Berkson's Paradox(twitter.com) |
Berkson's Paradox(twitter.com) |
Berkson's Paradox - https://news.ycombinator.com/item?id=18667423 - Dec 2018 (21 comments)
Berkson's Paradox - https://news.ycombinator.com/item?id=8264252 - Sept 2014 (20 comments)
Wikipedia was much clearer for me, https://en.wikipedia.org/wiki/Berkson's_paradox , but ymmv of course.
Another good statistical foible to be aware of along with Simpson's.
> For example, a person may observe from their experience that fast food restaurants in their area which serve good hamburgers tend to serve bad fries and vice versa; but because they would likely not eat anywhere where both were bad, they fail to allow for the large number of restaurants in this category which would weaken or even flip the correlation.
In this case it's https://threadreaderapp.com/thread/1373266475230789633.html
Edit to add: In this case I'd recommend wikipedia, the thread is quite short and light on details
To each their own, I guess. Sometimes a short explanation is plenty.
/meta
TBH, I'd say it's less that I dislike this form of presentation than that I hate all the anti-pattern bloat that Twitter adds, like clickable items not being detectable by extensions and previews being cut off.
Two different media for (occasionally) related work.
Calling whatever inverse relation was somehow crafted a "paradox" seems tendentious.
Do you think people who have a hard time in life are compelled to study hard and succeed, as if somehow people living in poverty or in third world countries are putting in significant amounts of effort to become smart? Of course not, not because people in poverty don't want to be smart of course, but because they are compelled to deal with time consuming hardships.
People who have it easy in life are far more compelled to study, to the point that the term "scholar" is literally the Greek word for "leisure".
I wouldn't be surprised if you drew out two axis, one measuring an individual's hardship in life and one measuring how "smart" they are, you'd reveal how paradoxical your statement is. The overall population would show that hardship places a huge burden that inhibits ones ability to learn and pursue intellectual endeavors while having an easier time in life facilitates it... and yet if you then filtered out the bottom left group (hard life and low "smart" score), you'd see the exact inverse correlation that Berkson's Paradox is all about.
Also "survival" taken literally is kinda interesting to think about in this framework. Like say there was some disaster so that the vast majority of people surviving would be either athletic or smart. This subset would likely have a negative correlation between athleticism and intelligence, even if they correlated positively in the general population. Except in this scenario the subset IS your new population.
So I wonder if there are real life traits that correlate negatively across all modern humans, but had no such correlation among our ancestors. Or is there too much regression to the mean with reproduction? Particularly if "opposites attract" is true.
The former is about correlations that appear in samples which are not representative of the general population, due to the way that those samples are selected.
> The former is about correlations that appear in samples which are not representative of the general population, due to the way that those samples are selected.
You just said the same thing twice. Think about it.
For one you used terms like "subgroups" and "pooled data" and for the other "samples" and "general population". Those are the same things.
Then you used "[the effect] appears in" and in the other "correlations". Well, Simpsons paradox can also manifest itself in correlations. So you just said the same thing twice.
Berkson's paradox: analyzing a single subgroup selected with a function aggregating two traits (additively?) will indicate an anticorrelation between the traits.
Simpson's paradox says you can't judge group trends from subgroup trends. Berkson's paradox says given a group selected in a specific way, it will have a certain property in itself. They're just different statements.
Berkson's paradox is a special case of Simpson's for the two subgroups selected and non-selected.
The difference is that Berkson's paradox involves selecting the subgroup a posteriori and in a particular way, Simpson's paradox assumes a selection a priori.
I've always learned of Simpson's paradox as relating more to different sample sizes when partitioning data, which can happen entirely arbitrarily - for example a baseball player getting injured part way through the season.
The fact that one player's at bats get partitioned differently than another's is not caused by the on field performance, so there's no "double dipping" going on like I would imagine with Berkson's. Conversely I'm having trouble fitting a Berkson's example into the framework of Simpson's paradox, since there's no reason the poorly-selected subpopulation can't theoretically be exactly half of the general population. And if all of the samples are of equal size Simpson's paradox doesn't exist anymore (because with equal bin sizes the mean of means is equivalent to the overall mean).
When you look at proportions based on binary outcomes it may be related to imbalanced groups but it's more general than that.
In the context discussed here of correlations between continous variables the groups can be of similar size.
See for example the chart here: https://towardsdatascience.com/simpsons-paradox-d2f4d8f08d42
I guess this paradox could then be thought of as a special case of Simpson's paradox? Since the out group will exclude people with both traits there should also be a negative correlation there, which disappears in the overall population. But in Berkson's case it seems they're implying the subgroup correlation is spurious whereas with Simpson's it could go either way.
In the first one you have a partition in subgroups A and B (or more than two) which show similar correlations, different from the correlation seen in A+B.
In the second one you have only a subgroup A (the implicit complement notA is not observed) where the correlation is not the same as in the (unobserved) full population A+notA. Nothing is said about the correlation in notA. It could be at either side of the correlation in the full population, while in Simpson’s paradox both subgroups are in the same side.
Edit: and I also mention "due to the way that those samples are selected" for Berkson's paradox where the selection is based on the variables of interest while in Simpson's paradox the subgroups are "external" (but influence the correlation between those variables).
Not necessarily. Imagine the traits are distributed uniformly and independently in [-1 1]. There is no correlation:
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If you select people with at least one positive trait you will find negative correlation in the group + but the correlation will still be zero in the group -. ++++++
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---+++According to Wikipedia, "paradox" can either mean "logically self-contradictory statement" or a "statement that runs contrary to one's expectation". I always thought that it meant the former only.
These two concepts should really really have separate words.