7 ms·

Berkson's Paradox

127 points by alfongj 5y ago

dang 5y ago
If curious, past threads: Berkson's Paradox - https://news.ycombinator.com/item?id=18667423 https://news.ycombinator.com/item?id=18667423 - Dec 2018 (21 comments) Berkson's Paradox - https://news.ycombinator.com/item?id=8264252 https://news.ycombinator.com/item?id=8264252 - Sept 2014 (20 comments)
- deleted 5y ago
  [deleted]
amelius 5y ago
Am I the only one who dislikes this form of presentation, i.e. as a series of tweets?
- anonymousiam 5y ago
  No, you aren't the only one. It has become even worse now that Twitter will not render without JavaScript enabled. Unfortunately, I still do not know what Berkson's Paradox is because I will not enable JavaScript for Twitter.
  - anonymousiam 5y ago
    Okay, I googled it. A non-hostile site hosts a definition here: https://en.wikipedia.org/wiki/Berkson%27s_paradox https://en.wikipedia.org/wiki/Berkson%27s_paradox
    - junippor 5y ago
      Thank you. Does anyone understand the difference between this and Simpson's paradox?
      - kgwgk 5y ago
        The latter appears when analyzing subgroups gives a different result than analyzing the pooled data. 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.
        junippor 5y ago
        > The latter appears when analyzing subgroups gives a different result than analyzing the pooled data. > 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.
        doubleunplussed 5y ago
        Eh. There is intentional splitting into subgroups, and there is accidental selection bias. I think that's the difference.
        caddemon 5y ago
        I think Berkson's paradox is more specific than just correlations arising from non-random sample selection. Correlations that are not representative of the general population could still be useful, if it's a meaningful correlation within some subgroup of interest. The problem is when the features you are correlating relate too closely to the features that were used for sample selection - then you can end up with a trivial result. 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).
  - 1vuio0pswjnm7 5y ago
    You do not need to enable Javascript, you only need to change your User-Agent header to one that is acceptable.
- rrmm 5y ago
  The series of tweets for me just wasn't illuminating and I didn't get what the actual 'paradox' was given the graphs. But my issue was more that the graphs weren't clear in pointing out what I should be looking at. Wikipedia was much clearer for me, https://en.wikipedia.org/wiki/Berkson's_paradox https://en.wikipedia.org/wiki/Berkson's_paradox , but ymmv of course. Another good statistical foible to be aware of along with Simpson's.
  - klyrs 5y ago
    Having selected for interesting content: quality of presentation is inversely correlated to length of a tweet thread?
  - billynomates111 5y ago
    If anyone's impatient like me, this example from wikipedia helped me get it: > 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.
- SilasX 5y ago
  You're not alone. I think it caught on because a long article (even with pictures) might seem like too much of an investment to a lot of people but a self-contained tweet that keeps getting extended is less intimidating. 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.
- anitil 5y ago
  I always go to threadreaderapp. In this case it's https://threadreaderapp.com/thread/1373266475230789633.html 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
  - Dylan16807 5y ago
    > 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.
- lurquer 5y ago
  Of the tweets I bother to read, I’ve found that the more interesting the tweet, the more likely it is to be poorly formatted. /meta
- deleted 5y ago
  [deleted]
- rkagerer 5y ago
  Yes it's one of the reasons I hate Twitter. It was designed with aversion to substance. Personally, I find older fashioned forums (with small communities of experts) more illuminating.
tejtm 5y ago
From the wikipedia page it seems to be a generalization on sampling below the Nyquist frequency can lead to incorrect interpretation of wave forms but in more dimensions.
- smitty1e 5y ago
  I don't understand why a good book/good movie are even included here. Two different media for (occasionally) related work. Calling whatever inverse relation was somehow crafted a "paradox" seems tendentious.
alexpetralia 5y ago
My favorite article on this: https://erikbern.com/2020/01/13/how-to-hire-smarter-than-the-market-a-toy-model.html https://erikbern.com/2020/01/13/how-to-hire-smarter-than-the...
- Arech 5y ago
  Excellent article, thank you very much for sharing! Infinitely better than everything else I read on the topic.
reactchain 5y ago
The argument here is that "smart people are worse looking" is actually a case of _of the people you encounter_ smart people are worse looking, but that overall there is no correlation. This makes sense, but I think it's more complex. If you took the entire population, I think you could still conclude the "smart people are worse looking" if you define smart to include non-innate, learned behaviour, for the simple reason that good looking people have an easier time in life (getting jobs and so forth) and are therefore less compelled to spend time and effort becoming "smart". So there's a self-balancing aspect that produces these correlations in the general population as well.
- Kranar 5y ago
  This doesn't make much sense and I think may actually be another instance of this paradox. For example, why would having an easier time in life dissuade someone from putting in effort to become smart (by your definition of smart)? 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.
reactspa 5y ago
As a Taleb follower, this concept seems similar to Survivorship Bias or Selection Bias.
- caddemon 5y ago
  I'd say it's a type of selection bias, but yeah seems very closely related to survivorship bias. 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.

127 points by alfongj 5y ago

dang 5y ago

If curious, past threads: Berkson's Paradox - https://news.ycombinator.com/item?id=18667423 https://news.ycombinator.com/item?id=18667423 - Dec 2018 (21 comments) Berkson's Paradox - https://news.ycombinator.com/item?id=8264252 https://news.ycombinator.com/item?id=8264252 - Sept 2014 (20 comments)

deleted 5y ago
[deleted]

amelius 5y ago

Am I the only one who dislikes this form of presentation, i.e. as a series of tweets?

anonymousiam 5y ago
No, you aren't the only one. It has become even worse now that Twitter will not render without JavaScript enabled. Unfortunately, I still do not know what Berkson's Paradox is because I will not enable JavaScript for Twitter.
- anonymousiam 5y ago
  Okay, I googled it. A non-hostile site hosts a definition here: https://en.wikipedia.org/wiki/Berkson%27s_paradox https://en.wikipedia.org/wiki/Berkson%27s_paradox
  - junippor 5y ago
    Thank you. Does anyone understand the difference between this and Simpson's paradox?
    - kgwgk 5y ago
      The latter appears when analyzing subgroups gives a different result than analyzing the pooled data. 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.
      - junippor 5y ago
        > The latter appears when analyzing subgroups gives a different result than analyzing the pooled data. > 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.
        doubleunplussed 5y ago
        Eh. There is intentional splitting into subgroups, and there is accidental selection bias. I think that's the difference.
        caddemon 5y ago
        I think Berkson's paradox is more specific than just correlations arising from non-random sample selection. Correlations that are not representative of the general population could still be useful, if it's a meaningful correlation within some subgroup of interest. The problem is when the features you are correlating relate too closely to the features that were used for sample selection - then you can end up with a trivial result. 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).
- 1vuio0pswjnm7 5y ago
  You do not need to enable Javascript, you only need to change your User-Agent header to one that is acceptable.
rrmm 5y ago
The series of tweets for me just wasn't illuminating and I didn't get what the actual 'paradox' was given the graphs. But my issue was more that the graphs weren't clear in pointing out what I should be looking at. Wikipedia was much clearer for me, https://en.wikipedia.org/wiki/Berkson's_paradox https://en.wikipedia.org/wiki/Berkson's_paradox , but ymmv of course. Another good statistical foible to be aware of along with Simpson's.
- klyrs 5y ago
  Having selected for interesting content: quality of presentation is inversely correlated to length of a tweet thread?
- billynomates111 5y ago
  If anyone's impatient like me, this example from wikipedia helped me get it: > 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.
SilasX 5y ago
You're not alone. I think it caught on because a long article (even with pictures) might seem like too much of an investment to a lot of people but a self-contained tweet that keeps getting extended is less intimidating. 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.
anitil 5y ago
I always go to threadreaderapp. In this case it's https://threadreaderapp.com/thread/1373266475230789633.html 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
- Dylan16807 5y ago
  > 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.
lurquer 5y ago
Of the tweets I bother to read, I’ve found that the more interesting the tweet, the more likely it is to be poorly formatted. /meta
deleted 5y ago
[deleted]
rkagerer 5y ago
Yes it's one of the reasons I hate Twitter. It was designed with aversion to substance. Personally, I find older fashioned forums (with small communities of experts) more illuminating.

tejtm 5y ago

From the wikipedia page it seems to be a generalization on sampling below the Nyquist frequency can lead to incorrect interpretation of wave forms but in more dimensions.

smitty1e 5y ago
I don't understand why a good book/good movie are even included here. Two different media for (occasionally) related work. Calling whatever inverse relation was somehow crafted a "paradox" seems tendentious.

alexpetralia 5y ago

My favorite article on this: https://erikbern.com/2020/01/13/how-to-hire-smarter-than-the-market-a-toy-model.html https://erikbern.com/2020/01/13/how-to-hire-smarter-than-the...

Arech 5y ago
Excellent article, thank you very much for sharing! Infinitely better than everything else I read on the topic.

reactchain 5y ago

The argument here is that "smart people are worse looking" is actually a case of _of the people you encounter_ smart people are worse looking, but that overall there is no correlation. This makes sense, but I think it's more complex. If you took the entire population, I think you could still conclude the "smart people are worse looking" if you define smart to include non-innate, learned behaviour, for the simple reason that good looking people have an easier time in life (getting jobs and so forth) and are therefore less compelled to spend time and effort becoming "smart". So there's a self-balancing aspect that produces these correlations in the general population as well.

Kranar 5y ago
This doesn't make much sense and I think may actually be another instance of this paradox. For example, why would having an easier time in life dissuade someone from putting in effort to become smart (by your definition of smart)? 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.

reactspa 5y ago

As a Taleb follower, this concept seems similar to Survivorship Bias or Selection Bias.

caddemon 5y ago
I'd say it's a type of selection bias, but yeah seems very closely related to survivorship bias. 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.