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> North: Democrat (145/154, 94 percent), Republican (138/162, 85 percent) > South: Democrat (7/94, 7 percent), Republican (0/10, 0 percent) > Overall: Democra

by nhebb 13y ago

> North: Democrat (145/154, 94 percent), Republican (138/162, 85 percent) > South: Democrat (7/94, 7 percent), Republican (0/10, 0 percent) > Overall: Democrat (152/248, 61 percent), Republican (138/172, 80 percent) This example is often cited for Simpson's Paradox, but because the South headcount for Republicans (10) and Democrats (94) had such a wide disparity and the Republican headcount was so low, it always seemed more like twisting the data to fit a political narrative than to make a statistical argument. Like other statistical methods, there should be a minimum population size for the paradox to be meaningful.

haldujai 13y ago
http://www.bmj.com/content/309/6967/1480.full http://www.bmj.com/content/309/6967/1480.full https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone_treatment https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone... Has larger sample sizes, all would be valid for statistical analysis. Although this paradox isn't really dependent on a sample size, it is not so much a statistical test. It's a trend that can be observed when looking at sub groups compared to overall averages. In the above example open surgery was better for both small and large kidney stones and is a prime example of Simpson's paradox. However, one should note that Simpson's paradox can also be subject to further confounding variables. Perhaps patients that were suitable for open surgery were in better medical condition and therefore the open surgery sample was non-random and caused the higher success rate. The presence of Simpson's paradox, similar to correlation, also does not imply causation.
jtc331 13y ago
And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights Act and vice versa), but rather than we're possibly using the wrong predictors. That is, rather than demonstrating that there is a different correlation between party and vote, it demonstrates that there is a (stronger) correlation between geography and vote.

by nhebb 13y ago

haldujai 13y ago

http://www.bmj.com/content/309/6967/1480.full http://www.bmj.com/content/309/6967/1480.full https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone_treatment https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone... Has larger sample sizes, all would be valid for statistical analysis. Although this paradox isn't really dependent on a sample size, it is not so much a statistical test. It's a trend that can be observed when looking at sub groups compared to overall averages. In the above example open surgery was better for both small and large kidney stones and is a prime example of Simpson's paradox. However, one should note that Simpson's paradox can also be subject to further confounding variables. Perhaps patients that were suitable for open surgery were in better medical condition and therefore the open surgery sample was non-random and caused the higher success rate. The presence of Simpson's paradox, similar to correlation, also does not imply causation.

jtc331 13y ago

And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights Act and vice versa), but rather than we're possibly using the wrong predictors. That is, rather than demonstrating that there is a different correlation between party and vote, it demonstrates that there is a (stronger) correlation between geography and vote.