that the
> cause of interest does not influence another variable associated with the
> effect, a test exists to determine
> whether SP can arise (see Pearl, 2000, chapter 6 for details).
>
> Note #1: Emphasis of the sentence containing Judah Pearl's statement that
> there is no single math property
> that underlie all instances of Simpson's Paradox. This implies that some
> cases of SP may be due
> to suppression but other mechanisms are probably operating to produce the
> pattern, hence the need
> for something like the author's R toolkit to investigate an instance of SP
> in detail.
>
> Note #2: I think that this article is helpful in thinking about Simpson's
> Paradox even though most of
> the examples are from psychology because it shows how it can appear in a
> wide variety of situations
> (sometimes unnoticed) as well as the difference between SP based on
> different groups of subjects
> and SP based on repeated measurements of individuals in different groups.
>
> 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 ---
>>
>
> No, I was trying to suggest that Simpson's paradox may reflect the
> operation of
> different mechanisms which is one reason why I pointed out that multilevel
> analysis
> is one strategy that some researchers are using to understand SP.
>
> -Mike Pallij
> New York University
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