Simpson's Paradox
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Simpson's Paradox
1–10 of 52 posts
Re: Simpson's Paradox
#2Reminds me of Anscombe's Quartet: four datasets that have the same mean, variance, correlation, and linear regression, but are really very different. http://en.wikipedia.org/wiki/Anscombe%27s_quartet
Re: Simpson's Paradox
#3Simpson's Paradox is scary if you've not seen it before, but you should not stop here and instead proceed immediately on to omitted variable bias and the conversation here (http://normaldeviate.wordpress.com/2013/06/20/simpsons-parad...).
In short, Simpson's paradox occurs because probability distributions and causal claims are distinct things which behave differently. It's nothing more than a particular, insidious example of correlation not implying causation. It's perfectly possible for a probability distribution to have a "contradictory" shape, but perfectly impossible for logical statements about the world to be contradictory.
The resolution is that you shouldn't let your probability distributions turn into logical statements without analyzing your causal assumptions. This will lead you to whether or not excluding a variable is omitted variable bias (and whether including an improper one will lead to included variable bias, which is rarely recognized).
Re: Simpson's Paradox
#4The Omitted Variable Problem is part of my mental framework that causes me to not believe most epidemiological studies, especially ones that confirm a popular belief.
The almost universally omitted variable is health-consciousness. Some people are health-conscious and some aren't. People who are health-conscious do a whole bunch of things, some of which help (like exercise, sleep well, eat moderately). They also do things that are widely believed to be good for you, like eating broccoli.
So if you do a study, you'll find that people who eat lots of broccoli are healthier. You'll be able to confirm pretty much any widely believed health folk wisdom, unless it's something quite harmful, as long as you omit health-consciousness as a variable.
Re: Simpson's Paradox
#5The Omitted Variable Problem is part of my mental framework that causes me to not believe most epidemiological studies, especially ones that confirm a popular belief. The almost universally omitted variable is health-consciousness. Some people are health-conscious and some aren't. People who are health-conscious do a whole bunch of things, some of which help (like exercise, sleep well, eat moderately). They also do t…
If it was a huge deal, wouldn't epidemiologists be slobbering over the statistical power they would get from using it?
That is, if they can control for it, they can make assertions about smaller effects.
Re: Simpson's Paradox
#6Reminds me of Anscombe's Quartet: four datasets that have the same mean, variance, correlation, and linear regression, but are really very different. http://en.wikipedia.org/wiki/Anscombe%27s_quartet
maybe we'll do that one next!
Re: Simpson's Paradox
#7The point of an interactive illustration like this is that it should make it more intuitive and easier to understand than the core concept, not more confusing.
What is the meaning of the green and purple lines on the graph, why do they have different gradients and why can't I adjust them? Why does the Simpson's Paradox apply sometimes and not others? Why are there so many bars and donut charts? What does the gray circle around the donuts mean? Information overload.
Re: Simpson's Paradox
#8The Omitted Variable Problem is part of my mental framework that causes me to not believe most epidemiological studies, especially ones that confirm a popular belief. The almost universally omitted variable is health-consciousness. Some people are health-conscious and some aren't. People who are health-conscious do a whole bunch of things, some of which help (like exercise, sleep well, eat moderately). They also do t…
Surely some studies account for this? If you look for people who do X and people who don't and just analyze their lives, yes this problem is likely to exist. But if you take two randomized samples of a the population and say to group A, "do X," and to group B "don't do X," you have an effective control group. At least I think so. Don't some dietary studies even provide the participants with custom food regimens to try to eliminate extra dietary differences between study participants?
Re: Simpson's Paradox
#9That is some sexy javascript.
Re: Simpson's Paradox
#10The Omitted Variable Problem is part of my mental framework that causes me to not believe most epidemiological studies, especially ones that confirm a popular belief. The almost universally omitted variable is health-consciousness. Some people are health-conscious and some aren't. People who are health-conscious do a whole bunch of things, some of which help (like exercise, sleep well, eat moderately). They also do t…
Surely some studies account for this? If you look for people who do X and people who don't and just analyze their lives, yes this problem is likely to exist. But if you take two randomized samples of a the population and say to group A, "do X," and to group B "don't do X," you have an effective control group. At least I think so. Don't some dietary studies even provide the participants with custom food regimens to tr…
You're describing a randomized controlled trial and not an epidemiological study.