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Questions tagged [simpsons-paradox]

Simpson's Paradox is an example of the Reversal Paradox, where an association appears in several different groups of data but disappears, or even reverses in sign, when these groups are combined.

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How to resolve Simpson's paradox?

Simpson's paradox is a classic puzzle discussed in introductory statistics courses worldwide. However, my course was content to simply note that a problem existed and did not provide a solution. I would like to know how to resolve the paradox. That…
Potato
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Basic Simpson's paradox

I have a question about something that my statistics teacher said about the following problem: There are two hospitals named Mercy and Hope in your town. You must choose one of these in which to undergo an operation. You decide to base your…
swiecki
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Understanding Simpson's paradox: Andrew Gelman's example with regressing income on sex and height

Andrew Gelman in one of his recent blog posts says: I do not think counterfactuals or potential outcomes are necessary for Simpson’s paradox. I say this because one can set up Simpson’s paradox with variables that cannot be manipulated, or for…
Abhimanyu Arora
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How to handle Simpson's paradox

Simpson's "paradox" is a well-known phenomenon that can be counter-intuitive for beginners: it is possible, say, for a medical trial to reveal that a certain treatment is beneficial to men as a group and to women as a group, but harmful to humans in…
Aryeh
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Examples of Simpson's Paradox being resolved by choosing the aggregate data

Most of the advice around resolving Simpson's paradox is that you can't decide whether the aggregate data or grouped data is most meaningful without more context. However, most of the examples I've seen suggest that the grouping is a confounding…
Richie Cotton
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Can you please explain Simpson's paradox with equations, instead of contingency tables?

I probably don't have a clear understanding of the Simpson's paradox. Informally I know that the average of response Y1, grouped over all possible levels of factor A, can be higher than the average of response Y2 over all levels of A, even if the…
DeltaIV
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Simpson's Paradox vs. Berkson's paradox

Can someone explain what is the difference between the two? They seem to me to be identical. In both paradoxes you start from a narrow distribution and find out the correlation switches when you move to the full distribution. So what's the…
Maverick Meerkat
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Does Simpson's Paradox cover all instances of reversal from a hidden variable?

The following is a question about the many visualizations offered as 'proof by picture' of the existence of Simpson's paradox, and possibly a question about terminology. Simpson's Paradox is a fairly simple phenomenon to describe and to give…
Mitch
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Is it possible that marginally independent random variables are conditionally dependent?

Suppose that $X,Y$ and $Z$ are random variables. If $X$ is independent of $Z$ and $Y$ is independent of $Z$, is it possible that $X$ is dependent on $Z$ given $Y$ and $Y$ is dependent on $Z$ given $X$? If so, what are some examples?
mhdadk
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Is this Simpson's Paradox on the Titanic data set?

With the well known "Survival of passengers on the Titanic" data set I get a strange behaviour by plotting the fare vs. the age (see below). Without a constraint on Pclass the correlation is positive. In contrast for all Pclasses the correlations…
chris elgoog
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Does adjusting for superfluous variables bias OLS estimates?

The usual textbook treatment of adjusting for superfluous variables in OLS states that the estimator is still unbiased, but may have larger variance (see, for example, Greene, Econometric Analysis, 7th ed., p. 58). The other day I stumbled upon…
Julian Schuessler
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Question about combining hazard ratios - Maybe Simpson's paradox?

I’m reviewing an article, and can’t give details but here is the situation, and it’s got me puzzled Patients were divided into 4 categories (call them A B C and D), which were exhaustive and exclusive. Adjusted hazard ratios were computed for these…
Peter Flom
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When does Simpson's Paradox "end"?

Disclaimer: This is not a duplicate of How to resolve Simpson's paradox. As given in this blog, the following is the data of people on the titanic: This is the same data when divided on basis of gender: A complete reversal of the results seen in…
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Is Simpson's Paradox always an example of confounding?

Is Simpson's Paradox always an example of confounding? Or is it possible to have a Simpson's paradox effect without an extra variable lurking in the background?
George
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Simpson's Paradox & Random Effects

Simpson's effect is key to understanding potential pitfalls in medical research, particularly in the area of meta-analysis, where multiple studies with dissimilar methodologies are brought together to provide a more definite answer to a problem. The…
Antoni Parellada
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